a u '0 ‘ . )I. . up 0 I 4"”..7‘: (if Huh) . , I. Ofi‘bl-JHOQ‘n 1?-.. .c... ‘0'! u' Q 5v: .10”! x I .OJ 5 nth .. 4- u“ 5. Untulh‘ 4.".' .‘I 'a"’.' a {.1- = " l 'I' .' 453-4.! ‘ My .c... A , ‘ h: “V ‘ .v I . .VK II‘ a u.‘... . ‘ v ,0. .1 . f ; c . ‘ I (It [ll 0’ ii. ‘ o .9. t . o. v- 1 -I ...-.L.v..: f- ‘ lvurlf . r0411- .77.l\l!¢ufl.;lto.nhvi tv:‘-‘|.'l. a .caluhuhc av . Inl' pit/5‘ illuvlfnlt. .‘Dvl $1.?! . .. . . . y .- . in .t1. $3211....om. ' ‘5’ 0 a ‘I “'>‘.‘AI' .‘L‘ b..' A .9'13 .I. .b;«u.-1f. . (I!!! J . >4 'I; . o - ill. )0I Vit'; In I \v a ’h’ot‘v’ljiltt I I'Iv'v IIHHWHOO’M..D Livif¢lnvflo u {II I all. . ‘ . u » 4|. : I t c. m. . ”1“” .u a ’1. I o no. :u. .v v WW” .0. A” v o . .. I I v ”N: . 3%? _ .. . , . , . ‘ .w A». .ll.l .rrldePhwwoban-E‘umfl .r . ‘ [r I V ‘ II! II libWWIWTTUHWIW| 3 1293 00097 6682 no We 9 g...” arr-'9‘? b ‘..-‘, an I I: a .- Ira-1 hv 1,;hi 'i .‘4';‘£--Msv-- “Vi—‘9 L?-...,__- 2.. _ ‘1 ”oi. f‘ 'g‘ "._ "‘---~- 1 v‘—“i’ This is to certify that the thesis entitled THERMODYNAMIC AND KINETIC ASPECTS OF HUMAN ERYTHROCYTE HEMOLYSIS IN HYPERTONIC SOLUTION OVER TEMPERATURE RANGE OF ~11) Ti) 2:} C presented by Amir M. Fallahi has been accepted towards fulfillment of the requirements for Ph.D degree in Mechanical Eng. Major professor Date Feb 6,1986 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution RETURNING MATERIALS: )VIESI_J Place in book drop to LIBRARIES remove this checkout from as; your record. FINES will 4___ be charged if book is returned after the date stamped below. m i ." r- rv t~‘<"~"“ I 2391')! mmmnmmc AND mumc ASPECTS or HUIAN mmaocmz annousrs IN armmurc scurrrou oven TEMPERATURE 11ch or -10 m 25°C. By Alix I. Fellehi A DISSBTATION Submitted to Iichigen Stete University In pertiel fullfillnent of the requirlente for the degree of DOCTOR OF PHILOSOPHY Depert-ent of lechenicel Engineering 1986 7Z>Eio§7;? Copyright by AMIR M FALLAHI 1986 ABS'IIACT mnmnmurc MD KINETIC espacrs 0F 1mm nmnocm amusrs IN nmmrc smUImN OVER MATURE RANGE 01? -10 m 25 c By Alli I. FALLABI Ihernodynenic end kinetic enelysis of bio-elbrenee subject to therlel end che-icel perturbetione is epplied using the hunen red blood cell ee e nodel systel. Since cheeicel end thernel effects occur sinulteneouely during the freezing end theeing of living cells. e complete dete bese in the for. of the he-olyeis kinetics es e function of solute concentretion end tenpereture is genereted for the hunen red blood cell. To decouple the cheeicel end the thernel effects en inproved stop-flow systel equipped with tenpereture control hee been designed end developed to neeeure the destruction dynelics of the red blood cell. The stop-flow technique provides very repid airing end therefore the denege dynenice for short tines (order of seconds) is obteined. This technique represents e definite edventege es oeupered to the etenderd technique for henolyis neeeure-ent (inferred by stetic neesureeent of the he-oglobin ebsorption) eith cherecteristic tines on the order of severel minutes. Specificelly. the he-olyeie kinetics for the hunen red blood cell populetion induced by un-buffered sodium chloride solution e beteeen 2- end 4- ere Amir I. Fel lehi presented for tempereturee between -5 end 25'C. It. :gt. of the destructive hemolysis reection is cherecteristicelly very repid et short times compered to thet et reletively long times for ell temperetures end concentretions. The eppeerence of neesureble delege in the stop flow device is deleyed for sub-embient temperetures. The cherecteristic tine (deley time) is on the order of 3.5 minutes for Zn concentretion. ebout 1 minute for the 2.5- concentretion end severel seconds for higher concentretions. Competed to room tempereture. the demege process et sub-embient temperetures proceeds et higher retes for reletively long tines. Thet is. the trensition from the initiel repid retes to the finel slow retes ere smoother end deleyed. The lergest effect of the reduced tempereture in survivel is observed when the isothermel tempereture is dropped from 25 to 10.0. Further decreeses in tempereture heve oomperetively less significent effect. The hemolysis process is treeted es s chemicel reection of the blood cell semple end hypertonic sodium chloride solution. The tempereture end the sodium chloride concentretion dependence of the hemolysis kinetics is interpreted in terms of the 1st end 2nd order rete lews for short exposure times. The thermodynemic ectivetion peremeters essocieted with these kinetics heve been enelysed. 0n the besis of these results. it is postuleted thet dissolution of one or lore membrene components is responsible for cell injury due to the exposure to hypertonic sodium chloride. A theoreticel ergument in support of the dissolution theory is given. Tb my perents. Jeved end Afkhem .. wife. Sims ... end sons. Kienoosh end liemere ACKNOILEDGEIENT I would like to thenk the nembers of my diesertetion committee Professor IcGreth. Professor Tien. Professor Anderson end Professor Atreye for their guidence throughout this effort. A speciel thenks is due to my thesis edvisor. John IcGreth. whose enthusiesn end dedicetion to reseerch inspired his students including the euthor of the present work. _His commitment to science end his fentestic personelity crested the most pleesent reseerch end leerning environment. My deepest epprecietiou nust go to ny perente end my wife whose love. encouregenent. end uuderstending helped us overcome the most difficult situetions throughout these neny yeers. ii TABLE OF (”NWT Pege Lfi't 0f T.bl.'0000000000.....OOOOOOOIOOOOO00.000.000.000.0.0.0'111 Li't Of Fi'u.‘OOOOOOCOOOOOOOOOOO0......00............OOOOOOOO x Ch‘pt.‘ I: InuodnctionOOOOOOOOO0.0.000...OOOOOOOOOOOOOOIOO... 1 A. B‘ck'toudeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee s B. .Od.. 0t Fr..z1n' Dn‘.........OOOOOOOOOOOOOIOOO0...... 11 Chepter II: Iembrene Structure. Function end Iodel lubrene Systems.................................. 24 A. The Cell Function...................................... 25 B. lembrene Structure end Function........................ 27 1. Chemicel Composition................................ 28 2. Physicel PrOperties of lubrene Components.......... 31 e. Lipids........................................... 32 b. Proteins......................................... 36 C. Inbrene Properties.................................... 37 1. Chemicel............................................ 37 2. lechenicel.......................................... 39 D. Forces end Iembrene Self Assembly...................... 45 3. “ht“. ‘“.1..OOOOOOOOOOCOIOOOO......OOOOOOOOIOOOOOOO 48 Chspter III: Osmotic Behevior of the Cell..................... 52 ‘C "t.: A..°°t.t.d '1th lubr‘n00 O O O O O O C O C C O I O O O O O O O O O O C O 55 B. ouotic Pt.‘.u.eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee a C. Osmotic Response of the Cell........................... 63 D. Description of Osmotic Demolysis....................... 69 Chepter IV: Brperimentel System............................... 74 A. Introduction to the Stop Flow Systen................... 76 B. Iejor Components....................................... 79 1. Delivery System..................................... 80 2. Opticel System...................................... 86 3. lining System....................................... 88 4. n.n.l conuOI sy.t-OOOOOOOOIOOOOOO......OCOOOOOIO ” Chepter V: Operetionel Cherecteristics end Celibretion of the Stop Flow System................................... 92 A. Generel Cherecteristics................................ 92 1. Initiel Trensient of Output Signel.................. 96 2. The Cell Volume Effect-Minimum Volume Stete......... 102 D. Celibretion of the System.............................. 107 1. Celibretion of Percent Demolysis es s Function of Nornelised Photocell Voltege........................ 108 2. Celibretion of Percent Demetocrit es s Function of n°t°°.11valt‘..eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee 113 iv Chepter VI: Bxperimentel Procedures for Determining Demolysis Kinetics.......................................... A. Cell Dendling.......................................... B. Procedure for the Determinetion of the Bemolysis Kinetics due to en Isothermel Dypertonic Step Chenge of the Entrecelluler Concentretion........................ C. Control Experiments.................................... D. Possible Source of Error in leesured Demolysis: Sheer B££.°t .. .R.‘u1t°f I‘Did “ixin'eeeeeeeeeeeeeeeeeeeee Chepter VII: Bxperimentel Results end Comperison 'ith Other Iorks............................................ A. llemolysis et Different Temperetures Due to Osmotic Perturbetion........................................... B. Comperison of Present Dete Iith Respect to Berlier 'ork By 0th.: I“..t1'.t“'.0000......OIOOOOCOO0.0.0.0000... Chepter VIII: Iechenism end Ceuse of Cell Injury es s Result of Erternsl Perturbetions....................... A. Ceuse end Iechenism of Injury.......................... 1. Ceuse............................................... 2e ".0huia0000.......0.............OOOOOOIOOOOOOOO.... B. Theoreticel Argument in Support of the Dissolution 119 119 121 125 127 136 137 165 173 173 174 177 Theory................................................. 1. Surfece Tension-Surfece Pressure.................... 2. Thermodynemic Development of Equetion of Stete of Bileyer lembrene-supporting the Loss of lembrene u.t.r1‘l.........OOOOOOOOOOOO......OOOICCOOCOOIOOOOO Chepter IX: Thermodynenic end Kinetic Treetnent of Eemolysis D. Dete.............................................. Introduction........................................... Eemolysis Ieection.................................... Pete Lew end Dete Constent............................. 1. First Order leection (lets Lew)..................... 2. Second Order leection (Dete Lew).................... 3. Iechenism........................................... Thermodynemics of Ieection letes....................... 1. Tmmpereture Dependence of the Pete of Reection: The Arrhenius Equetiou.................................. 2. Free Energy end Energy of Activetion................ 3. Enperimentel Activetion Energy...................... Chepter X: Conclusion end Suggestions for Future Iork A. conclu.i°nl......COOOOOOOOOOOOOO......OCOIOOOOOOIOOOOIO sn.‘.‘tion' for Fat“. 'orkOOOOO......OOOOOOOOOOOOOOCOO vi 185 186 190 200 200 203 205 210 211 213 214 214 216 219 240 249 '.£.t.nc.'0......OOOOOOOCOOOOCOOOO............OOOOOIOOOOOOOOIO 253 ApmndixOOOOOO00......0......0.0.............OOOOOOOOOOOOOOOOO 267 vii Teble 2.1 2.2 5.1 5.2 5.3 6.1 6.2 6.3 LIST OF TABLES Pege Approximete Protein end Lipid Content of Severel ‘-b:‘n..000000000000.0.0.0...IOOOOOOOOOOOOOOOOOOOO ” Overell Composition of Eunen Erythrocyte lembrene... 3O Normelised Photocell Voltege et 45 Eemetocrit es s motion at N‘Cl “al‘rity.........OOOOOIOOOOOOOOOOO 105 Celibretion of Percent Eemolysis es s Function of "M‘li'.d not“.ll valt".IOOOOCOOOOCCCO......... 111 Celibretion of Photocell Voltege es s Function of P.rc.‘t n-‘t°°r1t000000.00.00.00.00.......OOOOOOO. 116 Comperison of Percent Eemolysis for Enternelly lined end Innuelly Injected Semples with Semples lined end Delivered Through the Stop Flow System... 129 Percent Eemolysis es e Function of Injection Pressure(3m NeCI et.2981).......................... 131 Percent Eemolysis es s Function of Injection Pt."u.(3-N.CI ‘t 268‘)OOOOO.....OOOOOOIOOOOOO... 132 viii 6.4 6.5 7.1 7.2 7.3 9.2 9.3 Percent E-olysis es s Function of Injection ”...“.(4- N.c1 .t 298‘)OIIIOOOIOOOOOOOOO0.0.0.... Percent Euolysis es s Function of Injection Pr."u.(4- N.c1 ‘t 283‘)OOOOOO......OOOOOOOOOOOOOO "A" Velues (E5 - EtuA) for Different Time Int.".l..............00.000.000.00.......OOCOOOOOI lete of Percent Eemolysis et 40 end 60 Seconds..... Initiel Euolysis Eete (percent per second)........ Ieection Eete Consteut end Activetion Energies for 1st end 2nd Order Eeection lete Lews............... Activetion Peremeters for 1st end 2nd Order R0‘0t10n n‘t. Lu'OOCOOOOOOOOOOCOO......OOOOOIOOOO. The (Tc- DA S’Velues for Different Eeection c0“iti°‘.eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ix 133 134 147 149 lfl 212 222 236 LIST OF FIGURE Figure 1.1 1.2 2.1 2.2 3.1 ‘01 4.2 4.3 4.4 5.1 Survivel Signeture for Verious Cell Types.......... A Iethod for e Supercooled Cell to Achieve EquilibrinOOOO0.00.0000.........OOOOOOOOOOOOOOOOO Typicel Phospholipid Structures.................... Cross-Sectionel Diegrem of Steble Phospholipid su‘ctu.‘ in "t.r000000000......OOCOOOOIOOOOOO... Diegremetic Representetion of the Shepe Chenges. From Disk to Sphere which Occur During the Action 0‘.npi°.1Ly'ineeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee Stop m" sch-‘tic.00.000.000.000.........OOOOOOOO Top end Side Views of the Solutions Reservoir...... 8°h-.tic 0‘ a. “18111. uniteeeeeeeeeeeeeeeeeeeeeee Schemetic Representetion of the Shutoff lecheninn.. Percent Emmetocrit Delivered to the Observetion Pege 12 33 35 71 77 81 84 85 LIST OF FIGURES Figure 1.1 Survivel Signeture for Verious Cell Types.......... 1.2 A lethod for e Supercooled Cell to Achieve 2.1 2.2 3.1 4.1 4.2 4.3 4.4 5.1 Equlib‘inOOOC......OCOOOOOOO......OOOOOOO....... Typicel Phospholipid Structures.................... Cross-Sectionel Diegrem of Steble Phospholipid sunCtu.. in "t.r.OOOOIIOI0.00.0.0...00.0.0...... Diegremetic Representetion of the Shepe Chenges. From Disk to Sphere which Occur During the Action o:.hp1°.1Ly.in.......0............COOOOOOOOOOOI Stop F1" sch-‘t1c.......OOOOOOOOOOO......OOOOOOOO Top end Side Views of the Solutions Reservoir...... sch-‘t1001 th. .ixin‘ unitOOOOO......OOOOOOOOOOOO Schemetic Representetion of the Shutoff Iechenism.. Percent Eemetocrit Delivered to the Observetion Pege 12 33 35 71 77 81 84 85 5.2 5.3 5.4 5.5 5.7 7.1 7.2 Chember es s Function of Plunger Pressure.......... Nonnulised Photocell Voltege es s Function of NeCl .OI‘t‘ty in Ab..nc. 0‘ 3100‘0000000000000000......O Normelired Photocell Output es s Function of Normelised Lump Voltege for Opticel Chember Filled with Normel Seline end Blood et 4‘ E-etocrit...... The Initiel Trensient Effect of Cell Orientetion... Nurmelised Photocell Voltege es s Function of NeCl .01u1ty00000000.0.0.0.........OOOOOOOOOOOIOOI.0... Celibretion Curve for the Determinetion of Percent Eemolysis es e Function of Normelised Photocell valt".000000O............OOCOOOOOOOOO......OOOOOOO Nornelised Photocell Voltege es s Function of n-.to°rit....0.00.00.00.00.0.......OOOOOOOOOOOOOIO Typicel Photocell Voltege Output Due to Isothermel Step Chenge of the Entrecelluler Concentretion..... Percent Bemolysis es s Function of Exposure Time et xi 95 97 100 106 114 117 138 140 7.3 7.5 7.6 7.7 7.9 7.10 7.11 Percent E-olysis es s Function of Exposure Time et Percent Eemolysis es s Function of Exposure Time et 218‘000000000000000000.0.0.000...O ......OOCOOOOOOC Percent Eemolysis es s Function of Exposure Tine et 273‘0000000....0.0.0.0.0000.........OOOOOOOOOOOOOOO Percent Buolysis es s Function of Exposure Time et 26“.00.000.000.00...................COCOOOOOOOOOOO Initiel B-olysis Rete et 40 end 60 Seconds........ Percent Buolysis es s Function of Exposure Time et 2 moler NeCl Concentretion......................... Percent E-olysis es s Function of Exposure Time st 2.5 moler NeCl Concentretion....................... Percent E-olysis es s Function of Exposure Tine et 3.0 moler NeCl Concentretion....................... Percent E-olysis es s Function of Exposure Time et 3.5 moler NeCl Concentretion....................... xii 141 142 143 144 150 152 153 154 155 7.12 Percent Eemolysis es s Function of Exposure Time et 7.13 7.14 7.15 7.16 7.17 7.18 9.1 4.0 moler NeCl Concentretion....................... Initiel Buolysis Rete et Different NeCl C°n°.nu.ti°n.eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee Percent Initiel.flmnolysis Rete es s Function of N.CI hl‘tit’.t”8‘.nd213‘0000000000.0.0.000... Comperison of Eemolysis Kinetics et Selected Tumperetures end Concentretions of NeCl............ Percent Eemolysis for Exposure Times of 1 end 3 Iinutes es s Function of Thmpereture............. Normslised Photocell Voltege es s Function of n-.t°°rit...........OOOOOOOOOOOOO0.00.00.000.00... Conperison of Percent Bemolysis Celibretion Dete with the Results Reported by Others................ Cbmperison of Present Results with Results of Other In'..ti'.t“.....0.0.00.0000........OOOOOOOOOOOO... The Reletionship Betneen Free Energy of Activetion end NeCl Concentretion for 1st order Reection xiii 156 158 159 161 162 167 169 170 9.2 9.3 9.6 10.1 “.1000000000O0.0.000.........OOOOOOOOO00.0.0.0... 223 The Reletionship Between Free Energy of Activetion end NeCl Concentretion for 2nd Order Reection ladol...0.0.0.00....IO......OIOOOOOOOOOOOOOOOOOOIO. 224 The NeCl Concentretion Dependence of Pseudo- Reection Constent K for 1st Order Reection Iodel.. 226 The NeCI Concentretion Dependence of Pseudo- Reection Constent K for 2nd Order Reection lodel.. 