“III 3 HilllllllllllllllllllfllllljlllllUfllllllfllljl 293 ‘LIBRARY Michigan Scan: ' This is to certify that the thesis entitled PREDICTION OF SHEAR INDUCED ENZYME ACTIVITY LOSS IN FLOW SYSTEMS presented by Carl Robert Beck has been accepted towards fulfillment of the requirements for __E]:u_D.__degree in Chemical Engineering 1&1“ch /4 %‘@~/ Major professor Date 7/7/79 0-7 639 OVERDUE FINES ARE 25¢ PER DAY PER ITEM Return to book drop to remove this checkout from your record. PLEASE NOTE: In all cases this material has been filmed in the best possible way from the available copy. Problems encountered with this document have been identified here with a check mark ur’ . l. Glossy photographs . Colored illustrations Photographs with dark background Illustrations are poor copy °rint shows through as there is text on both sides of page aim-plum O Indistinct, broken or small print on several pages throughout 7. Tightly bound copy with print lost in spine 8. Computer printout pages with indistinct print 1// 9. Page(s) lacking when material received, and not available from school or author l0. Page(s) seem to be missing in numbering only as text follows ll. Poor carbon copy 12. Not original copy, several pages with blurred type 13. Appendix pages are poor copy l4. Original copy with light type l5. Curling and wrinkled pages l6. Other unmegéyfilms lntemanonal 300 N 2555 R0.. ANN ARBOR MI 48106‘313: 751.4700 PREDICTION OF SHEAR INDUCED ENZYME ACTIVITY LOSS IN FLOW SYSTEMS By Carl Robert Beck A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemical Engineering 1979 ABSTRACT PREDICTION OF SHEAR INDUCED ENZYME ACTIVITY LOSS IN FLOW SYSTEMS By Carl Robert Beck The exceptional catalytic potential of enzymes for industrial processes is limited by their fragile nature. This fragile nature is exemplified by a loss of catalytic activity in shear fields. Bovine liver catalase was used as a model system to study this effect in a stirred tank and in a Couette viscometer and this enzyme was found to have an activation energy of approximately 7 kcal/gmole for the "degradation" reaction. This suggests that the mechanism for enzyme damage in shear flow may be the breaking of one or two hydrogen bonds in the quaternary structure of the enzyme. A method is proposed here to predict the enzyme activity loss one might expect in industrial flow processes. The method requires the rate of activity loss of the pr0posed enzyme solution at a fixed shear rate to be measured experimentally in a viscometer. From this data, an activation energy and a frequency factor of degradation are calculated which relate the degradation rate to shear stress and temp- erature. This relationship is combined with a function describing the distribution of shear in the pr0posed process to predict the rate of activity loss in that process. A shear distribution function F is defined such that Fds is the fraction of fluid in the vessel which is experiencing a shear rate Carl Robert Beck between 5 and s+ds. Then the rate of degradation of enzyme in this volume fraction becomes RS Fds (l) where RS is the rate of deactivation of enzyme experiencing a shear rate 5, which must be determined experimentally. The total rate of deactivation is found by integrating over all shear rates Rt = [0 RS F ds (2) The shear distribution function is unknown for many important flow systems, such as the baffled stirred tank used in this study. Since the shear distribution function for such a process cannot be rigorously defined, several trial functions are examined: for Model l, it is assumed that most of the fluid in the tank is being sheared at a high rate; for Model 2 any shear rate (from zero up to a maximum value) is assumed equally likely; in Model 3 most of the fluid in the tank is under low shear; and for Model 4 the shear rate decays expon- entially with distance from the center of the tank. These four models were used, along with enzyme degradation data from a viscometer to derive an equation which predicts the rate of degradation in a stirred tank, as follows Rt = KZV(Pu/V)]/2a (3) where K is a constant which depends on the form of the shear distribu- tion function, P is the power input to the fluid, u is the viscosity, Zv is a parameter obtainable from measurements in a constant shear viscometer, and a is the concentration of active enzyme present. It Carl Robert Beck is shown further that K is not a sensitive function of the distribution function. Thus, enzyme degradation parameters from simple viscometer studies and a knowledge of the power input to the stirred tank are all that are required to estimate enzyme damage in a stirred vessel. Experimental degradation rates were consistent with the form of 1la) and were about equation (3) (i.e., they were proportional to P one-half the predicted rates. This deviation is considered good since Equation 3 contains no adjustable parameters. The degradation rates predicted using various shear distribution functions differed only slightly from each other (< 7%). Although this prevents drawing con- clusions on a "preferred" distribution function for stirred tanks, it has the advantage of making the choice of distribution function rela- tively unimportant to the prediction of enzyme damage. Finally, equations were derived for the predication of enzyme damage in laminar, tube flow. Two limiting cases were considered: (a) with complete, diffusive radial mixing and (b) with no radial mixing. Again, these limiting cases do not differ greatly from each other and are in agreement with the experimental results of Charm and Wong (Charm, S.E., and B. L. Wong. Enzyme inactivation with shearing. Biotech. and Bioeng. l2:ll03, 1970). To my wife Sue ii ACKNOWLEDGMENTS The author would like to express his deep appreciation to Dr. Donald K. Anderson for his assistance and support throughout the course of this work. Gratitude is expressed to Drs. Clarence Suelter, Krishnamurthy Jayaraman, Eric Grulke and Martin Hawley for their concern and interest. The author also acknowledges Don Childs and Carl Redman for their assistance in the design and construction of the experimental apparatus. The financial support of the Department of Chemical Engineering and the Division of Engineering Research is deeply appreciated. TABLE OF CONTENTS Page LIST OF TABLES ......................... vi LIST OF FIGURES ........................ vii NOMENCLATURE .......................... viii I. INTRODUCTION ...................... I II. BACKGROUND ....................... 4 Enzymes ...................... 4 Enzyme Degradation ................. 5 III. EXPERIMENTAL APPARATUS ................. 7 Viscometer ..................... 7 Stirred Tank .................... ll IV. ASSAY METHOD ...................... l3 V. RESULTS AND DISCUSSION ................. 17 Protein Adsorption to the Viscometer ........ l7 Catalase Degradation in a Constant Shear Field . . . l9 Shear Distribution Function ............ 22 Definition ................... 22 Application to a Stirred Tank ......... 24 Stirred Tank Power Measurement ........... 34 Activation Energy of Degradation .......... 39 VI. DEGRADATION IN POISEULLE FLOW ............. 43 Pipe Flow With Complete Radial Mixing ....... 43 Pipe Flow Without Radial Mixing .......... 45 VII. CONCLUSIONS ...................... SO BIBLIOGRAPHY .......................... 53 iv Page APPENDIX A: TABULATED DATA .................. 55 APPENDIX B: ASSAY COMPUTER PROGRAM .............. 75 LIST OF TABLES Table Page I. Industrial uses of enzymes ............ . . . . 2 2. Shear distribution function models ............ 25 3. Shear distribution function results ........... 29 4. Torque measurements ................... 55 5. Catalase adsorption to viscometer ............ 56 6. Boehringer-Mannheim catalase, viscometer degradation, 4°C ........................... 58 7. Worthington catalase, viscometer degradation, 2°C . . . . 60 8. Worthington Catalase, viscometer degradation, 10°C . . . . 6l 9. Worthington catalase, viscometer degradation, 20°C . . . . 63 10. Worthington catalase, stirred tank degradation, l°C . . . 65 ll. Worthington catalase, stirred tank degradation, l0°C . . . 68 12. Worthington catalase, stirred tank degradation, 20°C . . . 72 vi Figure 10. 11. 12. 13. 14. 15. LIST OF FIGURES Viscometer schematic .................. Viscometer torque versus rev./sec ............ Stirred tank, impeller and dynamometer schematic . . . . Schematic of the assay apparatus and the computer interface ....................... Loss of catalase activity without shear ........ Remaining activity versus exposure time in the viscometer ....................... Viscometer degradation rate constants versus shear stress ......................... Remaining activity versus exposure time in the stirred tank .......................... 1/2 Stirred tank degradation rate contents versus P Power Curve for stirred tank .............. Dynamometer measured torque versus RPM at 10°C ..... 1/2N Stirred tank degradation rate constants versus H 1 Viscometer degradation parameter, Zv versus T' . . . . 1 Stirred tank degradation parameter Zt versus T' . . . . Remaining activity after laminar flow through a tube . . . vii Page 10 12 15 18 21 23 30 33 36 37 38 4O 42 46 Symbol [A] NOMENCLATURE Definition concentration of ablumin activity ZVuL/D viscometer gap catalase concentration diameter activation energy shear distribution function gravitational acceleration height of fluid in stirred tank constant rate constant Length of tube Reynolds number exponent Froude number exponent frequency of revolution Froude number power number Reynolds number power pressure drop viii [S]. [510 Sv’ St’ S S vo’ Sp T T Subscripts .i lost Definition rate of enzyme degradation radius, gas constant radial distance substrate concentration degradation rate constant shear rate temperature torque time linear velocity volume variable volume, voltage weight u”max axial distance degradation parameter frequency factor viscosity shear stress kinematic viscosity density Definition shear distribution model index activity lost maximum ix Subscripts Definition min minimum 0 at t = 0 p pipe 5 due only to shear t stirred tank v viscometer I. INTRODUCTION Enzymes are globular proteins that display catalytic activity. In general, all chemical reactions in a living organism are made pos- sible only through the actions of enzymes (9), yet little is known in molecular terms about how they work. As catalysts they are extremely 20 times as fast as the effective, accelerating reactions 108 to 10 uncatalyzed reaction, while being so specific as to distinguish be- tween different substrate isomers. This remakable catalytic activity is achieved by the "active site" and the complex three dimensional structure of the enzyme. The active site is the place of attachment of a substrate molecule and it is surrounded by a three dimensional molecular structure which allows only preferred substrate molecules to fit. The catalytic activity of the molecule depends on the integrity of this active site which is maintained by covalent bonds, hydrogen bonds and van der Waal's forces. The industrial advantages of enzymes as catalysts are obvious and they are currently being used in many processes, Table 1. How- ever, the fragile nature of proteins and the susceptibility of the active site to chemical and mechanical degradation limits further ex- ploitation of many of the 2000 known enzymes. Enzyme degradation in a shear field has been observed by many investigators (22). Since shear is an ubiquitous component in any industrial or purification process and it is found in many physiological situations, it is an 1 Table l. 2 Industrial uses of enzymes (1) Enzyme Use Glucoamylase Invertase Pectic enzymes Cellulases Pancreatin Catalase Glucose isomerase Glucose oxidase Microbial protease Bromelain Papain Rennins Trypsin Pepsin a-Amylase Aminoacylase Laccase Glucose production; saccharification of dis- tillery and brewery mashes; manufacture of fermentation media. Production of confectionaries such as soft- center candies. Clarification of fruit juices and wines. Digestive aid; reduction of viscosity of vegetable gums such as those in coffee. Digestive aid. Removal of peroxide when it is used for sterilization, especially in milk. Production of high-fructose corn syrups. Removal of oxygen from food products; desugars eggs; diagnostic aid (glucose in diabetes). Detergent additive; bread baking; chill-proof— ing beer; meat tenderizer; leather bating. Digestive aid; anti—inflammatory preparations; meat tenderizer. Meat tenderizer; chill-proofing beer. Curdle milk in cheese formation. Digestive aid; leather bating. Digestive aid; rennet extender. Textile desizing; starch liquefaction; glucose production. Separating DL-acylamino acid into L-amino acid and D-acylamino