m... 3w. A- .ama.» ... mfiwéwuwammwwflrusm. V SW” , . "Wang _ «mm :c x.1....~#..¥m...$m kW... :26 l 7...... r. 3 i. u. 1». «ammJJWmn .. I. 1 .- .fl , .5: . , :43 33.4.3.4. at}. « .734.” .. A i. :.s Hiya“ . :. “E515 3 ‘90“ LIBRARY Michigan State University This is to certify that the dissertation entitled LOCAL SECONDARY STRUCTURE AND STRAND ARRANGEMENTS OF THE MEMBRANE-ASSOCIATED HIV-1 FUSION PEPTIDE OLIGOMERS PROBED BY SOLID-STATE NUCLEAR MAGNETIC RESONANCE presented by Zhaoxiong Zheng has been accepted towards fulfillment of the requirements for the Ph.D. degree in Chemistry Ema Pr Melitta Major Professor’s Sighature dam/L 524 .2 001 Date MSU is an affirmative-action, equal-opportunity employer oo-o-.-¢-n-o-o-o-o---‘-I-o-n-o-0-o--o-o-I-o-n-n-n-o-o-I-a-a-n-l-I-n-l-I-I-I-O-I-o-O-u-l-o--I-u-I-I-o-n--t-ICU-o-I-o-n-l. ____'__.‘_'--___ PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 6/07 p:/CIRC/Dale0ue.indd-p.1 LOCAL SECONDARY STRUCTURE AND STRAND ARRANGEMENTS OF THE MEMBRANE-ASSOCIATED HIV-1 FUSION PEPTIDE OLIGOMERS PROBED BY SOLID-STATE NUCLEAR MAGNETIC RESONANCE By Zhaoxiong Zheng A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 2007 ABSTRACT LOCAL SECONDARY STRUCTURE AND STRAND ARRANGEMENTS OF THE MEMBRANE-ASSOCIATED HIV -1 FUSION PEPTIDE OLIGOMERS PROBED BY SOLID-STATE NUCLEAR MAGNETIC RESONANCE By Zhaoxiong Zheng The HIV-1 fusion peptide (HFP) serves as a biologically relevant model for viral/target cell membrane fusion and previous studies have demonstrated that HFPs which are cross-linked at their C-termini to form trimers (HFPtr) catalyze fusion at a rate which is 15-40 times greater than non-cross-linked HFP monomers (HFPmn). Cross-polarization (CP) under magic angle spinning (MAS) was optimized by 1H to 13 C transfer efficiency for crystalline and membrane-associated samples at MAS frequency from 8 kHz to 13 kHz and CP was incorporated in all major pulse sequences in this work. Rotational-echo double resonance (REDOR), a solid-state nuclear magnetic resonance (NMR) heteronuclear dipolar recoupling technique, was tested and found quantitative in measuring l3CO-ISN distances (rCN) ~ 4 A. The technique development included investigation of two related homonuclear dipolar recoupling techniques, i.e., constant-time double-quantum buildup with finite pulses (prTDQBU) and constant-time finite-pulse rf-driven recoupling (prFDR-CT). Although prFDR-CT yielded higher signal-to-noise, it was impractical in measuring l3CO-13CO distances (rec) 2 5 A in membrane-associated samples due to complexity in transverse relaxation. On the other hand, prTDQBU was found useful in measuring rcc from 3 to 6 A in both crystalline and membrane-associated samples and was insensitive to relative CSA orientations and pulse imperfections. The REDOR and prTDQBU methods were applied to probe secondary structure and strand arrangements of membrane-associated HFP oligomers. Local chemical shift and intramolecular rCN measurements by REDOR showed that the conformation of the Len-7 to Phe-ll region of HF P has predominant helical conformation in membranes without cholesterol and fl strand conformation in membranes containing ~30 mol% cholesterol. Interstrand rcc and ray distance measurements respectively by prTDQBU and REDOR on HFPmn and HFPtr in membranes containing ~30 mol% cholesterol suggested a model of mixed parallel and antiparallel ,6 strand arrangements in the N- terminal region of HFP and loss of parallel fl sheet structure in the C-terminal region of HFP. Dedicated to Lu Dai, my beloved wife. iv Acknowledgements I would like to thank my advisor, Dr. David Weliky, the Weliky group and my guidance committee for their help and support during my time here at Michigan State University. I also want to thank my family and friends for all their support. This work would not have been possible without the Max T Rogers NMR Facility and the Computational Center in the Department of Chemistry, and the Mass Spectrometry Facility in the Department of Biochemistry and Molecular Biology. TABLE OF CONTENTS Pages LIST OF TABLES ................................................................................. viii LIST OF FIGURES ................................................................................. ix LIST OF ABBREVIATIONS AND SYMBOLS ............................................. xvii Chapter 1 Introduction ........................................................................ 1 References .......................................................................... 11 Chapter 2 Materials and Methods Chapter 3 Chapter 4 Chapter 5 Materials ........................................................................... 19 HF P Synthesis ...................................................................... 20 Model Compounds ................................................................ 21 Solid State NMR Sample Preparation ........................................... 23 Magic Angle Spinning and Cross Polarization ................................ 25 General Solid-State NMR Parameters .......................................... 26 CP MAS Spectroscopy .......................................................... 27 REDOR Spectroscopy ............................................................ 29 prTDQBU Spectroscopy ......................................................... 31 prFDR-CT Spectroscopy ...................................................... 34 Transverse Relaxation Measurement .......................................... 34 Experimental Data Analysis .................................................... 36 Solid State NMR Simulation and Fitting ....................................... 42 References .......................................................................... 52 Technique Development CP MAS Development .......................................................... 56 REDOR Development ........................................................... 58 prTDQBU Development ....................................................... 58 prFDRCT Development and Comparison with prTDQBU ............. 73 Conclusion of Technique Development ....................................... 77 References .......................................................................... 80 Fusion Peptide Structural Determination REDOR Measurements ............................................................ 81 prTDQBU Measurements ....................................................... 87 Structural Modeling ............................................................... 95 References ........................................................................ 105 Summary Technique Development ....................................................... 111 Fusion Peptide Structural Determination .................................... 112 Future Directions ................................................................ l 12 Appendix I Appendix II Appendix 111 Appendix IV References ......................................................................... 1 14 Determination of Corrections of REDOR, prTDQBU and prFDT- CT Data ........................................................................... 1 15 Location of NMR Data ........................................................ 131 List of New Pulse Programs and Macros ................................... 135 Simulation Examples and Procedures ..................................... 168 vii LIST OF TABLES Pages Table 1. 13CO principal CSA values used in SIMPSON simulation ......................... 49 Table 2. Experimental and model distances of HF Ptr-L7CF1 lN/LM3e ..................... 97 viii LIST OF FIGURES Pages Figure 1. Model (left) and Electron Microscopy (right) of the HIV virus (a) binding to host cell (b) fusion of viral and host cell membranes (c, (1) formation of large pore and infection of host cell. The triangle represents the viral RNA that enters the host cell ...... 2 Figure 2. Model of HIV infection. HFP = HIV-1 Fusion Peptide. Time sequence: Left to Right .................................................................................................... 4 Figure 3. Model for HIV -1/host celll fusion. In the left-most figure, a gplZO/gp40 trimer is displayed with the balls representing gp120 and rods representing gp41. “F” represents the fusion peptide and “A” represents the transmembrane anchorage of gp41. Fusion proceeds temporally from left to right with (i) initial state, (ii) receptor binding and fusion peptide membrane insertion, (iii) gp41 conformational change, and (iv) membrane fusion ................................................................................................... 5 Figure 4. Chemical structure of (a) 1-13C, N-13C doubly labeled N-acetyl leucine (D-NAL) and (b) 13c doubly labeled Glycyl-L-phenylalanyl-L-phenylalanine (D-GFF), in which the labeled l3c nuclei are in bold. The intrarnolecular labeled 130-130 distances in D-NAL and D-GFF crystals are 3.07 A and 5.40 A, respectively. ..................................... 24 Figure 5. 13 C CP MAS pulse sequence. Magnetization is transferred from 1H nuclei to 13 C nuclei during CP. lH continuous wave (CW) decoupling was applied acquisition. . . . . ....28 Figure 6. 1D l3C REDOR pulse sequences with (a) the "all-but-one 15N 7: pulse" version and (b) the "alternating 15N/13C 7r pulse" version. CP transfers lH magnetization to 13C. 13C magnetization is dephased (i.e., reduced) by l3C-ISN dipolar coupling mediated by either (a) two equally spaced 15N 71' pulses per rotor period except the one in the middle of the sequence or (b) one 15N 7r pulse 1per rotor period. One 13 C 71' pulse as in (a) or multiple 13C 71' pulses as in (b) refocuses the 3 C chemical shift ......................................... 30 Figure 7. prTDQBU pulse sequence. (a) The displayed prTDQBU pulse sequence included: (1) cross-polarization (CP) from 1H nuclei to 13C nuclei; (2) a constant-time (CT) period of (L + M + N)2'R duration where L, M, and N were integral multiples of 8 or 16, and TR was the duration of a single rotor period; and (3) an acquisition period during which 13 C NMR signals were detected. Continuous wave lH decoupling was applied during the CT and the acquisition periods. A pair of back-to-back 13C 7112 pulses separated the LTR and the M TR periods and another pair separated the M TR and the N TR periods. Variants of the pulse sequence during the CT period included (b) the “one-Ir-per- TR” version with one 13 C Irpulse per rotor period and (c) the “one-Ir-per-Z TR” version with one 13C Irpulse per two rotor periods. The 13C CP rf phase was §+ 71/2 and the phase of each 13C 71/2 and Irpulse is noted above the pulse. For g" = y or —y, l3C-BC dipolar couplings were averaged to zero and So data were obtained and for 4’ = x or —x, 13 C-13 C dipolar couplings were not averaged to zero and S1 data were obtained. The duration of ix the 13 C-13C dipolar recoupling or dephasing period 1'= 2L1'R, and data with increasing 1 were obtained by incrementing L and decrementing N while keeping constant M and constant (L + M + N) ............................................................................... 33 Figure 8. prFDR-CT pulse sequence. (a) The displayed prFDR-CT pulse sequence included cross-polarization (CP) from 1H nuclei to 13 C nuclei, a constant-time (CT) period, and an acquisition period during which 13C NMR signals were detected. Continuous wave lH decoupling was applied during the CT and the acquisition periods. The CT period contained K cycles of (2M + 4N) 1R duration where K was an integer, M and N were integral multiples of 8, and 17; was the duration of a single rotor period. Each (2M + 4N)1'R cycle contained intervals separated by 13C 72/2 pulses and panel b displays the series of 13C Irpulses in each of these intervals. The 13C CP r'f phase was y and the phase of each 13 C 7112 and erulse is noted above the pulse. Each (2M + 4N)1'R cycle could be understood to have a central 6N 1R WAHUHA period during which the l3C-13C dipolar couplings were averaged to zero. For M = N, the CT period can be considered as a series of WAHUHA periods and So data were obtained with no dipolar coupling period. For M > N, l3C-13C dipolar couplings were not completely averaged and S1 data were obtained. The total duration of the l3C-BC dipolar recoupling or dephasing period 1' = 2K x (M — N)1'R and data with increasing 1' were obtained by incrementing M and decrementing N while keeping (M + 2N) and K constant ..................................... 35 Figure 9. Carr-Purcell pulse sequence. The x-phase 13 C magnetization was transferred from 1H by cross-polarization, and 13C 7: pulse phases alternated between y and —y to prevent spin locking and to minimize effects of rf field inhomogeneity on the experimental echo decays. D was an even integer, P was an integer, and a data set consisted of echo signals with different values of P. .......................................... 37 Figure 10. The ORTEP representation. Illustrated here is a spatial second rank anisotropic interaction tensor in its principal axis system (PA), a crystallite—fixed coordinate system (C), the rotor-fixed coordinate system (R), and the laboratory-fixed coordinate system (L) along with the Euler angles Qxy = { axy, By, M } describing transformation between the various frames X and Y ............................................................................. 46 Figure 11. Plots of D-NAL and HFPmn-F8c/LMe CP MAS 13C signals with two Hartmann-Hahn matches and at various MAS frequencies. The match 1 was referred to 45 kHz lH 7d2, 45 kHz 1H CP and 13C ramp from 37 to 50 kHz rf fields, and the match 2 to 60 kHz lH 71/2, 60 kHz lH CP and 13C ramp from 43 to 54 kHz rf fields. The crosses (x) and squares were D-NAL ‘3 C CP signals of 128 acquisitions with match 1 and match 2, respectively, which were normalized by the signal with match 2 at 12 kHz MAS frequency. The down triangles and up triangles were HFPmn-F8c/LMe 13 C CP signals of 512 acquisitions with match 1 and match 2, respectively, which were normalized by the signal with match 2 at 10 kHz MAS frequency. The sample temperature, contact time and recycle delay were fixed at -50 °C, 3 ms and 1.25 s, respectively ............................ 57 Figure 12. 13 C REDOR spectra of the 14 peptide. For each lettered pair of spectra, the So spectrum is on the left and the S1 spectrum is on the right. The MAS fiequency = 8000 Hz, 17; = 125 us, and 1'= 8.25 ms (spectra a) or 1'= 32.25 ms (spectra b). Dotted lines are drawn at the peak So intensities. The 14 spectra were processed with 50 Hz Gaussian line broadening, and baseline correction was applied to all spectra. The numbers of acquisitions used to obtain each spectrum in panels were 32 .................. 59 Figure 13. (a) REDOR (AS/SOY” (filled squares) and (AS/SOY“ (crosses) vs. dephasing time for the 14 peptide. Each (AS/So)” was based on a (AS/So)” determined by integrations of 1 ppm regions in the So and S1 spectra. The integration region was centered at 178.8 ppm which is the peak shift in the So spectra. For each 1; there were 64 total (So + S1) scans. The values of 0“” are ~0.005 and the heights of the black squares are approximately equal to the average value of 2 x of". (b) A plot of )8 vs. dCN yields day = 44.78 :I: 0.22 Hz which corresponds to row = 4.110 :1: 0.007 A for the Ala-9 13'CO/Ala-13 15N labeled pair. The uncertainty was determined using the approach described in the Materials and Methods section. The (AS/So)“ values in plot a were calculated with the best-fit dCN .................................................................... 60 Figure 14. prTDQBU spectra of the GFF sample. The version of prTDQBU is one-7r- per-21R. For each lettered pair of spectra, the So spectrum is on the left and the S] spectrum is on the right. The MAS frequency = 8000 Hz, 1'3 = 125 us, the 13C Irpulse rf field = 10 kHz, M= 336, and the total constant-time = (L + M + N) x 1R = 84 ms. The values of L, N, and rare: 128, 208, 32 ms (spectra a); 192, 144, 48 ms (spectra b); 256, 80, 64 ms (spectra c); 320, 16, 80 ms (spectra (1). From left-to-right, each GFF spectrum has Phe-3, Phe-2 and Gly-l l3CO peaks at 180.3, 176.4, and 170.9 ppm, respectively. For each set of GFF spectra with the same 1', a dotted line is drawn at the peak So intensities of Gly-l. The spectra were processed with 50 Hz Gaussian line broadening, and baseline correction was applied to all spectra. The total numbers of scans used to obtain each spectrum in panels a, b, c, and d are 10240, 10240, 10240, and 8192, respectively ....... 61 Figure 15. Dependence of prFDR-CT of GFF Gly-l 13CO on 13C 71' pulse rf field, (AS/SOY” and (AS/So)” vs. dephasing time. The version of prTDQBU is one-7r-per-21'R. The MAS frequency = 8000 Hz, (23¢ ”mm,” = 175.7 ppm, M = 336, and the constant- time = 84 ms. The symbol legend is: squares, car, 10 kHz 13C Irpulse rf field; crosses, sim, 10 kHz field; diamonds, car, 43 kHz field; circles, Sim, 43 kHz field. Uncertainties are displayed for the cor points in plot a and lines are drawn. Each (AS/So)” was based on a (AS/So)” determined fiom spectral integrations over a 0.5 ppm region centered at the Gly—l 13 CO peak chemical shift. Each (AS/SOY” value was determined using intensities from 4096 total (So + SI) scans. The Sow" and 513"" were calculated with dcc é 42 Hz which yielded the best overall agreement between (AS/SOY" and (AS/So)“ values ................................................................................................. 63 Figure 16. (a) prTDQBU (AS/SOY” (open squares with error bars) and (AS/So)” (crosses) vs. dephasing time for GFF Gly-l 13CO. The version of prTDQBU is one-71:- per-2m The MAS frequency = 8000 Hz, the 13C Irpulse rf field = 10 kHz, r513c,,m,,,,-,,e, = 175.7 ppm, M = 336, and the constant-time = 84 ms. Each (AS/So)” was based on a (AS/So)” determined from spectral integrations over a 0.5 ppm region centered at the Gly-l l3co peak chemical shift. Each (AS/So)” value for 1'= 16, 24, 32, 4o, 48, 56, and xi 64 ms was determined using intensities from 20480 total (So + S1) scans and the (AS/So)” value for 1'= 72 ms was determined using intensities from 16384 total scans. (b) A plot of X2 vs dcc yields dcc = 42.3 :1: 0.5 Hz which corresponds to rcc = 5.67 :1: 0.02 A for the Gly-l/Phe—3 labeled pair. The (AS/S0)” values in panel a were calculated with dcc = 42.3 Hz ...................................................................................................... 65 Figure 17. 13c cne-zr-per- 1R prTDQBU spectra of (a) D-NAL with 1 = 13.33 ms, and (b) D-GFF with 1'= 28.00 ms. The MAS frequency was 12000 Hz and (a) CT = 20.0 ms, and (b) CT = 41.33 ms. For each lettered pair of spectra, the So spectrum is on the left and represented the sum of 5 = y and g = —y data and the S; spectrum is on the right and represented the sum of g = x and 4’ = —x data. Dotted lines are drawn at the peak labeled amide carbonyl So intensities. Each spectrum in panel a, or b, respectively represented the sum of 64, or 4000 scans and was respectively processed with 75, or 75 Hz Gaussian line broadening. Processing also included dc offset correction and polynorrrial baseline correction .............................................................................................. 66 Figure 18. Plots of D-NAL prTDQBU (a) (AS/So)” and (b) So vs dephasing time obtained with MAS frequency = 12000 Hz. Each (AS/So)” was calculated from a (AS/So)” determined with So and S1 spectra that each represented the sum of 32 scans. The integration regions were 1 ppm and were centered at 178.3 ppm which was the peak carbonyl shift. The of" were < 0.006. For plot b, the cross (x) value of So at 1'= 16.0 ms was set to 1.0 and the other So were normalized relative to this value. The symbol legend: squares, one-Ir-per-TR, 20.5 kHz l3C Irpulses, CT = 32.00 ms; crosses, one-Jr-per-21'R, 20.5 kHz l3C Irpulses, CT = 32.00 ms; up triangles, one-Ir-per- 1R, 35.0 kHz l3C Irpulses, CT = 32.00 ms; down triangles, one-Irr-per- 17;, 20.5 kHz l3C Irpulses, CT = 20.00 ms. . .68 Figure 19. (a) D-NAL and (b) D-GFF plots of prTDQBU (AS/SOY" and (AS/SOY“ vs dephasing time as a fimction of transmitter offset (A) calculated relative to the midpoint of the labeled carbonyl and carboxyl shifts. Acquisition parameters included one-mper— 1R, MAS frequency = 12000 Hz, 20.5 kHz 13’C Irpulses, and (a) CT = 20.00 ms or (b) CT = 41.33 ms. Each (AS/So)” was calculated from a (AS/So)” determined with So and S1 spectra that each represented the sum of (a) 32 or (b) 4000 scans. The integration regions were 1 ppm and were centered at (a) 178.3 or (b) 170.8 ppm which were the peak carbonyl shifts. The displayed (AS/S0)” were calculated with the best-fit (a) dcc = 296 Hz or (b) dcc = 49.4 or 44.6 Hz for A = 0 or —12.0 ppm, respectively. The symbol legend: squares, (AS/So)”, (a) A = —6.7 ppm or (b) A = 0 ppm; crosses, (AS/SOY“, (a) A = —6.7 ppm or (b) A = 0 ppm; up triangles; (AS/SOY", (a) A = —16.7 ppm or (b) A = —12.0 ppm; down triangles, (AS/So)“, (a) A = —16.7 ppm or (b) A = —12.0 ppm ................................................................................................... 70 Figure 20. (a) D-NAL and (b) D-GFF plots of prTDQBU (AS/S0)” and (AS/So ”I" vs dephasing time for 13 C Irpulses with different nutation angles. Acquisition parameters included one-Ir-per- 1R, MAS frequency = 12000 Hz, 20.5 kHz 13C Irpulses, and (a) A = — 6.7 ppm, CT = 20.00 ms or (b) A = 0 ppm, CT = 41.33 ms. The numbers of scans, sim integration parameters, and calculation of (AS/So) were the same as in Figure 19. The xii l3C nutation angle is denoted 6. The symbol legend: squares, (AS/So)”, 6 = 180°; up triangles; (AS/So)‘fm, 0 = 180°; crosses, (AS/So)“, (a) 6 = 170° or (b) 0 = 175°; down triangles, (AS/So)“, (a) 0 = 190° or (b) 6 = 185° .............................................. 72 Figure 21. (a) Plot of D-GFF prTDQBU (AS/S0)” (squares) and (AS/So)“ (crosses) vs dephasing time. Acquisition parameters included one-Ir-per- 1R, MAS frequency = 12000 Hz, 20.5 kHz 13C Irpulses, and CT = 41.33 ms. Each (AS/So)” was calculated from a (AS/So)” determined with So and S1 spectra that each represented the sum of 4000 scans. The integration regions were 1 ppm and were centered at 170.8 ppm which was the peak shift of the Gly-l 13CO in the So spectra. The 0”" were ~0.05. The displayed (AS/SOY” were calculated with the best-fit dcc = 49.4 i 1.2 Hz and corresponding rcc = 5.39 :l: 0.05 A for the Gly-l/Phe-3 13’CO labeled pair. The 12 = 8.4 for this best-fit value. (b) Plot of D-GFF prFDR-CT (SI/So)” (squares) and (St/So)“ (crosses) vs dephasing time. Acquisition parameters included MAS frequency = 10000 Hz, 15.2 kHz l3C Irpulses, and CT = 67.2 ms. Each (Sl/So)°°’ was calculated from a (SI/So)” determined with So and S1 spectra that each represented the sum of 2048 scans. The integration regions were 1 ppm and were centered at the Gly-l l3CO peak (170.8 ppm) and the of” were ~0.04. The displayed (Sl/So)‘i'" were calculated with the best-fit dcc = 59.0 :1: 3.0 Hz and corresponding rcc = 5.07 i 0.09 A. The 2’2 = 4.0 for this best-fit value ..................... 75 Figure 22. (a) Plot of prTDQBU (AS/So)” vs dephasing time for membrane-associated HFPmn-F8 (squares), HFPtr-A6 (crosses) and HFPtr-A15 (triangles). Acquisition parameters included one-mper- 1R, MAS frequency = 12000 Hz, 20.5 kHz l3C erulses, and CT = 64.00 ms for HFPmn-F8 and HFPtr-A15 or CT = 41.33 ms for HFPtr-A6. Each (AS/SOY“ was calculated from a (AS/So)” determined with So and S1 spectra that each represented the sum of 10000, ~40000, and 10000 scans for the HFPmn-F8, HFPtr-A6 and HFPtr-A15 samples, respectively. The integration regions were 2 ppm and the 0“” were ~0.10, 0.06 and 0.09 for the HFPmn-F8, HFPtr-A6 and HFPtr-A15 samples, respectively. (b) Plot of prFDR-CT (S1/So)°°' vs dephasing time for membrane- associated HFPmn-F8 (squares), HFPtr-A6 (crosses) and HFPtr-A15 (triangles). Acquisition parameters included MAS fiequency = 12000 Hz, 20.5 kHz 13 C Irpulses, and CT = 64.00 ms. Each (SI/So)” was calculated from a(S1/So)°’°’ with So and S1 spectra that each represented the sum of 12000, 33000, and 21000 scans for the HFPmn-F8, HFPtr- A6 and HFPtr-A15 samples, respectively. The integration regions were 2 ppm and the 0”” were ~0.04, 0.10 and 0.08 for the HFPmn-F8, HFPtr—A6 and HFPtr-A15 samples, respectively. The (AS/SOY" or (Sl/So)°°' in each plot were calculated with h = 1, i.e. all labeled 13 CO experienced the same homonuclear dipolar coupling .......................... 76 Figure 23. 13C spectra of HFPtr-F8cL9N associated with (a) PC-PG and (b) LM3 membranes and of HFPtr-L7CF1 1N associated with (c, d) PC-PG, (e) LM3, and (t) LM3e membranes. The HFPtrzlipid mol ratio was ~0.003 in the samples used to obtain spectra a andb and ~0.007 in the samples used to obtain spectra c-f. Spectra a, b, and c are REDOR-filtered with 1' = 1.0, 1.0, and 32.25 ms, respectively, and have 13CO peak chemical shifts of 178.4 (Phe-8), 172.5 (Phe-8), and 178.8 ppm (Leu-7), respectively. Spectra d, e, and f are REDOR So spectra with 32.25 ms dephasing period and have 13'CO peak chemical shifts of 178.6 ppm, 173.8 ppm, and 173.4 ppm, respectively. Each xiii spectrum was processed with 100 Hz Gaussian line broadening and baseline correction. The MAS frequency was 8000 Hz and the numbers of scans used to obtain spectra a, b, c, d, e, and f are 118784, 132864, 46048, 23024, 21760, and 98720, respectively. .8....2 Figure 24. 13 C REDOR spectra of HF Ptr-L7CF 1 IN associated with (a, b) PC-PG and (c, d) LM3e membranes. For each lettered pair of spectra, the So spectrum is on the left and the S1 spectrum is on the right. The MAS fi'equency = 8000 Hz, 17; = 125 us, and 1'= 8.25 ms (spectra a, c) or 1' = 32.25 ms (spectra b, d). Dotted lines are drawn at the peak So intensities. The HFPtr spectra were processed with 100 Hz Gaussian line broadening, and baseline correction was applied to all spectra. The numbers of acquisitions used to obtain each spectrum in panels a, b, c and d were 37710, 23024, 40528, and 98720, respectively. ......................................................................................................... 85 Figure 25. (a) REDOR (AS/So)” (open squares with error bars) and (AS/So)” (crosses) vs. dephasing time for the HFPtr-L7CF11N/PC-PG sample. Each (AS/So)” was based on a (AS/So)” determined from spectral integrations over a 1 ppm region centered at 178.6 ppm, the Leu-7 13CO peak chemical shift. The total (So + $1) numbers of scans used to obtain the (AS/So)” values for 1' = 8.25, 16.25, 24.25, and 32.25 ms were 75420, 52832, 41568, and 46048, respectively. (b) A plot of 12 vs. dCN yields dCN= 44.8 :I: 2.4 Hz which corresponds to rCN = 4.11 :l: 0.08 A for the Len-7 l3CO/Phe-ll ls'N labeled pair. The (AS/So)“ values in plot a were calculated with the best-fit dCN ......................... 86 Figure 26. (a) REDOR (AS/SOY" (open squares with error bars) and (AS/SOY“ (crosses) vs. dephasing time for the HFPtr-L7CF11N/LM3e sample. Each (AS/So)” was based on a (AS/So)” determined from spectral integrations over a 1 ppm region centered at 173.4 ppm, the peak shift in the So spectra. The total (So + St) numbers of scans used to obtain the (AS/So)” values for 1'= 8.25, 16.25, 24.25, and 32.25 ms were 81056, 76288, 172512, and 197440, respectively. (b) A plot of A? vs. dCN yields dCN= 15.8 :1: 1.8 Hz which corresponds to rCN = 5.8 :l: 0.3 A for the Leu-7 l3CO/Phe-ll 15N labeled pair. The (AS/So)“ values in plot a were calculated with dCN = 15.8 Hz ............................... 88 Figure 27. one-Ir-per- 1R prTDQBU spectra of (a) membrane-associated HFPmn-F8c with 1' = 29.33 ms, and (b) membrane-associated HFPtr-A15c with 1' = 30.67 ms. The MAS frequency was 12000 Hz and CT = 64.0 ms. For each lettered pair of spectra, the So spectrum is on the left and represented the sum of g = y and g" = —y data and the $1 spectrum is on the right and represented the sum of {= x and {= —x data. Dotted lines are drawn at the peak labeled amide carbonyl So intensities. Each spectrum in panel a, or b respectively represented the sum of 10000 scans and was respectively processed with 200, or 300 Hz Gaussian line broadening. Processing also included dc offset correction and polynomial baseline correction .................................................................... 89 Figure 28. prTDQBU “one-7r-per-21'R” spectra of (a-d) the HFPtr-L7CF11N/LM3e sample. For each lettered pair of spectra, the So spectrum is on the left and the S1 spectrum is on the right. The MAS frequency = 8000 Hz, 1'R = 125 us, the 13C Irpulse rf field = 10 kHz, M = 336, and the total constant-time CT = (L + M + N) x 1R = 84 ms. The values of L, N, and ram: 128, 208, 32 ms (spectra a); 192, 144, 48 ms (spectra b); 256, xiv 80, 64 ms (spectra c); 320, 16, 80 ms (spectra d). For each set of HFPtr spectra with the same 1; a dotted line is drawn at the peak So intensities of Leu-7 (HFPtr). The HFPtr spectra were processed with 250 Hz Gaussian line broadening, and baseline correction was applied to all spectra. For some of the HF Ptr spectra, there is a small glitch at ~178 ppm which is due to DC offset in the data. The total numbers of scans used to obtain each spectrum in panels a, b, c, and d are 77056, 80736, 102432, and 152064, respectively...91 Figure 29. prTDQBU “one-71-per-21'R” (AS/So)” and (AS/So)” vs. dephasing time for the HFPtr-L7CF11N/LM3e sample. The MAS frequency = 8000 Hz, the 13C Itpulse rf field = 10 kHz, (530 ”mm,” = 178.4 ppm, M = 336, and the constant-time CT = 84 ms. The (AS/So)” values are open squares with error bars. Each (AS/S0)” was based on a (AS/So)” determined from spectral integrations over a 1 ppm region centered at 173.4 ppm, the peak shift in the So spectra. The total (So + S1) numbers of scans used to obtain the (AS/So)” values for 1'= 32, 48, and 64 ms were 154112, 161472, and 204864, respectively. The (AS/So)“ values were calculated with two-spin and three-spin models in plots a and b, respectively. In plot a, the up triangles, crosses, and down triangles correspond to rice = 10, 15 and 20 Hz, respectively and in plot b, they correspond to (ICC = 8, l3, and 18 Hz, respectively. The best-fit values of dcc are ~15 Hz and ~13 Hz for the two-spin and three-spin models, respectively, and correspond to interstrand Len-7 l3CO-IB'CO distances of 8.0 A and 8.4 A. Reasonable upper limits on dcc in the two-spin and three-spin models are ~20 Hz and ~18 Hz respectively, and correspond to distances of 7.3 A and 7.5 A ................................................................................... 