227 The Reletionship Between the 1st Order Eyring Activetion Peremeters S end B for Rypertonic NeCl-Induced Eemolysis for 1st Order Reection I“.IOOOOOOOOO00......0.0.0..........OOOOOOOOOOOOOO 230 The Reletionship Between the 2nd Order Eyring Activetion Peremeters S end B for Rypertonic NeCl-Induced Bemolyeis for 2nd Order Reection “.100000000000000000000....OOOOIOOOOOOCOOOOOOOOOO 231 The Schemetic Representetion of e Iodel Describing the Effect of Bypertonic Solution on the lembrene sy.t~............OOOCOOOOOOOOOOOOO.........IOOOOO. 24s ixv CHAPTER I INTRODUCTION In recent yeers the surgicel technique of orgen trensplentetion hes been en eree of very ective experimentetion in medicine. New surgicel techniques heve been developed end orgen trensplentetions of heert. liver. end kidney heve become the most promising hope for extending humen life. Success of such e trensplent relies heevily upon the eveilebility es well es the viebility of orgens et the time of need. Tb overcome the time fector en effective preservetion technique needs to be developed. One of the most promising preservetion techniques et the present time is offered by low tempereture technology. deey through cryopreservetion techniques severel clesses of "simple" biometeriels such es blood. spermetoxoe. cornee. skin. end embryos ere reversibly preserved for periods es long es 3O yeers [1-5]. However. for the more complex biometeriels such es orgens no sueeessful cryopreservetion technique hes been developed. In order to extend the scope of cryopreservetion to more complex systems such es the heert or liver e deteiled understending of the celluler behevior et low temperetuxes is required. Fundementel thermodynenic enelysis in conjunction with kinetic theory of the reections end processes involved in e cryopreservetion protocol could provide the besis for the development of celluler behevior in response to low temperetures. The purpose of this work is eimed et providing e better understending of the demege susteined by living cells es s result of chenges which occur in the celluler environment during the process of freeze-preservetion. Specific environmentel chenges of interest ere the effects of high solute concentretion (e chemicel effect) end low tempereture exposure (e thermel effect). 'hen the liquid phese of weter is excluded from the cell suspension through the formetion of ice. there results en increese in the extrecelluler solute concentretion. This increese in the extrecelluler solute concentretion creetes en osmotic pressure which sets es s driving force for the flow of weter out of the cell. The chemicel effect end the strong tenpereture dependence of meny life processes constitute two mejor mechenisms in cell freezing. According to Resur's clessic two-fector hypothesis for freezing injury the slowly frozen cells ere demeged on the one hend by their reletively long exposure to high solute concentretions. This is the so-celled "solution effect". Furthermore. repidly frozen cells ere demeged es s result of intrecelluler ice formetion [6]. The chemicel end thermel fectors ‘ ere then necesserily inter-releted in e given freezing end thewing protocol. Thet is. The chemicel end thernel veriebles ere coupled during e freezing end thewing process. Therefore e complete. decoupled. end quentitetive understending of cell injury ceused by thermel end chemicel effects is essentiel for developing e thermodynemic nodel describing e freeze-then protocol. A decoupled study of the thermel end chemicel effects responsible for the cell demege during freezing should yield en importent understending of the degree end extent of injury ceused by eech perturbetion node. Cryopreservetion is e thermodynemic process where kinetics pley en importent role since it is known thet the survivel of biologicel systens is usuelly sensitive to cooling end werning retes [7]. Studies of the cell response to the thermel end chemicel perturbetions cen therefore generete kinetic informetion ebout the cell injury. Thermodynemic enelysis of kinetic informetion genereted by such studies provides dete for the development of e thermodynemic model for the cell injury mechenism(s). Therefore. the mein objective of this work wes to study independently the effects of thermel end chemicel perturbetions on the kinetics of red blood cell hemolysis. Specificelly it wee intended to determine the kinetics of demege to the humen red blood cell system induced by sodium chloride solutions of different concentretions st different tmnperetures. Even though hemolysis of erythrocytes hes been the subject of extensive studies essocieted with low tempereture preservetion [8-11]. the eree of study proposed here hes received little ettention. In this ,work the kinetics of hemolysis of the humen red blood cell in the fore of rete informetion is obteined. Demege histories of cells subject to "chemicel shock" is quentified et different temperetures. Specificelly. the demege induced by sodium chloride solutions between the concentretions of 1 molel end 4 molel is studied es s function of time for temperetures between-5C end 25C (the retionel for these renges of concentretion end tempereture is given in chepter IV). Tb enelyze the cell injury process. e thermodynemic epproech will be teken. The reection rete theory of Eyring will be employed to reduce the rete dete to obtein thermodynemic ectivetion peremeters such es enthelpy. entrOpy. end Gibbs free energy for the hemolysis process. The role of these peremeters in the stebility of the celluler system reletive to the proposed injury mechenism will be investigeted. Such en epplicetion of the principles of thermodynemics in conjunction with kinetic theory of reections will result in en importent clessificetion of thermel-chemicel effects on cell demege modes. This reseerch is expected to heve e significent impect on the eree of low tempereture preservetion. An improved understending of the effects of sinulteneous thermel end chemicel chenges eccompenying freezing should help to improve cryopreservetion protocols for e wider cless of biologicel systems including tissues end orgens. A better understending of the elteretions experienced by biologicel systems in terms of thermodynemic end reection rete theory hes the potentiel to provide e better conceptuel fremeuork for further reseerch from the theoreticel stendpoint. Furthermore. simuletions end predictions of celluler behevior in erbitery environments besed upon quentitetive models mey be possible in the future. Even though the model cell system for this study wee limited to the humen red blood cell. it is hoped thet the experimentel techniques end theoreticel nethods used here es well es the overell understending geined by this reseerch could be generelized to e lerger cless of biologicel systems. 'LW Living systems contein e substentiel emount of liquid weter end it is epperently necessery for e minimum emount of liquid weter to be present in most living systems to insure viebility. Therefore nost biologicel systems exhibit "nornel" behevior only et temperetures ebove OC. It hes been known for centuries thet the deterioretion process of bioneteriels could be severely slowed down or even stopped et low temperetures. This effect of low t-peretures in the reduction of metebolic ectivities of biologicel systems hes been employed in modern industriel scele food stuffs preservetions for meny yeers [12-14]. The potentiel of freezing preservetion es s promising clinicel technique for long term preservetion of biometeriels use not reelized until the 20th century. The fect thet living orgenisms ere in generel disesterously injured when exposed to subzero temperetures wes probebly the most importent fector limiting succesful cryopreservetion. The first successful freezing preservetion of biologicel systems occurred in 190 . when Polge. Smith. end Perks [15] reported the first successful freezing technique. Their work wee primerily concerned with the preservetion of humen end fowl spermetozoe. Since then the field of cryobiology hes been en eree of very ective experimentetion. This hes resulted in the development of clinicel scele reversible low tempereture preservetion techniques for severel biologicel systems including the humen erythrocyte. cornee. skin. end embryos [1.3.4.5]. Due primerily to its clinicel velue. the humen red blood cell hes received some of the most intensive oonsideretions. This hes in turn resulted in the development of very successful cryopreservetion protocols enebling blood benking for long periods of time [16-18]. The lerge biOphysicel dete bese eveileble for the humen red cell elso mekes this system e very ettrective model system. The generel uncontrolled effect of cooling of "living“ orgenisms to subzero centigrede temperetures results in injury end consequently "deeth" of such systems. A review of the cryopreservetion techniques in cryobiology reveels thet two of the most importent fectors controlling the fete of the biologicel system ere the cooling rete during freezing end the nermiug rete upon thewing [7319-24]. It is elso known thet the storege time end storege tempereture pley very importent roles in the success of e freeze-thew process. It should be pointed out here thet the presence of some crycphylectic egent. sometimes referred to loosely es entifreeze egent or simply entifreeze. is essentiel for the success of e cryopreservetion technique. The most commonly used cryophylectic egents ere glycerol end dimethylsulfoxide (DISO) [5.7.17. 