acid. Drying of laquer. interesting phenomenon to study. The object of this work is to examine the potential of a method with which one could measure shear sensitive parameters of an enzyme in a controlled shear situation and then to relate those parameters along with some measurable properties of the process flow system to predict the activity loss of the enzyme in that system. The procedure used requires that the rate of activity loss as a function of shear stress and temperature be determined. A Couette viscometer was designed for this purpose, consisting of two coaxial cylinders. One is held stationary while the other is rotated at a known rate. A fluid placed in the gap between the cylinders exper- iences a constant shear rate. With this relationship and a knowledge of the shear distribution in the process flow system, the rate of activity loss in the system could, in theory, be predicted. A baffled stirred tank was used to generate a shear field with an unknown shear distribution, and various hypothetical forms of this distribution were examined. This type of process vessel is comnon in many industrial enzyme processes. In addition, laminar flow of an enzyme solution in a pipe is examined by considering two models: (a) assuming complete radial mixing of the enzyme; (b) assuming no radial mixing. The enzyme catalase was chosen for this study because it can readily be assayed and it has previously been shown (4) to be ex- tremely sensitive to shear. II. BACKGROUND Enzymes The complex molecular structure of enzymes is necessary for catalysis. Globular proteins, of which enzymes are a class, can have as many as four levels of structure. The primary structure refers to the specific amino acid sequence along the covalent backbone of a polypeptide. The secondary structure refers to regular recurring arrangements of the polypeptide chain, such as the helical structure often formed by proteins. The tertiary structure refers to the bent and folded three dimensional shape. The quaternary structure refers to the arrangement of chains to form the unit molecule. The tertiary and quaternary structures of globular proteins fold compactly and allow very little space for solvent molecules. The internal space of the molecule contains nearly all the hydro- phobic groups of the amino acid monomers which further discourages the entry of water, while the external space of a globular protein contains nearly all the hydrophilic amino acid monomers which in- creases the solubility of the protein in water. The enzyme catalase possesses all four levels of structure. Catalase catalyzes the decomposition of hydrogen peroxide to oxygen and water. The use of hydrogen peroxide as a substrate as well as a hydrogen acceptor differentiates catalase from peroxidases which require a separate acceptor. Catalase activity is present in nearly all animal cells and in aerobic bacteria. Beef liver catalase has a molecular weight of 240,000 and consists of four subunits each with a molecular weight of 60,000. The catalase molecule has four trivalent iron heme groups which comprise the active group. Under optimum conditions, a single catalase molecule can decompose 5.6 million hydrogen peroxide molecules per minute (12). Catalase is used commercially to remove hydrogen peroxide used in pasteurizing milk prior to cheese making. Enzyme Degradation There is a significant amount of literature dealing with shear effects on immobilized enzymes but very little information is avail- able on the effect of shear on free enzymes in solution. The pioneer investigation which examined free enzymes in solution in a controlled shear field was performed by Charm and Wong (4). The enzymes rennet, catalase and carbozypeptidase were studied.in a viscometer and some measurements of activity loss of catalase in a teflon tube were re- ported. The authors reported activity losses of approximately 50% 1 for all three enzymes. This after 90 minutes of shear at 1155 sec- extreme sensitivity of enzymatic activity to shear led to the concep- tion of this work. The original publication was followed by several others by Charm and co-workers (5,6) in which different types of flow systems were examined and enzyme activity loss was predicted based on the results of the original work. One particular result worth noting because of its' applicability to this work is a 61% loss in catalase activity in a stirred tank after 4 hours of mixing at 1200 RPM. An exhaustive study of shear degradation of urease in a controlled shear field has been reported by Tirrell (19.20.23) who concluded that urease is permanently inactivated in a shear field only when certain conditions exist; (a) the enzyme must have formed high molecular weight aggregates, and (b) moieties which destroy the sulfhydryl group of cysteine residues are present (20). The oxidation of these sulfhydryl groups was concluded to be catalyzed by iron ions and promoted by shear. Additional studies conducted by Tirrel (20,21) demonstrated urease and lactic dehydrogenase inactivation to be a function of shear stress rather than shear rate as modeled by Charm. Shear stress is the force per area the adjacent fluid exerts on an enzyme molecule and is therefore a more logical parameter to study than shear rate if molecular deformation is the mechanism of enzyme inactivation. Shear stress is used in this work to model the effect of shear on enzyme activity loss. III. EXPERIMENTAL APPARATUS Viscometer An apparatus was constructed to shear enzyme solutions at con- trolled shear rates. A Couette viscometer was chosen as the best de- sign to shear a large volume of a low viscosity fluid. This design consists of two coaxial cylinders with the fluid to be sheared placed in the annular space between the cylinders, Figure 1. In this work, the outer cylinder was rotated at a fixed rate while the inner cylin- der was held stationary. This method allows stable laminar flow at higher Reynolds numbers than can be achieved by rotating the inner cylinder (18). If the gap between the cylinders is small compared to the di- ameter, the shear rate experienced by a fluid in laminar flow in the gap is s = u/b (I) where u is the linear velocity of the outer cylinder and b is the gap between the cylinders. The bottom of the fluid cavity was designed as a cone and plate viscometer to insure the same shear rate through- out the fluid. Since the fluid in the