92 Figure 30. Contour plots of )(2 for membrane-associated (a) HFPmn-F8c and (b) HFPtr- A6c. The X2 were calculated with comparison of (AS/Sp)” and (AS/SOY“ calculated with a two-parameter model. For this model, there was a population fraction (h) of labeled 13C which experienced measurable ‘3 C-13C dipolar coupling and a population fraction (1 — h) of labeled ‘3 C which experienced no 13C-1 C dipolar coupling. The horizontal and vertical axes are the measurable dipolar coupling and h parameters, respectively. The shading legend: black, (a) 1.0 <12 <1.1 or (b) 6 <12 < 7; dark gray, (a) 1.1 <12 < 2.0 or (b) 7 < 12 < 10; gray, (a) 2 <12 < 5 or (b) 10 <12 < 20; light gray, (a) 5 <12 <10 or (b) 20 < 12 < 50; white, (a) 12 > 10 or (b) 12 > 50 ....................................................... 94 Figure 31. Structural models for strand arrangements of LM3e-associated HFPtr: (a) parallel in-register; (b) parallel with adjacent strands two-residue out-of-register; and (c) antiparallel with adjacent strand crossing between Phe-8 and Leu-9. The sequence of the first sixteen residues is AVGIGALFLGFLGAAG fiom residue 1 to 16 ..................... 96 Figure 32. Chart of derivation of (AS/So)” for REDOR of the 14 peptide. Four pieces of information were shown from top to bottom in each box: the site description, its relative population, and its contributions to So (in brackets) and S 1 (in braces) ..................... 117 Figure 33. Chart of derivation of (AS/So)” for prTDQBU of the D-GFF sample. Four pieces of information were shown from top to bottom in each box: the site description, its relative population, and its contributions to So (in brackets) and St (in braces) ........... 124 XV Figure 34. Chart of derivation of (AS/S0)” for prTDQBU of the HFPtr-L7CF11N samples for 1'> 32 ms. Four pieces of information were shown from top to bottom in each box: the site description, its relative population, and its contributions to So (in brackets) and $1 (in braces) ................................................................................... 126 Figure 35. Chart of derivation of (AS/So)” for prTDQBU of the HF Pmn-F8c sample in a model of two structural populations. Four pieces of information were shown from top to bottom in each box: the site description, its relative population, and its contributions to So (in brackets) and 51 (in braces) ................................................................... 129 xvi LIST OF ABBREVIATIONS AND SYNIBOLS AB fl-alanine Boc tert-butyloxycarbonyl CD circular dichroism CP cross-polarization CSA chemical shift anisotropy; CT constant time CW continuous wave d dipolar coupling dcc 13 C-13 C dipolar coupling dCN l3C-ISN dipolar coupling DCM dichloromethane D-GF F doubly labeled GFF D-NAL 1-‘3c, N-‘3c doubly labeled NAL DTPC l ,2-di-O-tetradecyl-sn-glycero-3 -phosphocholine DTPG 1,2-di-O-tetradecyl-sn-glycero-3-phospho-rac-(1- glycerol) sodium salt DPhPE 1 ,2-di-O-phytanyl-sn-glycero-3 -phosphoethanolamine ESR electron spin resonance E(t) chemical shift echo intensity FID free induction decay F MOC 9-fluorenylmethoxycarbonyl xvii prTDQBU prFDR-CT F (t) GFF HEPES HIV HFP HFPdm HFPmn HF Ptr HPLC LM3 LM3e LMe LUV MAS Mtt NAL PC-PG PDB constant-time double-quantum buildup with finite pulses constant-time finite-pulse rf-driven recoupling dipolar echo intensity g1ycyl-L-phenylalanyl-L-phenylalanine N-(2-hydroxyethyl)piperazine-N '-2-ethanesu1fonic acid human immunodeficiency virus HIV fusion peptide HIV fusion peptide dimer HIV fusion peptide monomer HIV fusion peptide trimer hi gh-performance liquid chromatography infrared lipid mixture 3 ether-linked lipid mixture 3 8:2:5 DTPC:DTPG:cholesterol mixture large unilamellar vesicle magic angle spinning methyltrityl N-acetyl-L-leucine N-methylpyrrolidone nuclear magnetic resonance 4:1 POPC2POPG mixture Protein Data Bank xviii PI POPC POPE POPG POPS rCC rCN REDOR RFDR SIMPSON T2 TBME TFA TPPM WAHUHA TR TT phosphatidylinositol 1 -palmitoyl-2-oleoy1-sn-g1ycero-3—phosphocholine 1 -palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolarnine 1 -pa1mitoyl-2-oleoyl-sn-glycero-3 -phospho-rac-(l - glycerol) 1 -palmitoyl-2-oleoy1-sn-glycero-3 -phospho-L-serine radio frequency l3C-13C distance l3C-ISN distance rotational-echo double resonance radio frequency-driven recoupling simulation program for solid-state NMR spectroscopy transverse relaxation time t-butyl methyl ether trifluoroacetic acid two-pulse phase-modulation Waugh-Huber-Haberlen sequence chemical shift transmitter offset pulse nutation angle dephasing time duration of a rotor cycle duration of transverse relaxation xix Chapter 1 Introduction Membrane fusion is an important step in viral infection for widespread and serious diseases including measles, influenza and AIDS.(I-3) Understanding viral fusion is important as a key step in the viral life cycle and as a possible target for anti-viral therapeutics. Enveloped viruses such as human immunodeficiency virus (HIV) are surrounded by a membrane and infect cells through fusion between the viral membrane and the target cell membrane. After the fusion process the viral nucleocapsid is inside the target cell and can begin viral replication. HIV fuses directly with the plasma membrane and Figure 1 illustrates the three sequential steps of fusion in Hlebinding of two membranes, mixing of lipid membranes, and formation of a large pore through which the contents of both the virus and the host cell mix.(3-5) There is a high kinetic barrier to membrane fusion and the HIV virus has a “fusion peptide” (HF P) catalyst which increases the fusion rate.(6, 7) The HFP is the 20- residue apolar domain at the N-terminus of the ~170-residue HIV gp41 protein. The HFP construct is hidden within the envelope protein until a conformational change is triggered which exposes the HF P construct, and allows it to interact with the membranes of the target cell. The triggering event for HIV is binding of the protein to the target cell protein receptors. Figure 1. Model (left) and Electron Microscopy (right) of the HIV virus (a) binding to host cell (b) fusion of viral and host cell membranes (c, (1) formation of large pore and infection of host cell. The triangle represents the viral RNA that enters the host cell. Even in the absence of the rest of the fusion protein, the free fusion peptide catalyzes fusion between large unilamellar vesicles (LUVs) and between erythrocytes, serving as a good model system for understanding some aspects of HIV viral fusion.(8, 9) Mutational studies have shown strong correlations between HFP-induced fusion and viral/host cell fusion.(6, 7, 10) There are atomic-resolution structures of the “soluble ectodomain” of gp41 which deletes the ~30 N-terminal residues of gp41 (including the HF P).(3, 11-15) These structures are believed to correspond to the conformation after fusion has occurred and perhaps during some fusion steps.(16) The gp41 proteins form a trimer in the soluble ectodomain structure with the three N-termini in close proximity at the end of an in- register helical coiled-coil. It has therefore been hypothesized that during viral/target cell fusion, at least three HF Ps insert into the target cell membrane with their C-termini in close proximity. There is some antibody-based evidence for this hypothesis.(1 7) Current models of HIV-l/host cell infection include interaction of the fusion peptide with the host cell membrane as displayed in Figures 2 and 3.(13, 18) Fusion and infection are initiated by strong interactions of two viral enveloped proteins (gp41 and gp120) with the CD4 and chemokine (e. g. CXCR4) receptors of the human T and macrophage cells.(19, 20) The gp41 protein traverses the HIV-1 membrane and the fusion peptide region is located at the N-terminus of the gp41 extraviral ectodomain. W“ U” gm MM" . .mu . vf‘.‘ Figure 2. Model of HIV infection. HFP = HIV-1 Fusion Peptide. Time sequence: Left to Right. (i) (ii) (iii) (M 111111 lullllllllllllllllj'g W F C13: 013 Figure 3. Model for HIV-l/host cell fusion. In the left-most figure, a gplZO/gp40 trimer is displayed with the balls representing gp120 and rods representing gp41. “F” represents the fusion peptide and “A” represents the transmembrane anchorage of gp41. Fusion proceeds temporally from left to right with (i) initial state, (ii) receptor binding and fusion peptide membrane insertion, (iii) gp41 conformational change, and (iv) membrane fusion. A variety of experimental methods have shown that membrane-associated HF P can assume either helical or nonhelical structure.( 7, 8, 10, 21-31) Models for the helical structure have been developed based on nuclear magnetic resonance (NMR), electron spin resonance (ESR), infrared (IR), and circular dichroism (CD) data, as well as computer simulations.(32-38) A ,B hairpin model for non-helical structure has been proposed based on IR and surface activity measurements in membranes.(3 9) Fluorescence, ESR, IR, and solid-state NMR data also suggest that the nonhelical HFPs in membranes form oligomeric structures.(40-44) These oligomeric structures may be important as evidenced by envelope protein trimerization and by experiments and modeling which indicate that the fusion site contains multiple trimers and a correspondingly high HF P concentration.(13, 14, 45) Additionally, the V2E mutation in gp41 dominantly interferes with HIV fusion and infectivity and this suggests that oligomeric HFP is important in viral/target cell fusion.(40, 46) During the past five years, there has been progress in synthesis of HF Ps that reflect more closely HFP in gp41. In one effort, a longer “N70” peptide was made which contained the first 70 residues of gp41.(47) Relative to the 23-residue HFP, the N70 construct induced vesicle fusion at much lower peptide concentrations. In addition, the synthesis of the chemically cross-linked “HFPtr” construct which contained three HF P strands was motivated by those structures lacking gp41 .(2 7, 48) The significance of trimerization was indicated by a rate of vesicle fusion induced by HF Ptr that was as much as 40 times greater than the rate induced by single-strand “HFPmn”. One structural hypothesis for the increased fusion of N70 and HFPtr is formation of predominant parallel rather than mixed parallel and antiparallel ,6 strand arrangements. A parallel arrangement would place the most apolar N-terrrrinal regions of HFP strands close to one another and the resultant large apolar volume would cause greater perturbation of the membrane and more rapid fusion. Analysis of infrared spectra of membrane-associated N70 supported a parallel strand arrangement.(44) Without the need for crystallization or solvation, solid-state NMR is a useful method to probe membrane-associated HFP oligomer structure. Solid-state NMR studies have been done on peptides in either membrane bilayer dispersions or in bilayers aligned between stacked glass plates. Measurements of chemical shift (CS) and internuclear dipolar couplings (ds) provide information about the peptide conformation, oligomerization, and insertion angle and depth relative to the membrane. Magic angle spinning (MAS) solid-state NMR has shown helical, B strand, and random coil structures observed at specific residues in HFP and the distribution of conformations at specific residues depend on the lipid headgroup and cholesterol composition of the membrane.(24, 26, 28, 51, 52) Measurements of ds between HFPs showed that the [3- strand structure is oligomeric and contains interpeptide hydrogen bonding and that there are approximately equal populations of parallel and anti-parallel strand alignments.(43) Rotational-echo double-resonance spectroscopy (REDOR) is one of the most widely used MAS NMR techniques for analysis of molecular structure in the solid state.(53-5 8) REDOR has found application in detection of formation of chemical bonds and in resonance assignment of small peptides.(59-61) REDOR has recently been used to determine local secondary structure of membrane-associated HFP and to probe insertion depth of HF P in membranes by measuring 13C-ISN and 13 C-3 1P distances, respectively.(31, 62) The wide use of REDOR is primarily due to the relative simplicity and robustness of its pulse sequence and data analysis. In this work, the REDOR technique was applied to the filtered MAS observation of backbone carbons and to quantitatively measure heteronuclear recoupling in structural study of membrane- associated HFPS. A significant number of published studies were measurements of 13 C-13 C homonuclear dipolar recoupling (dcc) under MAS with which sharp peaks could be observed. The relationship between the internuclear distance rcc and dcc is rcc = (7740/dcc)1/3 where rcc and dcc have A and Hz units, respectively. A variety of methods have been deve10ped for measurement of these couplings including R2, RFDR, SEDRA, DRAMA, HORROR, DRAWS, c7, post-C7, CMR7, sc14j, R143, and SR26.(63-75) This work describes an investigation of the radiofrequency-driven recoupling (RF DR) or SEDRA method in which 13 C transverse magnetization evolves under trains of 13C Irpulses with one pulse per integral number of rotor periods.(73- 75) The RFDR setup is straightforward and rapid because the '3 C pulses are Itpulses with quadrature phases. Effects of 13C transverse relaxation may be reduced in constant-time (CT) versions of RFDR, in which there are a constant number of Itpulses and a single total duration of 13 C evolution for all dipolar dephasing times.(76, 77) Use of '3 C Iz'pulses which are an appreciable fraction of a rotor period is an additional modification and for such finite-pulse RFDR (prFDR) sequences, the average Hamiltonian is proportional to the static homonuclear dipolar coupling Hamiltonian.(78) The prFDR technique is relatively insensitive to 13 C chemical shifts and 13 C chemical shift arrisotropies and is well-suited to distance measurements in carbonyl (13CO)-labeled samples which are relatively inexpensive to prepare.(31, 78-80) Although prFDR was originally developed with small diameter and volume rotors for which the MAS frequency was >20 kHz, prFDR has also been applied at the ~10 kHz MAS fiequencies achievable with larger volume rotors.(31, 81) Higher Si gnals may be obtained with these rotors for samples which are concentration-limited, such as membrane-associated peptides and proteins. This work considers two variants of the prF DR sequence. For the constant-time double-quantum buildup with finite pulses (prTDQBU) method, the 13 C Irpulse train was divided into two parts, the first of which generated either 13 C dipolar evolution or dipolar refocusing, and the second of which only generated dipolar refocusing.(31, 76) The refocusing was achieved with solid echoes and selection of either evolution or refocusing was controlled by the phase of a 13 C 7112 pulse. The sum of the durations of the first and second periods was always a single constant time. The second variant, constant- tirne finite-pulse rf-driven recoupling (prFDR-CT), contained Waugh-Huber-Haberlen (W AHU HA) periods for dipolar refocusing.(79, 80, 82) Relative to solid echoes, the WAHUHA approach may result in higher signal because of better dipolar refocusing.(83, 84) This work provides some comparison between the prTDQBU and prFDR-CT methods in both polycrystalline model compounds and membrane-associated HIV fusion peptide (HFP) samples. An investigation was made of the necessity for constant-time in measurement of structurally interesting rcc ~ 5 A distances with dcc ~ 60 Hz. In addition, comparison was made between a version of prTDQBU with one 13 C Irpulse per two rotor periods and a version with one 13 C Irpulse per rotor period.(31) The latter version could generate more rapid dipolar evolution and permitted shorter durations of constant time with concomitant reduced transverse relaxation and higher signals. Investigations by experiment and simulation were also made of effects of transmitter offsets and pulse nutation angle errors on prTDQBU data and the derived ‘3 C-13 C distances. In addition to the examination of the prFDR techniques, the work also included application of prTDQBU for determination of ,6 strand arrangements in membrane- associated HFP samples. For peptides in amyloid fibrils, strand arrangements have been elucidated using measurements of interpeptide 13C-13C dipolar couplings in samples containing peptides with a single backbone l3CO label.(80, 85) For an in-register parallel strand arrangement, the l3CO-13CO rcc z 4.8 A with corresponding dcc z 70 Hz while an antiparallel arrangement would typically have greater rcc and much smaller dcc. This approach is the conceptual basis for the investigation of strand arrangements in membrane-associated HF P in this work. 10 (1) (2) (3) (4) (5) (6) (7) (3) (9) (10) (11) (12) (13) References Blumenthal, R., and Dimitrov, D. S. 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(2001) l3C-13C dipolar recoupling under very fast magic angle Spinning in solid-state nuclear magnetic resonance: Applications to distance measurements, 17 (79) (80) (31) (82) (83) (84) (85) spectral assignments, and high-throughput secondary-structure determination, J. Chem. Phys. 114, 8473-8483. Ishii, Y., Balbach, J. J ., and Tycko, R. (2001) Measurement of dipole-coupled lineshapes in a many-spin system by constant-time two-dimensional solid state NMR with high-speed magic-angle spinning, Chemical Physics 266, 231-236. Balbach, J. J ., Petkova, A. T., Oyler, N. A., Antzutkin, O. N., Gordon, D. J ., Meredith, S. C., and Tycko, R. (2002) Suprarnolecular structure in full-length Alzheimer's B-amyloid fibrils: Evidence for a parallel [S-sheet organization fi'om solid-state nuclear magnetic resonance, Biophys. J. 83, 1205-1216. Tseng, Y. H., Mou, Y., Mou, C. Y., and Chan, J. C. C. (2005) Double-quantum NMR spectroscopy based on finite pulse RFDR, Solid State Nucl. Magn. Reson. 27, 266-270. Waugh, J. S., Huber, L. M., and Haeberlen.U. (1968) Approach To High- Resolution NMR In Solids, Physical Review Letters 20, 180-182. Mehring, M. (1983) Principles of high-resolution NMR in solids, 2nd, rev. and enl. ed., Springer-Verlag, Berlin. Slichter, C. P. (1992) Principles of Magnetic Resonance, 3rd enl. and updated ed ed., Springer-Verlag, New York. Benzinger, T. L., Gregory, D. M., Burkoth, T. S., Miller-Auer, H., Lynn, D. G., Botto, R. E., and Meredith, S. C. (1998) Propagating structure of Alzheimer's [3- amyloid(10-35) is parallel B-sheet with residues in exact register, Proc. Natl. Acad. Sci. U.S.A. 95, 13407-13412. 18 Chapter 2 Materials and Methods Materials Resins and amino acids were purchased fi'om Advanced Chemtech (Louisville, KY), Calbiochem-Novabiochem (La J 011a, CA), and Peptides International (Louisville, KY). Labeled amino acids were purchased from Icon Services (Summit, NJ) and were fluorenylmethoxycarbonyl (FMOC)-protected using literature methods.(1, 2) The F MOC-l-13 C glycine was purchased fiom Sigma-Aldrich (St. Louis, MO). The 1- Palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1-palmitoyl-2-oleoyl-sn- glycero-3-phospho-rac-(l-glycerol) (POPG), 1-palmitoyl-2-oleoyl-sn-glycero-3- phosphoethanolamine (POPE), 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-L-serine (POPS), phosphatidylinositol (PI), sphingomyelin, 1,2-di-O-tetradecyl-sn-glycero-3- phosphocholine (DTPC), 1,2-di-O-tetradecyl-sn-glycero-3-phospho-rac-(1-glycerol) sodium salt (DTPG), and 1,2-di-O-phytanyl-sn-glycero-3-phosphoethanolarnine (DPhPE) were purchased fi'om Avanti Polar Lipids (Alabaster, AL). N-(2-hydroxyethyl)- piperazine-N'-2-ethanesulfonic acid (HEPES) was obtained from Sigma-Aldrich (St. Louis, MO). The buffer solution used in the study contained 5 mM HEPES (pH 7.0) with 0.01% NaN3. l9 HFP Synthesis The “HFPmn-FSC” was synthesized as a C-terrninal amide with sequence AVGIGALFLGFLGAAGSTMGARS and a 13co label at Phe-8 using a peptide synthesizer (ABI 431A, Foster City, CA) equipped for solid-phase FMOC cherrristry. The “HF Ptr-L7cFl 1N” fusion peptide trimer was synthesized with sequence (AVGIGALFLGFLGAAGSTMGARSWKKKKKK)3-Ap and with a 13co label at Leu-7 and a 15N label at Phe-ll on each strand, where AB refers to ,B-alanine. The related “HFPtr-F8CL9N” trimer was synthesized with sequence (AVGIGALFLGFLGAAGSTWMGARSKKKKKKh-Afl and with a 13co label at Phe-8 and a 15N label at Leu-9 on each strand. Residues in the N-termini of HFPtr correspond to the 23 N-terrninal residues (sequence AVGIGALFLGFLGAAGSTMGARS) of the LAV1a strain of the HIV-1 gp41 envelope fusion protein. HFPtr synthesis began with coupling of FMOC-Lys(Mtt) and activated ,B-Ala-Wang resin. A lysine trimer backbone was then formed with coupling of FMOC-Lys(Mtt) followed by coupling with N-a- FMOC-N'-e-tert-butoxycarbonyl-L-lysine (FMOC-Lys(Boc)). Prior to the second and third couplings, the Mtt group on the lysine side chain was removed with 1% trifluoroacetic acid (TFA) in dichloromethane (DCM). The rest of the trimer was then synthesized using standard solid-phase FMOC chemistry.(3) Syntheses of “HFPtr-A6c” and “HFPtr-A15c” began with chemical synthesis of a HIV fusion peptide with sequence AVGIGALFLGFLGAAGSTMGARSWKKKKKCAB and a fusion peptide with sequence, (AVGIGALFLGFLGAAGSTMGARSWKKKKKQXAVGIGALFLGFLGAAGSTMGA RSWKKKKKKAB). The sequences in parentheses represented individual peptide strands 20 and there was a chemical bond between the C0 of the underlined cysteine and the NH of the sidechain of the underlined lysine.(3) A fusion peptide trimer (HFPtr) was prepared by cysteine cross-linking these two peptides.(4) The non-native C-terminal lysines greatly improved aqueous solubility and the non-native tryptophan served as a 280 nm chromophore for peptide quantitation. HFPtr-A6c was l3CO labeled at Ala-6 on each strand and HFPtr-AISC was l3CO labeled at Ala-15 on each strand.(5, 6) HFPS were purified with reversed-phase HPLC using a preparative C13 column (V ydac, Hesperia, CA) and a water-acetonitrile gradient containing 0.1% TFA. Mass spectroscopy was used for peptide identification. Model Compounds 14 peptide. A 17-residue acetylated and amidated “I4” peptide with sequence Ac- AEAAAKEAAAKEAAAKA-NH2 was synthesized by the standard solid-phase FMOC method with a 13 CO label at Ala-9 and a 15N label at Ala-l3 as a setup compound for REDOR experiments.(1, 2) The solid-state NMR 14 peptide sample was lyophilized fi'om aqueous solution and is predominantly (83 :l: 6%) or helical at Ala-9(7) The two labeled nuclei should have a 13 C-lsN internuclear distance of ~4.1 A in the helical structure. N-acetyl-L-leucine WAL). 1-‘3c, N-‘3C doubly labeled NAL (D-NAL) was synthesized as a setup compound for prTDQBU and prFDR-CT experiments. The chemical structure of D-NAL is illustrated in Figure 4a. Synthesis of D-NAL began with addition of 1-13C, lsN leucine to glacial acetic acid and heating to 100 °C. 1-13C acetic anhydride was then added, the solution was cooled to 80 °C, and water was added to react with any excess acetic anhydride. The D-NAL product was washed with 21 cyclohexane, and the cyclohexane was subsequently removed under vacuum. Residual solvents were removed by water aspirator vacuum, drying in a vacuum dessicator and dissolution in water followed by lyophilization. Liquid-state 1H and 13 C NMR confirmed the identity, purity and labeling of D-NAL. The NAL sample for solid-state NMR was prepared by aqueous dissolution of a 1:9 mixture of D-NAL and unlabeled NAL (ICN, Aurora, OH) followed by slow evaporation of the water.(8, 9) The polycrystalline solid was ground with a mortar and pestle. The intramolecular 13 C-13 C distance of D-NAL in the crystal is 3.07 A.(10) Glycyl—L-phenylalanyl-L-phenylalanine ( GF F). Doubly labeled GFF (D-GFF) was synthesized withl3CO labels at Gly-l and Phe-3 and was a model compound for the prTDQBU experiments. D-GF F synthesis began with dissolution of FMOC-1-l3C-Phe in a N-methylpyrrolidone (N MP)/DCM mixture followed by 2 h coupling of the amino acid to unsubstituted Wang resin using a mixture of 1.0 M N,N’-dicyclohexylcarbodiirnide in NMP and 0.1 M 4-dimethylaminopyridine in dirnethylforrnamide. Unreacted anrino groups on the resin were benzoylated with benzoic anhydride. Standard FMOC chemistry was used for the remaining synthesis with 4 h and 8 h coupling times for FMOC-Phe and F MOC-l-UC-Gly, respectively. D-GFF was cleaved from the resin in a 3 h reaction with a rrrixture of TFA-water-phenol in a 33:2:2 volume ratio and precipitated by addition of t-butyl methyl ether (TBME). The yellowish-white precipitate was washed with TBME, centrifuged, lyophilized, dissolved in water, and passed through a 4-8 ,um filter. After slow evaporation of the water, colorless and needle-like D-GFF hemihydrate crystals were harvested. A small aliquot of the crystals was dissolved in dimethylsulfoxide-d6 and subsequent 1H and 13 C NMR 22 Spectroscopy confirmed the purity and labeling of D-GFF.(11) The solid-state NMR sample of GP F was prepared by aqueous dissolution of D-GF F and unlabeled GFF (Sigma-Aldrich) in a 1:49 ratio followed by slow evaporation of solvent. The crystalline solid was ground with a mortar and pestle. The intramolecular ” C-” C distance of D-GFF in the crystal is 5.40 A.(12) The chemical structures of D-NAL and D-GFF are illustrated in Figure 4. Solid-State NMR Sample Preparation Lipid preparation. HFP samples were prepared using three lipid/cholesterol mixtures: (a) "PC-PG" had POPC and POPG in a 4:1 mol ratio and had a headgroup composition similar to that used in previous fusion peptide and fusion protein biophysical studies;(13-16) (b) "LM3" had POPC, POPE, POPS, sphingomyelin, PI, and cholesterol in a 10:5:2:2:1 :10 mol ratio and reflects the lipid headgroup and cholesterol composition of cells infected by HIV;(1 7, 18) (c) "LM3e" had DTPC, DTPG, DPhPE and cholesterol in a 9:3:3:10 mol ratio and (d) LMe had DTPC, DTPG and cholesterol in an 8:2:5 mol ratio. Mixtures (c) and (d) were similar to LM3 in lipid headgroup and cholesterol composition but contained ether-linked rather than ester-linked lipids to eliminate natural abundance lipid ”CO signals.(5, 11) Lipid and cholesterol powders were dissolved in chloroform. 23 (a) O O H H II H3C—19C—N—CH—1ziC—OH 1H2 (EH-CH3 CH3 (1)) o o o 13“ H H H 13“ HzN—CIJH—C—N—(ISH c N (l‘.H—C—OH CH2 CH2 1/2 H20 Figure 4. Chemical structure of (a) 1-”C, N-”C doubly labeled N-acetyl leucine (D- NAL) and (b) 13c doubly labeled G1ycyl-L-phenylalanyl-L-phenylalanine (D-GFF), in which the labeled l3c nuclei are in bold. The intramolecular labeled 130% distances in D-NAL and D-GFF crystals are 3.07 A and 5.40 A, respectively. 24 The chloroform was removed under a stream of nitrogen followed by overnight vacuum pumping. Lipid dispersions were formed by addition of 5 mM pH 7.0 HEPES buffer followed by homogenization with 10 freeze-thaw cycles. Large unilamellar vesicles (LUVS) were prepared by extrusion through a filter with 100 nm diameter pores.(19) Solid-state NMR sample preparation. The samples were made in a manner similar to that used for functional fusion assays.(3) HFPtr (0.1-0.2 mol as determined by A230) was dissolved in ~2 mL of 5 mM HEPES buffer and LUVS (~30 umol total lipid) were prepared in ~2 mL of buffer. The peptide and LUV solutions were mixed and kept at room temperature overnight followed by ultracentrifugation at 35000 rpm for 5 h at 4 °C. The peptide/lipid pellet formed after ultracentrifugation was transferred by spatula to a 4 mm diameter MAS NMR rotor. Unbound HFPtr is predominantly monomeric under these conditions and does not pellet. For the HF Ptr and other samples, the rotor volume of ~40 11L was filled. Lyophilized I4 peptide (~29 ,umol), polycrystalline D-NAL (~260 total ram] with ~26 limo] doubly labeled compound) and polycrystalline D-GFF (~l40 total ,umol with ~2.8 ,umol doubly labeled compound) were ground before being packed in 4 mm diameter MAS NMR rotors. Magic Angle Spinning and Cross Polarization Molecular tumbling rates in most solids are usually much slower than the NMR frequency and the NMR peaks are therefore broadened by anisotropic effects, dipolar and quadrupolar interactions. These effects can be reduced and the peaks can be subsequently narrowed by magic angle spinning (MAS), whereby the NMR sample is rotated at kHz 25 fiequencies about an axis tilted at the “magic angle” tan’1 2 , or 54.7° relative to the static external magnetic field direction. An MAS spectrum contains peaks called centerbands at the isotropic chemical shifts, which would be observed in a typical liquid- state spectrum. Additional peaks can be observed which are separated from the isotropic peaks by integral multiples of the Spinning frequency and are known as spinning Sidebands. “Cross polarization” (CP) of magnetization from protons to ”C is a solid-state NMR technique which increases ”C signals. CP is accomplished by simultaneous rf radiation of both the 1H and ”C nuclei such that both isotopes effectively process at the same frequency. Magnetization transfer is mediated by heteronuclear dipolar coupling. Figure 5 Shows the typical pulse sequence for a ” C CP experiment. General Solid-State NMR Parameters Experiments were done on a 9.4 T Spectrometer (V arian Infinity Plus, Palo Alto, CA) using a MAS probe in double resonance ”C/IH or triple resonance 1'l’C/lH/ISN configuration. The NMR detection channel was tuned to ”C at 100.8 or 100.2 MHz, the decoupling channel was tuned to 1H at 400.8 or 398.6 MHz and the third l5N channel was tuned to 40.6 or 40.4 MHz only for triple resonance configuration. ”C Shifts were externally referenced to the methylene resonance of adarnantane at 40.5 ppm. Spacers were used to restrict samples to the central 2/3 rotor volume (~40 ,uL) in which the rf field variation was less than 10%.