23.25]. The presence of e cryophylectic egent will greetly complicete the enelyticel es well es experimentel enelysis. It will elso reduce the hemolysis reection rete considerebly meking it difficult to study the demege mechenism. Therefore. in the present work in order to simplify the system under study us well es emphesizing the demege to leern more ebout the ceuse. the effect of such egents vill not be considered. Among the controlling fectors mentioned eerlier. the effect of cooling rete hes received the most ettention. This is pertly due to the fect thet if the system is severely demeged during the freezing stege of the process. consideretion of the effect of other fectors becomes unnecessery. Figure 1.1 . shows representetive survivel percenteges of different cells es s function of cooling rete [23]. In spite of the feet thet optimel cooling retes differ from cell to cell (renging from 0.3 C/min for lymphocytes to 3000 C/min for humen erythrocytes) the cell survivel curves heve similer generel shepes. The results presented in Figure 1.1 reveel thet increesing the cooling rete of frosen cells is only beneficiel up to e point end once this point is reeched further increese of cooling rete will heve e negetive effect on the survivel. This hes suggested to some reseerchers the existence of two competing mechenisms responsible for detenining cell survivel [6.26]. Cooling the cells more slowly then et the optimel rete results in the injury thought to be due to the complex elteretions of the celluler environment due to the presence of extrecelluler ice. These physiochemicel elteretions ere collectively referred to es "solution effects" end include chenges in the concentretion of solutes. dehydretion of the cell. chenges in the pl of the solution. end subsequent decreese of the cell volume [8.9.27]. As the cooling rete is increesed the survivel increeses which is r23 eceeueuee Uuu veeeveuaeu. cook. :5 enoaue> ecu ensuing 155a an; enema.— .m. >2osu> 02.800 .0. am: m: w . . .b. \\\\ 10 interpreted to meen thet the increesed cooling rete reduces the solution effects. However. the survivel is diminished when biologicel systems ere cooled et supreoptimel retes. The demeging effect of supreoptimel cooling retes hes been cleerly demonstreted. both experimentely end theoreticelly. to be due to the intrecelluler ice formetion during freezing [24.29-35]. Thet is one ceunot increese the cooling rete beyond the retes et which lethel intrecelluler ice will form end survivel will be diminished. The ection of these tuo competing fectors is menifested in the survivel signeture of the cells (Figure 1.1). Studies of werming rete heve reveeled thet the effect of the werming rete is directly coupled with the cooling rete. For fest cooling rete the survivel is echieved et fest werming retes end similerly better results ere obteined st slow werming retes when the cooling rete is slow [7.8.23.32]. Storege time for systems stored et eny tempereture other then zero ebsolute tempereture will heve e negetie effect i.e. the survivel rete is improved es the storege tempereture is lowered [33.34]. Storege time effect studies on survivel retes reveel thet et temperetures below -6OC these effects ere minimel end thet the survivel of cell systems seems to be e strong function of storege tempereture in'the renge 0f ’5‘? to '60C [7s25s33e341e 11 LMfimflmn The generelly eccepted theory of freezing denege is due to Iezur [6.26]. where he proposes e two-fector model of freezing demege. Iezur's two-fector theory represents e convincing ergument in which en ettempt is mede to describe the low tempereture effects in biologicel systems subject to slow end repid cooling. Before discussing the freezing demege in deteil it is necessery to define severel terms commonly used in such e discussion. nemely such terms es "slow” end "repid" freezing. The concept of slow end fest freezing is generelly defined in light of intrecelluler crystel nucleetion or in terms of dehydretion of the cell. Freezing velocity is considered to be "slow” when only extrecelluler crystelizetion occurs. Vhen the freezing process results in intrecelluler crystel formetion the cooling rete is considered to be ”repid". It should be noted thet these terms ere reletive. so thet repid for e given cell type mey be slow for enother. In e freezing process regerdless of cooling velocity the weter trensport ecross the semipermeeble cell memhrene is directly linked with the survivel of the system under study. A simple model system presented in Figure 1.2 describes the weter trensport events essocieted with cell freezing. The system is considered es two compertments sepereted by e sphericel semi-permeeble menbrene resulting in en intrecelluler end en 12 m M M . em M M ICE M Mf‘ww m M \ :@’/: ; WATER FLUX M M M M M M M M M INT RACELLULAR ICE DEHYDRATION EAST CCKNJBKS .SLIMN'CCKNJhNS Figure 1.2: A Iethod for e Supercooled Cell to Achieve Equilibrium (reproduced from reference [31]). 13 extrecelluler compertment. At equilibrium the chemicel potentiel for solutes eble to diffuse ere equel in the intrecelluler end extrecelluler solutions. The formetion of ice in the extrecelluler solution results in e lowered chemicel potentiel of weter outside the cell with respect to the weter inside. A new equilibrium cen be reeched by either trensport of weter out of the cell or intrecelluler ice formetion. This metter will receive further ettentiou in conjunction with discussion of red blood cell h-olysis in Chepter 3. According to Iezur's two-fector hypothesis. when cells ere frozen slowly the demege is essocieted with reletively long exposure to the physio-chemicel elteretions of the cell system produced by crystelizetion of liquid weter (the so celled "solution effects" discussed eerlier). Vhen cells ere frozen with repid cooling retes the formetion of intrecelluler ice is the mejor fector responsible for demege. The implicit essumption here is thet the cells ere thewed et optimel werming retes. A quelitetive ergument eccounting for Iezur's theory besed on the model system given in Figure 1.2 follows. During e freezing process es discussed eerlier the tempereture reduction of the cell suspending medie results in crystelizetion of extrecellulet weter. During the eerly steges of freezing the membrene ects es s berrier to ice formetion within 14 the cell. As the extrecelluler liquid weter is trensformed to solid weter by ice formetion e solute concentretion gredient is developed ecross the supercooled cell such thet the system (the cell) is removed from it physiochemicel equilibrium stete. But since the cell membrene is permeeble to weter s new equilibrium stete cen be esteblished by wey of the flow of weter out of the cell. If the formetion of intrecelluler ice is to be evoided there should be sufficient time for the cell to loss its free weter to evcid supercooling. This meens if the cooling process is slow enough the cell will not freeze internelly or et leest lerge emcunts of weter will not solidify. At such slow cooling retes then. the cell will be exposed to high concentretions of solute for e reletively long period of time end the subsequent solution effects one result in injury. The slow cooling rete is cherecterized by the dominence of mess trensfer (weter flux ecross the cell membrene) over the best trensfer process. Now if the cooling rete is repid. intrecelluler supercooling occurs in e short time. The cell is uneble to lose e considereble portion of its weter content end it becomes increesingly probeble' thet the intrecelluler weter will freeze. Specificelly. et fest cooling retes the best trensfer process cherecteristicelly dominetes the mess trensfer process so thet the intrecelluler weter hes little time to leeve the cell end the ebundence of weter in the cell predisposes the interecelluler ice nucleetion to occur. 