viscometer must be in laminar flow for Equation 1 to be valid, experiments were performed to determine the maximum velocity at which the outer cylinder could be rotated without 7 force transducer 2.54 cm H enzyme solution'} _ L A f. p—br- 0.090m cooling fluid a I I 5 -ll.70cm *i g ‘ ”seem-J sampling 5'; port I I Figure l. Couette viscometer schematic. turbulence. This velocity in turn gives the maximum shear rate attainable in the viscometer. The torque transmitted to the fluid and in turn to the inner cylinder was measured by a force transducer as shown in Figure 1. Equation 2 gives the torque for laminar flow (18). _ 2 Tq " 2'” UhN '0"; - 2 (2) DE Di 01 where u is the viscosity of the fluid, h is the wetted height of the cylinders, N is the frequency of revolution of the outer cylinder, and 01 and D2 are the diameters of the inner and outer cylinders, respectively. Equation 2 and the experimental data of torque vs. frequency of revolution are plotted on Figure 2 such that one should get a straight line for laminar flow. The velocity at which the measured torque de- viates from the predicted straight line indicates the point at which flow becomes instable (i.e., laminar flow and constant shear rate can no longer be maintained) (18). The experimental points measured with the viscometer followed the theoretical line up to a velocity of 155 cm/sec. Thus for water, used in this work, the maximum shear rate attainable in the viscometer is 1700 sec-1. Since a fluid in a shear field generates heat by viscous fric— tion, the inner cylinder of the viscometer was filled with water at the control temperature to act as a heat sink. Computation of the maximum theoretical temperature rise, assuming the outer cylinder was perfectly insulated and the inner cylinder was at the control tempera- ture, gave an increase which was less than 0.01°C. The fluid 10 .mucmpzncau op comuwmcmcu mpcmmmcamc mcwp mwcu soc; :owumw>ou .3on inseam” mpcmmmcawc wcw_ cementum we» .omm\>mc msmgm> mzcgou cmumeoomw> .N mcamwu oom\>o¢ ‘ v 0%. m . m . i m m P I. o .J b an L. N N .6 1 x .Ir 0. l C -0 a r nu m 7v in low 11 temperature measured after several experimental runs was identical to the control temperature within the accuracy of the thermometer (< 0.1°C). Stirred Tank A schematic of the stirred tank and dynamometer used in this work are shown in Figure 3. The tank was designed to be geometrically similar to vessels commonly found in industry. The industry standard of four baffles, one twelfth the width of the tank diameter and a radial discharging six-blade turbine impeller was used. The other geometric relationships were based on the following Standard Tank Configurations (8): (a) a fluid depth equal to the tank diameter; (b) an impeller diameter equal to one third of the tank diameter; (c) the impeller distance from the bottom of the tank equal to one third of the tank diameter; (d) the impeller blade width equal to one fifth of the impeller diameter; and (e) the impeller blade length equal to one fourth of the impeller diameter. A cover was used to prevent the fluid from being thrown out at high impeller velocities. The temperature of the enzyme solution was maintained by circu- lating water at the control temperature through the tank jacket, pre- venting any increase in temperature by viscous heating. This pro- cedure was not necessary however, when measuring torque because of the short duration of the experiment. Temperature changes never exceeded 1°C in these experiments. The dynamometer was used to measure impeller torque. The torque transferred to the fluid is in turn transferred to the tank which rests on the dynamometer turntable. The product of the radius of the turntable pulley (1.59 cm) and the force measured on the force trans- ducer is the torque applied to the fluid by the impeller. 12 coofing water outlet 1 ‘l 2) psi mL \\\\‘o— -..-.. oww B—LLB 8.41am 0.7.3,? *1 2.80m|- % Impeller cooling 2'8 cm & (bottom view) vufler a: i. . J/ inlet coolln water jacket WA dynamometer turntable 7// re dynamometer .L___, force transducer Figure 3. Stirred tank, impeller and dynamometer schematic. IV. ASSAY METHOD Bovine liver catalase was purchased from Worthington Biochemical Corporation (code CTS) or Boehringer-Mannheim Biochemicals and was diluted to Bug/ml with 20 mM potassium phosphate buffer (pH 7.00). Some experiments were performed with the enzyme solution containing 500 ug/ml of bovine serum albumin purchased from Sigma Chemical Company. All experiments were conducted in a constant temperature room. The enzyme catalyzes the decomposition of hydrogen peroxide to water and oxygen 2H202 + 2H20 + 02 (2) The reaction as described by Maehly and Chance (l3) obeys pseudo first order kinetics. 1%? = KICJIS] = kIS] (3) where [S] is the concentration of substrate (hydrogen peroxide) and t is time. Since the enzyme concentration [C] is constant throughout the reaction, it may be incorporated in the reaction rate constant k. If [S]o is the initial concentration of hydrogen peroxide, Equation 3 can be integrated to give 1n [5] / [530 = -kt (4) 13 14 The rate constant is determined by following the concentration of hydrogen peroxide and since k is directly proportional to the activity of the enzyme (13), this parameter is used to monitor degradation. The concentration of hydrogen peroxide was measured spectro- photometrically by recording the absorbance at 240 nm in a Beckman DK - 2A spectrophotometer. The reference cuvette was filled with 3 ml of 50 mM potassium phosphate buffer (pH 7.00) and a 0.1 ml aliquot of the enzyme solution. The sample cuvette was filled with 3 ml of a solution of 50 mM potassium phosphate buffer (pH 7.00) and 10.5 mM hydrogen peroxide. For an assay, a 0.1 ml aliquot of the enzyme solution was removed from the shearing device with a syringe and injected into the sample cuvette, held at 25°C. Following each assay the sample cuvette was cleaned with a suspension of magnesium oxide in distilled water, rinsed, and then soaked in nitric acid as described by Beers and Sizer (2). The decomposition of hydrogen peroxide initially obeys first order reaction kinetics but after one minute the rate constant begins to decrease (13). Because the reaction is first order for such a short time it is difficult to assay catalase with precision. For this reason the spectrophotometer was interfaced with a computer. The output signal from the spectrophotometer was amplified and sent via an analog-to-digital converter, to an IBM 1800 computer, (see Figure 4). The computer was programmed to read these voltage signals 120 times over a period of 0.5 seconds, average them and store this value for each half second interval during the first minute of reaction (the program is listed in Appendix B). The voltage is dir- ectly proportional to absorbance read by the spectrophotometer. Since 15 . . ,._, Photo- "' ‘- O Amplifier multiplier (_J ‘— 7i amp BECKMAN SPECTROPHOTOMETER Amp 'onolog-to-__ ':_"1 ewrit .._.. digital yp er converter IBM 1800 —- lineprinter ,L__ \_.