(20) Experiments were performed at —50 °C rather than room temperature in order to achieve more efficient cross-polarization (CP) and greater signal per ”C nucleus. There were similar ”C backbone chemical shifts at both low 26 temperature and room temperature, suggesting that cooling the sample does not cause significant peptide structural changes.(21) CP MAS Spectroscopy The CP MAS pulse sequence was displayed in Figure 5. Two CP matches were tested to compare their 1H-” C CP efficiencies at various MAS frequencies on D-NAL and HFP-F8c/LMe. In “match 1”, the 1H rf fields of the 7172 pulse, CP and CW decoupling were respectively 45 kHz, 45 kHz and 90 kHz, while the rf field of ” C was ramped fiom 37 to 50 kHz. In “match 2”, the 1H rf fields of the 72/2 pulse, CP and CW decoupling were respectively 60 kHz, 60 kHz and 90 kHz, while the rf field of ”C was ramped from 43 to 54 kHz. There were 128 acquisitions for each D-NAL experiment with MAS fiequency at 8000, 9000, 10000, 11000, 12000 and 13000 Hz and 512 acquisitions for each HFP-F8c/LMe experiment with MAS frequency at 8000, 10000, and 12000 Hz. The contact time and recycle delay were respectively fixed at 3 ms and 1.25 s and phase cycling included 1H 72/2, x, —x, x, —x; 1H CP, y, y, y, y; ”C CP —y, —y, —x, -—x; receiver, —x, x, y, —y. The 1H and ”C pulse lengths were approximately obtained by direct pulsing adamantane and the CP matching condition was obtained by running ramped CP on D- NAL. Calibration of the 1H 7r/2, ” C 71/2 and ”C 7: pulses was done with the CP "Z-filter" sequence (CP — rr/2 — 1,. — 7r — acquisition) run on the D-NAL sample. 27 112/2 1H CP CW decouple 13‘0 CP Acquisition Figure 5. 13 C CP MAS pulse sequence. Magnetization is transferred from 1H nuclei to 13 C nuclei during CP. 1H continuous wave (CW) decoupling was applied during acquisition. 28 REDOR Spectroscopy The REDOR sequences were shown in Figure 6. The "all-but-one l5N 7t pulse" version was used to suppress natural abundance ”C Si gnals and selectively detect the labeled Phe-8 l3co signal of HFPtr-F8cL9N, of Figure 6a.(22, 23) An initial 2 ms CP was done with a ramped 40-50 kHz l3C rf field and a ~60 kHle rf field and was followed by a 1 ms dephasing period and then 13c detection. A single ~50 kHz 13(3 refocusing rt pulse was placed at the midpoint of the dephasing period, and two-pulse phase-modulation (TPPM) lH decoupling of ~90 kHz was applied during dephasing and detection.(24) The 13C transmitter was set to ~155 ppm and the ”N transmitter was set to ~115 ppm. An “So” and an “S1” acquisition were obtained. The dephasing period during the 51 acquisition contained a 40 kHz l5N 7t pulse at the midpoint and at the end of each rotor cycle except for the fourth and the eighth cycles. XY-8 phase cycling (x, y, x, y, y, x, y, x) was used for the ”N pulses.(25) The 15N pulses disrupted averaging of the l3C-”N dipolar coupling by MAS and led to selective attenuation of the Phe-8 13CO signal. The S0 acquisition did not contain ”N pulses and ”C-”N dipolar coupling was efficiently averaged by MAS and did not lead to ”C Signal attenuation. The selective Spectrum of Phe-8 13CO was obtained by subtracting the S1 signal from the So signal. 13CO-”\N distances were measured with an "alternating 15N/ ”C it pulse" version of REDOR, of Figure 6b.(26, 27) For the $1 acquisition, the dephasing period of length 1; included a ~40 kHz ”N rt pulse at the midpoint of each rotor cycle and a ~50 kHz ” C rt pulse at the end of each rotor cycle except for the last cycle. The S0 acquisition did not include l5N 7t pulses during the 29 1H | GP TPPM decouple l I 1 “It I l l I ‘30 I? [l :Acquisition: I I I I I I 1t 1t 1t TC 11: It I l I I 7 7 7 7 , _ I I | I T I Rotor 0 1 2 3 4 (b) 1t/2 ‘H ”Cp TPPM decouple l l I I It It It I I I I ‘30 6 H H H :Acquisition: I 1 ‘ ‘ ‘ I l I 1 1t 1t 1t 1t 1 l l I 7 7 _ l | l I I l Rotor 0 1 2 3 4 Figure 6. 1D ”C REDOR pulse sequences with (a) the "all-but-one 15N 7t pulse" version and (b) the "alternating ”N/ ” C 7t pulse" version. CP transfers lH magnetization to ”C. ”C magnetization is dephased (i.e., reduced) by ”C-”N dipolar coupling mediated by either (a) two equally spaced l5N rt pulses per rotor period except the one in the middle of the sequence or (b) one ”N rt pulse per rotor period. One ”C it pulse as in (a) or multiple ”C 7t pulses as in (b) refocus the ”C chemical Shift. 30 dephasing period. TPPM 1H decoupling of ~90 kHz was applied during dephasing and detection.(24) ”C signals were attenuated by l3C-”N dipolar coupling in the S1 acquisition but not in the So acquisition. Spectra were acquired for different 1;- and the difference between the 13C0 So and 51 signal intensities divided by the So Signal intensity (AS/So) was the experimental parameter used to determine l3CO-”N dipolar couplings and distances. XY-8 phase cycling was used for the 15N Itpulses and for all of the ”C 72' pulses except the final pulse. Individual So or S1 transients were added with phase cycling: 1H 702, x, —x, x, —x; 1H CP, y, y, y, y; ”C CP —y, —y, -x, —x; final l3C rtpulse, —y, -y, —x, —x; receiver, —x, x, y, —y. The S0 signal intensity of the 14 peptide was used to optimize 1H 7t/2, lH decoupling, the TPPM coupling pulse length, l3c 7t, and CP rf fields, and the AS/So values of the 14 peptide were used to optimize the ”N 7t rf field. prTDQBU Spectroscopy For both the prTDQBU and prFDR-CT experiments, typical parameters included MAS fiequency at 8000 :l: 2, 10000 i: 2, or 12000 :1: 2 Hz, ramped 50-60 kHz 13C and constant 65 kHle fields during the 3 ms CP period, 20.5 kHz ”C rtpulses, 50 kHz ”C 702 pulses, continuous-wave (CW) lH decoupling of 95 and 60 kHz during the firRFDR and acquisition periods, respectively, and 1.5 s recycle delay. Except when studying effects of transmitter offset, the ”C transmitter was set to 172.4 ppm for D- NAL, 175.5 ppm for D-GFF, 166.2 ppm for membrane-associated HFPmn-F8c and HFPtr-A6c, and 158.4 ppm for membrane-associated HFPtr-A150 Figure 73 displays the prTDQBU sequence that had the form CP;+ ,1/2 — 31 ()pRFDR)L — rt/2; 7t/2x -— 0pRFDR)M — 7t/2_x 7t/2y — (prFDR)N — acquisition where L, M, and N were integers and (firRFDRh, (prFDR)M, and ()pRFDR)N had durations L171, M IR, and N171 with 17; being the duration of a rotor cycle. Transverse ” C magnetization was generated during the CP period, evolved during the ijFDR periods, and was detected during the acquisition period. During the ijFDR periods, ”C chemical shift evolution was refocused by the rotor-synchronized ” C Itpulses. The 7172; 7t/2x (C = y, —y) and n/2_,rr/2, pulse pairs refocused the ‘3c-‘3c dipolar coupling, while the 71/2; r/2, (t: x, —x) pulse pairs did not refocus this coupling. For the latter case, there was homonuclear dipolar evolution during a period denoted tthat had duration 2L 1R. Increasing values of 1' were obtained by incrementing L and decrementing N by the same number while keeping M constant with an additional overall effect of having a constant time (C7) period of duration (L + M + N) 1);. For each set of L, M, N values, FIDS with C = x, y, —x, —y were recorded. The So signal (no 13’0” C coupling) was formed from addition of the FIDS with 4' = y and -y while the S1 signal (”C-”C coupling during 1) was formed with addition of the FIDS with 4' = x and —x. Two versions of the prTDQBU sequence were tested and were denoted “one-rt- per-1R” and “one-7t-per-2 17;” (Figure 6b, c). These versions differed during the ijFDR periods in having one ”C it pulse per rotor cycle or one ”’ C 7t pulse per two rotor cycles, respectively. XY-8 phase cycling was used for the ”C rtpulses and L, M, and N were integral multiples of 8 or 16 for the one-7t-per- 17; and one-7t-per-2 17; versions, respectively. 32 ‘H ” CP CW decouple CW decouple ‘30 CP Lt M1 N1 Acquisition J‘s + =I Rs 1) II N P----- :r it CT XYxYYx x 1 1,, U8, M/8 or Nl8 repeats (C) x y x y y x Y x [.IIILDJJIDJJLJ H 1,, Ll16, M/16 or Nl16 repeats Figure 7. prTDQBU pulse sequence. (a) The displayed prTDQBU pulse sequence included: (1) cross-polarization (CP) from 1H nuclei to ”C nuclei; (2) a constant-time (C7) period of (L + M + N)1'R duration where L, M, and N were integral multiples of 8 or 16, and 31;; was the duration of a single rotor period, and (3) an acquisition period during which 3C NMR signals were detected. Continuous wave H decoupling was applied dming the CT and the acquisition periods. A pair of back-to-back ”C 7112 pulses separated the L1); and the M1); periods and another pair separated the M111 and the N13 periods. Variants of the pulse sequence during the CT period included (b) the “one-rt-per- 17;” version with one ”C rtpulse per rotor period and (c) the “one-rt-per-2 1R” version with one 13C rtpulse per two rotor periods. The ”C CP rf phase was 6+ 7112 and the phase of each 13C 72/2 and 7t pulse is noted above the pulse. For f = y or —y, l3C-”C dipolar couplings were averaged to zero and So data were obtained and for 4’ = x or —x, ” C-” C dipolar couplings were not averaged to zero and S1 data were obtained. The duration of the l3c-“c dipolar recoupling or dephasing period 1'= 2L1'R, and data with increasing 1' were obtained by incrementing L and decrementing N while keeping constant M and constant (L + M + N). 33 prFDR-CT Spectroscopy Figure 8a displays the prFDR-CT sequence that had the form CPy — [WRFDRM — 7t/2x — (prFDR)N— 7t/2y — ()pRFDRhN — 7t/2.y - (ijFDR)N — 7t/2_x — 0pRFDR)M]K — acquisition where M and N were integral multiples of 8, (prFDR)M and ()pRFDR)N had durations M 1R and N 11;, and K was an integer. Transverse ” C magnetization was generated during the CP period, evolved during the prFDR periods, and was detected during the acquisition period. During the JpRFDR periods, ”C chemical shift evolution was refocused by the rotor-synchronized ”C rtpulses. For M = N = M), So data were obtained because each cycle of (prFDR)M — 7t/2x — (firRFDR)N — rt/2y — (prFDR)2N - 7t/2..,, — (firRFDR)N — 7t/2_x — (firRFDR)M can be considered as a series of WAHUHA periods with averaging of the ” C-” C dipolar couplings. For M > N, l3’C-”C dipolar couplings were not averaged during the initial (firRFDR)M_ N and final (@RFDRM- N periods of each cycle and SI data were obtained. Data with increasing dipolar coupling time 1'were obtained by incrementing M by “AM” which was an integral multiple of 16 and decrementing N by AM/2 so that 1'= 2K x (M — N)1'R = 3KAM1'R and the total CT = 2K x (M + 2N)1'R = 6KMo1'R. The full phase cycle included the (CPy 7t/2x rt/2y 7t/2.y 7t/2_x) ” C phases displayed in Figure 8a as well as the (CP_x 7t/2y 7t/2_x 7t/2x r/2_,), (CR, r/2_. r/2_, 7t/2y M2,), and (CPx, r/2_, a/2. n/2_, rr/2,,) l3c phases with y, -—x, —y, and x receiver phases, respectively. Transverse Relaxation Measurements For the prFDR-CT experiment, the ”C magnetization was longitudinal during the period between the first and second 7112 pulses and the period between the third and 34 (a) 11/2 1H CP CW decouple CW decouple I I x V -v -x : : : : 13C MtR NtR 2N1:R N‘ER MIR: Acquisition : 1' i K repeats 1 == CT = (b) XYXYYXYX 1 Ta Ml8, MB or 2N/8 repeats Figure 8. prFDR-CT pulse sequence. (a) The displayed prFDR-CT pulse sequence included cross-polarization (CP) from 1H nuclei to ”C nuclei, a constant-time (CT) period, and an acquisition period during which 13C NMR signals were detected. Continuous wave lH decoupling was applied during the CT and the acquisition periods. The CT period contained K cycles of (2M + 4N)1'R duration where K was an integer, M and N were integral multiples of 8, and 17; was the duration of a single rotor period. Each (2M + 4N)1'R cycle contained intervals separated by ”C #2 pulses and panel b displays the series of ”C rtpulses in each of these intervals. The 13C CP rf phase was y and the phase of each ”C 7112 and Itpulse is noted above the pulse. Each (2M + 4N)1'R cycle could be understood to have a central 6N 1'R WAHUHA period during which the ” C-” C dipolar couplings were averaged to zero. For M = N, the CT period can be considered as a series of WAHUHA periods and So data were obtained with no dipolar coupling period. For M > N, ” C-” C dipolar couplings were not completely averaged and 51 data were obtained. The total duration of the 13C-”C dipolar recoupling or dephasing period 1' = 2K x (M — N)1R and data with increasing 1' were obtained by incrementing M and decrementing N while keeping (M + 2N) and K constant. 35 fourth 7112 pulses. For the dephasing period 1'= 3KAM1'R, the total ”C transverse relaxation period 1'7 = 2K x (M + N) 1'}; = K X (4M0 + AM)1'R. Quantitative interpretation of the prFDR-CT data therefore required consideration of ”C transverse relaxation and ”C T 2 times were measured with a Carr-Purcell multiple echo sequence illustrated in Figure 9. The Carr-Purcell pulse sequence contains CPx — [D 1'}; — 75, — 2D1R — my — D1'R — detect] p where D was an even integer, P was an integer, and a data set consisted of echo Signals with different values of P.(28) For all samples, the echo intensities E(t) fitted well to a single exponential decay E(t) = E(O) exp(—t/T2) where t = 4DP1'R. The uncertainties in the fitted T2 values were < i 8%. Experimental parameters for the Carr-Purcell sequence included 10 kHz MAS frequency, ~65 kHz ”C Itpulses, and ~95 kHz CW 1H decoupling. Experimental data analysis For each pair of S0 and S1 REDOR or prTDQBU spectra with a particular dephasing time 1', integrated signal intensities in the isotropic carbonyl regions were denoted So and S1, respectively. A single experimental uncertainty 0 was calculated as the root-mean-squared deviation of integrated intensities in 24 regions of the So and S; spectra without signal. The integrated intensities were incorporated into the normalized dephasing parameter: exp E :50”): -5. (2.1) So So So The uncertainty in (AS/So)” was calculated:(29) 36 1t/2 ‘H CP CWdecouple T - “v : : l I ”c cp :Acquisflion: X 7 I I. e i .i. J 1 ' 'F ' " Prepeats Figure 9. Carr-Purcell pulse sequence. The x-phase l3C magnetization was transferred from 1H by cross-polarization, and 13C 7t pulse phases alternated between y and -y to prevent spin locking and to minimize effects of rf field inhomogeneity on the experimental echo decays. D was an even integer, P was an integer, and a data set consisted of echo signals with different values of P. 37 2 gexpzil+fl3=g_SL.l_2+_17 (2.2) So So So SI So The prFDR-CT data were similarly analyzed except that for each value of 1, there was only one spectrum. The 1'= 0 spectrum with no dipolar coupling period was denoted So and the other spectra with variable dipolar coupling periods were denoted S1. In addition, separate 030 and as, were calculated as the root-mean-squared deviations of integrated intensities in 12 regions of the So and S1 spectra without signal. The normalized dephasing parameter for the prFDR-CT data was (St/So)” and the uncertainty in (SI/S0)” was calculated: 2 2 2 2 2 a S o a 0 So So So SI 50 For 1'= 0,51/50 = 1 and 0”” = @030 /S0 . One goal of this study was quantitative comparison between the (AS/So)” or (SI/So)” and simulations done for two or three ”C nuclei coupled with either heteronuclei (in the case of REDOR) or homonuclei (in the cases of prTDQBU and prFDR-CT) at different internuclear distances. However, the experimental samples contained natural abundance ”C close to the labeled ”C and the experimental ”C labeling was ~99%. Values of (AS/SOY" and (Si/So)” were calculated from (AS/So)” and (SI/So)” to compensate for these effects and followed the correction methods detailed in literature.(1 1) As an example of correcting REDOR data, calculations of (AS/So)” for HFPtr- L7cF11N were based on the following approximations: 38 (1) There is 99% labeling of the Leu-7 ”CO and Phe-ll ”N sites. S1 = So for a labeled Len-7 ”CO in a peptide strand with a Phe-ll 14N. (2) S1 = 0 for a labeled Lou-7 ”CO separated by one or two bonds fi'om a natural abundance ”N at Phe-8 or Leu-7. The Len-7 S1 is not affected by other natural abundance ”N. (3) S1 = 0 for natural abundance backbone ”COS at Gly-10 or Phe-ll which are separated by one or two bonds from the labeled Phe-ll ”N. S1 = So for other natural abundance backbone ”CO sites. Criteria (1) and (2) are based on the close distance (5 2.5 A) and consequent strong (2 200 Hz) dipolar coupling of ”CO and ”N nuclei separated by one or two bonds. As described in Appendix I and the literature, an expression for (AS/So)” can be derived:(1 1 ) .A_Scor— 1_l]C+nAC gap_ 2Ac+2AN (2 4) So (l—UC_UN_2BN) So (1_UC_UN_2AN) . where Hg and UN are the fractional abundances of Leu-7 12CO and Phe-ll 14N, respectively, Ac and A N are the fractional ”C and ”N natural abundances, respectively, and n is the average number of unlabeled CO sites per peptide strand. For the HFPtr samples, values of Uc, UN, AC, AN, and n are 0.01, 0.01, 0.011, 0.0037, and 29.33, respectively. Eq. (2. 4) leads to (AS/So)°°'/(AS/So)"“"p ratios of ~1 .3. The value of of" was calculated by multiplying 0fo by the prefactor for (AS/So)” in Eq. (2. 4).(29) The calculations of (AS/So)” for the rest REDOR data are detailed in the Appendix I. As an example of correcting prTDQBU data, calculations of (AS/S0)” for D- GF F were based on the following approximations: 39 (1) ”CO signals from Gly-l, Phe-2, and Phe-3 were completely resolved. (2) Intermolecular 13C-”C dipolar coupling was not considered. For Gly-l ”CO, the closest intermolecular carbon nucleus was > 4 A away. (3) There was 99% labeling of Gly-l ”CO and Phe-3 13C0. SI = So for a molecule with a labeled Gly-l 13co and a Phe-3 12co. (4) SI values for a molecule with a labeled Gly-l 13CO and nearby natural abundance ”C were set with the following criteria: (4a) S1 = 0 when 1' $32 ms and the labeled Gly-l ”CO/natural abundance ”C nuclei were separated by one or two bonds. (4b) S1 = 0 when 1'> 32 ms and the labeled Gly-l ”CO/natural abundance ”C nuclei were separated by one, two, or three bonds. (4c) 51 was not affected by the natural abundance ”C if neither criterion (4a) nor (4b) was satisfied. The criteria were based on the ~l.5 A, ~2.5 A and ~3.8 A distances for one-, two- and three-bond ” C-” C separations, respectively, and the consequent 2200 Hz, 500 Hz, and 140 Hz dipolar couplings. (5) S1 = So for a natural abundance Gly-l 13CO in an unlabeled GFF molecule. The expression of (AS/So)” for D-GFF was: cor exp [as] = 1— UC1+ nAC (as) _ mAC (2.5) l—UC1_UC2_mAC 1_UC1_UC2—mAC So So where Um = 0.01 and U52 = 0.01 were the fiactions of Gly-l and Phe-3 12CO sites in D- GFF, respectively; Ac= 0.011 was the fractional ”C natural abundance; n = 49 was the ratio of unlabeled GFF to D-GFF molecules in the crystal; and m was the number of unlabeled carbon nuclei which satisfy either criterion (4a) or (4b). Incorporation of the previously noted parameter values for 1' £32 ms and m = 2 yielded: 40 cor exp 35- = 1.596 AS- — 0.023 (2.6) SO SO and for 1'> 32 ms and m = 4 yielded: cor exp g = 1.634 g — 0.047 (2.7) S0 S0 COI‘ The expressions for (AS/So) of D-NAL were determined in a manner similar to those of D-GFF and detailed in the Appendix I. The (AS/Sp)” of the membrane-associated HFPS were analyzed in the context of two structural populations. For one population with fraction h, there was a detectable dipolar coupling (dcc) between the labeled ”COS and for the other population with fraction 1 — h, dcc = 0. The resulting (AS/So)” had a general form: As_c°'_ l-UC+ nAC g””_ mAC (2 8) s0 _h(1—UC—mAC) sO h(1-UC— mAC) ' The prFDR-CT (SI/So)” expressions were similarly derived and yielded a general expression for D-GFF and D-NAL: cor exp {i} = l-UCl+nAC [31.] _ nAC+UC2 (2.9) 1_UC1—UC2—mAC So l—UCl—UCZ—mAC So The (AS/So)” or the (SI/So)” expressions had the general form a x (AS/So)” — b or a X (Sl/So)“p — b, respectively, where a and b were positive numbers. The 0°” associated with (AS/So)” and (Si/So)” were therefore a x 0“”. The overall data analysis included the goodness-of-fit metric 12 that had (om)-2 dependence. Although the h in the HFP analysis was a fitting parameter, the HFP a” were calculated with h = 1 and the Dr variations of 2’2 with h were therefore independent of ac . 41 Solid-State NMR Simulation and Fitting Theory. Prior to the introduction of the simulation and fitting methods in solid- state NMR, it is necessary to apply density matrix theory to analyze and simulate complex NMR experiments conducted in a building block fashion.(30, 31) For a two-spin system in which each nucleus has a spin of 1/2, there are four energy levels. The state functions describing these energy levels are given by 1111 = | aa >, 1,112 = | 01,8 >, 1,93 = | Bar >, and 1,114 = | BB >. An arbitrary state function, | ‘P > can be readily expanded by the a complete set of basis firnctions {ll/n} as |W>=ch|lyn). (2.10) In NMR experiments, I ‘1’ > is usually time-dependent and then the dependence of time is contained in the coefficients c,,(t). The expectation value of an operator, Up is given by (0p)=(\ll|op|\l')=2c;c,.(n|op|n’), (2.11) and its ensemble average is given by <0_p)=za. (2.12) The basis functions, w,- and the matrix elements, < i | Up | j > are time independent. The conjugate product terms of the coefficients, C;Cn' are conveniently considered as the matrix elements of the density operator ,0 czcn, -=- (n'lpln). (2. 13) By recalling ZIn)(n| =1, Eq. (2. 12) above becomes 42 (612—):Z=Tr(p0p) =Tr(0pp), (2.14) where symbol Tr is called trace and defined as the sum value of all diagonal elements of a matrix. From the operator product formalism above, one finds it significant to calculate or to simulate the time evolution of the density operator ,0 during an NMR experiment assuming that the initial value p(0) at thermal equilibrium or resulting from a given preparation sequence is known. A convenient approach of simulation of an NMR experiment is based on the numerical evaluation of the Liouville—von Neurnann equation of motion d . Ep(t)=-1[H(t),p(t)]a (215) where H(t) is the time-dependent Hamiltonian describing the relevant spin interactions and external operations, e. g. rf irradiations. Neglecting spin relaxation, the formal solution to Eq. (2. 15) is p(t)=U(t, 0) p(0) U“(t, 0), (2.16) where U(t, 0) is the unitary propagator responsible for the Spin dynamics in the period from time 0 to time t and If 1(t, 0) is the inverse operator of U(t, 0). The propagator U(t, 0) is related to the Hamiltonian as I U (r, 0) = T exp {—i [H (t’)dt'}, (2. 17) o where T is the Dyson time-ordering operator relevant for Harniltonians containing noncommuting components. Furthermore, U(t, 0) can be efficiently and numerically approximated by replacing the integral in Eq. (2. 17 ) by a simpler time-ordered product 43 U (t, O) = fi exp{—iH (kAt) At} , (2. 18) k=0 where k is the number the number of infinitesimal time intervals At over each of which the Hamiltonian may be considered time-independent and which overall span the fllll period flom 0 to t = [At (32) In the most typical cases in solid-state, the Hamiltonian is described by the high-field truncated components in the Zeeman interaction flame, i.e. the rotating flame. For a Spin system consisting of multiple spins 1,- consisting only 1/2 spins, being of the same or different spin species, the Hamiltonian has the form H=Hext+Hint=Htf+HCS+Hd’ (2.19) where H,f = 2| wif (t) | (1,, cos a, +4., singoi) (2.20) i Hcs= 241C, 0(112 (2.21) H0): in}; 0j.()(3l,.,1j,— —1,. 1].) (2.22) with subscripts i and j specifying the involved spins and 1,- representing the vector sum of 1g, 11,, and [,2 spin operators. Here are some detailed descriptions of each term of the Hamiltonian. Under the rotating flame and neglecting relaxation, the only external Hamiltonian is contributed by a series of (pi-phase rf irradiation pulses with an angular nutation frequency, wine For 1/2 spin systems in the solid state, J coupling is usually negligible and quadrupolar interaction is not present. Therefore, the internal Hamiltonian is contributed by chemical shift (CS) and magnetic dipole-dipole coupling (d). 44 For the internal Harrriltonians H, with A = CS or d, the flequency coefficients i.e. afCS o and (02’ o , are functions of time and relative orientations, which are of zeroth rank and second rank for isotropic and anisotropic parts of the interaction A, respectively. The dependencies may be expressed in terms of a Fourier expansion in the context of MAS, 2 a)”. (t) = Z mmmlm) eima’r’, (2.23) m = —2 where ark/211 is the MAS flequency and the Fourier coefficients (0mm, (m) depend on the intrinsic interaction (60A, ,3.) and/or 60A, m) and some separate rotations between several reference flames, which relate the principal-axis flame (PA) of the interaction to a crystal- fixed flame (C), C to a rotor-fixed flame (R), and also R to the laboratory-fixed flame (L), respectively. The various flames are displayed in Figure 10 with the ORTEP-type representation as described by Mehring.(32, 33) For the convenience in mathematics, Euler angles relating flame X and flame Y are usually employed to describe the rotation for a certain interaction A and denoted as {2A Xy =[aA Xy, BA Xy, 7A 2”,]. QRL and OCR are not involved in rotations relating flame P A and are therefore independent of A, where A can be CS, d and etc. Furthermore, QRL can be set as [6012 t, tan"1 \f2- , 0] for MAS experiments within the high-field approximation, which is generally satisfied by modern NMR spectrometers. QCR appears in the expression of simulated “expectation values” and can be evaluated with power averaging methods detailed in the literature.(32) Once the information of {2,1, pc, spin system and pulse sequence is known, the evolution of density matrix can be numerically simulated. 45 21. X Z X C ZP R ZR X pr A C Y y C yp R Q A L yL Q L‘ QRL R‘ CR C ‘ A,PC P A Figure 10. The ORTEP representation. Illustrated here is a spatial second rank anisotropic interaction tensor in its principal axis system (PA), a crystallite-fixed coordinate system (C), the rotor-fixed coordinate system (R), and the laboratory-fixed coordinate system (L) along with the Euler angles Qxy = { aXy, By, M } describing transformation between the various flames X and Y. 46 Simulations. SIMPSON is a computer program for fast and accurate numerical simulation of solid-state NMR experiments, which was developed by the Nielsen Group in Denmark and designed to emulate a NMR spectrometer by letting the user specify high-level NMR concepts such as spin systems, nuclear spin interactions, RF irradiation, flee precession, phase cycling, coherence-order filtering, and implicit/explicit acquisition.(32) (AS/SOY” were calculated as a function of internuclear distances between two or three labeled nuclei and as a function of 1;. The simulations were done with the SIMPSON program and incorporated the MAS flequency and the 13C and ”N rf fields, pulse lengths, timing, and phases, as well as ” C resonance offsets and CSA principal values and axis directions. The REDOR Simulations were based on a single ” CO/ ”N spin pair and did not consider the ”N chemical Shift or CSA. The prTDQBU and prFDR-CT simulations were based on either two or three l3C0 nuclei and did not consider 15N spins. In the experiments, the effects of 1H and 14N spins were largely removed by 1H decoupling, constant-time and MAS, and these spins were not incorporated in any of the simulations. Orientation-dependent Simulation input parameters included 13C0 CSA principal values, the Euler angles which relate the ”CO CSA principal axis system(s) to a fixed crystal axis system, and the Euler angles which relate the ”CO-”N or 13'CO-”CO internuclear vectors to the crystal axis system. Although distance determination by REDOR, prTDQBU and prFDR-CT experiments is not strongly dependent on these parameters, an effort was made to use reasonable values for the parameters. The (A1, 522, 633) CSA principal values for all samples were listed in Table 1. Those values for 14 Ala- 47 9, HFPtr-L7CF1 lN/PC-PG Leu-7, HF Ptr-L7CF1 lN/LM3e Leu-7, HFPmn-FSC/ LMe Phe- 8, HFPtr-A6c/ LMe Ala-6 and HFPtr-AISC/ LMe Ala-15 13 COs were based on experimentally measured isotropic chemical shifts and literature CSA values.(11, 34, 35) The Gly-l and Phe-3 of GFF and the carbonyl and carboxyl of NAL CSA principal values were determined by fitting experimental centerband and spinning sideband intensities with the Herzfeld-Berger method.(1 I, 36) The Euler angles which relate a 13 CO CSA principal axis system to the crystal axis system can be considered in terms of the relative orientation of the principal axis system and the 13 CO chemical bonds and the structure and orientation of the molecule relative to the crystal axes. For 14 Ala-9, HFP, NAL and GFF Gly-l '3 COS, the principal axis/chemical bond orientations were: (1) the 63,3 axis perpendicular to the peptide plane; and (2) the 6;; axis tilted 130° from the CO-N bond.