15 Besed on the ebove ergument it is evident thet the following cell peremeters cherecterize the optimel cooling rete for survivel: (i) the permeebility of the cell to weter (ii) the emount of celluler free weter (iii) the surfece eree to volume retio. As pointed out eerlier end is evident from the proceeding ergument the mechenisms of freezing injury ere very involved end compliceted phenomene which ere yet to be resolved. Bowever. et the present time there exists substentiel evidence suggesting thet the elteretion of the plesme membrene could be e mejor if not the only. mechenism responsible for freezing demege [45.46]. At this point heving discussed the problems involved in cryopreservetion end heving emphesized freezing es the nejor ceuse of injury. e few words ere in order to clessify the mechenism of injury. The formetion of ice in the freezing process. intrecelluler or extrecelluler. could definitely introduce considereble stress end therefore mechenicel demege to the cell et the membrene site en well es et the internel level. The demege to the cell could occur either during the freezing or when the system is thewed. However. the hemolysis phenomenon due to freezing of red blood cells in isotonic seline solution is. in some ceses dupliceted by 16 the hemolysis due to hypertonicity of the extrecelluler solution in the ebsence of freezing [8]. Furthermore freeze-induced chenges of spinech thylekoids hes been observed to he similer to those observed by trensferring thylekoids from en isontonic to hypotonic [37] or hypertonic medie [38]. Thet is the neture of thermel shock demege is similer to osmotic shock.demege. Severel biologicel menbrene systems heve been studied with respect to the biochemicel end structurel elteretions of the membrene induced by freezing or osmotic stress in the ebsence of freezing [35-42]. The object of such studies is the phenomenon of cell demege due to extrecelluler perturbetions which hes been postuleted to be e result of membrene elteretions. he notion thet freezing injury is due to injury to the plesme membrene wss first proposed by leximov in 1921 [43]. he importent role of the plesme membrene in the function of the cell. end the feet thet the emount of demege incurred by the presence of externel ice is considerebly lower then the level of demege introduced by intrecelluler ice formetion ere in direct egreement with this notice. The direct involvement of the membrene constituents in the phencmene of cell demege due to osmotic or thermel shock hes been observed [8.44]. It hes elso been shown thet intect red blood cells or ghost cells exposed to hypertonic sslt conditions resulted in solubilisetion end releese of membrene proteins~ end phospholipids [10.11]. Perheps the most intringing ere 17 observetions mede by Areki [45] end Areki et el [46]. where they found thet red blood cells exposed to osmotic stress st or below 0C lose their nembrsne lipids end proteins by virtue of relessing cholesterol-enriched microvesicles. A similer observetion hes been mede on rst hepstocyte cells recovered from freezing [47]. In his studies releted to the effect of hypertonic treetment of membrene structures et low tuperetures. Areki showed thet such treetments result in the releese of microvesicles. Be showed thet the lipid end protein content of the microvesicles were different from the red cell membrene. Be wee elso eble to show thet the retio of cholesterol:phospholipid (C:P) in microvesicles wss dependent upon the tempereture of the treetment. The lower the tempereture of the treetment. the higher the (C:P) retio [45]. Areki et el further found thet the totel protein content of the microvesicles decreeses with decreesing tempereture [46]. These observetions suggest e tempereture end tonicity dependent preferentiel segregetion of membrene constituents due to osmotic stress end low tempereture exposure. The noleculer segregetion end mechenism of vesicle formetion induced st low temperetures ere not cleerly understood. Nevertheless. occurence of such processes suggest e significent tempexture end tonicity dependence of the membrene protein-phospholipid intersction end consequently e membrene domine ted injury mechenism. 18 Grunze et el in their studies observed moleculer segregetion of the red blood cell membrene et room tenpereture due to treetment with long-chein elcohols [48]. Such treetment results in development of rod-sheped projections. The rods cen be sepereted from the cell without significent hemolysis. Preferentiel l’ipid segregetion in the membrene wes observed where protein content of the cells end the rods remeined the sums. Despite the ebundence of studies concerning the red cell shepes due to environmentel pertubetions. the question of "whet is responsible for the red cell shepe in generel end shepe chenges in perticuler:is it the bileyer or the spectrierectin network?" hes been e controversiel issue. In the study of hypertonic cryohemolysis (the erythrocyte hemolysis in e hypertonic environment when the tempereture is lowered to below ebout 120 is celled “hypertonic cryohemolysis" [49-51l). Green et el heve presented evidence for the possible indirect effect of the hypertonic environment on the spectrinrectie cytoskeletel system [44]. These investigstors suggest thet the membrene lipid intersction with the cytoskeleton mey be responsible for injury. This notion is in line with results suggested by severel studies where the red cell membrene shepes ere due to elteretions in the cytoskeletel network [52-55]. On the other hend. Lenge et el concluded from their studies on the shepe of the red cell membrene thet the membrene bileyer end not the cytoskeletel proteins is 19 responsible for ghost cell crenetion [42]. They believe thet oemoticelly induced redistribution of lipids between the two leeflets of the membrene bileyer proceeds end results in the ghost creenetion. Concerning whet constitutes freezing or hypertonic exposure injury st the celluler end moleculer level. it is believed thet the loss of membrene msterisl pleys en importent role [47.48]. This notion is strongly supported by Areki's findings frtn his work on the red blood cell thet the low t-pereture induces lipid end protein segregetion in the membrene end es s result of hypertonic exposure et sub-zero temperetures the membrene msterisl is lost in the form of microvesicles [45.46]. Furthermore Steponkus end co-workers besed on studies on spinech protoplest propose thet freezing demege is due to loss of membrene msterisl [47.48.79]. Specificelly. they propose e hypothesis of exchenge of msterisl between the plume of the membrene end e reservior of membrene msterisl induced by en increesed tension imposed in the membrene during freezing. The erguments given here suggest thet freezing or hypertonicelly induced stresses result in tension or increesed pressure in the plene of the cell membrene. This is concomittent with e significent redistribution end loss of membrene constituents end consequently of the surfece eree end cell volume. 20 Therefore the notion thet the membrene is the site of demege or et leest thet mejor demege is st the membrene site is e well justified essumption. All the evidence end theories put forwerd emphesize thet in order to resolve the uncerteinties of the demege processes end mechenisms. e complete understending of the neture of forces end moleculer interections et the moleculer level is required . Due to the biologicel neture of the problem it hes been extremely difficult to errive et such en in depth insight st the moleculer level. This. however. does not meen one should eweit such en edvencement end ben exploring different end in some ceses simpler epproeches. No theoreticel epproech could eccount for ell the peremeters of such e complex system. end direct experimentel meesurements should elweys be considered the most relieble method to check the theoreticel findings. One such epproech is provided by thermodynemics. Thenmodynemics in connection with biologicel systems hes been e reletively forgotten tool in meny ceses even though it offers quentitetive es well es quelitetive methods of enelysis. The process of cryopreservetion is in feet e thermodynemic process. The ultimete goel of such e process is to errive et cryopreservetion protocols such thet the system under consideretion is returned to its initiel thermodynemic stete. thet is the tesk involved here is to design e cyclic thermodynemic process for the cell. Therefore methods of enelysis of such 21 process should be besed on fundementels of thermodynemics. Thermodynemic