| . start I“; switch Figure 4. Schematic of the assay apparatus and computer interface. 16 Beer's law relates concentration to absorbance, the hydrogen peroxide concentration is proportional to the voltage and Equation 4 becomes 1n (v/vo) -k t (5) where v0 is the voltage at t = 0. A linear regression analysis per- formed by the computer of In v vs. time yields the rate constant k. The computer was also programmed to plot the results and to analyze the rate constants as a function of shear exposure time. V. RESULTS AND DISCUSSION Protein Adsorption to the Viscometer When a buffered Worthington catalase solution was allowed to remain in the viscometer without the application of shear, the activ- ity of the solution decreased exponentially with time to a steady state level of activity (curves 0, E, F, Figure 5). It is speculated that this is due to adsorption of the enzyme on the walls of the viscometer. Enzymes have previously been reported to adsorb to polypropylene test tubes, lucite and glass (7,10,16). The speculation that the enzyme was adsorbing to the walls of the viscometer is supported by other results: (a) increasing the concentration of catalase decreased the fraction of "adsorbed" en— zyme, (curves 0 and E, Figure 5); (b) increasing the temperature in- creased the fraction of “adsorbed" enzyme, (curves E and F, Figure 5); (c) the application of shear after the "adsorption" loss reached steady state, increased the activity of the solution (curves 0 and F, Figure 5). Here, the applied shear stress is assumed to remove some of the enzyme from the viscometer walls. All of this experimental evidence is consistent with a previous report that proteins at a water-solid interface conform to a Langmuir model of adsorption (11). The addition of albumin to Worthington catalase solutions in the viscometer suppressed the "adsorption" of enzyme (curve C, Figure 5). Presumably, the albumin, which was at a much higher concentration 17 18 .cmumEoomw> .o u H .o u H .o n H .PE\mE m.o ”(a ._E\m: m u Hog .u°o~ ”Same negates .o ”(H .Fe\aa m u Hui .UOON II II H II PHHH .3238 535533 > T: .mmepmamu :oumcwgpcoz Av Amv .3338 coumcmficoz 0 EV .mmmpmamu coumcwcucoz AV Auv h .3288 835583 0 8V memymsoomw> .o u Hwuum mmmpmumo mo mmog mmSEE .mE. ._. 00m OWN OON On. 00. Om cl] T I d id 1 \xiw 11$. b. r \\ L l \ o m >\ 1 O D p I. o o iiiOlii O 0 Oil! o . . . - O J o o O i /o o r o .a . _< _o Dal i-W‘ U uilllllsf - 4 .m weaned No no H m co m. no w. D mo 0 D so W. ,M mo D . W mo 0 o._ 19 (500ug/ml) than catalase (Sug/ml), was preferentially adsorbed to the viscometer walls. Albumin was therefore added to all Worthington catalase solutions prepared for viscometer shear experiments. It was unnecessary to add albumin to catalase solutions in the stirred tank since there was no measurable catalase adsorption in the tank (curve 8, Figure 5). This was fortunate since the addition of albumin caused extensive foaming when stirred, which prohibited an assay of the solution. Both the viscometer and the tank were con- structed of stainless steel but the viscometer had a much larger sur- face area to volume ratio and was therefore more susceptible to ad- sorption. Shear experiments carried out with and without albumin in the Couette apparatus indicated that albumin does not affect the shear damage phenomenon. The Boehringer-Mannheim enzyme did not display the same adsorp- tion phenomenon (curve A, Figure 5). Since the methods of purification used in the preparations are unknown, 'it is difficult to hypothesize on this discrepancy. However, according to the supplier the Worthing- ton enzyme was sterilized by filtration through a 0.22 um pore size membrane which may have removed microbiological contaminants that pre- vented adsorption of the Boehringer-Mannheim enzyme. Catalase Degradation in a Constant Shear Field Since the rate constant for hydrogen peroxide decomposition, k, is proportional to enzymatic activity, a, a0 (units of activity/ volume) will be used in lieu of k, k0 respectively. Assuming a first order reaction mechanism, the rate of shear deactivation in a batch reactor is given by 20 - -da _ Rv-—d—t—-Sva (6) where Sv’ the rate constant for activity loss, is expected to be a function of the shear field and the sensitivity of the enzyme to shear. The first order assumption (rate of activity loss proportional to remaining activity) is an intuitive model which fits the experi- mental data reasonably well, Figure 6. Upon integration, Equation 6 yields a/a0 = e'svt (7) Sv and a can be obtained from measured values of activity as a 0 function of exposure time. Linear regression was used to estimate the values of Sv and a Several experiments were run at different 0‘ temperatures and shear stresses to determine the effect of these var- iables on the rate constant Sv‘ Shear stress I for a Newtonian fluid is defined by r = us (8) where u is the viscosity of the fluid and s is the shear rate. By substituting Equation 1 for s in Equation 8, it is apparent that the shear stress applied to the enzyme solution in the viscometer can be controlled by varying the linear velocity u, of the viscometer outer cylinder. 1 = (u/b) u (9) The viscosities of all enzyme solutions used in this work (including those that contained albumin) were essentiaerthe same as that of m ._-uwm apa.m u on ._-umm e-oi x mam.m u >m .UoN n ._. “NEU\mm:>._u mm.om n P .LmvwEoumw> 9.3. .5. $5.5. 9»szwa mamLm> Xvw>wuum mcwcwgmm .0 9:5?