(34) GFF Phe—3 has ionic COO“ rather than amide functionality and its 633 axis was perpendicular to the 0C0 plane and its 6“ axis bisected the OCO angle.(3 7, 38) The crystal flame Euler angles for the l3CO principal axis systems and the internuclear vectors were calculated using a Mathematica program whose inputs were atomic coordinates from high-resolution structures and the previously detailed 13CO CSA principal axis directions. The atomic coordinates for GFF were obtained fiom its crystal structure while for parallel ,6 strand and antiparallel ,6 strand structures, coordinates were obtained respectively from the crystal structure of cutinase (PDB file name lcex) and fiom the crystal structure of human gamma-D crystalline R58H mutant (PDB file name 1h4a).(12, 39, 40) The latter two 48 Table 1. 13'CO principal CSA values used in SIMPSON simulation. Sample and labeled 13‘CO 511 (PPm) 522 (1)1331) 533 (PPm) Literature 14 peptide Ala-9 246 203 86 (11, 41) HFPtr-L7CF11N/ PC-PG Len-7 248 202 85 (11, 41) HFPtr-L7CF11N/ LM3e Len-7 242 195 83 (I I, 41) GFF Gly-l 255 168 91 (11, 36) GFF Phe-3 243 193 106 (II, 36) NAL carbonyl 246 201 87 (11, 36) NAL carboxyl 258 172 109 (I I, 3 6) HFPmn-FSC/ LMe Phe-8 242 191 85 (II, 35, 41) HFPtr-A6c/ LMe Ala-6 240 193 85 (II, 35, 41) HFPtr-A1 5c/ LMe Ala-15 242 195 87 (11, 35, 41) 49 structures have been refined to 1.0 and 1.15 A resolution, respectively. For REDOR simulations of the 14 and HFPtr-L7CF11N/PC-PG samples, the Ala-56 CO and Glu-6O N coordinates of cutinase were used. These residues are in a helical region of cutinase and the labeled l3co chemical shifis of the two solid-state NMR samples correlate with helical conformation. The REDOR simulation of the HFPtr-L7CF1 lN/LM3e sample used coordinates of Len-114 CO and Gly-118 N in a ,6 strand region of cutinase because the 13 CO shift of this sample correlated with ,B strand conformation. The two-spin prTDQBU simulation of the HF Ptr-L7CF1 lN/LM3e sample used cutinase Ile-37 CO and Ala-116 CO coordinates, and the three-spin prTDQBU simulation of the HFPtr- L7CF11N/LM3e sample used cutinase I1e-37 CO, Ala-116 CO and Thr-144 CO coordinates. In cutinase, these are in-register residues in a parallel ,B strand region and this was our initial structural model for ,8 strand HFPtr. Some SIMPSON simulations were done on a PC with a WINDOWS operating system and a 1.7 GHz processor while other simulations were performed on a LINUX cluster using two 1.8 GHz processors. As noted earlier in this chapter, the prFDR-CT dephasing period 1'= 3KAMTR and the transverse relaxation period If = K(4Mo + AM)2'R, and the effect of differential transverse relaxation was empirically incorporated into the simulation results with multiplication of (SI/so)“ by exp(— T/3 T2). Fitting of internuclear distances. For the REDOR and prTDQBU experiments, comparison was made between (AS/So)” and (AS/So)‘i’"calculated as a function of dipolar coupling d and the best-fit d was determined by X2 fitting: 50 . 181:“1841‘1 where the i subscript refers to a particular dephasing time t and N was the number of 2' (2. 24) periods. For the prFDT-CT experiments, the analogous analysis was done using (Si/So)” and (S 1/S0)5i’" in the 22 expression. In units of A, the l3C-BN distance rCN = (3110 Hz/dCN)“3 and the l3C-l3C distance rcc = (7720 Hz/dcc)“3.(42) The best-fit d is the one for which A} has the global minimum value 12",," and the uncertainty 0;; is set by the values of d corresponding to ,1} = [min + 1.(29) According to statistics theory, the most likely value of 32",," is the number of degrees of freedom of the fit, i.e., N — 1 in the REDOR, prTDQBU and prFDR-CT analyses.(43) The [m values in the fittings were close to V and were consistent with reasonably accurate evaluation of the 02“” in Eq. (2. 24). 51 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) References Chang, C. D., Waki, M., Ahmad, M., Meienhofer, J ., Lundell, E. O., and Haug, J. D. (1980) Preparation and properties of N-0L-9-fluoreny1methyloxycarbonylamino acids bearing tert-butyl side chain protection, Int. J. Pept. Protein Res. 15, 59-66. Lapatsanis, L., Milias, G., Froussios, K., and Kolovos, M. (1983) Synthesis of N- 2,2,2-(trichloroethoxycarbonyl)-L-amino acids and N-(9- fluorenylmethoxycarbonyl)-L-amino acids involving succinimidoxy anion as a leaving group in amino-acid protection, Synthesis-Stuttgart 8, 671-673. Yang, R., Prorok, M., Castellino, F. J., and Weliky, D. P. (2004) A trimeric HIV - 1 fusion peptide construct which does not self-associate in aqueous solution and which has 15-fold higher membrane fusion rate, J. Am. Chem. Soc. 126, 14722- 14723. Yang, R., Yang, J., and Weliky, D. P. (2003) Synthesis, enhanced fusogenicity, and solid state NMR measurements of cross-linked HIV-1 fusion peptides, Biochemistry 42, 3527-3535. Zheng, Z., Qiang, W., Weliky, D. P. Investigation of F inite-Pulse Radiofrequency-Driven Recoupling Methods for Measurement of Intercarbonyl Distances in Polycrystalline and Membrane-Associated HIV Fusion Peptide Samples, Submitted to Magnetic Resonance in Chemistry. Qiang, W., Weliky, D.P. unpublished work. Long, H. W., and Tycko, R. (1998) Biopolymer conformational distributions fiom solid-state NMR: alpha-helix and 3(10)-helix contents of a helical peptide, J. Am. Chem. Soc. 120, 7039-7048. Williamson, K. L. (1994) Macroscale and Microscale Organic Experiments, 2nd ed., Heath and Company, Lexington, Massachusetts, Toronto. Bodner, M. L. (2006) Solid state nuclear magnetic resonance of the HIV-1 and influenza fusion peptides associated with membranes, Ph. D. thesis, Michigan State University, East Lansing. Waskowska, A., Lukaszewicz, K., Kuzmina, L. G., Strutshkov, Y. T. (1975) The Crystal Structure of N-acetyl-L-leucine, Bull. Pol. Acad. Sci, Ser. Sci. Chim. 23, 149-153. Zheng, Z., Yang, R., Bodner, M. L., and Weliky, D. P. (2006) Conformational flexibility and strand arrantements of the membrane-associated HIV fusion peptide trimer probed by solid-state NMR spectroscopy, Biochemistry 45 , 12960- 1297 5. ’52 (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) Precigoux, G., Cotrait, M., and Geoffre, S. (1986) Structure of glycyl-L- phenylalanyl-L-phenylalanine hemihydrate, Acta Crystallogr. Sect. C 42, 315- 317. Macosko, J. C., Kim, C. H., and Shin, Y. K. (1997) The membrane topology of the fusion peptide region of influenza hemagglutinin determined by spin-labeling EPR, J. Mol. Biol. 267, 1139-1148. Han, X., Bushweller, J. H., Cafiso, D. S., and Tamm, L. K. (2001) Membrane structure and fusion-triggering conformational change of the fusion domain from influenza hemagglutinin, Nat. Struct. Biol. 8, 715-720. Afonin, S., Dur, U. H. N., Glaser, R. W., and Ulrich, A. S. (2004) 'Boomerang'- like insertion of a fusogenic peptide in a lipid membrane revealed by solid-state l9F NMR, Magn. Reson. Chem. 42, 195-203. Wasniewski, C. M., Parkanzky, P. D., Bodner, M. L., and Weliky, D. P. (2004) Solid-state nuclear magnetic resonance studies of HIV and influenza fusion peptide orientations in membrane bilayers using stacked glass plate samples, Chem. Phys. Lipids I 32, 89-100. Aloia, R. C., Tian, H., and Jensen, F . C. (1993) Lipid composition and fluidity of the human immunodeficiency virus envelope and host cell plasma membranes, Proc. Natl. Acad. Sci. U.S.A. 90, 5181-5185. Brugger, B., Glass, B., Haberkant, P., Leibrecht, I., Wieland, F. T., and Krasslich, H. G. (2006) The HIV lipidome: A raft with an unusual composition, Proc. Natl. Acad. Sci. U.S.A. 103, 2641-2646. Hope, M. J ., Bally, M. B., Webb, G., and Cullis, P. R. (1985) Production of large unilamellar vesicles by a rapid extrusion procedure - characterization of size distribution, trapped volume and ability to maintain a membrane-potential, Biochim. Biophys. Acta-Biomembr. 812, 55-65. Yang, J. (2003) Solid-state nuclear magnetic resonance structural studies of the HIV-1 fusion peptide in the membrane environment, Michigan State University, East Lansing, MI. Bodner, M. L., Gabrys, C. M., Parkanzky, P. D., Yang, J ., Duskin, C. A., and Weliky, D. P. (2004) Temperature dependence and resonance assignment of 13 C NMR spectra of selectively and uniformly labeled fusion peptides associated with membranes, Magn. Reson. Chem. 42, 187-194. Gullion, T., and Schaefer, J. (1989) Rotational-echo double-resonance NMR, J. Magn. Reson. 81 , 196-200. Yang, J ., Parkanzky, P. D., Bodner, M. L., Duskin, C. G., and Weliky, D. P. (2002) Application of REDOR subtraction for filtered MAS observation of 53 (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) labeled backbone carbons of membrane-bound fusion peptides, J. Magn. Reson. 159,101-110. Bennett, A. E., Rienstra, C. M., Auger, M., Lakshmi, K. V., and Griffin, R. G. (1995) Heteronuclear decoupling in rotating solids, J. Chem. Phys. 103, 6951- 6958. Gullion, T. (1998) Introduction to rotational-echo, double-resonance NMR, Concept Magnetic Res. 10, 277-289. McDowell, L. M., Holl, S. M., Qian, S. J., Li, B., and Schaefer, J. (1993) Inter- tryptophan distances in rat cellular retinol-binding Protein Ii by solid-state NMR, Biochemistry 32, 4560-4563. Anderson, R. C., Gullion, T., Joers, J. M., Sha iro, M., Villhauer, E. B., and Weber, H. P. (1995) Conformation of [1-13C,l ]acetyl-L-carnitine. Rotational- echo, double-resonance nuclear magnetic resonance spectroscopy, J. Am. Chem. Soc. 117, 10546-10550. Carr, H. Y., and Purcell, E. M. (1954) Effects Of Diffusion On Free Precession In Nuclear Magnetic Resonance Experiments, Physical Review 94, 630-63 8. Bevington, P. R., and Robinson, D. K. (1992) Data Reduction and Error Analysis for the Physical Sciences, 2nd ed., McGraw-Hill, Boston. Farrar, T., Harriman, J E (1998) Density Matrix Theory and Its Applications in Spectroscopy, Third Ed. ed., The Farragut Press, Madison, WI. Slichter, C. P. (1992) Principles of Magnetic Resonance, 3rd enl. and updated ed ed., Springer-Verlag, New York. Bak, M., Rasmussen, J. T., and Nielsen, N. C. (2000) SIMPSON: A general simulation program for solid-state NMR spectroscopy, J. Magn. Reson. 14 7, 296- 330. Mehring, M. (1983) Principles of high-resolution NMR in solids, 2nd, rev. and enl. ed., Springer-Verlag, Berlin. Oas, T. G., Hartzell, C. J., McMahon, T. J ., Drobny, G. P., and Dahlquist, F. W. (1987) The carbonyl 13 C chemical-shift tensors of 5 peptides determined from 15N dipole-coupled chemical shift powder patterns, J. Am. Chem. Soc. 109, 5956- 5962. Ando, S., Yamanobe, T., Ando, 1., Shoji, A., Ozaki, T., Tabeta, R., and Saito, H. (1985) Conformational Characterization Of Glycine Residues Incorporated Into Some Homopolypeptides By Solid-State C-13 NMR-Spectroscopy, Journal Of The American Chemical Society 107, 7648-7652. 54 (36) (37) (38) (39) (40) (41) (42) (43) Herzfeld, J., and Berger, A. E. (1980) Sideband intensities in NMR spectra of samples spinning at the magic angle, J. Chem. Phys. 73, 6021-6030. Naito, A., Ganapathy, S., Akasaka, K., and McDowell, C. A. (1981) Chemical shielding tensor and ‘3 C-MN dipolar splitting in single crystals of L-alanine, J. Chem. Phys. 74, 3190-3197. F acelli, J. C., Gu, Z. T., and McDermott, A. (1995) Carbon-13 chemical-shift tensors of carboxylic-acids: GIAO calculations in acetic-acid + methylamine dimer, Mol. Phys. 86, 865-872. Longhi, S., Czjzek, M., Larnzin, V., Nicolas, A., and Cambillau, C. (1997) Atomic resolution (1.0 A) crystal structure of F usarium solani cutinase: stereochemical analysis, J. Mol. Biol. 268, 779-799. Basak, A., Baternan, O., Slingsby, C., Pande, A., Asherie, N., Ogun, O., Benedek, G. B., and Pande, J. (2003) High-resolution X-ray crystal structures of human 7D crystallin (1.25 A) and the R58H mutant (1.15 A) associated with aculeiform cataract, J. Mol. Biol. 328, 1137-1147. Oas, T. G., Hartzell, C. J ., Dahlquist, F. W., and Drobny, G. P. (1987) A New Approach To Least-Squares Fitting Analysis Of NMR Powder Patterns, Biophysical Journal 51, A80-A80. Schmidt-Rohr, K., and Spiess, H. W. (1994) Multidimensional Solid-State NMR and Polymers, 2nd ed., Academic Press, San Diego. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1996) Numerical Recipes in FORTRAN 77: The Art of Scientific Computing, Vol. Fortran Numerical Recipes, 2nd ed., Cambridge, New York. 55 Chapter 3 Technique Development CP MAS Development Cross polarization (CP) from 1H to 13 C has a four-fold advantage in signal intensity over direct 13 C polarization, which is significant especially for membrane- associated HF P samples, which contain fewer ‘3 C spins and usually undergo longer dephasing periods in structural determination. Hence REDOR, prTDQBU, prFDR-CT and Carr-Purcell sequences each include a CP fi'om 1H to 13 C. The CP efficiency, i.e. the relative ‘3 C signal after CP, usually depends on MAS frequency and sample temperature but different CP matches may even have different CP efficiencies at fixed MAS fiequency and sample temperature. The temperature effect was previously studied by our research group and the sample temperature was controlled at - 50 °C in this work.(1) Figure 11. showed the efficiency of two different CP matches and their dependence on MAS fiequency, which were done on D-NAL and HFPmn-F8c/LMe samples. Match 1 was set to 45 kHz 1H 702, 45 kHz lH CP and 37 to 50 kHz l3C ramp rf fields, and match 2 to 60 kHz 1H 72/2, 60 kHz 1H CP and 43 to 54 kHz 13 C ramp rf fields. The overall CP efficiency of match 2 was ~75 % and ~30 % higher than that of match 1 when performed on D-NAL and HFPmn-F8c/LMe samples, respectively. Furthermore, the CP efficiency of match 1 decreased (especially for the HFPmn-FSC/LMe sample), 56 1.0- It 1:1 g a :1 R '3 g 0.8- v V ,9 0.6- v 8 x X - X g 0.4- 0.2- 0.04 8 5'1 1'0 1'1 12 1'3 MAS frequency (kHz) Figure 11. Plots of D-NAL and HFPmn-FSC/LMe CP MAS l3c signals with two matches and at various MAS frequencies. Match 1 refers to 45 kHz 1H 7112, 45 kHz lH CP and 13C ramp from 37 to 50 kHz rf fields, and match 2 to 60 kHz 1H 7112, 60 kHz lH CP and 13C ramp from 43 to 54 kHz rf fields. The crosses (X) and squares were D-NAL l3C CP signals of 128 acquisitions with match 1 and match 2, respectively, which were normalized by the signal with match 2 at 12 kHz MAS frequency. The down triangles and up triangles were HFPmn-FSdLMe l3C CP signals of 512 acquisitions with match 1 and match 2, respectively, which were normalized by the signal with match 2 at 10 kHz MAS frequency. The sample temperature, contact time and recycle delay were fixed at - 50 °C, 3 ms and 1.25 s, respectively. 57 when MAS frequency increased, while the CP efficiency of match 2 had less pronounced dependency on MAS frequency. Match 2 was a better match in terms of efficiency, convenience and robustness in experimental setup and therefore mostly used in REDOR, prTDQBU, prFDR-CT and Carr-Purcell experiments of this work. REDOR Development The REDOR distance-measurement experiment was first validated on helical I4 peptide with Ala-9 ‘3 CO and Ala-l3 15N labels using the “alternating 15N/'3C 1: pulse” version (cf. Figure 12a, b and Figure 13). As Twas increased from 8.25 to 32.25 ms, there was a regular decrease in S 1 mgr’/So'3""’ values and concomitant increase in (AS/So)” values. Therefore, (AS/S0)” depend on dam" and (AS/So)” increase as dCNt'increase within a certain range for a specific sample. Using the approach and equations described in Chapter 2 and Appendix I, the (AS/S0)” were calculated fiom the (AS/So)” and then fitted to the (AS/SOY“ calculated for an array of dCN values. The resulting doc = 44.78 i 0.22 Hz and rCN = 4.110 :1: 0.007 A are consistent with a helical structure between Ala-9 and Ala-l 3 and serve to validate REDOR measurements on HFP samples. prTDQBU Development Early development of firC T DQBU The one-n—per-ZrR version of prTDQBU experiment was first validated using the GFF sample for which there is a ~2% fraction of D-GFF molecules with 13CO labels at Gly-l and Phe-3. D-GFF has an intramolecular l3CO/BCO distance of 5.40 A and dcc ~ 49 Hz. The GFF prTDQBU spectra have Phe-3, Phe-2 and Gly-l 13(:0 peaks at 180.3, 176.4, and 170.9 ppm, respectively (Figure 14). As twas increased from 16 to 80 ms, there was a general decrease in S 1“” /S0e"p values for the Phe—3 and Gly-l peaks. 58 Juanita 180160 180160 ppm Figure 12. 13 C REDOR spectra of the 14 peptide. For each lettered pair of spectra, the So spectrum is on the left and the S1 spectrum is on the right. The MAS fi'equency=8000 Hz, TR = 1251.18, and 1' = 8.25 ms (spectra a) or 1’ = 32.25 ms (spectra b). Dotted lines are drawn at the peak So intensities. The 14 spectra were processed with 50 Hz Gaussian line broadening, and baseline correction was applied to all spectra. The number of acquisitions used to obtain each spectrum in each panel was 32. 59 a) 12 10“ x 0.8 — rt Oti- AS/So OAR- OJ?“ 00- 1 1 1 0 10 20 30 Dephasing time (ms) 4 l l I l 444’ 446 448 451) 452 Dipolar coupling (Hz) Figure 13. (a) REDOR (AS/Sp)” (filled squares) and (AS/So)” (crosses) vs. dephasing time for the 14 peptide. Each (AS/Sp)” was based on a (AS/So)” determined by integrations of 1 ppm regions in the So and Sr spectra. The integration region was centered at 178.8 ppm which is the peak shift in the So spectra. For each 2; there were 64 total (So + St) scans. The values of 0“” are ~0.005 and the heights of the black squares are approximately equal to the average value of 2 x 02“”. (b) A plot of A; vs. dCN yields day = 44.78 a: 0.22 Hz which corresponds to rat = 4.110 r 0.007 A for the Ala-9 l3CO/Ala-13 15N labeled pair. The uncertainty was determined using the approach described in the Materials and Methods section. The (AS/So)” values in plot a were calculated with the best-fit dCN. 6O will .11.“th militia nt‘iu. 180 1&0 180 180 ppm Figure 14. prTDQBU spectra of the GFF sample. The version of prTDQBU is one-1r— per-2m For each lettered pair of spectra, the So spectrum is on the left and the S1 spectrum is on the right. The MAS frequency = 8000 Hz, 7R = 125 118, the 13C n'pulse rf field = 10 kHz, M = 336, and the total constant-time = (L + M + N) x 1); = 84 ms. The values of L, N, and rare: 128, 208, 32 ms (spectra a); 192, 144, 48 ms (spectra b); 256, 80, 64 ms (spectra 0); 320, 16, 80 ms (spectra d). From left-to-right, each GFF spectrum has Phe-3, Phe-2 and Gly-l 13CO peaks at 180.3, 176.4, and 170.9 ppm, respectively. For each set of GFF spectra with the same 1', a dotted line is drawn at the peak So intensities of Gly-l. The spectra were processed with 50 Hz Gaussian line broadening, and baseline correction was applied to all spectra. The total number of scans used to obtain each spectrum in panels a, b, c, and dis 10240, 10240, 10240, and 8192, respectively. 61 This is consistent with the ~65% contribution to these signals from D-GF F molecules for which there is significant Gly-l 13CO/Phe-3 13 CO dipolar coupling. By contrast, the Phe- 2 peak has Slap/Soap ~ 1 for all r'which is consistent with the ~98% contribution to this signal from unlabeled GFF molecules for which there are large 13 CO/ ” C distances and corresponding small dcc values. The labeled Gly-l and Phe-3 13COs have significant (AS/So)”, which increase as dccz'increase. As the magnitude of the constant-time parameter increases, transverse relaxation causes a decrease in 13 CO signal intensity for all values of rand consequent lower signal- to-noise ratio. It was therefore desirable to use the smallest constant-time which allowed observation of the full (AS/So) buildup for a ~5 A l3co-‘3co distance. Because RFDR is affected by 13C pulse duration, an investigation was made of the effect of the ”C erulse rf field on the (AS/So) buildup rate of the GFF sample.(2) For the Gly—l l3C0 signal, smaller 13C rtpulse rf fields yielded faster buildup in both experiment and simulation (Figure 15) but also led to smaller So and S1 signal intensities, perhaps because of larger resonance offsets and poorer refocusing of chemical shift evolution.(3) prTDQBU experiments were done in the one-u-per—ZrR version with a 10 kHz 13C rtpulse rf field. Figure 16a displays comparison and fitting of GFF Gly-l l3C0 (AS/So)” and (AS/S0)“ over a wide range of 2'. The analysis focused on Gly-l l3C0 because it is has carbonyl rather than carboxyl functionality and is thus more relevant to the HFPtr sample. The fitting yielded dCC = 42.3 :1: 0.5 Hz and corresponding rcc = 5.67 :1: 0.02 A for the Gly-l l3CO/Phe-3 l3CO labeled pair. Variation of ” CO CSA axis orientations relative to the GFF atomic geometry did not greatly affect (AS/S0)” and 62 0.8 m 0.6 — 0.4— l i l i 0.0 — AS/So 1 I 1 0 20 4O 60 80 Dephasing time (ms) Figure 15. Dependence of prTDQBU of GFF Gly-l 13co on 13C It pulse rf field, (AS/So)” and (AS/So)“ vs. dephasing time. The version of prTDQBU is one-rt-per-2IR. The MAS frequency = 8000 Hz, 613C pmmme, = 175.7 ppm, M = 336, and the constant- time = 84 ms. The symbol legend is: squares, cor, 10 kHz ”C rtpulse rf field; crosses, sim, 10 kHz field; diamonds, cor, 43 kHz field; circles, sim, 43 kHz field. Uncertainties are displayed for the cor points in plot a and lines are drawn. Each (AS/Sp)” was based on a (AS/So)” determined from spectral integrations over a 0.5 ppm region centered at the Gly-l l3CO peak chemical shift. Each (AS/SOY" value was determined using intensities from 4096 total (So + S1) scans. The Sow" and S15“ were calculated with dcc = 42 Hz which yielded the best overall agreement between (AS/Sp)” and (AS/So)” values. 63 the fitted values of dcc. For example, different sets of (AS/SOY” were calculated with each set having a randomly generated principal axis orientation. Each set of (AS/SOY“ was then fitted to (AS/So)” and the resulting dcc was always within a range of 37 - 47 Hz. In Figure 16, the only systematic disagreement between (AS/Sp)” and (AS/SOY” occurs at large values of rfor which (AS/Sp)” decreases more rapidly than (AS/SOY“. The best-fit rec is ~5% larger than the 5.40 A crystallographic distance.(4) Overall, the GFF studies demonstrate that ” C-13 C distances in the ~5 A range can be reasonably accurately determined with the prTDQBU method although there is still room for further improvement of this technique. Improvement and optimization of ij T DQBU Figure 17 displays example ”C prTDQBU spectra of setup compounds, which were done in the one-n-per—IR version. For each panel, peak shifts in ppm and assignments were: (a), 180.1, carboxyl; and 178.4, amide COs of D-NAL; and (b), 180.3, Phe—3; 176.7, Phe-2; and 170.8, Gly-l COs of D-GFF. In Figure 17a, (AS/So)” > 0.9 for the D-NAL spectra which was a reasonable result because dcc = 270 Hz and deer: 3.6. In Figure 17b, (AS/So)” z 0.55 for the D-GFF spectra with dcc = 49 Hz and dcct= 1.4. The Gly—l and Phe-3 signals included ~3 5% contribution from natural abundance 13C08 and the natural abundance sites had (AS/So) z 0. (AS/So)"“"pdepend on deer, and (AS/So)” increase as dcct'increase within a certain range for a specific sample. As detailed in Chapter 2 and Appendix I, after (AS/S0)” is calculated by (AS/So)”, which is obtained as a function of 2', a best-fit dcc can be achieved by fitting (AS/So)“ to (AS/S0)”. 64 0.8 — x 9: E i E 0.6 — I O a) a 0.4 — 9: <1 I 0.2 — i 0.0 — 1 r 1 0 20 4o 60 80 Dephasing time (ms) b) 12 O O 11 — O 8. . ° 0 O O 10 — ' , O . O . O .000. 9 1 r 41.5 42.0 42.5 43.0 Dipolar coupling (Hz) 65 Figure 16. (a) prTDQBU (AS/S0)” (open squares with error bars) and (AS/So)” (crosses) vs. dephasing time for GFF Gly-l 13CO. The version of prTDQBU is one-7r- per-21'R. The MAS frequency = 8000 Hz, the ”C n'pulse rf field = 10 kHz, fi3cpmmme, = 175.7 ppm, M = 336, and the constant-time = 84 ms. Each (AS/S0)” was based on a (AS/So)” determined from spectral integrations over a 0.5 ppm region centered at the Gly-l 13co peak chemical shift. Each (AS/SOY" value for r= 16, 24, 32, 40, 48, 56, and 64 ms was determined using intensities fi'om 20480 total (So + S1) scans and the (AS/So)” value for t'= 72 ms was determined using intensities from 163 84 total scans. (b) A plot of X2 vs dcc yields dcc= 42.3 :1: 0.5 Hz which corresponds to rcc= 5.67 :1: 0.02 A for the Gly-l/Phe-3 labeled pair. The (AS/So)” values in panel a were calculated with dcc = 42.3 (a) (b) I I I I I I 190 170 ppm I I 190 170 Figure 17 . ”C one-mper- TR prTDQBU spectra of (a) D-NAL with 2' = 13.33 ms, and (b) D-GFF with 2' = 28.00 ms. The MAS frequency was 12000 Hz and (a) CT = 20.0 ms, and (b) CT = 41.33 ms. For each lettered pair of spectra, the So spectrum is on the left and represented the sum of 5 = y and 4’ = —y data and the $1 spectrum is on the right and represented the sum of 4’ = x and g“ = —x data. Dotted lines are drawn at the peak labeled amide carbonyl So intensities. Each spectrum in panel a, or b, respectively represented the sum of 64, or 4000 scans and was respectively processed with 75 Hz Gaussian line broadening. Processing also included dc offset correction and polynomial baseline correction. 66 It was shown in a previous development that use of longer rather than shorter ”C 71' pulses in the prTDQBU experiment resulted in faster buildup of (AS/So)” with 11(3) Faster buildup allowed use of smaller CT values with the concomitant effect of increasing So and S1 signal intensities. However, for the moderate 12 kHz MAS fiequency of our experiments, longer n'pulses also reduced chemical shift refocusing with the effect of decreasing So and S1 signal intensities. For samples with dcc z 50 Hz, an examination was made of (AS/S0) buildup rates, corresponding reasonable CT values, and So signal intensities as a function of trpulse length and it was found that there was a broad signal- to-noise maximum near 20 kHz Irpulse field. Much of the optimization was done using SIMPSON simulations and these calculations were experimentally validated by spectra obtained with the D-GF F and D-NAL samples. Most of the subsequent prTDQBU experiments were done with 20.5 kHz n'pulses.(5) The original implementations of the transverse RFDR or prF DR experiments for quantitative 13C-”C distance determination were done in the one-rt-per-Z TR version, cf. Figure 7 c.(3, 6) The ratio of (total Itpulse time)/ tfor the one-rt-per- 2'}; version was two times larger than for the one- 7t-per-2 2']; version and the one- It-per- 2); version might therefore exhibit a larger finite pulse effect and a more rapid buildup of (AS/So). This more rapid buildup was experimentally demonstrated for D-NAL and can be observed by visual comparison of the squares and crosses in Figure 18a. Use of shorter 35.0 kHz 7: pulses in the one-n-per- 7R version decreased the buildup rate, cf. up triangles in Figure 18a. 67 B) 1.2 10: vvv'v x x x E a a E 5 6 A 08- v A x u 9 A D goe- v4 x 4 n X 0.4" A X V 0.2-1 A x E X 0.0 0 5 10 15 20 25 30 Dephasing time (ms) b ()12 10 X X X x X g X x V 08 xva VV x Relative So 9 O) > .0 b 1 D D 0.0 - o 5 18 lb 20 25 do Dephasing time (ms) Figure 18. Plots of D-NAL prTDQBU (a) (AS/So)” and (b) So vs dephasing time obtained with MAS frequency = 12000 Hz. Each (AS/SOY” was calculated from a (AS/So)” determined with S0 and S1 spectra that each represented the sum of 32 scans. The integration regions were 1 ppm and were centered at 178.3 ppm which was the peak carbonyl shift. The 0“” were < 0.006. For plot b, the cross (X) value of So at 1'= 16.0 ms was set to 1.0 and the other So were normalized relative to this value. The symbol legend: squares, one-rt-per- 27;, 20.5 kHz ”C Itpulses, CT = 32.00 ms; crosses, one-7t—per-21'R, 20.5 kHz ” C rtpulses, CT = 32.00 ms; up triangles, one-rt-per- TR, 35.0 kHz l3C It'pulses, CT = 32.00 ms; down triangles, one-rt-per- TR, 20.5 kHz ”C Jz'pulses, CT = 20.00 ms. 68 Because the ratio of (number of rtpulses)/ twas two times larger for the one—71:- per-rR version than for the one-JI-per-Z TR version, the one-It-per- 1'}; version might exhibit reduced chemical shift refocusing and decreased S0 and S1 signals. This reduction was experimentally demonstrated for So signals, cf. squares vs crosses in Figure 18b. The S0 signal could be partially recovered in the one-It-per— TR version by using 35.0 kHz 7: pulses, cf. up triangles. A reasonable compromise was 20.5 kHz rrpulses in the one-It- per- TR version with reduced CT, cf. down triangles in Figure 18a, b. Relative to longer CT data, the So intensity was twice as large and a rapid buildup rate was retained for (AS/SOY”. All of the So data sets of Figure 18b had an inverted parabola shape with a maximum near r/CT = 0.5 and ~20% reduction in signal for r/CT z 0.1 or 0.9. The dipolar echo periods during the So acquisition had durations 2 rand CT — 2 z'and Sp z F (2 1' ) x F (C T — 2 2') where F (t) was the dipolar echo amplitude. The variation of S0 with 2' suggested that F may have both exponential and non-exponential decay components. Figure 19 displays the effect of ”C transmitter offset on prTDQBU (AS/So) of (a) D-NAL and (b) D-GFF. The offset parameter in ppm was defined as A = dwmmirm — 8,er where 4,901, was the average shift of the 13C0 labeled sites. For D-NAL in Figure 19a, there was little difference between (AS/So)” determined with A = —6.7 or —16.7 ppm and similar invariance to offset was seen for (AS/SOY“. Invariant (AS/So)” and (AS/So)“ were also observed for A = 12.7 ppm (not shown). For the same A, there were systematic differences between (AS/SOY" and (AS/SOY“ at large values of 2', which are not 69 (a) 1.2 'l.0'l V O R a 0.8“ . 