is e quentitetive subject end it cen be employed to enhence our quentitetive understendings of structure end function of living system. For exemple. regerding the membrene system. equetion of stete informetion besed on principles end fundementels of thermodynemics cen in principle be derived by direct meesur-ents. Furthermore. concerning the development of Physics of the membrene interections end knowledge of ultrestructure of such systems. cherecterizetion end quentitetive clessificetion of thermodynemic peremeters such es entropy. enthelpy. end energy is required. Fcr exemple. the entropy end enthelpy chenges essocieted with the hemolysis intersction form e velueble besis for the interpretetion of the thermodynemic peremeters concerning the moleculer orgenizeticn of the cell membrene es releted to environmentel peremeters. A clessicel thermodynemic method of enelysis is concerned with equilibrium stetes. i.e.. it yields stetic informetion. however. es discussed eerlier. the survivel end degree of injury es s result of freezing end thewing is very sensitive to cooling end werming retes involved in such e process. Therefore to clessify the injureous cherecteristics of such e dynemic process. kinetic informetion is needed. Thet is to study the hemolysis intersction. e kinetic reection rete theory is required to compluent the thermodynemic enelysis. The present effort deels 22 with the hypertonicelly induced osmotic hemolysis kinetics of humen red blood cels et different temperetures. Specificelly the osmotic shock espect of the so-celled "solution effect" freezing injury is considered. The dete obteined here is in the form of demege histories obteined when humen red blood cells ere subject to step chenges in extrecelluler concentretion et verious isothermsl set points. As discussed eerlier Lovelock showed thet injury due to freezing of red cells could be dupliceted by exposure to hypertonic sodium chloride if the cells were returned to the isotonic stete [26]. Be elso concluded thet hypertonic exposure elone is not in itself demeging enough to explein the totel emount of injury observed when red blood cells ere frozen end thewed. In light of Lovelock's findings the erythrocyte hemolysis hes been re-exemined here for the following reesons. It is well known in cryobiology thet frozen end thewed cell recovery cen be very sensitive to the rete of freezing end thewing. It is therefore importent to study the demege process on e rete besis in order to ccrrelete the extent of demege with the exposure time et verious temperetures end concentretions. Dete of this form ere not eveileble in the litereture. Also. hypertonic sodium chloride induced hemolysis hes never been interpreted in terms of the Eyring rete equetion. This hes been done for the present results to suggest the mechenism by which osmotic thock ceuses en 23 instebility in the humen erythrocyte membrene. thereby lending to hemolysis. As will be seen the mechenism suggested by thermodynemic ectivetion properties derived from the Eyring equetion is consistent with the membrene dissolution theory offered by Lovelock [57]. Chepter II IENBRANE STRUCTURE. FUNCTION AND NDDEL IEIBRANE SYSTEMS In order to pursue the cell freezing problem end ecquire en understending of fectors or processes effecting the extent of the subsequent cell injury. one neturelly must ecquire sue primery knowledge of the cell end cell membrene structure end function es well es the properties of the constituent elements comprising such structures. Furthermore. study of the neture of the intersctions end forces between membrene constituents which ere responsible for the formetion end stebility of such syst-s is essentiel for interpreting the celluler response to externel perturbetions. In this chepter. the cell function will be discussed first. Secondly. since the cell membrene pleys e significent role with respect to e successful freezing protocol emong other things. membrene structure. function end composition will be discussed in deteil. Third. generel properties of the membrene ere discussed in reference to the effects of the externel perturbetion imposed on the cell. Fourth. the self-essembly of the lipid end protein 24 25 molecules into e membrene structure in en equeous medium end the roles pleyed by the intermoleculer forces in connection with such e process is discussed. Finelly. membrene models will be considered. 1.1119111211931123 The living cell is the fundementel unit of structure in biology. It is the besic unit meking up en orgeniem of greeter complexity. The besic types of cells heve been cherecterized: prokeryotes end eukeryotes. Prokeryotic cells ere cherecteristicelly smell end posses minimel interecelluler structure. Specificelly they do not possess nuclei. nucleer membrene or chromosomes. On the other hend. eukeryotic cells ere much lerger end contein numerous interecelluler orgenelles in perticuler nuclei end chromosomes [59]. leny reletively lerge orgenisms mey posses e single cell (the protists). The unity principle in biology is errived et due to striking similerities emong the structure end functionel orgenizeticn of cells in orgenisms. Regerdless of the complexity of the celluler structure of en orgenism. it is essentiel for the survivel of the cell. es en individuel end es s species. thet eech cell cerries out its besic functions. These functions include: 26 1)Acquisition of nutrients end energy sources. 2)Disposel of unuseble end toxic meteriels. 3)Reproduction 4 )Locomoti on 5)Interection with the environment To cerry out the forementioned functions every cell must regulete between its internel ectivities end the environment. An outstending cherecteristic of the cell is thet the reletionship between the intrecelluler ectivities end the extrecelluler environment is reguleted by en encepsuleting envelope. The interior of the cell is mede up of needed components end orgenelles of widely differing structure. chemicel composition end functionel behevior. Iithin the cell the ectivities mey occur either in e reletively undifferentieted internel milieu or in e series of functionelly distinct. but coordineted. regions which ere themselves sepereted by en envelope. The integrity of these components end consequently by the cell's internel mechinery necesserily depend on the encepsuleting envelopes. 27 memm The cell envelope. celled the plesme membrene elso known es the cytoplesmic membrene or cell-surfece membrene. encepsuletes the cytoplesm end defines the bounderies of the cell while creeting internel components in which essentiel functions ere cerried out. This mey exist elone or be pert of s more complex cell-surfece structure. No single structure for the membrene cen be described. Its complexity veries considerebly. end cen teke on e number of forms eccording to the physiologicel functionel role of the cell [60]. A single cell cen elso heve severel different erees of plesme membrene with different morphology end function [60]. Biologicel membrenes et the cell sufece end within the cell ere of lipoprotein structure. i.e.. ere mostly composed of lipid end protein molecules Electron microscopy hes reveeled e cherecteristic trilemeller feeture of the lipoprotein membrenes [61]. The microgreph imeges of these membrenes eppeer es peirs of perellel dense .1ines sepereted by e less dense region. This trilemeller feeture corresponding to the plesme membrene in different cells is typicelly 70-1501 in 'idth. In membrenes of intrecelluler orgenells the thickness is 50-801. 28 meuwm Two mejor constituents of biologicel membrenes ere proteins end lipids. Composition of membrenes veries from cell to cell but in generel the dry weight of the membrene is 405 lipid end 60% protein. The lipid content of the bit-embrenes renge from 20% in becteriel end inner mitochondriel to 80% in myelin plesme membrene of the dry membrene weight [$.60.62.63]. Protein end lipid content of some membrenes ere compered in Teble 2.1. end the overel composition of humen erythrocyte membrene is given in Teble 2.2. In eddition to lipid end protein the membrene conteins weter. the most importent constituent of eny known biologicel system. lembrenes contein ebout 20b of their totel weight es weter which is e very ective perticipent in ell membrene intersctions [64.65].Iuch informetion ebout the weter in the membrene hes been obteined from celorimetric end nucleer megnetic resonence (NI) studies [65-68]. These experiments distinguish e weter component in the membrene possessing different properties then bulk weter. This weter is referred to es “bound" weter. Another technique which hes provided very useful informetion ebout the stete of weter in membrenes is x-rey diffrection. (The metter of weter in the membrene will be discussed further in Chepter III.) Such 29 TABLE 2.1 Approximate Protein and Lipid Content of Several Menbrances Cholesterol; W III E .1... Myelin o 3 1.00 Liver Plasma Menbrene 1.0 0.40 Red Blood Cell 1.0 0.30 EndOpIasmic Reticulun 1.0 0.06 Mitochondrial Otter Meninanc 1.0 0.06 Mitochondrial Inner Meubrsne 3.0 0.03 3.0 Bacterial Mentrene 0.00 .Weight Ratio “Molar Ratio. 