“— mueooom .o—Eu cove. cows 0 W M q H o' nae Bugugetuaa d °B/B “HA o; 22 water (17). At each temperature (2°C, 10°C, 20°C) measurements were made at different shear stresses to find the effect on Sv' The degra- dation rate constant appears to increase linearly with an increase in shear stress (Figure 7), such that one may write: Sv = Zvr + Sv0 (10) where Zv and Sv0 are the slope and intercept of a plot of Sv versus r. Sv0 is the rate constant of activity loss in the viscometer in the absence of shear and is a function of the properties of the viscometer. The rate of loss due only to shear then becomes R = S a = Z (r)a = Zv(us)a (11) where the subscript 5 refers to the shear effect only. Equation 11 describes the rate of degradation at shear rate 5. Shear Distribution Function Definition It would be useful to be able to predict shear deactivation in a flow process from information about the shear sensitivity of the enzyme (obtained from Couette type data), and information that is re- lated only to the shear field in the process. This type of modeling could in theory be achieved if the distribution of shear throughout the flow system were known. One can define a shear distribution function in the following way. Let F ds be the fracthniof'fluid in the vessel which is exper- iencing a shear rate between s and s + ds. Then the rate of 23 .F-umm a-o_ x we.m n om .m\uam so a-o_ x Po m .UOe n h .nu.c_ssapm uaozpwz mmmpmumo smogccmzlcwmcwcsmom “F-0mm olop x mo.m u cm .38.. B Z: x as. u 3 .38 u » .DJBB i: x 8; " cm .38... .5 Z: x 5.... 5.2 u c .378. T2 x Ba- u m .38... 5 Z: x a: n J JR u c .4552... new: mmmpepmu cogmcwcucoz .mmmeum cemcm mamem> museumcou mum; compmumcmmc LmumEoumw> «com 5036mm? 595 can Qmm 0.5 08 oo. om. ow ow A 4 a Q 9'. .N mczmmu OI x’ts ‘luoisuoo elm uoglopoibaq 'OBS ‘ 24 degradation of enzyme in this volume element is: RS F ds (12) where RS is the rate of deactivation of enzyme experiencing a shear rate 5 (see Equation 11), which can be measured in a viscometer. Then the total rate of deactivation of enzyme in the process vessel is found by integrating Equation 12 over all shear rates Rt =f0 RS F ds (13) Thus, if one has data for deactivation as a function of shear (i.e., RS from viscometer type data) and a shear distribution function F for the process vessel, one should be able to calculate the total rate of degradation in the vessel. Application to a Stirred Tank In general F is an unknown function. This difficulty was approached by assuming functions of F and examining the resultant rate expressions. Four models of F were proposed (Table 2): Model 1 assumes that most of the fluid in the tank is being sheared at a high rate; Model 2 assumes that the various shear rates (up to a maximum value) are equally likely; Model 3 assumes that most of the fluid in the tank is under low shear; and Model 4 assumes that shear rate de- cays exponentially with distance from the center of the tank as re- ported by Holland and Chapman (8). A comparison of experimental deg- radation rates with predicted rates from the various models might be expected to give some insight into the actual distribution of shear in the tank. 25 Table 2. Shear distribution function models. Model Plot F(s) 1 1 F _2_ S 2 Smax s 2 F 1. Smax s 3 I F 2 (smax - s) 2 Smax s 4 1 F : 2 1n(s/smax) : [1"(Smin/Smax)]2 S I 26 The method used to derive shear distribution functions can be explained by examining Model 1, in which F increases linearly with S, such that F=Ks for Ogsgsmax (14) where smax is the maximum shear rate allowed by this model. The constant K can be evaluated in terms of smax with the use of the restriction 1.0 = f”F ds (15) 0 which is apparent from the definition of F. By substituting Equation 14 into 15 and integrating the result, one obtains an expression to replace K in Equation 14, thus F = (2/s2 )s (16) max which is the form of Model 1 shown in Table 2. A similar procedure was used to derive Models 2 and 3. If Equations 16 and 11 are substituted into Equation 13, the total rate of enzyme degradation R in the tank becomes t 2 Rt = {fzv(us) a {_2 1 ds (17) Smax This equation contains the enzyme activity (a) which will be treated as a constant with respect to s. This is valid if one assumes that there exists packets of fluid which are experiencing a shear rate 5, and the packets are continuously being destroyed and reformed 27 (micromixing), such that the activity of the entire volume of fluid is nearly the same at any given instant. This is consistent with the idea of a shear distribution function which assumes that there is always the same distribution of shear but a given molecule is not necessarily confined to a constant shear region. In fact, in many turbulent flow systems there may not be any constant shear regions. With this assumption Equation 17 can be integrated to give R - 2 z - '3— US a (18) which expresses the total rate of degradation in the tank as a func— tion of Smax’ One method for estimating smax employs the rate of energy dis- sipation in a fluid with shear rate 5, which is given by (3): - _ 2 dP/dV — us (19) where P is power, and V is the volume of the tank. It is assumed that Equation 19 is valid for all of the fluid with shear rate 5, so that the total rate of energy dissipation is given by P = {favsz Fds (20) If Equation 16 is used to replace F in Equation 20 and the resulting expression is integrated over all allowable shear rates, one obtains ' s an expre551on for max’ ..-<—> <2» This equation can be substituted in Equation 18 to yield - gal/2 .. e. Rt - Ki Zv ( v) a - -dt St a (22) 28 where the index i refers to a particular distribution model (e.g., K1 = 0.943). The other models produced a similar result, differing only in the value of Ki’ see Table 3. Integration of Equation 22 gives a theoretical relationship describing the remaining catalase activity as a function of exposure time in the stirred tank a/a = e t (23) The measured activity of catalase after exposure to shear in the tank is plotted in Figure 8 and appears to be consistent with the assumed first order rate of degradation. Experimental values of the degra- dation rate constant St’ obtained from such data are listed in Table 3. The derivation of Model 4 required a different approach because it has a more fundamental origin. Model 4 may be written 5 = s e (24) where r is the radial distance away from the center of the tank, and k is constant. F ds (the volume fraction of fluid which is experienc- ing a shear rate between s and s+ds) when equated to a differential volume element is Fds = ——- (25) where dv is the differential volume and V is the total volume of the system. The shear distribution function can now be expressed 1H =1.