0.6 -1 ASlSo 0.4 - ¥ 0.2 .. ‘D 0.0.. q r 0 4 8 12 16 20 Dephasing time (ms) (b) 1.2 1.0- 0.8 1 0.6-1 g x 83130 0.4 " a 0.2- g A 0.0 T r . r 0 10 20 30 40 Dephasing time (ms) Figure 19. (a) D-NAL and (b) D-GFF plots of prTDQBU (AS/So)” and (AS/So 5"" vs dephasing time as a function of transmitter offset (A) calculated relative to the midpoint of the labeled carbonyl and carboxyl shifts. Acquisition parameters included one-mper- TR, MAS frequency = 12000 Hz, 20.5 kHz l3C rtpulses, and (a) CT = 20.00 ms or (b) CT = 41 .33 ms. Each (AS/SOY" was calculated fiom a (AS/S0)” determined with So and S1 spectra that each represented the sum of (a) 32 or (b) 4000 scans. The integration regions were 1 ppm and were centered at (a) 178.3 or (b) 170.8 ppm, which were the peak carbonyl shifts. The displayed (AS/SOY“ were calculated with the best-fit (a) dcc = 296 Hz or (b) dcc = 49.4 or 44.6 Hz for A = 0 or —12.0 ppm, respectively. The symbol legend: open squares, (AS/So)”, (a) A = —6.7 ppm or (b) A = 0 ppm; crosses, (AS/SOY”, (a) A = —6.7 ppm or (b) A = 0 ppm;half-filled up triangles; (AS/SOY”, (a) A = -16.7 ppm or (b) A = -12.0 ppm; half-filled down triangles, (AS/SOY“, (a) A = —16.7 ppm or (b) A = — 12.0 ppm. 70 currently understood. The best-fit dcc fiom (AS/So)” was also ~10% larger than the dcc calculated from the ” CO-13 CO distance in the crystal structure. For D-GFF in Figure 19b, similar (AS/So)” were observed for A = 0 or —12.0 ppm and yielded best-fit dcc= 49.4 or 44.6 Hz, respectively. The ” CO-” CO distance in the GFF crystal structure corresponded to doc = 49 Hz. Figure 20 displays the effect of variation of the ” C 7: pulse nutation angle (19) on (AS/So) of (a) D-NAL and (b) D-GFF. Each plot includes (AS/So)” and (AS/SOY“ calculated for o = 180° and best-fit dcc. The plots also include (AS/So)” calculated with this dcc value but with different values of 6. For D-NAL, very similar (AS/So 3"" were obtained for 19 = 170°, 180°, or 190° while for D-GFF, there was some variance of the (AS/SOY“ calculated for o = 175°, 180°, or 185°. The D-GFF (AS/So)” calculated with o = 175° were subsequently considered as an “experimental” data set and were fitted to (AS/S0)” calculated with 6 = 180° and different values of dcc. The new best-fit dcc was ~10% different fiom the value originally determined using the (AS/So)” values. A similar variance was obtained when fitting (AS/SOY“ calculated with 6 = 185°. 71 o co «in O A “a «a 0 4 8 12 16 20 Dephasing time (ms) O m CIX “X D )1 OX! >004 X D 0 1'0 20 3b 40 Dephasing time (ms) Figure 20. (a) D-NAL and (b) D-GFF plots of prTDQBU (AS/S0)” and (AS/So 5"" vs dephasing time for ”C Itpulses with different nutation angles. Acquisition parameters included one-rt-per- TR, MAS fi'equency = 12000 Hz, 20.5 kHz 13C Itpulses, and (a) A = - 6.7 ppm, CT = 20.00 ms or (b) A = 0 ppm, CT = 41.33 ms. The numbers of scans, integration parameters, and calculation of (AS/SOY” were the same as in Figure 19. The ”C nutation angle is denoted 19. The symbol legend: open squares, (AS/So)”, 6 = 180°; half-filled up triangles; (AS/SOY”, B = 180°; crosses, (AS/SOY”, (a) 6 = 170° or (b) 6 = 175°; half-filled down triangles, (AS/So)”, (a) o = 190° or (b) o = 185°. 72 prFDR-CT Development and Comparison with prTDQBU Besides the prTDQBU method, prFDR-CT is an alternative method using finite 72' pulses to restore homonuclear dipolar coupling under MAS and it was investigated with both model compounds and HFP samples, and compared with prTDQBU. For all of the prTDQBU methods in this work, there was a So and a S1 acquisition for each dephasing period 2'. For the prFDR-CT method, there was only one So acquisition per data set and consequent higher sensitivity because for a fixed total time for data acquisition, more time was available for signal averaging of S1 spectra. On the other hand, data analysis for this version of prFDR-CT had greater complexity because the prFDR-CT dephasing period 2'= 3KAMTR and the transverse relaxation period t’T = K(4Mo + AM) TR = 4KMO TR + 7/3 , the contribution of transverse relaxation was 2'- dependent. Figure 21 displays an initial comparison of the two experiments using the D-GFF sample for which the labeled ” CO-” CO distance was comparable to the structurally interesting distances in the HFP samples. The (AS/So)” derived from the prTDQBU experiment were fitted to (AS/SOY” calculated as a function of rice and Figure 4a displays (AS/S0)” and best-fit (AS/SOY” plotted as functions of r. The best-fit value of dcc was 49.4 i 1.2 Hz with corresponding rcc = 5.39 i 0.05 A, which agreed with rcc = 5.40 A in the crystal structure.(4) As displayed in Figure 21b, a similar analysis was done for the (s1 /so)°‘°' calculated from the prFDR-CT data and (51 /so)“'" which incorporated the experimentally-derived T 2 = 54 ms. The best-fit dcc = 59 i 3 Hz corresponded to rcc = 5.07 i 0.09 A. Comparison of the prTDQBU and prFDR-CT results for microcrystalline GF F showed that the prTDQBU method was more quantitative and the 73 prFDR-CT method yielded higher signal-to-noise which agreed with expectations for the two approaches. Figure 22 displays plots of prTDQBU (AS/So)” vs rand prFDR-CT(S1/So)°°' vs rfor the membrane-associated HFP samples. Figure 22a shows qualitative differences between the prTDQBU data of the three samples with the largest (AS/So)” buildup for the HFPmn-F8 sample and (AS/S0)” == 0 for the HFPtr-A15 sample when r< 35 ms. There were much less pronounced differences among the prFDR-CT data which might be understood from the measured T 2 z 15 ms for these samples and the expected exp(-r /45 ms) decay that would be d-independent. The Figure 22 data suggested that l°CO-”CO distances in the membrane-associated HFP samples would be more straightforwardly derived from the prTDQBU experiment and this method was the focus of our subsequent study. 74 (a) 1.2 1.0-l XI) 0.8 1 . 0.6 4 XI: ASISo 0.4 J a 0.2 . XD 0 10 20 30 40 Dephasing time (ms) 0 1To 20 80 43 60 60 Dephasing time (ms) Figure 21. (a) Plot of D-GFF prTDQBU (AS/So)” (squares) and (AS/so)“ (crosses) vs dephasing time. Acquisition parameters included one-rr-per- rR, MAS fiequency = 12000 Hz, 20.5 kHz ” C Irpulses, and CT = 41 .33 ms. Each (AS/So)” was calculated fiom a (AS/So)” determined with So and S1 spectra that each represented the sum of 4000 scans. The integration re 'ons were 1 ppm and were centered at 170.8 ppm which was the peak shift of the Gly-l 300 in the sO spectra. The omr were ~0.05. The displayed (AS/So)“ were calculated with the best-fit dcc = 49.4 i 1.2 Hz and corresponding rcc = 5.39 d: 0.05 A for the Gly-l/Phe-3 l°CO labeled pair. The 12 = 8.4 for this best-fit value. (b) Plot of D-GFF prFDR-CT (Sr/So)” (squares) and (Sr/SOY” (crosses) vs dephasing time. Acquisition parameters included MAS frequency = 10000 Hz, 15.2 kHz ”C n'pulses, and CT = 67 .2 ms. Each (SI/S0)” was calculated fiom a (Sr/So)” determined with So and S1 spectra that each represented the sum of 2048 scans. The integration regions were 1 ppm and were centered at the Gly-l 13C0 peak (170.8 ppm) and the 17°” were ~0.04. The displayed (Sr/SOY“ were calculated with the best-fit dcc = 59.0 r 3.0 Hz and corresponding rcc = 5.07 :l: 0.09 A. The 12 = 4.0 for this best-fit value. 75 0 10 20 30 40 Dephasing time (ms) 0 To 20 3'0 4'0 5'0 60 Dephasing time (ms) Figure 22. (a) Plot of prTDQBU (AS/Sp)” vs dephasing time for membrane-associated HFPmn-F8 (squares), HFPtr-A6 (crosses) and HF Ptr-Al 5 (triangles). Acquisition parameters included one-rr-per- rR, MAS fiequency = 12000 Hz, 20.5 kHz ”C rrpulses, and CT = 64.00 ms for HFPmn-F8 and HFPtr-A15 or CT = 41.33 ms for HFPtr-A6. Each (AS/So)” was calculated from a (AS/So)” determined with So and Sr spectra that each represented the sum of 10000, ~40000, and 10000 scans for the HFPmn-F8, HFPtr-A6 and HFPtr-A15 samples, respectively. The integration regions were 2 ppm and the a” were ~0.10, 0.06 and 0.09 for the HFPmn-F8, HFPtr-A6 and HFPtr-A15 samples, respectively. (b) Plot of prFDR-CT (S 1/S0)°°' vs dephasing time for membrane- associated HFPmn-F8 (squares), HFPtr-A6 (crosses) and HFPtr-A15 (triangles). Acquisition parameters included MAS fi'equency = 12000 Hz, 20.5 kHz ”C n'pulses, and CT = 64.00 ms. Each (Sr/So)” was calculated from a(S1/So)°xp with So and S1 spectra that each represented the sum of 12000, 33000, and 21000 scans for the HFPmn-F8, HFPtr- A6 and HFPtr-A15 samples, respectively. The integration regions were 2 ppm and the of" were ~0.04, 0.10 and 0.08 for the HFPmn-F8, HFPtr-A6 and HFPtr-A15 samples, respectively. The (AS/So)” or (SI/So)” in each plot were calculated with h = 1, i.e. all labeled 13C0 experienced the same homonuclear dipolar coupling. 76 Conclusion of Technique Development Two matches for CP from 1H to ” C were compared and the one with higher 1H and ” C CP rf fields yielded higher CP efficiency and was therefore applied to complex pulse sequences. The alternating 15N/ ” C 71' pulse version of REDOR sequence was tested with a model compound 14 peptide. It was found useful in measuring rCN ~ 4.1 A or day ~ 40 Hz and therefore ready to probe local secondary structure and strand arrangements in membrane-associated HF P samples. This work included investigation of two related methods for these measurements which are based on rotor-synchronized finite ”C erulses, i.e. pulses which are a significant fraction of a rotor period.(6-8) Strengths of these sequences include: (I) nearly all pulses are 71' pulses with quadrature phases; (2) the sequences are amenable to measurements on samples with inexpensive ”CO labeling; (3) the setup is straightforward and rapid; and (4) the data are relatively insensitive to chemical shifts and chemical shift anisotropy.(2, 3, 8) The constant-time aspect of prTDQBU allowed neglect of transverse relaxation in the data analysis but also led to reduced signal because of transverse relaxation during the long CT period. Versions of prTDQBU which incorporate shorter CT should therefore yield higher signal-to-noise data. Previous prTDQBU studies had used the one-n-per-2 rR version while in the present study, it was shown that the one-n—per- 232 version led to more rapid buildup of AS/So presumably because there was a larger finite pulse effect.(2, 3, 6) For rcc ~ 5 A and dcc ~ 60 Hz, CT could be reduced by a factor of ~06 to ~40 ms, cf. Figures 21 a, 22a. The sensitivity improvement should be significant for samples such as membrane-associated HFPS which have T2 ~ 15 ms. An additional 77 advantage of the one-n—per- 17; version was (AS/So)” and (AS/SOY” of ~0.9 at large d ras compared to ~0.75 for the one-n-per-Z rR version, cf. Fig. 4a.(3) This study also showed that reasonable transmitter offsets and errors in the ”C n'pulse nutation angle reduced best-fit dcc by ~10% and the corresponding best-fit rcc by ~3%. This error was small compared to the variation in fee among different HFP structural models and the method should therefore be useful for distinguishing among the models. This work also includes some investigation of the related prFDR-CT sequence for ” C-13 C distance measurement in HFP samples. One advantage of the chosen version of prFDR-CT was its use of multiple WAHUHA cycles for refocusing of ” C-” C dipolar coupling rather than the solid echo used in prTDQBU.(9, 10) Comparison of So spectra between the two sequences for GFF indeed showed ~1.5 times higher signal for prFDR-CT. For this version of prFDR-CT, there was variation of the transverse relaxation period with dephasing time but multiplication of (SI/SOY” by exp(—r/3 T2) led to accurate determination of dcc and rec in GFF which had T2 = 55 ms. This simple approach to transverse relaxation correction was more problematic in the HFP samples 00" because T2 z 15 ms and the decay time constant of (Sr/So) with rwas comparable to 3 T2. One difference between the versions of prTDQBU and prFDR-CT presented in this work was the acquisition of an S0 spectrum for each rin prTDQBU and acquisition of a single So spectrum in prFDR-CT. This difference resulted in higher sensitivity for prFDR-CT. If So were independent of rfor prTDQBU, data analysis could also be done with a single So spectrum, but Figure 18b showed ~20% variation of S0 with maximum So for rz CT/2 and minimum So for 2'2 0 and rz CT. Considering So(r) z 78 F ( 2) x F (C T — r) where F (t) was the dipolar echo intensity, it appeared that F (t) had a non—exponential decay component which caused greater signal loss at larger t. After all, the REDOR and one-n-per-tR prTDQBU sequences presented in this work are useful methods to respectively probe ray and rec in model samples. They were employed in the investigation of chemical shifts and strand arrangements of membrane- associated HFP samples, which will be detailed in the next chapter. 79 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) References Bodner, M. L., Gabrys, C. M., Parkanzky, P. D., Yang, J ., Duskin, C. A., and Weliky, D. P. (2004) Temperature dependence and resonance assignment of ”C NMR spectra of selectively and unifomrly labeled fusion peptides associated with membranes, Magn. Reson. Chem. 42, 187-194. Ishii, Y. (2001) ” C-” C dipolar recoupling under very fast magic angle spinning in solid-state nuclear magnetic resonance: Applications to distance measurements, spectral assignments, and high-throughput secondary-structure determination, J. Chem. Phys. 114, 8473-8483. Zheng, Z., Yang, R., Bodner, M. L., and Weliky, D. P. (2006) Conformational flexibility and strand arrantements of the membrane-associated HIV fusion peptide trimer probed by solid-state NMR spectroscopy, Biochemistry 45, 12960- 1297 5. Precigoux, G., Cotrait, M., and Geoffre, S. (1986) Structure of glycyl-L- phenylalanyl-L-phenylalanine hemihydrate, Acta Crystallogr. Sect. C 42, 315- 317. Zheng, Z., Qiang, W., Weliky, D. P. Investigation of Finite-Pulse Radiofi'equency-Driven Recoupling Methods for Measurement of Intercarbonyl Distances in Polycrystalline and Membrane-Associated HIV Fusion Peptide Samples, Submitted to Magnetic Resonance in Chemistry. Bennett, A. E., Weliky, D. P., and Tycko, R. (1998) Quantitative conformational measurements in solid state NMR by constant-time homonuclear dipolar recoupling, J. Am. Chem. Soc. 120, 4897-4898. Ishii, Y., Balbach, J. J ., and Tycko, R. (2001) Measurement of dipole-coupled lineshapes in a many-spin system by constant-time two-dimensional solid state NMR with high-speed magic-angle spinning, Chemical Physics 266, 231-236. Balbach, J. J ., Petkova, A. T., Oyler, N. A., Antzutkin, O. N., Gordon, D. J ., Meredith, S. C., and Tycko, R. (2002) Suprarnolecular structure in full-length Alzheimer's B-arnyloid fibrils: Evidence for a parallel B-sheet organization from solid-state nuclear magnetic resonance, Biophys. J. 83, 1205-1216. Mehring, M. (1983) Principles of high-resolution NMR in solids, 2nd, rev. and enl. ed., Springer-Verlag, Berlin. Slichter, C. P. (1992) Principles of Magnetic Resonance, 3rd enl. and updated ed ed., Springer-Verlag, New York. 80 Chapter 4 Fusion Peptide Structural Determination REDOR Measurements ”C0 chemical shifts. Liquid-state and solid-state NMR studies on proteins have shown an empirical correlation between the 13CO chemical shift and local conformation, with higher shifts correlating with helical structure and lower shifts correlating with ,B strand structure.(l-3) In the present study, ” CO shifts at Len-7 and Phe-8 were measured for membrane-associated HFPtr and it was observed that there is a strong dependence of shifts on membrane composition. The Phe-8 chemical shift in membrane-associated HFPtr-F8CL9N was specifically detected using REDOR filtering (Figure 23a, b) and peak shifts of 178.4 and 172.5 ppm were observed in PC-PG and LM3 membranes, respectively. These values correlate with database distributions of Phe ”CO shifts for helical (177.1 m 1.4 ppm) and ,B strand (174.2 i 1.6 ppm) conformations.(3) As displayed in Figure 23c, the REDOR-filtered peak Leu-7 l3co shift in HFPtr-L7CF11N/PC-PG was 178.8 ppm. This shift agreed better with the database distribution of Leu ” CO in helical conformations (178.5 d: 1.3 ppm) than with the distribution in ,B strand conformations (175.7 i 1.5 ppm). In the HFPtr-L7CF1 lN/LM3 sample, there were relatively small values of AS/So and the Leu-7 13C0 peak was not observed in the REDOR-filtered spectrum. 81 Wain 170 ppm1eo' Figure 23. ” C spectra of HFPtr-F8CL9N associated with (a) PC-PG and (b) LM3 membranes and of HFPtr-L7CF1 12.; associated with (c, d) PC-PG, (e) LM3, and (f) LM3e membranes. The HFPtrzlipid mol ratio was ~0.003 in the samples used to obtain spectra a and b and ~0.007 in the samples used to obtain spectra c-f. Spectra a, b, and c are REDOR-filtered with r = l. 0,1 .0 and 32. 25 ms, respectively, and have l3CO peak chemical shifts of 178. 4 (Phe-8), 172. 5 (Phe-8), and 178. 8 ppm (Leu-7), respectively. Spectra d, e, and f are REDOR So spectra with 32. 25 ms dephasing period and have °CO peak chemical shifts of 17 8 6 ppm, 173. 8 ppm, and 173 .4 ppm, respectively. Each spectrum was processed with 100 Hz Gaussian line broadening and baseline correction. The MAS frequency was 8000 Hz and the number of scans used to obtain spectra a, b, c, d, e, and f is 1187 84, 132864, 46048, 23024, 21760, and 98720, respectively. 82 REDOR So spectra were therefore used to obtain additional chemical shift information for the HFPtr-L7CF11N samples. The S0 spectrum of the HF Ptr-L7cFl lN/PC-PG sample (Figure 23d) is a combination of a sharper signal peaked at 178.6 ppm and a broader signal centered near 176 ppm. Comparison with the REDOR-filtered spectrum (Figure 23c) suggests that the downfield Signal is primarily due to the labeled Leu-7 l°CO while spin-counting and published spectra of ”CO labeled lipid samples suggest that the upfield Signal is primarily due to natural abundance lipid l3’CO.(4) For the HFPtr-L7CF1 lN/LM3 sample (Figure 23c), there is a single signal which is a superposition of intensity fi'om the labeled Leu-7 and natural abundance lipid ” COS with a smaller contribution from natural abundance HF Ptr ”COS. The HFPtr-L7CF l lN/LM3e sample contains ether-linked rather than ester-linked lipids with consequent elimination of natural abundance 1°CO lipid signals in the spectrum (Figure 23f). The HFPtr-L7CF1 lN/LM3e spectrum is narrower than the HFPtr-L7CF1 lN/LM3 spectrum but the peak shift of the LM3e spectrum (173.4 ppm) is very similar to the peak shift of the LM3 spectrum (173.8 ppm) and suggests that the HF Ptr conformation is insensitive to ether- vs. ester-linked lipids. The peak shifts are more consistent with Leu chemical shifts in B strand conformations (175.7 i 1.5 ppm) than in helical conformations (178.5 i 1.3 ppm). Overall, the Lou-7 and Phe-8 peak HFPtr l3co chemical shifts correlate with local helical conformation in PC-PG and with ,B strand conformation in LM3 and LM3e. Other studies of HIV and influenza fusion peptides suggest that the absence of cholesterol in PC-PG and its presence in LM3 and LM3e is an important determinant of peak chemical shifts and local conformations.(5, 6) 83 I 3 C 0—1 5 N distances. HFPtr-L7CF11N conformation was probed more quantitatively with REDOR determination of the distance between the labeled Leu-7 ”CO and Phe-11 ”N nuclei. If the Leu-7 to Phe-11 region has a regular 01 helical conformation, the distance will be ~4.l A, while if the region has a regular ,6 strand conformation, the distance will be ~11 A. These distances correspond to dipolar couplings (day) of ~45 Hz and ~3 Hz, respectively. The REDOR experiment was first validated using the helical I4 peptide with Ala-9 ”CO and Ala-13 ”N labels, which is detailed in Chapter 3. REDOR experiments were then performed on the HFPtr-L7CF11N/PC-PG sample. For the Len-7 l°CO peak at 178.6 ppm, Spectra with r at 8.25 and 32.25 ms yielded Slew/502x12 values which were in semi-quantitative agreement with the SIM/Soap values from the 14 sample (Figure 24). In the HFPtr Spectra, the upfield natural abundance lipid ”CO signals near 175 ppm have (S1 exp /Soe"p) ~ 1 for all r, which is consistent with the expected large l3CO-”N distances and corresponding small dCN values for these nuclei. Fitting of the Len-7 (AS/So)” to (AS/SOY” yielded day = 44.8 :1: 2.4 Hz and ray = 4.11 5: 0.08 A for the Leu-7 ”CO/Phe- 11 15N labeled pair (Figure 25). These values are consistent with an or helical structure between the labeled nuclei and correlate with the previously discussed downfield Leu-7 ”CO chemical Shift. 84 Mt ............. it 81.1. .............. .1. 180160 180160 180160 180160 ppm Figure 24. ”C REDOR spectra of HFPtr-L7CF11N associated with (a, b) PC-PG and (c, d) LM3e membranes. For each lettered pair of spectra, the So spectrum is on the left and the S1 spectrum is on the right. The MAS frequency = 8000 Hz, 1'}; = 125 us, and 1'= 8.25 ms (spectra a, c) or r= 32.25 ms (spectra b, d). Dotted lines are drawn at the peak So intensities. The HFPtr spectra were processed with 100 Hz Gaussian line broadening, and baseline correction was applied to all spectra. The number of acquisitions used to obtain each spectrum in panels a, b, c and dis 37710, 23024, 40528, and 98720, respectively. 85 a) 1 .2 1.04 0.8- as" 0.6- AS/ 0.4- 0.2 - 0.0- I 10 T 20 Dephasing time (ms) 30 .. .... 40 42 454 46 la Dipolar coupling (Hz) 50 Figure 25. (a) REDOR (AS/S0)” (open squares with error bars) and (AS/SOY” (crosses) vs. dephasing time for the HF Ptr-L7cFl lN/PC-PG sample. Each (AS/So)” was based on a (AS/So)” determined fiom spectral integrations over a 1 ppm region centered at 178.6 ppm, the Leu-7 ”CO peak chemical shift. The total (So + Sr) number of scans used to obtain the (AS/So)” values for 1'= 8.25, 16.25, 24.25, and 32.25 ms is 75420, 52832, 41568, and 46048, respectively. (b) A plot of )(2 vs. dCN yields dCN= 44.8 :1: 2.4 Hz which corresponds to rev = 4.11 :1: 0.08 A for the Leu-7 1°CO/Phe-ll l5N labeled pair. The (AS/So)” values in plot a were calculated with the best-fit day. 86 REDOR spectra of the HFPtr-L7CF11N/LM3e sample yielded S1 exp /S0°xp values which were Significantly smaller than the S 1°” /So‘°"’ values for the 14 sample and suggest that the region between Len-7 and Phe-11 has non-helical conformation (Figures 12 and 24). Fitting of (AS/So)” to (AS/SOY” yielded dc); = 15.8 :1: 1.8 Hz which corresponds to rev = 5.8 :1: 0.3 A for the Len-7 ”CO/Phe-ll 15N labeled pair (Figure 26). This distance is longer than the ~4.1 A distance expected in a or helical conformation and shorter than the ~11 A distance expected in a ,B strand conformation. This result is discussed after presentation of the prTDQBU analyses; briefly, structural models suggest that the REDOR data reflect an interpeptide distance and provide information about the register of residues in adjacent fl strands. prTDQBU Measurements fioCTDQBU spectra. The prTDQBU experiment was first validated using the GF F sample as detailed in Chapter 3. Figure 27 displays example ” C prTDQBU spectra of different samples: a, 172.6, C0 of membrane-associated HFPmn-F8c/LMe; and b, 174.9, CO of membrane-associated HFPtr-A15c/LMe. The 13C0 Signals of the membrane-HFP samples had ~75% and ~25% respective contributions from labeled and natural abundance sites. The peak Shift of the HFPmn-FSdLMe spectra agreed better with the database distribution of ,6 strand ” CO shifts for Phe (174.3 i 1.6 ppm) than with the distribution of helical Shifts (177.1 i 1.4 ppm).(3) A ,B strand conformation at this Site was also supported by previous torsion angle measurements.(7) The peak shift of the HFPtr-A6c/LMe spectra was 173.7 ppm with ~3 ppm peak width and lineshape Similar to those of the HFPmn—F8c/LMe spectra. 87 1.2 1.0- 0.8- (0° 0.6- AS/ 0.4 - 0.2 - 0.0 - E E E 1'0 20 I 30 Dephasing time (Hz) I I l 12 13 1'4 15 1'6 1'7 18 19 Dipolar coupling (Hz) Figure 26. (a) REDOR (AS/So)” (open squares with error bars) and (AS/So)” (crosses) vs. dephasing time for the HFPtr-L7cF11N/LM3e sample. Each (AS/So)” was based on a (AS/So)” determined from spectral integrations over a 1 ppm region centered at 173.4 ppm, the peak shift in the So Spectra. The total (So + S1) number of scans used to obtain the (AS/So)” values for r= 8.25, 16.25, 24.25, and 32.25 ms is 81056, 76288, 172512, and 197440, respectively. (b) A plot of 22 vs. dCN yields day = 15.8 r 1.8 Hz which corresponds to my = 5.8 :1: 0.3 A for the Leu-7 l°CO/Phe-11 l5N labeled pair. The (AS/S0)” values in plot a were calculated with day = 15.8 Hz. 88 I I I I 190 170 190 170 Figure 27. one-rr-per- rR prTDQBU spectra of (a) membrane-associated HFPmn-F8c with r= 29.33 ms, and (b) membrane-associated HFPtr-AISC with r= 30.67 ms. The MAS frequency was 12000 Hz and CT = 64.0 ms. For each lettered pair of spectra, the So spectrum is on the left and represents the sum of {= y and {= —y data and the S1 spectrum is on the right and represents the sum of {= x and {= -x data. Dotted lines are drawn at the peak labeled amide carbonyl So intensities. Each spectrum in panel a, or b respectively represented the sum of 10000 scans and was respectively processed with 200, or 300 Hz Gaussian line broadening. Processing also included dc offset correction and polynomial baseline correction. 89 The HFPtr-A6c/LMe shift was also more consistent with the database distribution of )6 strand shifts for Ala (176.1 i 1.5 ppm) than with the distribution of helical shifts (179.4 :1: 1.3 ppm).(3) The peak shift of the HFPtr-A15c/LMe spectra was also consistent with ,B strand conformation but the peak was broader than the other two HFP samples which may indicate greater conformational heterogeneity near Ala-15. The membrane-associated HF P Spectra of Figure 27 were obtained with rz 30 ms and offered an interesting contrast with (AS/S0)” z 0.5 for HF Pmn-F8c/LMe and < 0.1 for HFPtr-A1 SdLMe. The signals had ~25% contribution from natural abundance Sites and comparison with the GF F Spectra qualitatively suggested labeled l°CO-”CO distances close to 5 A in the HFPmn-F8c/LMe sample and much greater than 5 A in the HFPtr-A1 SdLMe sample. I 3 C 0—1 3 C0 distances. An in-register parallel ,B strand model for the HF Ptr-L7CF1 lN/LM3e sample was tested with prTDQBU measurements of adjacent interstrand Len-7 l°CO/Leu-7 ” CO dipolar couplings and distances. If the model is correct, the distance will be ~4.8 A with dcc ~ 70 Hz. The prTDQBU one-n-per-IR So/Sl spectra of the HFPtrL7cF11N/LM3e sample are displayed in Figure 28. Relative to the Gly-l and Phe-3 l3C0 peaks in the GFF Spectra (Figure 12), the HFPtr spectra have larger Sl/So ratios which are consistent with a doc smaller than in D-GFF and a Len-7 13 CO/Leu-7 ” CO distance longer than that in D- GFF. The r = 32, 48, and 64 ms points were fitted in the context of a “two-spin” or a “three-spin” model (Figure 29). The 80 ms point was not included in the fitting because of the systematic disagreement between (AS/So)” and (AS/So)” at large values of rin the GF F analysis (Figure 16a). 90 (b) ‘ 1141 1W 411 W 2601'50 2601'50 ppm Figure 28. prTDQBU “one-7t-per-2 1);” spectra of (a-d) the HFPtr-L7cFl lN/LM3e sample. For each lettered pair of spectra, the So spectrum is on the left and the S1 Spectrum is on the right. The MAS frequency = 8000 Hz, T); = 125 us, the ”C rrpulse rf field = 10 kHz, M = 336, and the total constant-time CT = (L + M + N) x rR = 84 ms. The values of L, N, and rare: 128, 208, 32 ms (spectra a); 192, 144, 48 ms (spectra b); 256, 80, 64 ms (spectra c); 320, 16, 80 ms (spectra (1). For each set of HFPtr spectra with the same 2', a dotted line is drawn at the peak So intensities of Leu-7 (HFPtr). The HFPtr spectra were processed with 250 Hz Gaussian line broadening, and baseline correction was applied to all spectra. For some of the HFPtr spectra, there is a small glitch at ~178 ppm which is due to DC offset in the data. The total number of scans used to obtain each spectrum in panels a, b, c, and d is 77056, 80736, 102432, and 152064, respectively. 91 a) 0.8 - 0.6 - AS/So 0.4 - i i 8 l l I 0 20 4O 60 80 Dephasing time (ms) b) 0.8—1 0.6 - 0.4— , i i 0.0- AS/So 0 ‘20 40 60 80 Dephasing time (ms) Figure 29. prTDQBU “one-n-per-Z TR” (AS/So)” and (AS/Sp)” vs. dephasing time for the HFPtr-L7CF1 lN/LM3e sample. The MAS frequency = 8000 Hz, the ”C rrpulse rf field = 10 kHz, 53c ”mm-“e, = 178.4 ppm, M = 336, and the constant-time CT = 84 ms. The (AS/So)” values are open squares with error bars. Each (AS/So)” was based on a (AS/So)” determined fiom spectral integrations over a 1 ppm region centered at 173.4 ppm, the peak shift in the So spectra. The total (So + Sr) number of scans used to obtain the (AS/So)” values for r= 32, 48, and 64 ms is 154112, 161472, and 204864, respectively. The (AS/So)” values were calculated with two-spin and three-Spin models in plots a and b, respectively. In plot a, the up triangles, crosses, and down triangles correspond to dcc = 10, 15 and 20 Hz, respectively and in plot b, they correspond to doc = 8, 13, and 18 Hz, respectively. The best-fit values of dcc are ~15 Hz and ~13 Hz for the two-spin and three—spin models, respectively, and correspond to interstrand Len-7 ” CO-13 CO distances of 8.0 A and 8.4 A. Reasonable upper limits on dcc in the two-spin and three-spin models are ~20 Hz and ~18 Hz respectively, and correspond to distances of 7.3 A and 7.5 A. 92 The two-spin (three-spin) model has two (three) adjacent in-register parallel B strands and the Simulations are based on two (three) ” COS, each of which is at the same residue position in its respective strand. The interstrand distance and corresponding dcc value were input parameters for the simulations. In the three-spin model, the two outside strands were always equidistant from the central strand. The fitting is based on three points with relatively large uncertainties and visual comparison was used to assess best-fit dcc and its uncertainty. The best-fit values of dcc in the two-spin and three-Spin models are ~15 Hz and ~13 Hz, respectively, and correspond to rcc of 8.0 A and 8.4 A. Reasonable upper limits on dcc in the two-spin and three-spin models are ~20 Hz and ~18 Hz, respectively, and correspond to rcc of 7.3 A and 7.5 A. The lower limits on dcc and upper limits on rcc are more difficult to assess because of the uncertainties in (AS/So)” and weak dependence of (AS/SOY” on dcc at small values of dcc. Overall, experimental values of dcc and rcc do not support the in- register parallel B model for which dcc ~ 70 Hz and rcc ~ 4.8 A. For the HFPtr-A1 SdLMe sample, Figure 26a shows that (AS/So)” z 0 for r < 35 ms and comparison with simulations suggested an upper limit of ~1 5 Hz on dcc or a lower limit of ~8 A on rcc. The HFPmn-F8c/LMe and the HFPtr-A6c/LMe samples both had fairly rapid buildup of (AS/So)” calculated with h = 1, i.e. all labeled '3 CO were 60" considered to have the same value of dcc. However, the (AS/So) at large r were between 0.4 and 0.6 and these values were about half of the expected (AS/So)” (cf. Figure 21 a). AS noted in Eq. (2. 