30 TABLE 2.2 Overall (imposition of l-hxnen Erythrocyte Mcnbranes Caucasus. W Protein 49.2 Lipid (total) 43.6 Phospolipid 32.5 Cholesterol 11.1 Carbohydrate (total) 7 Sialic Acids l chosemines 2. Neutral Sugars 4 31 studies have confirmed the essential importance of the water content for the integrity end maintenance of the biological membrane structure [59.60.69.70]. From these experiments the water associated with the membranes is broken down as i) bulk water 90$ ii) bound water 105 iii) irrotetionelly bound water 10-20 molecules. ‘Irrotetionelly bound water molecules are known to be located within the protein interior. LMWMWW In general membrane components are emphiphetic; i.e.. they posess two different natures. polar and nonpoler. The polar nature is due to the fact that they are charged species. These emphiphetic molecules are in active interactions with one another and polar water molecules. From energy considerations the optimal stability of the system is attained when the free energy of the system is minimized. Therefore. the emphiphetic molecules in an aqueous environment. should form a structure such that polar elements comprise one phase and nonpoler elements. the other [71-73]. The structure of an emphipatic molecule is shown schematically in Figure 2.1. 32 Characteristic mejor lipid components of the cell membrane are phosphoglycerides (more commonly referred to as phospholipids). The red blood cell contains four major phospholipids and one major neutral lipid [59.60.74]. The different types of phospholipids differ in size. shape and electric charge of their polar heed groups. However. these molecules have a similar overall structure as illustrated in Figure 2.1. They possess two hydrocarbon chains derived from long chain fatty acids. The hydrocarbon chains are normally 14-24 carbons long. Various types of lipids exist in harmony in the cell membrane. These lipids are esymetrically arranged with respect to the two halves of the bileyer [75.76]. For example. in the erythrocyte membranes. amino phospholipids (i.e.. phosphatidylserine and phosphatidylethenoleminc) are mostly found to be located in the inner layer. where lipids in the outer half are mainly phosphatidylcholine and sphingomyelin [76]. All phospholipids (at pH7) have a negative charge essicieted with the phosphate group. Phosphetidylcholine and phosphatidylethenclamine (at pH7) ere dipolar zwitterions with no net charge. as their head groups have a positive charge. Besides the variations in the head 33 T x.“ 8'93 rm: ‘ (l) mu PEOSPEATEATIDTLE‘EB‘QANINE P READ x""cng'Cls""'.' (CB,), /|0 HOSFBATIDYLGG. IN E Circe-cu. Nut (I) (I) Notroue x—tn,-¢|:n-coo" (Ii-0 l0"0 TAILS HOSFEOTIDYLSBINB a. L Figure 2.1: Typical Phospholipid Structures. (8. and R. are Hydrocarbon Chains 14-24 Carbons Long). 34 group charge and size. the hydrocarbon tails vary in length and degree of saturation. These considereble variations are believed to play a significant role in the functional and structural classification of biological membranes. To represent lipid molecules. the following shorthand representation is adopted. The polar head groups. are represented by filled circles. whereas the hydrocarbon tails are represented by straight or wavy lines. According to minimum free energy analysis. the hydrophilic region also called the polar head group should be in‘ contact with the aqueous environment [73]. On the other hand. fatty acid chains in order to be stable should be sequestered from contact with the aqueous environment. Now in light of this thermodynemic consideration we shall consider the arrengment of such emphiphetic molecules in an aqueous environment. The thermodynamic stability criteria can be accomplished by lipid molecules forming a "micelle". A cross sectional diagram of a micelle is shown in Figure 2.2 where it is illustrated that the polar heed groups are on the surface in contact with water and the hydrocarbon tails are hidden from the aqueous environment and form an internal hydrophobic phase. In the hydrophobic phase the hydrocarbon tails are mostly in interactions with one another. 36 Another arrangement fullfilling the stability criteria is formation of a biomolecular sheet structure generally called a "lipid bileyer". Due to its nature such a lipid bilayer in an aqueous medium will form a completely closed structure. A schematic diagram of such a closed vesicular bileyer structure is represented in Figure 2.2. The matter of molecular organization of the membrane lipid will be further discussed later. Lannie! Proteins are responsible for many of the biological activities of the cell membrane [77]. Proteins also play very important role in the structural makeup of the cell mubrane [78.79]. For exemple the red blood cell cytoskeleton protein network is essential for cellular functional and structural integrity [77.79]. Iembrane proteins are classified in two categories: intrinsic or integral proteins and extrinsic or peripheral proteins. Extrinsic. also referred to as membrene-essocieted. proteins are electrostatically loosely bound and are easily separated from the membrane by such treatment as reducing the ionic strength or altering the pH of the suspending medium. However. the intrinsic proteins are deeply embedded in the 37 m-bxane and are associated with lipids. lembrane proteins are responsible for most of the dynamic processes carried out by the membrane such as transport. communication. and energy transduction. Some proteins are very mobile. and freely move in the lipid matrix. These proteins include. rhodopsin [80]. bacteriorhodopsin [81] and those associated with ion transport. The red cell membrane contains about 40 types of proteins [74]. The stability criteria discussed for lipid molecules is applicable for protein molecules as well. The non-polar nine acid residues of these molecules should be sequestered from contact with the aqueous environent and the ionic and polar regions should be in contact with the aqueous medium. Lhahrmhnnuin Lmlfxmmn hbrane processes take place through chemical reactions. The constituent molecules of membranes are mostly lipids and proteins. and their specific distribution give the membrane its unique ch-ical identity. Therefore any kinetic or thermodynamic analysis of the membrane cyst- must take into account the chuical nature of the processes involved. For example. importent 38 properties of the membrane system such as activation energy or the total energy are purely due to chemical reactions in such a systn. Ibmbranes are very selective pcrmeeblility barriers. This is due to the existence of specific molecular pumps and gates at the membrane which regulate the selective transport of matter across the biomenbrene. Besides regulating the active transport the mubrane composition is also important to regulate passive transport. The major constituents of thet-umbrenes. lipid and protein molecules. work in a very cooperative manner to give the cell its characteristic transport properties. The relatively small lipid molecules form layers which act as barriers to the flow of polar molecules. On the other hand the larger protein molecules serve as gates. pumps. energy transducer. and enzymes. Another important aspect of the chuical properties of the cell membrane is that its shape is astrong function of the chemical composition of the environment. In the .... of the erythrocyte cell. depending upon the chemical make up of the suspending media the normel biccncave shape goes through several variations. such as. stometocyte (cup shepe). echinocyte (creeneted spheres) and a class of shapes commonly referred to aa myelin figures [82-84]. Vhile some of these shepe transformations are reversible. some are associated with hemolysis [82.85.86]. 