—:<-—> 1... where the "chain rule" has been utilized to separate dv/ds into two 29 m.o u xa5m\=e5mi mm.~ _N.~ . _mu=mevemaxm _m.F F_.P emm.o .e m~._ Na.o new.o m mm._ mm.o eem.o N ee._ ao._ mem.o _ goow u c goo? u we Fave: _-=_e mo_ x um 2am scam u z i>\a:v >N cg u 3m «\— .mu_:mmc cowuuczw :owpzawcumwo Lemcm .m epoch 3O .vvu .uoom u h .ZQm ooom u z o . . .F-uam mp.m u a _-=.e e-o_ x mm Q, n pm .xcep umgcwum on» cw we?“ mcamoaxm mzmem> xuw>wuom mcwcmmEmm $535.: .05: Agar .w mesmwm a ‘9 C) :5 °e/e ‘Kiganoe Bugugewau 31 easily acquired derivatives. The derivative of r with respect to s (from Equation 24) is _ 1 ' k? (27) (1'0. U’ '5 The change in volume fraction of the tank with respect to r is 1 dv _ 2nhr V3?" v (28) where h is the height of the fluid in the tank. By substituting Equations 27 and 28 into 26 one obtains _ Znhr F — Vks (29) When Equation 24 is substituted for r in Equation 29 the shear distri- bution function becomes ~2nh ln(s/s Vk2 s x) which is a function of the variables 5 and the unspecified constants k and Smax' Equation 24 can be rearranged to express k as a function of s (the minimum shear rate which the fluid experiences at the 'min wall of the tank). k _ -1" (Smin/Smax) (3]) - R Substitution of Equation 31 into 30 yields the form of Model 4 which is shown in Table 2. F = [ln(s -2 112 ]n(:/Smax) (32) min/Smax Unlike the other models examined, Model 4 is a two parameter model (Smin’ Smax)’ therefore the e1im1nat1on of Smax with Equat1on 20 y1e1ds 32 a value of K4 which is a function of s . . m1n The maximum value of K4 is obtained when 5 equals Smax’ which min is tantamount to a process which has a single shear rate, such that Equation 19 becomes P)]/2 V5' (33) s=( One can, therefore express the rate of degradation directly from Equation 11 as R. = ZV a (3%)”2 (34) which implies that K4 equals one. The deactivation rates predicted by the various models (as a 1/2) and the experimental degradation rate constants function of P measured in the stirred tank are shown in Figure 9. Because of the small differences in the predicted rates, it is difficult to choose the better model, however this is advantageous since it implies that the predicted rate is insensitive to the form of the shear distribu- tion function. The agreement between the predicted rates and the ex- perimental rates is acceptable when one considers that Equation 22 contains no adjustable parameters, and the viscometer experimental error inherent in measuring such small deviations from the initial activity. The attractive aspect of this result is that the form of the prediction is consistent with the data (i.e., degradation rate is proportional to P1/2). Degradatlon rate constant. St x103, Figure 9. 33 3 — ll 2 L- ‘. 14a 1 2 ’ 4b 3 1 " 4c .1 «4d 1 J- (J 15 1C) ‘1 2 53 1 2 P/ X 10 , lorg/eecll 1/2 Stirred tank degradation rate constants versus P . 0 Experimental points. Numbers refer to shear distribu- tion models. T = 20°C. 4c, Smin/Smax 0.010; 4d, Smin/Smax 0.100; 0.001. 34 Stirred Tank Power Measurement The use of Equation 21 to predict the rate of enzyme degradation requires knowledge of the power requirements of the tank. The dimen- sionless equation for agitator power in a stirred tank is given by (15): (35) where ND is the power number, NRe is the Reynolds number and ”Fr is the Froude number. These dimensionless numbers are defined by the equivalent equation: N335p = K (Qifl)m(ll_:_0_)n (35a) where: P = power N = frequency of revolution 0 = impeller diameter v==kinematic viscosity p = density 9 = gravitational acceleration K, m, n = empirical parameters. In general, at high Reynolds numbers (3_104) m is equal to zero, and if the tank is baffled n is equal to zero, therefore the power number is constant and power is proportional to N3 (8). For stirred tanks, power is related to torque by P = Tq (2nN) (36) where the quantity in parenthesis is the rate of angular displacement. 35 Dynamometer measurements of torque were used to calculate power in the stirred tank at various values of N and v, Figure 10. Although this tank was baffled, the power number is constant with respect to Reynolds number only for constant Froude numbers, which is similar to the re- sults obtained by Rushton gt a1, (15) in unbaffled tanks. The Froude number represents a ratio ofinertialto gravitational forces and affects the shape of the liquid surface (24). Large waves were observed near the baffles, and since maintainance of a vortex in an unbaffled tank is responsible for a Froude number dependence (24), it is presumed that these waves produced a similar result in this tank. This effect would be minimized in a larger tank where the waves would be dissipated over the larger surface area. Because of the Froude number effect, torque was found to be linear with the frequency of revolution N (see Figure 11) such that one may write: T = K' N (37) where K' is constant. If Equations 36 and 37 are substituted into Equation 22 one obtains t T T Equation 38 suggests that the degradation rate constant is propor- 1”N which can be seen in a plot of experimental data itional to p measured at various temperatures, Figure 12. The intercepts on Figure 12 could not be distinguished from zero for an 80% confidence interval (14). A similar result would be expected in a stirred tank operating 401 P 36 V + a 2 g NFr.Oo79 A .0 W H‘— S 10- : : NFrI1.79 o a A g — n‘ a 1- 0 NFr'3.17 — NFr.4096 —-—O— p,— 4" NF,- 1.14 ‘T l l l l l 1 A l J L J L l L] 4 10 10 RGYnolds number, "Re Figure 10. Power curve for stirred tank. 1) = 0.01307 cmz/sec o 0 = 0.01002 cmZ/sec o v = 0.00326 cmZ/sec A 37 000m .omm\~Eo Nompo.o OOON :_E\>om > .zam mzmcm> mzacou umcsmmme emmeoEeczo COOP .FF acsmci is. lCON LOOm 8. wo-au/(p ‘01 x alleOL 38 .725 to x 2:3 u SN .28 u 2 $.72... mv.2 x m: u SN .22 u 2 6.725 -2 x 24 u N .9; n 2 .< .z N: o : mzmcm> magnumcoo mum; cowumomemmc xceu umccwum uric... N\_ 80m ESE .z a: 3. 