8), this discrepancy could be reduced with a two- population model in which a fraction (h) of the labeled l°CO experienced a Single non- zero value of dcc and a fraction (1 — h) experienced dcc = 0. 93 0.2 l l I ‘I 20 4O 60 80 100 Dipolar coupling (Hz) (b) 1 .o - 0.84 0.4 - 0-2 r r r 20 40 60 80 100 Dipolar mupling (Hz) Figure 30. Contour plots of x2 for membrane-associated (a) HFPmn-F8c and (b) HF Ptr- A6c. The x2 were calculated with comparison of (AS/So)” and (AS/So)” calculated with a two-parameter model. For this model, there was a population fraction (h) of labeled ” C which experienced measurable 1°C-”C di olar coupling and a population fraction (1 — h) of labeled 13C which experienced no 1°C- 3 C dipolar coupling. The horizontal and vertical axes are the measurable dipolar coupling and h parameters, respectively. The shading legend: black, (a) 1.0 <12 < 1.1 or (b) 6 <12 < 7; dark gray, (a) 1.1 <12 < 2.0 or (b) 7 < 22< 10; gray, (a) 2 <22 < 5 or (b) 10 <22 < 20; light gray, (a) 5 <22 < 10 or (b) 20< 22 < 50; white, (a) 22 > 10 or (b) 22 > 50. 94 For the HFPmn-F8c/LMe data, {(d, h) was determined using (AS/So)” calculated for 0.2 S h S l and (AS/So)“ calculated for 20 Hz 5 dcc S 100 Hz, cf. Figure 30a. The f contour plot had a well-defined minimum centered at h = 0.78 and dcc = 80 Hz (rcc = 4.6 A) and the most likely dcc and h were within the black and dark gray regions of this plot.(8) A similar analysis was done for the HFPtr-A6c/LMe data and yielded best-fit parameter values h = 0.99 and dcc = 49 Hz (rcc = 5.4 A), cf. Figure 30b. The black and dark gray good-fit regions had a curved Shape that approximately extended from the best-fit parameter values to h z 0.5 and dcc z 80 Hz (rcc = 4.6 A).(9) Structural Modeling Strand arrangement models. Figure 31 displays three models: (a) parallel B strand with all strands in-register; (b) parallel B strand with adjacent strands two residues out-of- register; and (c) antiparallel B strand with adjacent strand crossing between Phe-8 and Len-9. Each model is shown with three strands, although we do not have information about the numbers of strands in the LM3e-associated HFPtr oligomer. Table 2 displays Len-7 CO/Phe-ll N and interstrand Len-7 CO/Leu-7 CO distances fiom REDOR and prTDQBU experiments and from the models. The model distances are averages for parallel strand regions of cutinase and antiparallel strand regions of human gamma-D crystalline R58H mutant whose crystal structures have been refined to 1.0 A and 1.15 A, respectively.(1 0, I 1 ) 95 a) AVGIGALFLGFLGAAG —> AVGIGALFLGFLGAAG -—> AVGIGALFLGFLGAAG —> b) AVGIGALFLGFLGAAG —> AVG | GALFLGFLGAAG —> AVGI GALFLGFLGAAG —> 6) AVGIGALFLGFLGAAG —> <— GAAGLFGLFLAGIGVA AVGIGALFLGFLGAAG —> Figure 31. Structural models for strand arrangements of LM3 e-associated HFPtr: (a) parallel in-register; (b) parallel with adjacent strands two-residue out-of-register; and (c) antiparallel with adjacent strand crossing between Phe-8 and Len-9. The sequence of the first Sixteen residues is AVGIGALFLGFLGAAG fi'om residue 1 to 16. 96 Table 2. Experimental and model distances of HF Ptr-L7CF 1 lN/LM3e ° rCN (13K)!) rCC (1°06 Experiment 5.8(3) 8.2(9) Parallel in-register modeld 1 1.0(3) 4.8(2) Parallel out-of-register 6.5(3) 8.2(3) Antiparallel modelf 6.1(3) 8.5(3) ° Each model distance was determined from a region of a high- resolution crystal structure which has the same strand arrangement as the model. Several internuclear distances were measured in this region. An average distance is reported in the table as well as the standard deviation in units of 0.1 A in parentheses. b Len-7 CO/Phe-ll N distance. ° Interstrand Leu-7 CO/Leu-7 CO distance. dModel distances were determined from the region of the cutinase protein corresponding to residues 34-39, 113-120, and 143-148. e Adjacent strands are two-residues out-of-register. Model distances were determined from the cutinase protein. f Adjacent strands cross between Phe-8 and Leu-9. Model distances were determined from the region of the human gamma-D crystalline R58H mutant protein corresponding to residues 2-7, 14-18, and 34-38. 97 There are significant differences between the experimental distances and in- register parallel strand model distances. The experimental Len-7 l°CO/Phe-11 l5N distance is ~6 A which is much Shorter than the ~11 A intrastrand or interstrand distance in the model. The lower limit on the experimental interstrand Leu-7 l°CO/Leu-7 ” CO distance is >7 A and is significantly longer than the 4.8 A distance in the model. Distances in the out-of-register parallel strand and antiparallel strand models are more consistent with the experimentally derived distances. There are ~6 A interstrand Len-7 CO/Phe-ll N distances because of the strand registers in the models. In addition, the interstrand Leu-7 CO/Leu-7 CO distances are ~8 A. Calculations of REDOR and prTDQBU (AS/So)“ for the two models agreed reasonably well with (AS/So)”. The data were more poorly fit by other strand arrangement models. Further experiments are required to distinguish between the two models. For example, we recently observed Ala-6 1°C/G1y-10 '3 C crosspeaks in 2D Spectra of LM3- associated HFP which was uniformly '3 C labeled at Ala-6 and Gly-10.(12) The crosspeaks were generated by magnetization exchange due to proton-driven spin diffusion which typically occms between ”C nuclei separated by < 6 A. For the out-of- register parallel and antiparallel models, the closest distance between Ala-6 and Gly-10 ”CS is ~7 .1 A and ~4.5 A, respectively, and the spectra are more consistent with the antiparallel model. Future experiments could be based on the REDOR approaches used to recently elucidate strand arrangements in the PG-l antimicrobial peptide.(l3) A turn structure in the Leu-7 to Phe-11 region could also be consistent with the experimental Leu-7 CO/Phe-ll N distance. Although this possibility cannot be definitively ruled out, measurements of ”C chemical shifts for nuclei in this region of 98 LM3-associated HFP are all consistent with a B strand conformation.(12, 14) We also note the possibility of populations of distinct strand arrangements which would necessitate fitting REDOR and prTDQBU Si grrals with populations of distinct Spin geometries. With the assumption of Single structural model of HFP, the REDOR and prTDQBU (one-n—per-ZTR) data are consistent with a parallel strand arrangement with adjacent strands two-residues out-of-register and with an antiparallel arrangement whose adjacent strand crossing is between Phe-8 and Len-9. The data are not consistent with an in-register parallel strand arrangement. Recently, the prTDQBU (one-n—per-rR) data was analyzed in the context of a mixture of two structural models. In one model, adjacent HFP strands are parallel to one another and are in-register. Example hydrogen bonds between adjacent strands would be Ala-6 CO"'HN Leu-7, Phe-8 CO"'HN Leu-9, and Ala-15 CO"'HN Ala-16. In this model, the distance between labeled ”COS on adjacent strands is ~4.8 A for the HFPtr- A6c/LMe, HFPmn-F8c/LMe, and HFPtr-A15c/LMe samples. In a second model, adjacent HF P strands are antiparallel to one another with strand crossing between Phe-8 and Len-9. Example hydrogen bonds between adjacent strands are then Ala-6 CO'“HN Phe-11, Phe-8 CO"'HN Len-9, and Ala-15 CO"'HN Val-2. A key feature of the antiparallel model is the variation among the different samples of the distance between labeled 13cm on adjacent strands, eg. ~4.8 A in HFPmn-F8c/LMe and 215 A in HFPtr- A6c/LMe and HFPtr-A1 SdLMe. The clearest data analysis could be done for the HFPmn-FSC/LMe sample, cf. Figure 30a, and yielded best-fit doc z 80 Hz, rcc z 4.6 A, and h z 0.8. The best-fit 99 distance was generally consistent with the predicted distances of either the parallel or the antiparallel model. For the parallel model, the same dcc z 80 Hz would be predicted for the HFPtr-A6c/LMe sample and the good-fit region of the f plot for this sample includes dcc z 80 Hz with accompanying h z 0.5, cf. Figure 30b. The antiparallel model predicted rCC z 15 A and dcc z 2 Hz for HFPtr-A6c/LMe and was a poor fit to the data. The parallel strand arrangement did not appear to extend to Ala-15, as evidenced by (AS/SOY” z 0 for r< 35 ms in the HFPtr-A1 SdLMe data, of. Figure 22a. The upper limit on dcc for this sample was ~15 Hz. Conformational plasticity. The structural plasticity of membrane-associated viral fusion peptides has been observed by several groups using a variety of experimental probes, and it is known that they can exist in helical or nonhelical forms.(l5) Other investigators have developed structural models for the helical form of the peptides based principally on liquid-state NMR, ESR, and IR data.(16-20) IR and solid-state NMR studies of the B strand form of HFP and its oligomeric constructs have Shown a parallel strand arrangement, an anti-parallel strand arrangement and a mixture of parallel and antiparallel arrangements.(21-23) In the present study, the structure of membrane- associated HF Ptr was explored with solid-state NMR methods including chemical Shift, heteronuclear distance, and homonuclear distance measurements. The data suggest that the region of HFPtr between Leu-7 and Phe—11 is or helical when associated with membranes without cholesterol and is B strand when associated with membranes which have a lipid headgroup and cholesterol composition similar to that of host cells of the virus. These results are consistent with our observations that for a single FP:lipid mol 100 ratio, cholesterol favors formation of the B strand conformation of fusion peptides.(5, 6) This conformational difference has been seen at room temperature as well as at the —50 °C temperature of the experiments in this work.(14) The observed fusion peptide conformations appear to be equilibrium rather than kinetically-trapped structures.(24) The presence of cholesterol in membranes is known to increase the lateral molecular packing density and membrane tensile strength, decrease in-plane elasticity and permeability of water through the membrane, and promote formation of the “liquid- ordered phase”.(25-30) This phase is characterized by a rapid lateral molecular translational diffusion coefficient Similar to that of the “liquid-disorder ” phase and high configurational order of the lipid acyl chains similar to that of the “solid-ordered” phase.(30, 31) These latter phases exist for non-cholesterol containing membranes at higher and lower temperature, respectively. Fluorescence data suggest that HFPmn in its helical form inserts more deeply into the membrane than HFPmn in its B strand form.(32) The higher molecular packing density in the cholesterol-containing membranes may make HF Ptr insertion more difficult and thus favor a more surface-associated B strand form. Because the rapid fusion rate of HF Ptr is observed both for vesicles which contain cholesterol and for vesicles which do not contain cholesterol, one reasonable hypothesis is that both the helical and B strand structures of HFPtr are highly fusogenic.(33) Other investigators have proposed that the peptide structure responsible for fusion is irregular and may be transient.(34, 35) Although the present work does not directly address these issues, it is noted: (1) cholesterol-associated structural variation is also observed for the influenza virus fusion peptide (5, 6); and (2) pH-triggered fusion can be observed both 101 for helical influenza fusion peptide bound to non-cholesterol containing membranes and for B strand influenza fusion peptide bound to cholesterol-containing membranes.(36) These results argue in favor of fusogenic activity of both helical and B strand structures. Lentz and coworkers have proposed that fusion peptides catalyze fusion by filling void spaces in nonbilayer fusion intermediates and that this function can be done by peptides in either helical or B strand conformation.(3 7) Our results are consistent with this model and two firsogenic conformations may allow the virus to fuse with a wider variety of membrane compositions. Membranes of uninfected host cells of the virus contain ~30 mol% cholesterol and there is some depletion of cholesterol in these membranes after HIV infection.(38, 39) The HIV membrane contains ~45 mol% cholesterol and there is some evidence that HIV fuses with cholesterol-rich regions of host cell membranes.(40) The 15-40 fold higher rate of HFPtr-induced lipid mixing relative to HFPmn is observed both with PC-PG vesicles for which the final HFPtr conformation is helical and with LM3 vesicles for which the final conformation is B strand. For either conformation, there is a higher local concentration of peptide strands at the membrane surface with HF Ptr than with HFPmn and this larger concentration could cause greater perturbation of the membrane and provide a general model for the increased fusion rate of HFPtr. Other possible differences between HFPtr and HFPmn are their depths and angles of membrane insertion as well as the arrangement and interactions of individual helices or strands. Strand arrangement. Previous solid-state NMR REDOR data for HFPmn associated with cholesterol-containing membranes were consistent with a mixture of parallel and antiparallel strand arrangements.(23) A predominant parallel strand 102 arrangement is an appealing structural model to explain the increased fusion rate of B strand HF Ptr because it places the apolar N-terminal regions of the strands close to one another and thereby provides a larger apolar volume to perturb the membrane. The solid- state NMR data of this work are consistent with a parallel model with adjacent strands two residues out of register. The data are also consistent with antiparallel strands with adjacent strands crossing between Phe-8 and Leu-9. For this antiparallel arrangement, the sixteen N- terminal apolar residues (A1 to G16) could form a hydrogen-bonded B strand oligomer and the more polar C-terminal residues would be outside the hydrogen-bonded oligomer. If residues A1-G16 form a single B strand without turns, then a structural building block could be based on two HFPtr molecules “A” and “B”. The A1, A2, and A3 strands would run in the same direction (as enforced by the cross-linking) and the B1, B2, and B3 strands would run in the opposite direction. Arr antiparallel interleaved arrangement could be AlB3A2B2AgBl; i.e. residues in strand B3 are hydrogen bonded to residues in strands A1 and A2. This antiparallel structure would place the bulky C-terminal regions of the HFPtr molecules on either Side of the oligomer and could allow more efficient assembly of multiple HF Ptr trimers at the membrane surface with consequent greater membrane perturbation and fusion rate. The total number of strands in a hydrogen-bonded oligomer may not be large as evidenced by poor room-temperature cross-polarization and the inferred high molecular mobility.(l4) For membrane-associated HF Pmn, IR data from several groups support an antiparallel strand arrangement.(22, 3 7, 41, 42) However, IR data on constructs which contain the first 34 or 70 residues of gp41 support an in-register parallel strand 103 arrangement.(21) These latter constructs contain the 23-residues of HFPmn as well as an additional 11 or 47 C-terminal residues. The variation in strand arrangements among the constructs may be due to sequence or cross-linking differences.(43) An overall HFP model consistent with the data in this study was: (1) a rrrixture of parallel and antiparallel strand arrangements in the region of HFP which included Ala-6 and Phe-8; and (2) loss of parallel B sheet structure in the Ala-15 region. Supporting evidence for point 1 included the larger h of the HF Pmn-FSdLMe sample relative to the HFPtr-A6c/LMe sample. This result correlated with: (1) the large dcc predicted by both parallel and antiparallel models for HF Pmn-F 8dLMe; and (2) the large and small dcc values predicted for HF Ptr-A6c/LMe by the parallel and antiparallel models, respectively. Previous measurements of interstrand homonuclear and heteronuclear dipolar couplings in HFP samples were also consistent with a mixture of parallel and antiparallel strands.(23, 44) As noted above, evidence for loss of parallel B sheet structure near Ala-15 included (AS/Sp)” z 0 for the HFPtr-A1 SdLMe sample. This C-terminal “fi'aying” of the parallel B Sheet was also consistent with larger Ala-15 ”CO linewidths and with previous measurements of interpeptide l3CO-”N dipolar couplings.(23) Previous studies have also shown that the Ala-15 ”COS were in close 5-6 A proximity to the 31P in the lipid headgroups while distances between Ala-6 or Phe-8 ”COS and lipid 31PS were > 8 A.(45) The combination of the different data suggests a general structural model in which: (1) residues in the apolar N-terminal region of HF P are located in the low water content acyl chain region of the membrane and form a regular B sheet structure; and (2) residues in the 104 more polar C-terminal region are located in the lipid headgroup region and have greater structural disorder because of hydrogen bonding with water.(7) 105 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) References Kricheldorf, H. R., and Muller, D. 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(2004) De novo design of conforrnationally flexible transmembrane peptides driving membrane fusion, Proc. Natl. Acad. Sci. U.S.A. 101, 14776-14781. Parkanzky, P. D. (2006) Solid state nuclear magnetic resonance studies of the influenza fusion peptide associated with membrane bilayers, Ph. D. thesis, Michigan State University, East Lansing. Haque, M. E., Koppaka, V., Axelsen, P. H., and Lentz, B. R. (2005) Properties and structures of the influenza and HIV fusion peptides on lipid membranes: Implications for a role in fusion, Biophys. J. 89, 3183-3194. Aloia, R. C., Tian, H., and Jensen, F. C. (1993) Lipid composition and fluidity of the human immunodeficiency virus envelope and host cell plasma membranes, Proc. Natl. Acad. Sci. U.S.A. 90, 5181-5185. Brugger, B., Glass, B., Haberkant, P., Leibrecht, I., Wieland, F. T., and Krasslich, H. G. (2006) The HIV lipidome: A raft with an unusual composition, Proc. Natl. Acad. Sci. U.S.A. 103, 2641-2646. Ono, A., and Freed, E. O. (2005) Role of lipid rafts in virus replication, in Virus Structure And Assembly (Roy, P., Ed.) pp 311-358, Elsevier Academic Press, San Diego. Nieva, J. L., Nir, S., Muga, A., Goni, F. M., and Wilschut, J. (1994) Interaction of the HIV-1 fusion peptide with phospholipid vesicles: different structural requirements for fusion and leakage, Biochemistry 33, 3201-3209. Castano, S., and Desbat, B. (2005) Structure and orientation study of fusion peptide FP23 of gp41 from HIV -1 alone or inserted into various lipid membrane models (mono-, bi- and multibi-layers) by FT-IR Spectroscopies and Brewster angle microscopy, Biochim. Biophys. Acta-Biomembranes 1 715, 81-95. Gordon, D. J ., Balbach, J. J ., Tycko, R., and Meredith, S. C. (2004) Increasing the arnphiphilicity of an amyloidogenic peptide changes the beta-sheet structure in the fibrils fi'om antiparallel to parallel, Biophys. J. 86, 428-434. Zheng, Z., Yang, R., Bodner, M. L., and Weliky, D. P. (2006) Conformational flexibility and strand arrantements of the membrane-associated HIV fusion peptide trimer probed by solid-state NMR spectroscopy, Biochemistry 45 , 12960- 1297 5. Qiang, W., Yang, J ., and Weliky, D. P. (2007) Solid-state nuclear magnetic resonance measurements of HIV fusion peptide to lipid distances reveal the 109 intimate contact of beta strand peptide with membranes and the proximity of the Ala-l4-Gly-l6 region with lipid headgroups, Biochemistry 46, 4997-5008. 110 Chapter 5 Summary Technique Development The CP match with higher 1H and ”C CP rf fields was tested to be more efficient and robust for CP from 1H to '3 C under MAS frequency ranging fiom 8 kHz to 12 kHz for both crystalline and membrane-associated samples. The alternating lSN/ '3 C it pulse version of REDOR sequence is a useful and accurate method in quantitatively measuring ~4 A l3CO-”N distances and thus probing hydrogen-bonding and secondary structure in membrane-associated HF P samples. Two finite-pulse radiofi'equency-driven recoupling methods, i.e. prTDQBU and prFDT-CT, were examined and compared in measuring 3-6 A l3CO-”CO distances. For the prTDQBU method, the optimal experimental condition is reached by 20.5 kHz finite 7t pulses and the one-rt-per-rR version under MAS frequency = 12 kHz and this method is proved to be semi-quantitative and relatively insensitive to chemical shift anisotropy (CSA), spin relaxation, pulse and phase imperfections and ”C transmitter offset. On the other hand, although the prFDR-CT method has relatively higher Si gnal-to-noise ratio because of its better performance in refocusing spins, it is not a true constant-time experiment in terms of total transverse spin relaxation. Therefore, prTDQBU is a more straightforward method in measuring 13CO-”CO distances in membrane-associated HFP samples which have relatively short transverse relaxation time (T2 ~ 15 ms). 111 Fusion Peptide Structural Determination REDOR-filtered chemical Shift and REDOR intramolecular ”CO-”N distance measurements Show that the conformation of the Len-7 to Phe-ll region of HFPS has predominant helical conformation in membranes without cholesterol and B strand conformation in membranes containing ~30 mol% cholesterol. To study the strand arrangement, further prTDQBU l°CO-”CO distance measurements were conducted on HFP samples in membranes containing ~30 mol% cholesterol, which were singly labeled with 13C0 on each strand at residue Ala-6, Leu-7, Phe-8 and Ala-15, respectively. A set of earlier prTDQBU data suggests two-residue out-of-register parallel B strand or antiparallel B strand under the assumption of a single structural arrangement, while the interpretation of recent prTDQBU data supports a model with mixed parallel B and antiparallel B strand arrangements at the N-terminal region of HFPS and also suggests the loss of structural ordering towards the C-terminal region of HFPS. Future Directions The current version of prTDQBU experiments have variation in So Signal intensities over the dephasing time t, which may be reduced by using higher '3 C It'pulse phase cycles like XY -1 6 in the sequence or by adding more refocusing solid echoes to lower the length of each echo period.(I) Other homonuclear recoupling sequences such as the one introduced by Y. Ishii in 2001 and the more recent one by R. Tycko may be the alternative solutions to the above problem.(2, 3) Once the variation in So signal intensities is significantly reduced, prTDQBU experiments can be run in a fashion similar to that of prFDR-CT which acquires a Single So Signal and multiple S1 signals 112 for a set of data, and the total signal acquisition time of a set of data will subsequently be reduced by almost 50%. 113 (1) (2) (3) References Gullion, T., Baker, D. B., and Conradi, M. S. (1990) New, Compensated Carr- Purcell Sequences, J. Magn. Reson. 89, 479-484. Ishii, Y. (2001) 1°C-” C dipolar recoupling under very fast magic angle spinning in solid-state nuclear magnetic resonance: Applications to distance measurements, spectral assignments, and hi gh-throughput secondary-structure determination, J. Chem. Phys. 114, 8473-8483. Tycko, R. (2007) Symmetry-based constant-time homonuclear dipolar recoupling in solid state NMR, Journal Of Chemical Physics 126, 064506. 114 Appendix I Determination of Corrections This section considers determination of (AS/So)”, the contribution to (AS/So)” due only to the labeled nuclei. (AS/Sp)” is equivalently described by the parameter “f” , the Sl/So ratio for the labeled l3C0 nuclei considering only other labeled nuclei. Comparison of (AS/Sp)” to (AS/SOY” yields the labeled nuclei internuclear dipolar couplings and distances. Contributions to So and S1 are considered for ”CO nuclei in different environments. A. REDOR analysis of 14 peptide The following parameters/approximations are used: Al. There is 99% labeling of the Ala-9 13co and Ala—13 ”N sites. 51 = so for a labeled Ala-9 13CO in a molecule with an Ala-l3 l4N. A2. Effects of natural abundance 15N on 13C0 Signals are evaluated using the following criteria: (1) S1 = 0 for a labeled Ala-9 l°CO separated by one or two bonds fiom a natural abundance ”N at Ala-10 or Ala-9. Ala-9 S1 is not affected by other natural abundance ”N. (2) S1 = 0 for natural abundance backbone ”COS at Glu-12 or Ala-13 which are separated by one or two bonds from the labeled Ala-13 15N. S1 = So for other natural abundance backbone ”CO sites. Criteria (1) and (2) are based on the close distance (S 2.5 A) and consequent strong (2 200 Hz) dipolar coupling of ”CO and ”N nuclei separated by one or two bonds. 115 A3. Ten percent of the Ala-9 ”CO So is due to molecules in random coil structures. The Ala-9 13C0 in these structures have S1 = 0 if criterion A2-(l) is satisfied and have S1 = So otherwise. Previous solid-state NMR experiments suggest that the 14 peptide has 17 i 6% random coil structure but a lower random coil population is chosen in our analysis because some of the random coil 13CO shifts are outside the 1 ppm integration range used to calculate So and S1 intensity values.( J. Am. Chem. Soc., 120, 7039-7048, 1998) The (AS/S0)” expression is calculated using the following parameters: Uc and UN, the fractions of Ala-9 12CO Sites and Ala-13 l4N sites, respectively; AC and AN, the '3 C and ”N natural abundances, respectively; n, the total number of natural abundance peptide backbone CO Sites in an 14 molecule; and h, the fraction of the Ala-9 ”CO So signal due to molecules with regular secondary structure. A chart for the determination of (AS/Sp)” is given in Figure 32. Derivation Express Soexp as the sum of contributions from labeled ” CO nuclei (So'°°) and from natural abundance ”CO nuclei (S0"'°'): sgxp = sgab + 831 =1— UC + n AC (AI. 1) with: 53"” = h(1—UC —UN)+hUN +(1-h)(1—UC —UN)+(1—h)UN (AI. 2) and: saw- : 2 AC + (n — 2) AC (AI. 3) 116 Site description Relative popdation [SO contribution fraction ] {S1 contribution fraction } without nearby n.a. 15N h (1 -UC- UN) 11] m l l YT A913CO 1 [l {} HelicalA; 1300 Non-heliehlA913 co h 1-h [l [l {l {} 15N A913006n1y ' A13 15N only 15:" A913CO only A1315Nonly h (1 - UC- UN) hl'tJlN “(31° (1 -h) (1 -uc- UN) (1 -[t:)]UN (1 'lhO'luc ii {1} {0} H {1} {or /\ A91300andA1315N A913COandA1315N A9 13CO and A13 15N with nearby no. 15 N without nearby no. 15 N with nearby n.a. 15 N h(1-UC-UN) h(t -UC- UN) h(1 -UC- UN) [1] [1] [1] L {or {11 10} n.a. 13CO nAC [l i} // \ E12. A14 n.a. 13CO other no. 1300 2AC (n-2)AC l1] [1] {0} {1} Figure 32. Chart of derivation of (AS/Sp)” for REDOR of the I4 peptide. Four pieces of information were shown fiom top to bottom in each box: the site description, its relative population, and its contributions to So (in brackets) and S1 (in braces). 117 Express Slap as the sum of contributions from labeled 13C0 nuclei (S1’°°) and from natural abundance '3 CO nuclei (S1"'°'): $fo = 8,10” + s,”- (AI. 4) with: Sllab=h(1_UC_UNXl-2AN)f+hUN (AI 5) +(1-hX1—UC-U~X1-24~)+(1‘h)UN ' and: Slna. = (n —2)AC (AI. 6) and the parameterfi f=Sl =1_§0__i_=1- g (A17) 550' Si” 50 Incorporate Eq. (AI. 7) into Eq. (AI. 5): Slab = h(l-UC —UN)(1—2AN)[l—[%S-Jwr]+(l—hXI—UC —UN)(1—2AN)+UN s,” =(1—UC —UN)(1—2AN)—h(l—UC -UN)(1—2AN)[%) +UN. (AI. 8) 0 UC, UN, and 2AN are much less than 1 so that: (l-UC—UNX1—2AN)El—UC—UN—2AN (AI. 9) and: 0 118 Incorporate Eqs. (AI. 6) and (AI. 10) in Eq. (AI. 4): Sfxp =1—UC —2AN —h(1—UC -UN —2AN{-:£] +(n-2)AC. 0 Combine Eqs. (AI. 1), (AI. 2), (AI. 3), and (AI. 11): SSXP "Slexp =[1-UC + "Ac] —1—UC —2A,, —h(l—UC —UN 4.4%?) +(n—2)AC] 0 and simplify: 0 Combine Eqs. (AI. 1) and (AI. 13): 0 So AS exp and rewrite: as °°’_ l—UC+nAC AS “°_ 2AC+2AN sO h(l-UC—UN-ZAN) s0 h( l-UC—UN—ZAN) (AI. 11) (AI. 12) (AI. 13) (AI. 14) (AI. 15) Incorporate UC = 0.01, UN= 0.01, AC = 0.011, AN= 0.0037, n = 17, and h = 0.9: 119 (Al. 16) B. REDOR analysis of HFPtr-L 7CF1 1 N samples The following parameters/approximations are used and B1 and B2 are based on Al and A2 for the 14 peptide. Bl. There is 99% labeling of the Leu-7 ”CO and Phe-ll ”N Sites. S1 = So for a labeled Leu-7 13C0 in a peptide strand with a Phe-11 l4N. BZ. (1) S1 = 0 for a labeled Leu-7 13CO separated by one or two bonds from a natural abundance ”N at Phe-8 or Leu-7. The Leu-7 S1 is not affected by other natural abundance ”N. (2) S1 = 0 for natural abundance backbone ”COS at Gly-10 or Phe-11 which are separated by one or two bonds from the labeled Phe-ll ”N. 51 = So for other natural abundance backbone ”CO sites. 133. In the HFPtr-L7CF11N/PC/PG sample, the natural abundance lipid l3co signal is resolved from the Len-7 labeled 13C0 Signal and does not contribute to S0 or S1. Using h = 1, Eq. (AI. 15) is modified: cor exp (AS) _ l—UC+nAC (AS) 2AC+2AN (AI.17) s—0 —1—UC—UN—2AN S,- -1—UC—UN-2AN Consider n as the average number of unlabeled backbone CO Sites per strand. Using UC = 0.01, UN = 0.01, AC = 0.011, AN = 0.0037, and n = 29.33: cor eJCp [g] = 1.350[£j — 0.030 (A1. 