00¢ Omm COM 0mm CON On. 00. On .N_ meamta 1 ID 1 9 1 1n 0 N 1 IO N 0 r0 |_'u1ul ‘v01xlg ‘luoisuoa 910; uouopoibeg 39 in the viscous region where Equation 37 would also be valid. In general however, with a baffled stirred tank in the turbulent range, 3)1/2 the degradation rate should be proportional to (uN but this has not been demonstrated here. Activation Energy of Degradation Increasing temperature accelerated the rate of deactivation in the viscometer (Figure 7). If one assumes the rate of enzyme degra- dation in a shear field follows classical reaction kinetics, temper- ature dependence of the rate (Equation 11), can be described by an Arrhenius relationship: 2 = z e'E/RT v v0 (39) where the parameter 2 and E are the frequency factor and activation vo energy respectively, and R is the gas constant (1.987 cal/g mole °K). Values of Zv obtained from Figure 7 for various temperatures were fit to Equation 39, see Figure 13. Equation 11 now becomes R = 2 Te- a (40) The frequency factor 2 and the activation energy E obtained from a v0 least squares fit of the data were 0.262 cm sec/g and 7564 cal/g mole respectively. Equation 40 implies that catalase molecules must acquire a critical energy E from the shear field before they will degrade. The 'E/RT therefore, is the fraction of molecules that Boltzmann factor e have attained this energy, and the product ZvoT is the rate at which this fraction degrades. 40 m —r O) 7 Degradation parameter, valo, cm-seC/g A O) I l J 1 .1. 9° .5 3.5 3L6 l/T x 10‘”, 1/°K 1 Figure 13. Viscometer degradation parameter, Zv versus 1' . E = 7564 cal/gmole. O Worthington catalase; o Boehringer- Mannheim catalase. 41 Experiments using the Boehringer-Mannheim catalase (without albumin) were also carried out and the resultant values of Sv and Zv are shown in Figures 7 and 13. These results were not used to calcu- late the Arrhenius parameters of Worthington catalase (with albumin), but were included to show that they are consistent. As observed in the viscometer the rate of activity loss in the stirred tank increased with temperature, Figure 12. If shear induced catalase degradation is an activated process, then the activation en- ergy should be the same in any flow system. The Arrhenius relation- ship for the stirred tank (Equation 38) is 2 =2 43/“ (41) t e to Experimental values of Zt versus T'1 are shown in Figure 14. The activation energy from the stirred tank was 6825 cal/g mole, which is consistent with the value of 7564 cal/g mole obtained from vis- cometer data. This excellent agreement in activation energy in two greatly different flow systems supports the theory that enzyme deg- radation is an activated process and that the activation energy is quite small. 42 1/2 lcm- sec/9| 6) Degradation parameter, Zt x10, J l I l 3.4 3.5 3 _1 3.6 1/1 x10, K Figure 14. Stirred tank degradation parameter, Zt versus T']. E = 6825 cal/gmole. VI. DEGRADATION IN POISEULLE FLOW Laminar fluid flow in a pipe (Poiseulle flow) exhibits a radial velocity profile which is maximum at the center of the pipe and de- creases parabolically to zero at the wall. The analysis of Poiseulle flow of an enzyme solution through a pipe is an interesting problem because it possesses characteristics of both the viscometer and the stirred tank. There is a distribution of shear in the pipe as in the stirred tank, but at any radial position the shear rate is constant as in the viscometer. In the analysis of the stirred tank it was assumed that the fluid was well mixed and the activity throughout the fluid was constant which allowed the integration of Equation 17. In laminar pipe flow however, a fluid particle remains in its' lamina as it travels down the length of the pipe and mixing occurs primarily through molecular diffusion. This situation was examined by develop- ing two limiting cases: (a) assuming the fluid is radially well mixed, and (b) assuming no radial diffusion. These results are com- pared to the experimental data of Charm and Wong (5). Pipe Flow with Complete Radial Mixing If radial mixing is assumed, the shear distribution function can be used to estimate the rate of deactivation in the pipe. This function can be derived with the use of Equation 26. Shear rate in Poiseulle flow is given by 43 44 s = -Apr/2uL (42) where r is the radial distance from the center and Ap is the pressure drop along the length L of the pipe (3). The derivative of r with respect to s is then: Let ds AP (43) The derivative of v with respect to r is given by Equation 28 and the product becomes 2 F = EEL_EI = IBELE. (44) VAp DzAp where D is the diameter of the pipe. Substitution of r with Equation 42 gives the shear distribution function for the pipe. uL}ZS =32 155—p (45) If Equations 11 and 45 are used with Equation 13 the folowing integral is obtained: 2 _U_L)S _ s - I’max Zv (us) a 32 (DTp ds (45) This is analagous to Equation 17 derived for the stirred tank and as previously discussed the activity will be treated as a constant in the radial direction. An expression for smax can be obtained from Equation 42 by substituting the pipe radius for r. The integration of Equation 46 yields: 12439021,Ha (47) 9 6L which is the total rate of activity loss in the pipe. Since this 45 model assumes complete radial mixing, the shear exposure time is the residence time in the pipe which is given by (3): t = "—RO—X (48) where R is the radius, 0 is the volumetric flow rate and y is the axial distance. Thus the rate of degradation in the pipe can be ex- pressed in terms of pipe length with the use of Equation 48. 2 R : :_d_a_ : _-Q. d_a_= 9.9—2. Fig. (49) p dt 0R2 dy 32 L dy Substitution of Equation 47 into 49 and integrating the result yields an expression for the remaining activity in the fluid leaving the tube -16 '—§— B a/a = e (50) o B = Zv U L/D (51) where B has been defined far later reference. Equation 50 is a model predicting the remaining activity expected after an enzyme solution has passed through a pipe of length L and diameter D in laminar flow, assuming complete radial mixing (curve 8, Figure 15). This is the same result obtained by Charm and Wong (5) using a different approach. Pipe Flow Without Radial Mixigg Since the activity of enzyme varies radially in this model, the shear distribution method (i.e., Equation 13) is not appropriate. A different method is used in which the degradation rate in a differential element of fluid (andrdy), with constant activity, is integrated over the length of pipe L, then over radius to give the total rate of deg- radation in the tube. The ratio of total rate of degradation to the 46 new Scene 50cm mew mucwoa Feocmswcmaxm one .Aev ago: .mcwxwe Pawnee mumpgsou mossmwm m m>c=u .mcwxwe Parent 0: mosammm < o>c=u .mnzu m canoes“ zap» emcwsmp emcee >u_>waom mcwcmemm > 9.1 Nnm -o. -o. -o. . _d3. U 0 ho hb Z 0 4m m w Cm CC I 0 m~Q Z4 3 2&4 Cw 0 w 01 G 0L1...“ C u. 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