18) S0 S0 120 C. fiC T DQBU analysis of the D-GFF solid-state NMR sample The following parameters/approximations are focused on the Gly-l 13 CO nuclei because So and $1 signals from these nuclei are used in the experimental data analysis. C1. 13C0 signals from Gly-l, Phe-2, and Phe-3 are completely resolved. C2. Intermolecular '3 C-13C dipolar coupling is not considered. For Gly-l 13 CO, the closest intermolecular carbon nucleus is > 4 A away. c3. For D-GFF, there is 99% labeling of Gly-l ”co and Phe-3 ”co. s1 = so for a molecule with a labeled Gly-l ”co and a Phe-3 12co. C4. St values for a molecule with a labeled Gly-l 13CO and nearby natural abundance 13 C are set with the following criteria: (1) S1 = 0 when 2' s 32 ms and the labeled Gly-l 13CO/natural abundance 13 C nuclei are separated by one or two bonds. (2) S1 = 0 when r> 32 ms and the labeled Gly-l l3CO/natural abundance 13 C nuclei are separated by one, two, or three bonds. (3) $1 is not affected by the natural abundance 13 C if neither criterion (1) nor (2) are satisfied. The criteria are based on the ~1.5 A, ~2.5 A and ~3.8 A distances for one-, two- and three-bond l3C-13C separations, respectively, and the consequent 2200 Hz, 500 Hz and 140 Hz dipolar couplings. C5. S1 = So for a natural abundance Gly-l 13CO in an unlabeled GF F molecule. Each (AS/So)” value is calculated using the following parameters: UCl and ch, the fractions of Gly-l and Phe-3 12CO sites in D-GFF, respectively; Ac, the fractional 13 C natural abundance; n, the ratio of unlabeled GF F to D-GFF molecules in the crystal; and m, the number of unlabeled carbon nuclei which satisfy either criterion C4-( 1) or C4-(2) (cf. Figure 33). The prTDQBU expression for (AS/SOY" is: 121 COI‘ exp The values of Uct, Ucz, Ac, and n are 0.01, 0.01, 0.011, and 49, respectively. For 15 32 ms, m = 2 and numerical evaluation of Eq. (AI. 19) yields: cor exp [5'3] = 1.596(A—S] - 0.024 (A1. 20) For 1'> 32 ms, m = 4 and numerical evaluation of Eq. (AI. 19) yields: cor exp [55—] = 1.634(gj - 0.047 (A1. 21) S0 S0 The prTDQBU analysis of D-NAL followed that of D-GFF. For D-NAL, the values of Ugl, U02, AC, n and m are 0.01, 0.01, 0.011, 9 and 2, respectively and numerical evaluation of Eq. (AI. 19) yields: (gjw’ = 1.173 [£19m — 0.024 (A1. 22) So 50 D. ij T DQBU analysis of the HFPtr-L7CF11N sample The following parameters/approximations are used: D1. There is 99% labeling of Leu-7 ”co. D2. SI values for a Leu-7 13 CO with nearby natural abundance 13 C are determined by the following criteria: (1) S1 = O for 2' s 32 ms and Leu-7 l3CO/natural abundance 13C separated by one or two bonds. (2) $1 = O for T > 32 ms and Leu-7 l'"CO/natural abundance l3C separated by one, two, or three bonds. (3) S1 is not affected by natural abundance ”c if neither criterion (1) nor (2) are satisfied. 122 D3. The following criteria are used to set S1 values for natural abundance backbone 13 CO sites: (1) For the Ala-6 and Phe-8 sites, $1 = So for IS 32 ms and St = O for r> 32 ms, these values are in accord with D2-(1) and D2-(2). (2) For other sites, 51 = So for all values of 2'. (Figure 34) Each (AS/So)” value is calculated using the parameters Uc, AC, n and m where: UC is the fraction of Leu-7 12CO sites; Ac is the fiactional '3 C natural abundance; n is the average number of unlabeled backbone CO sites per peptide strand; and m is the number of natural abundance sites which satisfies either D2-(1) or D2-(2) (c.f. Figure 32.). A derivation similar to that for Eq. (AI. 19) yields an expression for 1'3 32 ms: 123 Site description Relative population [SO contribution fraction] {81 contribution fraction} l L7 1300 n.a. 13co 1 n AC [1 l] l} {} !//" \\\\: %///\\: labeled L7 1300 l unlabeled L7 13CO A6. F8 n.a. 13CO other n.a. 1300 1 - UC UC 2AC (n - 2) AC [1 [0] [1] [1] l } {0} {0} {1} //\\‘\\ / \ labeled L7 13CO withoutl labeled L7 13CO with nearby n.a. 130 i nearby n.a. 13C (1-UC)(1-mAC) ; (1-UC)mAC [1] . [1] {t} j {0} Figure 33. Chart of derivation of (AS/So)” for prTDQBU of the D-GFF sample. Four pieces of information were shown from top to bottom in each box: the site description, its relative population, and its contributions to So (in brackets) and S1 (in braces). 124 COI‘ l—U + A exp A g = C n C AS. _ m C (AI.23) The values of Uc, AC, n, and m are 0.01, 0.011, 29.33, and 3, respectively, and numerical evaluation of Eq. (AI. 23) yields: cor exp [lg] = 1.372 [Q] — 0.034; (A1. 24) For r> 32 ms, the contribution to S1 of natural abundance Ala-6 and Phe-8 l3COS slightly modifies Eq. (AI. 22): [Asjw _ l—UC +nAC [ASJCXP (m+2)AC (AI 25) E,— _1—UC—mAC }; _1—UC—mAC The values of Uc, Ac, n, and m are 0.01, 0.011, 29.33, and 7, respectively, and numerical evaluation of Eq. (AI. 24) yields: cor exp [£J = 1.438(3‘5] — 0.108 (A1. 26) S0 so In Eqs. (AI. 22) and (AI. 24), the small fraction of Leu-7 12CO (denoted by the parameter UC) is considered in the calculation of total signal but is neglected in the calculation of the effect of 13 C-13 C dipolar coupling on S1. This latter approximation neglects the possibilities of a Leu-7 l3CO being near either one or two Leu-7 12COS in adjacent strands. The approximation makes a much smaller contribution to the uncertainty in (AS/So)” than does uncertainty in (AS/S0)”. 125 Site description Relative population [SO contribution fraction ] {S1 contribution fraction } ‘ A913CO 1 [l {} Helical A5 13 co Non-helical A913 co h 1-h I] [I i} {} Agwcgfidma A913COonly l A1315N only 15;" A913COonly A1315Nonly h(1_UC_UN) hUN huc (1-h)(1-UC-UN) (1-h)UN (1-h)UC ll [1] [0] [l [1] [0] u {1} {0} A/fl\:u {0} ‘9.'3°°'ll;:l;l;l; lA913c0andA1315N A913COandA1315N A91300andA1315N ! ”“33”” l wlmnearbyn.a.15N withoutnearbyna.15N mmabyn.a.15l~l . h(1-UC-UN) . h(1-UC-UN) h(1-UC-UN) h(1-UCoUN) l m I [1] [1] l1] _ g, 1 {0} {1} {0} n.a.13CO nAC ll % t} /\\ E12. A14 n.a.13CO other n.a. 13CO 2AC (n-2)AC [1] [1] {0} {1} Figure 34. Chart of derivation of (AS/So)” for prTDQBU of the HFPtr-L7CF11N samples for z'> 32 ms. Four pieces of information were shown from top to bottom in each box: the Site description, its relative population, and its contributions to So (in brackets) and S1 (in braces). 126 E. ij T DQBU analysis of HFPmn-F 8c/LMe in a model of two structural populations The following parameters/approximations are used: E1. There is 99% labeling of Phe-8 13 CO. E2. S1 values for a Phe-8 ‘3 CO with nearby natural abundance 13 C are determined by the following criteria: (1) S1 = 0 for r s 32 ms and Phe-8 l3CO/natural abundance l3C separated by one or two bonds. (2) $1 = 0 for 2' > 32 ms and Phe-8 13CO/natural abundance l3C separated by one, two, or three bonds. (3) S1 is not affected by natural abundance ”c if neither criterion (1) nor (2) are satisfied. E3. The following criteria are used to set 51 Values for natural abundance backbone 13CO Sites: (1) For the Ala-6 and Phe-8 Sites, S1 = So for IS 32 ms and $1 = 0 for 1'> 32 ms, these values are in accord with E2-(1) and E2-(2). (2) For other Sites, St = So for all values of 2'. E4. Two structural populations of local Phe-8 13 COS were assumed. For one population with fraction h, there was a detectable dipolar coupling (dcc) between the interstrand labeled Phe-8 ”cm and stab/50’” = f(0 < f< 1), while for the other population with fraction 1 — h, dcc = 0 and Sllab/Solab = l. The derivation followed REDOR analysis on 14 peptide and prTDQBU analysis on HFPtrL7c sample and the resulting (AS/Sp)” had a general form: AAim: 1’U0+"AC 93m: mAC (AI.27) s0 h(l—UC— mAC) so h(l—UC— mAC) Each (AS/Sp)” value is calculated using the parameters h, Uc, Ac, n and m where: h is the normalized population of Phe-8 l3COS with detectable interstrand dcc; Uc is the fraction of Phe-8 12CO sites; AC is the fractional 13C natural abundance; n is the average 127 number of unlabeled backbone CO Sites per peptide strand; and m is the number of natural abundance Sites which satisfies either E2-(1) or E2-(2) (c.f. Figure 35 .). For r§2 ms, the values of Uc, AC, 11, and m are 0.01, 0.011, 22, and 3, respectively, and the evaluation of Eq. (AI. 27) yields: So h __ AI. 28 So ( ) [AST- 1.2s7[as]‘°"’_ 0.034 h For r> 32 ms, the values of UC, AC, 12, and m are 0.01, 0.011, 22, and 6, respectively, and the evaluation of Eq. (AI. 27) yields: cor exp g = 1.333 g _ 0.071 (A1. 29) so h so h The prTDQBU analysis of HFPtr-A6c/LMe and HFPtr-AISdLMe in a model of two structural populations followed that of HF Pmn-F8c/LMe shown above in Eq. (AI. 27). For 7332 ms, the values of UC, AC, n, and m are 0.01, 0.011, 29.33, and 3 respectively, and the evaluation of Eq. (AI. 27 ) yields: cor exp g = 1.372 g _ 0.034 (A1. 30) so h so h For r> 32 ms, the values of UC, AC, n, and m are 0.01, 0.011, 29.33, and 5 respectively, and the evaluation of Eq. (AI. 27) yields: cor exp _2_1S_ = 1.404 g _ 0.059 (A131) so h so h 128 Site description Relative population [SO contribution fraction] {S1 contribution fraction} L713CO i n.a. 1300 1 ' n AC [1 [l { } 1' { } !/' III; \\\“\: / \\\: labeled L7 1300 unlabeled L7 1300 A6. F8 n.a. 1300 other n.a. 1300 1 - UC ; UC 2AC (n - 2) AC [1 I [0] [1] [1] { } {0} {0} {1} /"// - \\\\\ AK/ \\\A labeled L7 13CO withoull labeled L7 13CO with l nearby n.a. 130 . nearby n.a. 130 l (1-U0)(1-mAC) ! (1-U0)mA0 l [11 [1] I {I} {0} l Figure 35. Chart of derivation of (AS/So)” for prTDQBU of the HFPmn-F8c sample in a model of two structural populations. Four pieces of information were Shown from top to bottom in each box: the site description, its relative population, and its contributions to So (in brackets) and $1 (in braces). 129 F. firRFDR-C T analysis ofD-GFF solid-state NMR sample Sl/So was used in prFDR-CT experiments and its analysis was a simple analog to that of AS/So because Sl/So = l — AS/So. The expression for (SI/So)” is: cor exp The values of Uc1, Ucz, Ac, and n are 0.01, 0.01, 0.011, and 49, respectively. For 75 32 mS, m = 2 and numerical evaluation of Eq. (AI. 32) yields: cor exp [£15] = 1.596(g] — 0.573 (A1. 33) SO SO For r> 32 ms, m = 4 and numerical evaluation of Eq. (AI. 32) yields: (30" exp [Q] = 1.634(£] — 0.587 (A1. 34) S0 S0 130 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Appendix 11 Location of NMR Data squares: /home/zxz4b/data/setup/N-acet-Leu/cpr-prk-122006 (x = 8, 9, 10,11,12 and 13) crosses: /home/zxz4c/data/setup/NAL/cp-spxk-check-081306 (x = 8, 10 and 12) up triangles: /home/zxz4b/data/FP/FPmnF8CL9N-LM3e/cpr-prk-122006 (x = 8,10 and 12) down triangles: fhome/zxz4b/data/FP/FPmnF8CL9N-LM3e/cprlf-prk- 122006 (x = 8,10 and 12) (a): /home/zxz4b/data/I-4PEPTIDE/redorxypm-O8ms-sum (b): fhome/zxz4b/data/I-4PEPTIDE/redorxypm-32mS-sum (a): /home/zxz4b/data/I-4PEPTIDE/redorxypm-xms-sum (x = 08, 16, 24 and 32) (a): /home/zxz4b/data/GFF/2C-GFF/rfdrctcw-16-Sum2 (b): /home/zxz4b/data/GFF/2C-GFF/rfdrctcw-24-sum2 (c): /home/zxz4b/data/GFF/2C-GFF/rfdrctcw-32-Sum2 (d): /home/zxz4b/data/GFF/2C-GFF/rfdrctcw-40-suml /home/zxz4b/data/GFF/2C-GFF/rfdrcw-array-0201 05 (a): /home/zxz4b/data/GFF/2C-GFF/rfdrctcw-x-sum2 (x = 08, 12, 16, 20, 24, 28, and 32), and /home/zxz4b/data/GFF/2C-GFF/rfdrctcw-40-sum1 131 Figure 17 Figure 18 Figure 19 Figure 20 Figure 21 Figure 22 (a): /home/zxz4b/data/setup/NAL-2007/ctdqbu1-array-01 1607b (b): /home/zxz4b/data/setup/GFF/2C-GFF/ctdqbu1-array01 1607 squares: /home/zxz4b/data/setup/N-acet-Leu/ctdqbu1-array-01 1407 crosses: /home/zxz4b/data/Setup/N-acet-Leu/ctdqbu2-array-O1 1407 up triangles: /home/zxz4b/data/setup/N-acet-Leu/ctdqbul -fp3 5k-01 1407 down triangles: /home/zxz4b/data/setup/NAL—2007/ctdqbu1T240-array- 01 1607 (a): /home/zxz4b/data/setup/NAL-2007/ctdqbu1-array-01 1607b (b) squares: /home/zxz4b/data/setup/GFF/2C-GFF/ctdqbu1 -array01 1 607 up triangles: /home/zxz4b/data/setup/GFF/2C-GFF/ctdqbu1 -array03 0807 (a): /home/zxz4b/data/setup/NAL-2007/ctdqbu1 -array-01 1 607b (a) squares: /home/zxz4b/data/Setup/GFF/2C-GFF/ctdqbul -array01 1 607 (b) squares: /home/zxz4b/data/setup/GFF/2C-GFF/fp1 5krfdrct-k2672- 092006 (a) squares: /home/zxz4b/data/FP/FPmnF 8CL9N-LM3 e/ctdqbul -array- 01 2 1 07 crosses: /home/zxz4b/data/FP/FPtrA6C-LM3e/ctdqbul -L40-O3 1307 /home/zxz4b/data/FP/FPtrA6C-LM3e/ctdqbul-L104-03 1207 /home/zxz4b/data/FP/FPtrA6C-LM3e/ctdqbul-L168-03 1007 /home/zxz4b/data/FP/FPtrA6C-LM3e/ctdqbul -L232-03 0907 triangles: /home/zxz4b/data/FP/FPtrA1 5CA1V2M19N-LM3e/ctdqbul- L016-012807 132 Figure 23 Figure 24 /home/zxz4b/data/FP/FPtrA1 5CA1V2M19N-LM3 e/ctdqbul - L05 6-sum1 /home/zxz4b/data/FP/FPtrAl 5CA1V2M19N-LM3 e/ctdqbul - L120-012507 /home/zxz4b/data/FP/FPtrAl 5CA1V2M19N-LM3 e/ctdqbul - Ll 84-012507 /home/zxz4b/data/FP/FPtrAl 5CA1V2M19N-LM3 e/ctdqbul - L248-012707 /home/zxz4b/data/FP/FPtrAl 5CA1V2M19N-LM3e/ctdqbu1- L256-012807 (b) squares: /home/zxz4b/data/FP/FPmnF8CL9N-LM3 e/rfdrct-t768- 033007 crosses: /home/zxz4b/data/FP/FPtrA6C-LM3e/rfdrct-t768-O40507 triangles: /home/zxz4b/data/FP/FPtrAl 5CA1V2M19N-LM3e/rfdrct- t768-032807 (a): /home/mb4b/data/Rong/trimer-PC-PG-1 -1 00-22604-REDOR-sub (b): /home/mb4b/data/Rong/trimer-LM3 - 1 - 1 00-sum-223 04-REDOR-Sub (c): /home/zxz4b/data/FP/FPtrL7CF1 1N-PCPG/trL7CF1 1N-32ms- 060104-REDOR-sub (d): /home/zxz4b/data/FP/FPtrL7CF 1 1N-PCPG/trL7CFl 1N-32mS-060104 (e): /home/zxz4b/data/FP/FPtrL7CF1 1N-LM3/redorxypm-32mS-06 l 604 (f): /home/zxz4b/data/FP/FPtrL7CF1lN-eLM3/redorxypm-32-sum1 133 Figure 25 Figure 26 Figure 27 Figure 28 Figure 29 (a): /home/zxz4b/data/FP/FPtrL7CF1 1N-PCPG/trL7CF1 1N-08mS-060404 (b): /home/zxz4b/datafFP/FPtrL7CFl 1N-PCPG/trL7CF1 1N-32ms-060104 (c): /home/zxz4b/data/FP/FPtrL7CF 1 1N-eLM3/redorxypm-08-120304 (d): /home/zxz4b/data/FP/FPtrL7CF1 1N-eLM3/redorxypm-32-sum1 (a): /home/zxz4b/data/FP/FPtrL7CF1 1N-PCPG/trL7CFl 1N-08ms—060404 /home/zxz4b/data/FP/FPtrL7CF1 1N-PCPG/trL7CF1 lN-l 6ms-sum /home/zxz4b/data/FP/FPtrL7CF1 lN-PCPG/trL7CF1 1N-24mS-060404 /home/zxz4b/data/FP/FPtrL7CF1 1N-PCPG/trL7CF1 1N-32mS-060104 (a): /home/zxz4b/data/FP/FPtrL7CFl lN-eLM3/redorxypm-08-suml /home/zxz4b/data/FP/FPtrL7CF1 1N-eLM3/redorxypm-16-120304 /home/zxz4b/data/FP/FPtrL7CF1 1N-eLM3/redorxypm-24-sum1 /home/zxz4b/data/FP/FPtrL7CF1 1N-eLM3/redorxypm-32-sunr1 (a): /home/zxz4b/data/FP/FPmnF8CL9N-LM3e/ctdqbu1-L176-012107 (b): /home/zxz4b/data/FP/FPtrA15CA1V2M19N-LM3e/ ctdqbul-L184- 012507 (a): fhome/zxz4b/data/FP/FPtrL7CF1 1N-eLM3/rfdrctcw-16-050605 (b): /home/zxz4b/data/FP/FPtrL7CFl1N-eLM3/rfdrctcw-24-Sum1 (c): fhome/zxz4b/data/FP/FPtrL7CF1 lN-eLM3/rfdrctcw-32-sum (d): /home/zxz4b/data/FP/FPtrL7CF11N-eLM3/rfdrctcw-40-sum fhome/zxz4b/data/FP/FPtrL7CF1 1N-eLM3/rfdrctcw-16-050605 /home/zxz4b/data/FP/FPtrL7CF1 1N-eLM3/rfdrctcw-24-suml /home/zxz4b/data/FP/FPtrL7CF1 lN-eLM3/rfdrctcw-32-sum 134 Appendix 111 List of New Pulse Programs and Macros Pulse Programs /home/zxz4b/pulse_programs/cpc/cpramp_cpy2 Description: Carr-Purcell T2 measurement sequence with CW lH decoupling followed by lH-13C CP ramp. The phase of 13C CP is x, and the phase of n'pulses are +y and —y, cf. Figure 9. name "cpramp_cpy2“; title "cross polarization with a ramp on X channel followed by Carr- Purcell echo sequence to measure t2"; ! COMPILED WITH OPTIMIZATION ON ! $Header: /usr2/users/applab/CFR/I+/ppg/cp.s,v 1.2 2000/06/27 19:43:03 applab Exp $ ! InfinityPlus Compatible ! composed by Z. Zheng and last modified on 10/19/2006 1 Ref: Balback, J. J., Biophys. J., 2002, vol. 83, 1205-1216 ! 130 magnetization is prepared with x phase under rotating frame and there is no phase cycling. NMRchnls RF: chl ch2; NMRacq; data .phase H90 = 180; lH90 phase .phase Hmix = 90; leix phase .phase Hdec = 0; 1H dec phase .phase Xmix = 180; leix phase .phase list X180[] = 90,270; !X pi pulses with phase cycle of y and -y .time TAUl, TAU2, TAU3, TAU4; ltiming parameters .time TRI; lcp ramp interval .ampl list ramp[20]; .ampl extern achmod = O. .ampl extern aX180 "X 180 ampl" = l 0 ; 1 cp ramp change 0.1; 135 .long extern list abph[] = 0, 0, 0, 0; lacq phase cycling .long I; .long extern echo_size "pts per echo“ = 64; .long extern MG_loops = 1; .long list dummies[] J = 0, \ ‘ ‘ C>Z Zlfitfl l o<3c>c>o ‘0 include "../includes/STANDARD_PARAMS"; include "../includes/1D.inc"; ! Define error codes specific to this pulse program I define TAU4_ERR 0x110 define TAU4_ERROR_CODE USER_ERROR_BASE + TAU4_ERR comment "ERROR "TAU4_ERROR_00DE "Too many points per echo. Reduce echo_size or dw, or lengthen tau."; define TAU_ERR 0x120 define TAU_ERROR_CODE USER_ERROR_BASE + TAU_ERR comment "ERROR "TAU_ERROR_CODE “Too many points per echo. Reduce echo_size or dw, or lengthen tau."; 1 update Spinsight with calculations. 1 ___________________________________________ .update "rb = 1.30 * sw"; .update "al = (MG_loops * echo_size)"; .update "aqtm = (MG_loops * 2.0 * tau) "; lthe aqtm is the longest echo time. .update "extm = (pw90H + ct + aqtm +pd)"; .update "txdutyl = (pw90H + ct + aqtm ) / extm"; .update "timeld = ((na + dp) * extm) / 60.0“; ! Executed once at Start of Experiment I __________________________________________ .program dpc = dp; TAUl = (tau / 2.0) — tMX - (pw180X / 2.0); TAU2 = tau - tMX - (pw180X / 2.0); TAU3 = (tau / 2.0) - (pw180X / 2.0) - ad; TAU4 = (tau / 2.0) - (dw * echo_size) - tMX - (pw180X / 2.0); txdutyl = (pw90H + ct + aqtm ) / extm; if (txdutyl > 0.2) {error(TXDUTY_ERR);} TRI = (0.05*Ct); for(I=0, I<20, I++l 136 ramp[I] = ach + (2.0 * (I-lO) * achmod) / 19.0; abph = abph.start; txdutyl:(pw90H+(2.0*ct)+ad+rd+aqtm)/extm; if (txdutyl > 0.2) {error(TXDUTY_ERR);} if (TAU4 < Sus) {error(TAU4_ERR);} if (tau <= (2*dw*echo_size)) {error(TAU_ERR);} ! actual pulse prog. runtime loop lDuty factor too large start aqph = @abph++; ramp = ramp.start; X180 = X180.start; out time(3u) chl: SC(scX) ch2: SC(scH); out time(lu) chl: P(Xmix) ch2: MK I AP(aH, H90); lpreset phase, ampl.& MX out pw90H chl: MX ch2: TG; loutput pi/2 pulse do (20) { out time(TRI) chl: TG | A(@ramp++) ch2: TG I AP(chp,Hmix); } out time(TAUl) chl: A(aX180) Hdec)|TG; do (MG_loops) { ch2: AP(aHdec, out tMX chl: MX ch2: TG; out pw180X chl: P(@X180++) | TG ch2: TG; out time (TAU2 ) ch2 : TG; out tMX chl: MX Ch2 : TG; out pw180X chl: P(@X180++) | TG ch2: TG; out time(TAU3) chl: TB ch2: TG; out ad chl: TB | RE ch2: TG; outAQ dw chl: TB | RE ch2: TG, echo_size; out time(TAU4) ch2: TG; } scan pd; .end /home/zxz4b/pulse_programs/cpc/fpctdqbu_cw1 Description: the “one-Ir-per-rR” version of prTDQBU sequence, cf. Figure 7a and 7b. 137 name title and 1 01/14/ "fpctdqbu_cw1.s"; "Ramp CP, finite pulse CTDQBU w/ CW decoupling, pi pulse every rotor cycle."; xy8 phase cycle COMPILED WITH OPTIMIZATION ON $Header: /usr2/users/applab/CFR/I+/ppg/REDOR_pm.s,v 1.1 2007 21:25:19 applab Exp $ InfinityPlus Compatible ! ref. Bennett, A. et al. J. Am. Chem. Soc., 120: 4897 (1998). 1 ref. Ishii, Y. J. Chem. Phys., 114: 8473 (2001) ! programmed by Z. "Norm" Zheng on 01/17/2007. NMRchnls RF: ch1 ch2; NMRacq; ! __________________________________________ ! .data section is for compiler definitions I __________________________________________ data .time TAUl, TAU2, TAU3, TAU4, TAUS; .time TRI; ' cp ramp interval .time extern Tr "rotor period“ = 200us; .time extern Trl "half rotor period" = 100us; .time AQTM = 10 ms; .long extern l "L rotor prds" = 64; .long extern m "M rotor prds" = 320; .long n; .long extern total "Total rotor prds” = 656; .long pi_l; .long pi_m; .long pi_n; .long quadral = 4; .phase list H90[] = 180, O, 0, 180, lH90 phase list .phase Hmix = 90; .phase list Xmix[] = 270, 180, 270, 180, !X CP phase list .phase Hdec = 0; .phase list X90_ksi[] = 0, 90, 180, 270, lX90_ksi refocus phase list for RFDR 90phi .phase X9OA = 0; 1X90 var .phase X9OB = 0; .phase X900 = 180; .phase X90D = 90; .phase list X180_rfdr[] = 0, 90, O, 90, 90, 0, 90, 0; lrefocus phase list on X channel for RFDR .ampl extern aH9O ”H 90 ampl“ = 0.1; .ampl list ramp[20]; ! cp ramp amplitude .ampl extern achmod = 0.0; ! cp ramp change .ampl extern aX180 "fp X 180 ampl" = 0.01; .ampl extern aX9O "X 90 ampl" = 0.1; .ampl extern aHacq "H acq ampl“ = 0.1; 138 .long Cphase_Flag; .long I; .long list abph[] = 0, 0, O, 0; lreceiver phase debug l.long list dummies[] I = O, ! J=0, ! K=0, ! L 0, l M = 0; include “../includes/STANDARD_PARAMS"; include "../includes/1D.inc"; lchanged from 2D ! Parameters are updated and reported to the acq panel by updates .update "rb = 1.30 * sw"; .update "n = total - l - m"; .update "Tr = (1.0 / (1000.0 * speed))"; .update "Trl = Tr / 2.0"; .update "aqtm = (dw * al / 4)"; l4 fids. .update "extm = (pw90H + 2 * ct + (Tr * total) + rd + aqtm + pd)”; .update "txdutyl = (pw90H + 2 * ct + (Tr * total) + rd + aqtm) .update “timeld = (4 * (na + dp) * extm) / 60.0"; ! Executed once at start of experiment I ____________________________________________________ .program AQTM = rd + aqtm; X90B = 0; X900 = 180; X90D = 90; TAUl = Trl — ( pw180X / 2 ) - tMX; TAU2 = Tr - pw180X - tMX; TAU3 = Trl - ( pw180X / 2 ) - pw90X - tMX; TAU4 = Trl - ( pw180X / 2 l - rd; TAUS = Tr * total; ldecoupling time at 90kHz TRI = (ct / 20.0); for(I = 0, I < 20, I++) { ramp[I] = ach + (2.0 * (I - 10) * achmod) / 19.0; 139 / extm"; abph = abph.start; quadral = al / 4; n = total - l - m; pi_l = l — 1; lno. of repeating pulses of the rfdr sequence pi_m = m - 1; if (n > O) pi_n = n - 1; else pi_n = 0; txdutyl = (pw90H + 2 * ct + (Tr * (2 * (a12 - 1) + total)) + rd + aqtm) / extm; lrev needed lif (txdutyl > 0.2) {error(TXDUTY_ERR);} lDuty factor too large lif (L02_redor < 8) {error(L02_redor_ERR);} 11 must be equal or greater than 8. lif (TAU2 < lOOns) {error(TAU2_ERR);} lerror in pw180Y or spin. lif (TAU3 < lOOns) {error(TAU3_ERR);} lerror in pw180X. lif (TAU4 < lOOns) {error(TAU4_ERR);} ! actual pulse prog. runtime loop .start H90 = H90.start; Xmix = Xmix.start; X90_ksi = X90_ksi.start; aqph = @abph; for (Cphase_Flag = 0, Cphase_Flag < 4, Cphase_Flag++) { X180_rfdr = X180_rfdr.start; ramp = ramp.start; X90A = X90_ksi[Cphase_Flag]; out time(3u) chl: SC(scX) ch2: SC(scH); out time(1u) chl: P(@Xmix++) ch2: MX | AP (aH90, @H90++); out pw90H chl: MX ch2: TG; do (20) { out time(TRI) chl: TG | A(@ramp++) ch2: TG | AP(chp, Hmix); } Async; Ch++ chl; out time(TAUl); do (pi_l) 140 out tMX chl: MX | AP(aX180, @X180_rfdr++); out pw180X chl: TG; out time(TAU2); out tMX chl: MX | AP(aXlBO, @x180_rfdr++); out pw180X chl: TG; out time(TAU3); out tMX chl: MX | AP(aX90, X90A); out pw90X chl: TG; out pw9ox chl: TG | P(X9OB); out time(TAU3); do (pi_m) { out tMX chl: MX | AP(aX180, @X180_rfdr++); out pw180X chl: TG; out time(TAU2); } out tMX chl: MX | AP(aX180, @X180_rfdr++); out pw180X chl: TG; out time(TAU3); out tMX chl: MK I AP(ax90, X90C); out pw90X chl: TG; out pw90X chl: TG I P(X90D); if (pi_n > 0) { out time(TAU3); do (pi_n) { out tMX chl: MX | AP(aX180, @X180_rfdr++); out pw180X chl: TG; out time(TAU2); out tMX chl: MX I AP(aX180, @X180_rfdr); out pw180X chl: TG; out time(TAU4) chl: TB; } else { out time(lu) chl: TB; } out rd chl: TB; out ad chl: RE | TB; outAQ dw chl: RE I TB, quadral; 141 if (Cphase_Flag == 3) { scan pd; } else { out pd; } Sync; Ch--; ch++ ch2; out time(TAUS) ch2: TG | AP(aHdec, Hdec); out time(AQTM) ch2: TG | AlaHacq); waits; Ch--; } abph++; .end /home/zxz4b/pulse_programs/cpc/fp_rfdrxy8_ct_cw Description: the “one-Ir-per-ZrR” version of prTDQBU sequence, cf. Figure 7a and 7c. name "fp_rfdrxy8_ct_cw"; title "Ramp CP, finite pulse RFDR, Constant time w/ CW decoupling, xy8 phase cycle"; ! COMPILED WITH OPTIMIZATION ON l $Header: /usr2/users/app1ab/CFR/I+/ppg/REDOR_pm.s,v 1.2 01/19/2007 applab Exp $ ! InfinityPlus Compatible ! ref. Bennett, A. et al. J. Am. Chem. Soc., 120: 4897 (1998). 1 ref. Ishii, Y. J. Chem. Phys., 114: 8473 (2001) ! last revised by Z. Norm Zheng on 01/19/2007, NMRchnls RF: chl ch2; NMRacq; ! .data section is for compiler definitions .time TAUl, TAU2, TAU3, TAU4, TAUS; 142 .time TRI; 1 cp ramp interval .time extern Tr "rotor period" = 200us; .time AQTM = 10 ms; .long extern l ”L rotor prds" = 64; .long extern m "M rotor prds" = 320; .long n; .long extern total "Total rotor prds" = 656; .long pi_l; .long pi_m; .long pi_n; .long quadral = 4; .phase list H90[] = 180, 0, 0, 180, lH9O phase list .phase Hmix = 90; .phase list Xmix[] = 270, 180, 270, 180; !X CP phase list .phase Hdec = 0; .phase list X90_ksi[] = 0, 90, 180, 270; lX90_ksi refocus phase list for RFDR 90phi .phase X90A = 0; 1X90 var .phase X90B = 0; .phase X900 = 180; .phase X90D = 90; .phase list X180_rfdr[] = 0, 90, 0, 90, 90, 0, 90, 0; lrefocus phase list on X channel for RFDR .ampl extern aH90 "H 90 ampl“ = 0.1; .ampl list ramp[20]; ! cp ramp amplitude .ampl extern achmod = 0.0; ! cp ramp change .ampl extern aX180 "fp X 180 ampl" = 0.01; .ampl extern aX90 "X 90 ampl" = 0.1; .ampl extern aHacq "H acq ampl' = 0.1; .long Cphase_Flag; .long I; .long list abph[] = 0, 0, 0, 0; lreceiver phase debug !.long list dummies[] I = 0, ll ‘ N \ beC—l II 0000 \0 include "../includes/STANDARD_PARAMS"; include "../includes/1D.inc"; lchanged from 2D ! Parameters are updated and reported to the acq panel by updates 143 .update "rb = 1.30 * sw"; .update "n = total - l - m"; .update "Tr = (1.0 / (1000.0 * speed))"; .update I‘aqtm (dw * a1 / 4)"; l4 fids. .update "extm = (pw90H + 2 * ct + (Tr * total) + rd + aqtm + pd)"; .update "txdutyl = (pw90H + 2 * ct + (Tr * total) + rd + aqtm) / extm"; .update "timeld = (4 * (na + dp) * extm) / 60.0"; ! Executed once at start of experiment I ____________________________________________________ .program AQTM = rd + aqtm; X9OB = 0; X900 = 180; X90D = 90; TAUl = Tr - ( pw180X / 2 ) - tMX; TAU2 = Tr * 2.0 - pw180X - tMX; TAU3 = Tr - ( pw180X / 2 ) - pw9OX - tMX; TAU4 = Tr — ( pw180X / 2 ) - rd; TAUS = Tr * total; ldecoupling time at 90kHz TRI = (ct / 20.0); for(I = 0, I < 20, I++) { ramp[I] = ach + (2.0 * (I — 10) * achmod) / 19.0; abph = abph.start; quadral = a1 / 4; n = total - l - m; pi_l = l / 2 -1; lno. of repeating pulses of the rfdr sequence pi_m = m / 2 —1; if (n > 0) pi_n = n / 2 -1; else pi_n = 0; txdutyl = (pw90H + 2 * ct + (Tr * (2 * (a12 - 1) + total)) + rd + aqtm) / extm; lrev needed lif (txdutyl > 0.2) {error(TXDUTY_ERR);} lDuty factor too large lif (L02_redor < 8) {error(L02_redor_ERR);} ll must be equal or greater than 8. !if (TAU2 < lOOns) {error(TAU2_ERR);} lerror in pw180Y or spin. lif (TAU3 < lOOns) {error(TAU3_ERR);} lerror in pw180X. lif (TAU4 < lOOns) {error(TAU4_ERR);} 1 actual pulse prog. runtime loop 144 .start H90 = H90.start; Xmix = Xmix.start; X90_ksi = X90_ksi.start; aqph = @abph; for (Cphase_Flag = 0, Cphase_Flag < 4, Cphase_Flag++) I X180_rfdr = X180_rfdr.start; ramp = ramp.start; X9OA = X90_ksi[Cphase_Flag]; out time(3u) chl: SC(scX) ch2: SC(scH); out time(lu) chl: P(@Xmix++) ch2: MX I AP (aH90, @H90++); out pw90H chl: MX ch2: TG; do (20) { out time(TRI) chl: T0 | A(@ramp++) ch2: TG | AP(chp, Hmix); } Async; ch++ chl; out time(TAUl); do (pi_l) { out tMX chl: MK I AP(aX180, @X180_rfdr++); out pw180X chl: TG; out time(TAU2); out tMX chl: MX | AP(aX180, @Xl80_rfdr++); out pw180X chl: TG; out time(TAU3); out tMX chl: MX I AP(aX90, X90A); out pw90X chl: TG; out pw90X chl: TG I P(X90B); out time(TAU3); do (pi_m) { out tMX chl: MX I AP(aX180, @X180_rfdr++); 145 out pw180X out time(TAU2); out tMX chl: out pw180X out time(TAU3); out tMX chl: out pw90X chl: out pw90X chl: if (pi_n > 0) { out time(TAU3); do (pi_n) { out tMX @X180_rfdr++); out pw180X out time(TAU2); out tMX @X180_rfdr); out pw180X out time(TAU4) } else { out time(lu) } out rd out ad chl: outAQ dw chl: if (Cphase_Flag == ) { scan pd; } else { out pd; } Sync; Ch--; ch++ Ch2; out time(TAUS) ch2: out time(AQTM) ch2: waitS; 146 chl: TG; MX | AP(aXl80, @X180_rfdr++); chl: TG; MK I AP(aX90, x90cl; TG; TG | P(X90D); chl: MK I AP(aX180, chl: TG; chl: MK I AP(aX180, chl: TG; chl: TB; chl: TB; chl: TB; RE | TB; RE I TB, quadral; TG I AP(aHdec, Hdec); TG | A(aHacq); Ch--; abph++; .end /home/zxz4b/pulse_programs/cpc/fprfdrctxy8whh4b Description: the prFDR-CT sequence, cf. Figure 8. This version does not incorporate the pulsed Spin locking during acquisition. name "fprfdrctxy8whh4b"; title "Ramp CP, finite pulse RFDR with Constant time, WAHUHA-4, CW decoupling, xy8 phase cycle and cyclops acq"; ! COMPILED WITH OPTIMIZATION ON 1 $Header: /usr2/users/applab/CFR/I+/ppg/ applab Exp $ ! InfinityPlus Compatible ! ref. Balbach, J. J. et al. Biophys. J., 83: 1205-1216 (2002). (for prFDR-CT) ! ref. Haeberlen, U. and Waugh, J. S. Phys. Rev., 175: 453—467 (1968). (for WAHUHA-4) ! programmed by Zheng, Z.X. on 09/19/2006 and last revised on 09/19/2006. ! This version sets M, K and total rotor prds as variables so that N can be automatically calculated. NMRchnls RF: chl ch2; NMRacq; .data .time TAUl, TAU2, TAU3, TAU4; ! timing parameters .time TRI; ! cp ramp interval .time extern Tr "MAS rotor prd" = 200us; .time AQTM = 10 ms; .long extern m "M rotor prds" = 64; .long extern n "N rotor prds" = 8; .long extern k "K repeats" = 4; .long extern total "Total rotor prds" = 656; .long pi_l; .long pi_2; .long pi_3; .phase list H90[] = 180, 180, 0, 0; EH90 phase list 147 .phase Hmix = 90; .phase list Xmix[] = 180, 270, 180, 270; .phase Hdec = 0; .phase list X90A[] = 270, 0, 90, 180; .phase list X90B[] = 0, 90, 180, 270; .phase list X9OCI] = 180, 270, 0, 90; .phase list X90B[] = 90, 180, 270, 0; .phase list X180[] = 0, 90, O, 90, 90, 0, prFDR .ampl extern aH9O "H 90 ampl" = 0.1; .ampl list ramp[20]; ! .ampl extern achmod = 0.0; .ampl extern aX180 “fp X 180 ampl" = 0.01; .ampl extern aX90 "X 90 ampl" = 0.1; .ampl extern aHacq “H acq ampl'I = 0.1; .long I; .long list abph[] = 0, 1, 2, 3; include "../includes/STANDARD_PARAMS"; include "../includes/1D.inc"; 1X CP phase list 90, 0; lchanged from 2D lWHH-4 X90A IWHH-4 X9OB lWHH-4 X90C lWHH-4 X90D !XY-8 for cp ramp amplitude cp ramp change lreceiver phase debug ! Parameters are updated and reported to the acq panel by updates I _________________________________________________________________ .update "rb = 1.30 * sw"; .update "n = ( (total / (2*k)) - m ) / 2"; lCalc. the acq. panel .update "Tr = (1.0 / (1000.0 * speed))"; .update "aqtm = (dw * al)“; .update "extm = (pw90H + ct + (Tr * total) .update "txdutyl = (pw90H + 2 * ct + (Tr * total) .update "timeld = (na * extm) / 60.0"; ! Executed once at start of experiment I ____________________________________________________ .program AQTM = rd + aqtm; H90 = H90.start; Xmix = Xmix.start; X90A = X90A.start; X9OB = X9OB.start; X900 = X9OC.start; 148 + rd + aqtm) of N and update + rd + aqtm + pd)"; / extm"; X90D = X9OB.start; TAUl = (Tr / 2) - (pW180X / 2) - tMX; TAU2 = (Tr / 2) - (pW180X / 2); TAU3 = (Tr / 2) - (pw180X / 2) - (pw90X / 2) - tMX; TAU4 = Tr * total; !decoupling time at 90kHz TRI = Ct / 20.0; for(I = 0, I < 20, I++) { ramp[I] = ach + (2.0 * (I - 10) * achmod) / 19.0; } abph = abph.start; txdutyl = (pw90H + 2 * ct + (Tr * (2 * (a12 - 1) + total)) + rd + aqtm) / extm; !if (txdutyl > 0.2) {error(TXDUTY_ERR);} !Duty factor too large !if (L02_redor < 8) {error(L02_redor_ERR);} ll must be equal or greater than 8. !if (TAU2 < lOOns) {error(TAU2_ERR);} !error in pw180Y or spin. !if (TAU3 < lOOns) {error(TAU3_ERR);} !error in pw180X. !if (TAU4 < lOOns) {error(TAU4_ERR);} 1 actual pulse prog. runtime loop .start aqph = @abph++; X180 = X180.start; ramp = ramp.start; n = ( (total / (2*k)) - m ) / 2; !Calc. of N pi_l = m - 2; !no. of repeating pulses of the rfdr sequence pi_2 = n - 2; pi_3 = 2 * n - 2; out time(3u) chl: SC(scX) ch2: SC(scH); out time(lu) chl: P(@Xmix++) ch2: MX I AP (aH90, @H90++); out pw90H chl: MX Ch2; TG; do (20) I out time(TRI) chl: TG I A(@ramp++) ch2: TG I AP(chp, Hmix); } Async; ch++ chl; do (k) l K repeats { out time(TAUl) chl: AP(aX180, @X180++); !Unit 1B 149 Unit 1 Unit 1 of Unit 1 out tMX chl: MX; out pw180X chl: TG; out time(TAU2); do (pi_l) !(M—2) repeats of { out time(TAUl) chl: P(@X180++); out tMX chl: MX; out pw180X chl: TG; out time(TAU2); } out time(TAUl) chl: P(@X180++); !Unit 2A out tMX chl: MX; out pw180X chl: TG; out time(TAU3) chl: AP(aX90, @X90A++); out tMX chl: MX; out pw90X chl: TG; out time(TAU3) chl: AP(aX180, @X180++); !Unit 3 out tMX chl: MX; out pw180X chl: TG; out time(TAU2); do (pi_2) !(N-2) repeats of { out time(TAUl) chl: P(@X180++); out tMX chl: MX; out pw180X chl: TG; out time(TAU2); } out time(TAUl) chl: P(@X180++); !Unit 28 out tMX chl: MX; out pw180X chl: TG; out time(TAU3) chl: AP(aX90, @X90B++); out tMX chl: MX; out pw90X chl: TG; out time(TAU3) chl: AP(aXl80, @X180++); !Unit 3 out tMX chl: MX; out pw180X chl: TG; out time(TAU2); do (pi_3) !(2*N-2) repeats { out time(TAUl) chl: P(@X180++); out tMX chl: MX; out pw180X chl: TG; out time(TAU2); } out time(TAUl) chl: P(@X180++); !Unit 20 out tMX Chl: MX; 150 out pw180X chl: TG; out time(TAU3) chl: AP(aX90, @X90C++); out tMX chl: MX; out pw90X chl: TG; out time(TAU3) chl: AP(aX180, @X180++); out tMX chl: MX; out pw180X chl: TG; out time(TAU2); do (pi_2) Unit 1 { out time(TAUl) chl: P(@X180++); out tMX chl: MX; out pw180X chl: TG; out time(TAU2); } out time(TAUl) chl: P(@X180++); out tMX chl: MX; out pw180X chl: TG; out time(TAU3) chl: AP(aX90, @X90D++); out tMX chl: MX; out pw90X chl: TG; out time(TAU3) chl: AP(aX180, @Xl80++); out tMX chl: MX; out pw180X chl: TG; out time(TAU2); do (pi_l) Unit 1 { out time(TAUl) chl: P(@X180++); out tMX chl: MX; out pw180X chl: TG; out time(TAU2); } out time(TAUl) chl: P(@X180++); out tMX chl: MX; out pw180X chl: TG; out time(TAU2); } out rd chl: TB; out ad chl: RE | TB; Acq dw chl: RE | TB; scan pd; Sync; Ch--; ch++ ch2; 151 !Unit 3 !(N-2) repeats of !Unit 2D !Unit 3 !(M-2) repeats of !Unit 1 out time(TAU4) ch2: TG I AP(aHdec, Hdec); out time(AQTM) ch2: TG I A(aHacq); waitS; Ch--; .end lhome/zxz4b/pulse_programs/cpc/redorxy8xypi_pm Description: the “alternating 15N/ 13 C 7r pulse” version of REDOR sequence, cf. Figure 6b. name "redorxy8xypi_pm"; title "REDOR w/ TPPM decoupling and C N pi pulses"; ! COMPILED WITH OPTIMIZATION ON ! $Header: /usr2/users/applab/CFR/I+/ppg/REDOR_pm.s,v 1.1 1999/11/10 21:25:19 applab Exp $ ! InfinityPlus Compatible ! ref. Y. Pan, T. Gullion, and J. Schaefer, J. Magn. Reson., 90: 330 (1994). ! Obtain deltaS/S values with REDOR_PIKER or XY_REDOR macros. ! modified from REDOR_pm by Jun Yang, to apply pi pulses in both carbon and nitrogen ! channels in each rotor period according to Dr. Terry Gullion. 2001/12/13. NMRchnls RF: chl ch2 ch3; NMRacq; data .time TAU1,TAU2,TAU3; .time extern Tr "rotor period" = 200us; .long extern lcl "no. rotor periods": 2; .long x,L02; .long halfal = 4; .phase list H90[] = 0,180; !H90 phase list .phase Hmix = 90; !Hmix&decoup1e phase list .time TRI; ! cp ramp interval .ampl list ramp[20]; 1 cp ramp amplitude 152 .ampl extern achmod = 0.0; 1 cp ramp change .phase list Xmix[] = 270,270,180,180; !X phase list .phase list x180A[] .phase list X180[] .ampl extern aX180 "X 180 ampl" 270,270,180,180; O,90,0,90,90,0,90,0; 0.1; .phase list Y180[] = 0,90,0,90,90,0,90,0; .ampl extern aY180 = 0.1; .ampl aY180_on = 0.0; .phase autofix p2 = 15.0; !Hdec phase excursion .phase autofix p0 = 90.0; !Hdec phase excursion .long cycles "no. of TPPM cycles" = 8; .ampl autofix a_tmp = 0; .time AQTM = lOms; .time dec_cycle = 10us; .long AB_Flag; .long extern list abph[] = 2,0,1,3; !receiver cycling .long list dummies[] I = 0, ‘ Kt‘NCl l c>c>o<3 ‘0 include "../includes/STANDARD_PARAMS"; include "../includes/1D.inc"; !changed from 2D.inc 1 Define error codes specific to this pulse program I ___________________________________________________ define L02_ERR 0x100 define LC2_ERROR_CODE USER_ERROR_BASE + LC2_ERR comment "ERROR "L02_ERROR_CODE "too few rotor periods: lcl"; define TAU1_ERR 0x101 define TAUl_ERROR_CODE USER_ERROR_BASE + TAU1_ERR comment "ERROR "TAU1_ERROR_CODE "pw180Y too long or spinning speed too fast"; define TAU2_ERR 0x102 define TAU2_ERROR_CODE USER_ERROR_BASE + TAU2_ERR comment "ERROR "TAU2_ERROR_CODE "pw180X too long or spinning speed too fast"; define TAU3_ERR 0x103 define TAU3_ERROR_CODE USER_ERROR_BASE + TAU3_ERR comment "ERROR "TAU3_ERROR_CODE "rd too long or spinning speed too fast"; 153 ! Parameters are updated and reported to the acq panel by updates .update "rb=1.30*sw“; .update “Tr = (1.0/(1000. .update "aqtm=(dw*al/2)"; O*speed))"; .update "extm=(pw90H+ct+(Tr*lcl)+rd+aqtm+pd)"; .update "txdutyl:(pw90H+(2.0*ct)+(Tr*lc1)+rd+aqtm)/extm"; .update "time1d=(2.0*(na+dp)*extm)/60.0"; .update “time2d=(a12*2.0*(na)*extm)/3600.0"; ! Executed once at start of experiment I ________________________ .program p2 = p2 + p0; a_tmp = aHdec; dec_cycle = (2.0 * pW); AQTM = (rd + aqtm); dpc = dp; pw90Y= (pw180Y/2.0): pw90X: (pw180X/2.0); TAUl = ((Tr/2.0) - pw90Y TAU2 = ((Tr/2.0) - pw90Y TAU3 = ((Tr/2.0) - pw90Y TRI = (ct/20.0); for(I = O, I < 20, I++) { - tMX); - pw90X - tMX); - rd); ramp[I] = ach + (2.0*(I-10)*achmod)/19.0; } ramp = ramp.start; halfal = al/2; L02 = (lcl - 2); abph = abph.start; H9O = H90.start; Xmix = Xmix.start; X180A= X180A.start; X180 = X180.start; Yl80 - Y180.start; cycles = ceil(((lc1 * Tr) cycles = cycles - l; + AQTM + 100u)/(dec_cycle)li txdutyl=lpw90H+(2.0*ct)+(Tr*(2*(a12—1)+lc1))+rd+aqtm)/extm; if (txdutyl > 0.2) {error(TXDUTY_ERR);} !Duty factor too large if (L02 < 0) {error(L02_ERR);} !lcl must be equal or greater than 2. if (TAUl < lOOns) {error(TAUl_ERR);} lerror in pw180Y or spin. if (TAU2 < lOOns) {error(TAU2_ERR);} lerror in pw180X. if (TAU3 < lOOns) {error(TAU3_ERR);} 154 actual pulse prog. .start aqph=@abph; runtime loop for(AB_Flag = 0, AB_Flag < 2, AB_Flag++) { X180 Y18O ramp out if (AB_Flag == 0) { aY180_on = } else { aY180_on = } X180.start; Y180.start; ramp.start; time(lOu); Async; ch++ chl; time(3u) out time(lu) out pw90H out Ct do (20) { out out time(TRI) } out time(TAUl) out tMX; out pw180Y; for(x=0, x 0.2) {error(TXDUTY_ERR);} !Duty factor too large if (L02 < 0) {error(L02_ERR);} !lcl must be equal or greater than 2. if (TAU2 < lOOns) {error(TAU2_ERR);} lerror in pw180Y or spin. if (TAU3 < lOOns) {error(TAU3_ERR);} lerror in pw180X. if (TAU4 < lOOns) {error(TAU4_ERR);} ! actual pulse prog. runtime loop .start aqph=@abph; for(AB_Flag = 0, AB_Flag < 2, AB_Flag++) { if (AB_Flag == 0) { aY180_on = 0.0; 1 else { aYl80_on = aY180; } Y180 = Y180.start; ramp = ramp.start; out time(lOu); Async; ch++ chl; out time(3u) chl: SC(scX); out time(lu) chl: P(@Xmix); out pw9OH chl: MX; 1 out ct chl: TG; do (20) { out time(TRI) chl: TG I A(@ramp++); } out time(TAUl) chl: AP(aX180,@Xl8OA); 160 out tMX; out pw180Y; for(x=0, x 0 ) {sleep time;} average = average/no_pos; sd = 0.0; /* calculate standard deviation */ for (pos_index = 0; pos_index < no_pos; pos_index++) { sd = sd + pow((intensity[pos_index] - average),2); } sd = sqrt(sd/(no_pos - 1)); sd_ave = sd_ave + sd; sprintf(stringS, "average is %6.3f; ", average); strcat(stringl, string5); sprintf(stringS, "standard derivation is %6.3f", sd); strcat(stringl, string5); fd = fopen (data_file,a); fprintf (fd,"%s", stringl); 164 fclose (fd); } sd_ave = sd_ave/no_rows; fd = fopen (data_file,a); fprintf (fd, "the average standard derivation from all spectra is %f", sd_ave); sprintf(output, "the average standard derivation from all spectra is %f", sd_ave); info output; fprintf (fd, ' "); fprintf (fd, “end_data"); fclose (fd); View -d1; dis; sprintf(output,"Results are saved in the file with noise_integrals and integration width as the suffix."); info output; /home/zxz4b/macros_utiI/RFDR_extractions Description: a process macro of prTDQBU data, eg. jpctdqbudata, which contains four FIDS. This macro adds up the second and fourth FIDS in buffer SO, save the sum as fpctdqbudata—sO, adds up the first and third F IDS in buffer 31, saves the sum as jpctdqbudata-sl, subtracts S1 from S0 in buffer SUB and saves the subtraction as firctdqbuda ta-S UB. /* RFDR_extractions */ /* Created on 07/04/04 */ /* Macro to create two extracted fids and one subtracted fid from the RFDR data set.*/ no_size = getproc sizel; quarter_size = no_size / 4; time = query “Enter view time for each row (5): ; /***** Generate the 50 output file *****/ filesuffix = "-sO"; fullpath = getproc filepath; sprintf(data_file, "%s", fullpath); strcat(data_file, filesuffix); 165 setsize quarter_size; first = copy -a active; second = copy -a active; third = copy -a active; fourth = copy -a active; templ view first -r O; templ extract templ; dis templ; if (time > 0 ) {sleep time;} temp2 = view second -r l; temp2 = extract temp2; dis temp2; if (time > 0 ) {sleep time;} temp3 = view third -r 2; temp3 = extract temp3; dis temp3; if (time > O ) {sleep time;} temp4 = view fourth -r 3; temp4 = extract temp4; dis temp4; if (time > 0 ) {sleep time;} sO = temp2 + temp4; sl = templ + temp3; SUB = sO - sl; dis sO; if (time > O ) {sleep time;} data_file = write s0; /***** Generate the 51 output file *****/ filesuffix = “-sl"; fullpath = getproc filepath; sprintf(data_file, "%s", fullpath); strcat(data_file, filesuffix); dis 51; if (time > 0 ) {sleep time;} data_file = write s1; /***** Generate the SUBl output file *****/ filesuffix = "-SUB"; fullpath = getproc filepath; sprintf(data_file, "%s", fullpath); strcat(data_file, filesuffix); dis SUB; if (time > 0 ) {sleep time;} data_file = write SUB; 166 delete first; delete templ; delete second; delete temp2; delete third; delete temp3; delete fourth; delete temp4; /*delete fifth; delete temp5;*/ /*delete sixth; delete temp6;*/ /*delete seventh; delete temp7;*/ /*delete eighth; delete temp8;*/ /*SUB = read data_file;*/ sprintf(output,“done, you may display buffer $0, $1 or SUB"); info output; /home/zxz4b/macros_util/RFDR_cleaner Description: a process macro of prTDQBU data in association with RFDR_extrationS. It deletes the SO, SI and SUB buffers generated by macro RFDR_extrations, without any modification of original or processed files. /* RFDR_cleaner */ /* Created on 07/06/04 */ /* Macro to clean up buffers */ delete sO; delete sl; delete SUB; sprintf(output,“Done, buffers named $0, $1 and SUB are deleted."); info output; 167 Appendix IV Simulation Examples and Procedures An example of calculation of Euler angles for carbonyl CSA (0pc). Group FI‘P/Norm/PhD/mathedit/GFF—Glyl.nb (written and composed with Mathematica 5.0) Description: This Mathematica program reads the nuclear coordinates of a carbonyl carbon, an a-carbon, an amide nitrogen and a carbonyl oxygen on the same peptide plane in frame C, constructs and normalizes relating internuclear vectors, uses the geometry to calculate unit vectors of 51 1, 622 and (533 directions of the carbonyl carbon, i.e., “Ndl 1”, “Nd22” and “Nd33” in program, according to literature. (Oas et. al., J. Am. Chem. Soc., 109, 5956-5962, 1987) One can obtain deapc, ,ch, ypc) by comparing the numerical matrix formed by {Nd11, Nd22, Nd33} and the Euler rotation matrix R'l(apc, ,ch, ypc), which is cos (1pc cos ,BPC cos- sin dpc sin rpc sin apc cos .ch cos 7pc + cos apc Sin 7pc —sin ,BPC cos 7pc cos arc cos ,BPC sin- sin arc cos 7pc —sin aPC cos 1613c Sin 7% + cos arc cos 7pc sin flPC Sin 7pc COS arc sin .BPC Sin arc sin ,BPC COS flpc (Mehring, M., Principles of high-resolution NMR in solids, Springer-Verlag, Berlin, 2nd ed.l983) Anglelitt = n*130/180; angleOCN = n*124/180; angleOCCa = n*121.2/180; angleNCCa = n*114.8/l80; CoordC = {12.054, 3.758, 2.599}; CoordCa = {12.249, 4.927, 1.697}; CoordN {13.298, 4.651, 0.701}; Coord0 {12.907, 2.890, 2.703}; VctrCO = CoordO — CoordC; NVctrCO = VctrCO/Norm[VctrCO] //N 168 VctrCN = CoordN - CoordC; NVctrCN = VctrCN/Norm[VctrCN] //N VctrCCa = CoordCa - CoordC; NVctrCCa = VctrCCa/Norm[VctrCCa] //N d22 = NVctrCO+Tan[n*130/180—n/2]*NVctrCN; Nd22 = d22/Norm[d22] //N dll = NVctrCN+Tan[n*130/180-angleOCN]*NVctrCCa; Ndll = dll/Normldlll //N Nd33 = Cross[Ndll,Nd22] //N An example of calculation of Euler angles for dipolar coupling (0pc). GroupFl‘P/NormlPhD/pubs/Dissertation/Appendices/IVSIMPSON_MATH_SIMM OL/ligd_dipolar.mol Description: SIMMOL is a useful tool in specification and visualization of anisotropic interaction tensors especially for polypeptides and proteins. (Bak et al., J. Magn. Reson. 154, 28-45, 2002) This SIMMOL program reads a model protein PDB file (1igd.pdb), selects two carbonyl carbons and returns a Spin system with dipolar coupling information and the Euler angles relating the internuclear tensor and frame C (0pc). #ver. 1.0 last revised on 08/16/07 by Z. Norm Zheng regsub ".mol" $argv0 {\1.spinsys} spinsys set m [mload ”1igd.pdb"] mloadtensors $m -default #mloadjcouplings $m -default msetspinsysfile $m $spinsys -numbered mselect $m 1 atom 72 mselect $m 2 atom 429 #mset $m —solid -ellipsoid shielding -color cpk -nice mdipole Sm 1 2 0AA 15AA #mclosespinsysfile $m munload $m puts "Generated: $spinsys" 169 The output for this SIMMOL file is the following and one can incorporate the output line with “dipole 1 2” into the related part of SIMPSON simulation. spinsys { # l 2 # 72C 429C # channels 13C nuclei 13C 13C dipole 1 2 —71.8948 0 75.071 8.3447 1 An example of SIMPSON input of REDOR GroupFI‘P/Norm/PhD/pubs/Dissertation/Appendices/IVSIMPSON_MATH_SIMM OL/redorxy8xy-i4-03 1907 .in Description: this SIMPSON input describes the spin systems in the spinsys section, specifies experimental and user-defined parameters in the par section, and calculates the evolution of density matrix in the proc pulseq section. In the proc main section, further functions includes (i) phase cycling, (ii) arrays of dipolar coupling day and dephasing time 2', (iii) simulation of 50““, s3” and (AS/soy”, (iv) obtaining (AS/So)” from an external file redor-i4-cor.fid Shown below, (v) calculation of 12 between (AS/So)“ and (AS/So)”, and (vi) also output of x2 as a fimction of rim to file redorxy8xy-i4-03 I 907. out Shown below. The code lines with “#” are comments and details of Simulation to help readers in understanding. # REDOR simulation for pulse sequence redorxy8xy_pm for freezedried i4 peptide ver. 1.0, last revised on 03/19/07 w/ all real pulses no cp phase cycling no output of sO and $1 coordinates based on Ala-56 CO and Glu60 N in helical domain of lcex Corrected the CSA and offset #41:=fl==fl==fl= 170 spinsys { } channels 130 15N nuclei 13C 15N dipole l 2 $par(dp12) 0 0 0 shift 1 178p -81.0p 0.7284 0 116.08 -104.96 par I } proton_frequency 400.779784e6 spin_rate 8000 sw 50000 np 4 crystal_file replOO gamma_angles 18 start_operator le detect_operator Ilp verbose 1101 variable Crf 40000 variable Nrf 47600 variable dp12_min 35 variable dp12_max 55 variable dp12_incr 1 variable bestkaisqr 1e6 variable c_off 16500 variable n_off 0 proc pulseq I} I global par maxdt 1 set Ct180 [expr 0.5e6/$par(Crf)] set Nt180 [expr 0.5e6/$par(Nrf)] set tr [expr O.5e6/$par(spin_rate)] set trl [expr $tr-0.5*$Ct180] set tr2 [expr $tr-O.5*$Ct180-0.5*$Nt180] reset offset $par(c_off) $par(n_off) delay $tr2 pulse $Nt180 O x $par(Nrf) x delay $tr2 pulse $Ct180 $par(Crf) x O x store 1 #s1 reset offset $par(c_off) $par(n_off) delay $tr2 pulse $Nt180 0 y $par(Nrf) y delay $tr2 pulse $Ct180 $par(Crf) y 0 y store 2 #51 171 reset offset $par(c_off) $par(n_off) delay $tr2 pulse $Nt180 0 x $par(Nrf) x delay $tr2 pulse $Ct180 $par(Crf) x 0 x delay $tr2 pulse $Nt180 0 y $par(Nrf) y delay $tr1 store 3 #81 reset foreach i {l 2 1 2 2 1 2 1} { prop $i } store 8 #51 reset offset $par(c_off) $par(n_off) delay $tr2 pulse $Nt180 0 x 0 x delay $tr2 pulse $Ct180 $par(Crf) x 0 x store 4 #50 reset offset $par(c_off) $par(n_off) delay $tr2 pulse $Nt180 0 y 0 y delay $tr2 pulse $Ct180 $par(Crf) y 0 y store 5 #sO reset offset $par(c_off) $par(n_off) delay $tr2 pulse $Nt180 0 x 0 x delay $tr2 pulse $Ct180 $par(Crf) x 0 x delay $tr2 pulse $Nt180 0 y 0 y delay $trl store 6 #sO reset foreach i {4 5 4 5 5 4 5 4} { prop $i } store 9 #50 for {set j 8} I$j <= 32} {incr j 8} { 172 reset prop $par(swtch1) $j prop $par(swtch2) acq } proc main {} { global par set exp [fload redor-i4—cor.fid] set fl [file exists $par(name).out] if I$fl == 1} I file delete $par(name).out } for {set par(dp12) $par(dp12_min)} {$par(dp12) <= $par(dp12_max)} {set par(dp12) [expr $par(dp12)+$par(dp12_incr)]} { foreach p {{0 9 6} {1 8 3}} { set par(swtchl) [lindex Sp 1] set par(swtch2) [lindex Sp 2] set f [fsimpson] set g[lindex $p 0] [fdup Sf] } #fsave $g0 $par(namel-Spar(dp12)-sO.fid #fsave $gl $par(name)-$par(dp12)-sl.fid set gsub [fdup $gO] fsub $gsub $gl for {set j l} {$j <= $par(np)} liner 3} { set a0 [findex $g0 $j -re] set a1 [findex $gsub $j -re] fsetindex $g1 $j [expr $a1/Sa0] 0 } #fphase $g1 -scale $par(scl_avg) fsave $g1 $par(name)-$par(dp12).fid set kaisqr 0 for {set k 1} {$k <= $par(np)} {incr k} { set b0 [findex $g1 $k -re] set b1 [findex $exp $k -re] set c [findex $exp $k -im] set cume [expr ($b0—$bl)*($b0-$b1)/$C/$c] set kaisqr [expr $kaisqr+$cume] } if {$kaisqr < $par(bestkaisqr)} { set par(bestkaisqr) Skaisqr set dp12_opt $par(dp12) fsave $gl $par(name)-opt.fid } puts "dp12=$par(dp12) kaisq=$kaisqr bestkaisqrzspar(bestkaisqr)" set outpt [open $par(name).out a+ 0600] 173 puts $outpt "$par(dp12) $kaisqr" close $outpt } #set outpt [open $par(name).out a+ 0600] #puts $outpt "$dp12_opt $par(bestkaisqr)" #close $outpt #funload GroupFI‘P/Norm/PhD/pubs/Dissertation/Appendices/IVSIMPSON_MATH_SIMM OL/redor-i4-cor.fid Description: the associated file with REDOR (AS/So)” (on the left column) and ems/50f” (on the right column) of 14 peptide. SIMP NP=4 SW=50000 TYPE=FID DATA 0.12916 0.0089 0.43257 0.00686 0.78875 0.00482 0.99543 0.01038 END GroupFI‘P/Norm/PhD/pubs/Dissertation/Appendices/IVSIMPSON_MATH_SIMM OL/ redorxy8xy-i4-03l907.out Description: the output file with day (on the left column) and 12 (on the right column) of 14 peptide REDOR Simulation. 35 2390.70482557 36 1839.73313007 37 1366.63944623 38 969.367258135 39 645.43214659 4O 391.887699375 41 205.477637589 42 82.6023016007 43 19.4340789519 44 11.970640534 45 56.0508461683 46 147.462383488 47 281.938977348 48 455.2169525 174 49 663.12061251 50 901.50180335 51 1166.4060966 52 1453.93385228 53 1760.40721465 54 2082.3368734 55 2416.41005902 An example of SIMPSON input of pr T DQB U GroupFI‘P/NormlPhD/pubs/Dissertation/Appendices/IVSIMPSON_MATH_SIMM OL/ctdqbul-fpmnf8c-elm3-hnew.in Description: similar to the previous example of REDOR simulation, this SIMPSON input describes the spin systems in the spinsys section, Specifies experimental and user-defined parameters in the par section, and calculates the evolution of density matrix in the proc pulseq section. In the proc main section, fiirther functions includes (i) phase cycling, (ii) arrays of dipolar coupling dcc, (iii) dephasing time 2' and in-register parallel ,8 strand population h, (iv) Simulation of 505"", 513"" and (AS/SOY”, (v) obtaining (AS/So)” from an external file (ctdqbuI-fpmnf8c-elm3expfid) listed below, (vi) internal calculation (AS/So)” from (AS/So)”, (vii) calculation of X2 between (AS/SOY“ and (AS/So)”, and (viii) output of f as a function of both dcc and h to file ctdqbuI-jpmnch-elm3- hnew.out1, which is not displayed because of its length and has (ICC, h and f in the left, central and right columns, respectively. The code lines with “#” are comments and details of simulation to help readers in understanding. #ctdqbul-fpmnf8c-e1m3-hnew.in #Last revised 05/21/2007 by Z. Norm Zheng, ver. 8.0 real for fp X180 and idea for high-field x90 with array of 1 and cp phase cycle #Kai-square fit HFPmnFBC-eLMB simulation to the ORIGINAL expt data written in ctdqbul-fpmnch-elmBexp.fid #The dipolar coupling, i.e., the distance between homonuclei is the only parameter to fit and the scaling factor is set to a fixed value 175 #fit dipole_1_2, dipole_2_3(dipole_2_3=dipole_l_2), dipole_1_3(dipole_1_3=dipole_1_2/8) for HFPmnF80L9N-eLM3 #CSA approx values and orientations are obtained from AT&T Bell Lab Reference book and crystal file lcex.pdb. #Start: In; detect: Inp #The normalized population of in-register beta parallel conformation (h) is arrayed and exp = a*cor/h - b/h for the correction eq. spinsys { channels 130 nuclei 13C 13C shift 1 170.6p shift 2 170.6p shift 3 170.6p dipole 1 2 $par(dp12) dipole 1 3 $par(dp13) 13C -75.67p 0.91189 -75.67p 0.91189 -75.67p 0.91189 0 75.071 0 75.071 dipole 2 3 $par(dp23) 0 75.071 } par { spin_rate 12000 proton_frequency 400.779784e6 crystal_file gamma_angles detect_operator 50000 sw np verbose variable fp variable rf variable m variable variable variable variable variable variable variable variable variable variable } h_min c_off proc pulseq I} I global par maxdt 1.0 set tr [expr set x90 [expr set x180 [expr set trl [expr reset replOO 18 Inp 7 1101 20500 55000 48 dp12_min -100 dp12_max —2 dp12_incr 2 0.02 h_max l h_incr 0.02 bestkaisqr 1e6 a 1.2874 b 0.03450 16299 ooooooooo 109.37 -17l.38 109.37 -171.38 109.37 -17l.38 .3447 .3447 .3447 1.0e6/$par(spin_rate)] 0.25e6/$par(rf)] 0.5e6/$par(fp)] ($tr*0.5)-(0.5*$x180)] offset $par(c_off) pulseid $x90 $par(rf) 270 pulseid $x90 $par(rf) 0 store 0 176 reset offset $par(c_off) pulseid $x90 $par(rf) 0 pulseid $x90 $par(rf) 0 store 1 reset offset $par(c_off) pulseid $x90 $par(rf) 90 pulseid $x90 $par(rf) 0 store 2 reset offset $par(c_off) pulseid $x90 $par(rf) 180 pulseid $x90 $par(rf) 0 store 3 reset offset $par(c_off) delay $tr1 pulse $x180 $par(fp) 0 delay $tr1 store 11 reset offset $par(c_off) delay $tr1 pulse $x180 $par(fp) 90 delay $tr1 store 22 reset offset $par(c_off) pulseid $x90 $par(rf) 180 pulseid $x90 $par(rf) 90 store 4 reset foreach i {11 22 11 22 22 11 22 11} { prop $i } store 7 foreach l {2 6 10 14 24 30 38} I set n [expr $par(m)—$1] reset prop 7 $1 prop $par(type) prop 7 $par(m) prop 4 prop 7 Sn acq 177 proc main I} I global par set exp [fload ctdqbul-fpmnf8c-elm3exp.fid] set fl [file exists $par(name).out] if {$fl == 1} { file delete $par(name).out } for {set par(dp12) $par(dp12_min)} {$par(dp12) <= $par(dp12_max)} {set par(dp12) [expr $par(dp12)+$par(dp12_incr)]} { set par(dp23) $par(dp12) set par(dp13) [expr $par(dp12)/8] foreach p IIO Inx} {1 Iny} {2 —Inx} {3 -Iny}} { set par(type) [lindex Sp 0] set par(start_operator) [lindex $p 1] set f [fsimpson] set g[lindex Sp 0] [fdup $f] } fadd $g0 $g2 fadd $g1 $g3 #fsave $g0 $par(name)—sO.fid #fsave $gl $par(name)-sl.fid set gsub [fdup $g0] fsub $gsub $g1 for {set j 1} {$j <= $par(np)} liner 1} I set a0 [findex $g0 $j -re] set a1 [findex $gsub $j -re] fsetindex $g2 $j [expr $a1/$a0] O } #fphase $g2 —scale $par(scl_avg) fsave $g2 $par(name)$par(dp12).fid for {set h $par(h_min)} {$h <=$par(h_max)} {set h [expr $h+$par(h_incr)]} { - $par(b)/$h)] set kaisqr 0 for {set k 1} {$k <= $par(np)} {incr k} { set b0 [findex $g2 $k -re] set temp [findex $exp $k -re] set bl [expr ($par(a)*$temp/sh set c [findex $exp $k -im] set cume [expr ($b0-Sb1)*($b0-$b1)/$c/$c] set kaisqr [expr $kaisqr+$cume] } if {$kaisqr < $par(bestkaisqr)} { set par(bestkaisqr) $kaisqr set dp12_opt $par(dp12) set h_opt $h fsave $g2 $par(name)-scaled.fid 178 set outpt [open $par(name).out a+ 0600] puts $outpt "$par(dp12) Sh $kaisqr" close $outpt } } set outpt [open $par(name).out a+ 0600] puts $outpt "$dp12_opt $h_opt $par(bestkaisqr)" close $outpt #funload GroupFTP/Norm/PhD/pubs/Dissertation/Appendices/IVSIIVIPSON_MATH_SIMM OL/ctdqbul-fpmnf8c-elm3exp.fid Description: the associated file with prTDQBU (AS/So)” (on the lefi column) and trm/50f” (on the right column) of HFPmn-F8CL9N/LMe. SIMP NP=7 SW=50000 TYPE=FID DATA 0.071762 0.065670 0.152774 0.070136 0.226882 0.058087 0.393600 0.087761 0.451378 0.073625 0.480053 0.085385 0.418892 0.099848 END Procedures of SIMPSON simulation SIMPSON Simulation of AS/So in REDOR or prTDQBU experiments includes the following steps, which are not necessary in the same order in code lines of SIMPSON input files. (Bak et al. J. Magn. Reson., 147, 296-330, 2000) (i) In the proc pulseq section, correctly and efficiently rewrite the pulse sequence with details including timing and phases of pulses, delays and acquistion in coding of SIMPSON. Pay necessary attention to the different versions of pulse sequences such as 179 “all-but-one 15N pulse” and “alternating 13 C/ 15N pulse” in REDOR, and “one-7r-per— TR” and “one- 7r-per-2 1'11” in prTDQBU, so that the proc pulseq section correctly Should simulate the pulse sequence of interest. Since the REDOR and prTDQBU sequences used in this work are based on phase-cycled Irpulses, the proc pulseq section Should be developed by combination of saved and reused units and subunits in density matrix propagation, which are the “reset store” units. Hence a pulse sequence can be correctly simulated and the simulation time can be significantly saved by an optimized proc pulseq section. (ii) In the spinsys section, achieve the information of Spin system from crystal structure of the sample (for crystalline samples) or its model protein (for non-crystalline samples), which includes chemical Shift(s) (CS) and dipolar coupling(s) (d) of simulated nuclei. There are two previous examples of calculating Euler angles from crystallographic coordinates for CSA and dipolar coupling in Mathematica and in SIMMOL, respectively. Most of SIMPSON simulation inputs in this work were written in array of d, which is handled by the proc main section described later. (iii) In the par section, list the experimental parameters mandated by SIMPSON and also user-defined parameters. The necessary experimental parameters include MAS frequency (spin_rate), 1H NMR frequency of spectrometer (proton fiequency), powder sampling profile (crystal _file), number of y angle pairs in powder sampling (gamma_angles), sweep width (sw), number of acquisition points, i.e. number of (AS/So)“ in this work, (np), initial operator (start_operator) and detect operator (detect_operator). Some extra user-defined parameters, which include pulse field of 13 C 7: pulses, ‘3 C transmitter offset, timing parameters, lower bound, upper bound and 180 increment of dipolar coupling, lower bound, upper bound and increment of in-register parallel ,B strand population and correction coefficients from (AS/So)” to (AS/Sp)”, and these parameter can also facilitate the programming. (iv) In the proc main section, specify phase cycles, array of fitting parameters including d and h, as well as reading and writing of files. The progress of the Simulation can be controlled by adding conditional cycles within the following general form of proc main section. Proc main I} I global par set f [fsimpson] fsave $f $par(name).fid In the previous examples of prTDQBU Simulation file ctdqbuI firmnch-elm3-hnew. in, several conditional cycles were applied and they are listed with respective controlling variable within parentheses and brief function within braces. The indentation Shows the function range of each cycle in the logic flow. for (d) { foreach (number of four prTDQBU FIDs){ phase cycling } for (index j){ . . . calculation of.&fim, sfm‘and (AS/Swim } for (h){ for (index klI calculation of (AS/5mm” and 0(AS/Sficm from (AS/3mg” and O'IAS/Solexp x2 calculation } 181 After all, various user-defined controls are allowed be readily implemented in the proc main section, such that input and output of SIMPSON simulations can be readily automated. (v) Manually generate some extemal file if it is needed. In the examples of REDOR and prTDQBU Simulation, external files were generated with [AS/Soc", aAS/Soco'] and [AS/Soap, GAS/30w], respectively. The SIMPSON Simulation in this work focused on the numerical simulation of (AS/SOY“ and )(2 fitting it to (AS/SOY” to get best-fit dipolar coupling and/or structural population. However, the use of SIMPSON iS not limited to the type of simulation described above, and it covers simulations of CSA powder pattern, 2D spectra and etc. (Bak et al. J. Magn. Reson., 147, 296-330, 2000) 182 llIIIIIIIIIIIIIIIIIIIIIIIIl