39 In haehanical £1221£111£ An important consequence of the perturbation of the cell system is the observed shepe changes. This implies the existence of mechanical stress and physical forces on the membrane. Any descriptive analysis of the membrane system then must include the mechanical properties of the membrane. Thermodynemically speaking. the ultimate goal is to arrive at the thermodynamic equation of state of the model membrane system. Such an equation could be derived from direct measuruents of the mechanical properties such as interfaciel membrane tension as a function of tapereture and surface density. A classic theoretical development of mechanical behavior of membranes by Evans and Skelek [87] deals with the above topic. The monolayer system is a much simpler system than the bilayer system and has been studied extensively over the years. For this reason this syst- has been used to interpret the mechanical and thermodynamic properties of membrane systems. Ioncleyer surface pressure versus area behavior is studied for nuercus lipid molecules which gives the internal equation of state of such a system. However. one can not define a surface pressure for a closed membrene syst- in the same manner defined for the monolayer systu. Furthermore. the surface pressure of a membrane system cannot be directly measured in contrast with the 40 monolayer system. The definition of the surface pressure could eventually lead to the development of an internal equation of state. Since the surface pressure could be considered as a negative tension. surface pressure and surface tension within the membrane are suetimes referred to as interfaciel membrene tension. The surface pressure is a strong function of temperature and surface density and therfore area changes by definition. On the other hand the surface tension is a weak function of area changes [87]. The red cell membrane for example is very resistant to changes in area. In fact a few percent membrane area increase results in membrane rupture whereas it can be sheared easily. his is due to the fact that the red cell membrane elastic shear modulus is 4 to 5 orders of magnitude smaller than the area compressibility modulus (Bending modules. a. 1. of order 10*13 to 10'"2 dye/cm [87]). From the thermodynamic point of view the energy expenditure associated with bending a red cell m-brane is quite small and negligible compared with membrane tension [88]. (Sheer modulus. in. and compressibility modules. k. are of the order 10"2 dye/cm and 10'-10' dye/cm respectively [87]). However free energy variation caused by local deformations in the outer layer of, the membrane with respect to the inner layer could result in 41 relatively large bending moments (essential for the shape stebility). Therefore considereble energy storage in bending may result: such is the case for example for e creaneted cell or echinocyte formations. mmmumw The formation of lipid structures such as micelles. lipid bilayers. and liposomes is e self-assembly process. This process is due to the structural and functional characteristics of the fundamental units of such systems. namely their amphipathic character. Any physical and thermodynamic understanding and analysis of the bicmembrene system requires a fundamental understanding of the intermolecular interactions involved in the self-assembly process. All the theoretical analysis for the red cell in this work will be based upon our model system. namely lipid vesicles or liposome. LNatmssd-Rnlsufficrm Surfece phenomena in general and stability and formation of lipid bileyers in particular are a direct consequence of interatomic and intermolecular forces. For exemple the existence 42 of a surface or interfaciel tension is due to the unsymmetrical force field at the interface. Molecular orientation at any liquid interface is also a direct consequence of intermolecular forces. The hydrophilic head-groups of lipids in bileyers are subject top strong interactions with each other. with the surrounding aqueous medium. and with nearby bileyers (if such bileyers are near). These interactions and hydrocarbon chain interactions are all interdependent and it is this intimate interdependence which manifests itself in the formation and is responsible for the stability of lipid bilayers. Three importent interactions encountered in surface physics will now be considered. 1.31.2111! ion A strong repulsive force arises when atoms or molecules are brought in or near contact. Basically. the repulsion effect is a manifestation of the Pauli exclusion principle (that the electron clouds could not overlap each other). Steric interaction depends upon the size of the atoms or molecules and it strongly depends upon the seperation distance of such particles. For steric interaction various functional forms for the potetial energy of the interaction have been proposed. A classic form is 43 E(r) ' W‘ ' g~12 lhere E(r) is the potential energy function and r is the distance between two particles (atoms or molecular groups). Another functional form E(r) is E(r) I b‘EKP(P/t) This latter form is preferred due to the fact that quantum mechanical erguments suggest that the interaction should be closer to being exponential than an inverse power. This functional form is used when molecules are modeled as hard. impenmaeable particles. e.g. hard spheres. discs or cylinders [89]. This repulsion is important only at atomic distances (<41), LWW The potential energy of interaction of two particles with °h|3803 1; and q. which are separated by distance r. is given by Coulomb's law as E(r) ' $413,: For two dipoles interacting with the field of the other the 44 interaction energy is given by E(u.n) ' -2n/r’ where n is the dipole moment. If the dipole were free to move which is the case in the biological system such as with bileyers. the combined effect of the dipole‘dipole interaction and thermal agitation should be considered. One such analysis due to Keesom [92] gives stand“... .. -zu‘lar‘rs‘ where K is the Boltzmen's constant and T is temperature. In case of complicated charge distribution one needs to also consider possibilities of higher level interactions such as dipole-quadrepole. dipole-octapole. quadrapole-quadrapole. etc. interactions. The electrostatic interactions play an important role in bileyers as the lipid heed groups are charged. The ionic or zwitterionic charges on the polar head groups are subject to mutual interactions while interacting with the dipole moments associated with water molecules. It is known that the extrinsic proteins are bound to membranes vie electrostatic and 45 hydrogen-bond interactions. Furthermore. the aqueous phase usually contains an appreciable amount of charged solute species. An ionizable nembrene surface will preferentially attract the oppositely charged ions and repel like charged ions. creating a region of nonuniform ion concentration. This region is referred to es the electrical double layer or the diffuse double layer. Exact treatment of the actual charge distribution is impossible due to its decorate nature. The Sony-Chapman theory combined with the specific ion adsorption and uniform charge distribution assumptions [90-91]. gives the surface charge density 0 and potential t of the charged membrenes. For the case in_ which the charge binding sites are negatively charged. the surface charge density is given by " ' ‘i/(1‘*‘co) [2.1] '50:. 61 is the initial charge density. K is an association °°“t“t' “d °0 is the concentration of free cations at the membrane surface. memmmm The origin of dispersion forces lie in the van der Veels 46 state equation of gases. This force also called the van der Iaals attraction force exists between neutral (uncharged) particles (atoms. molecules or group of molecules). The credit for the theoretical understanding is due to the works of Debye. Keesom. and London [92.93]. Debye in 1920 introduced induction or Debye forces and Keesom in.l921 introduced orientation or Keesom forces. which exist due to the permanent dipole moments of the atoms. Ihen these forces are comphred with the forces deduced from the van der Vaals equation. it is apparent that they do not account for all the existing forces. Furthermore. there exist forces between atoms or molecules possessing no permanent dipole moments such as rare gas molecules Hh N.. CH.. etc. pbtc.‘ of the type which exist between such neutral atoms or molecules are called Dispersion. forces. first introduced by Vang in 1927. An explanation for nature of these forces was set forward by London [92.93]. he noted that the neutral atoms and molecules do posses instantaneous dipole moments due to their zero point motion. This motion which is a direct consequence of the uncertainty principle creates a fluctuating dipole at the site of the atom or molecule. London gives the dispersion energy as E(r) ' -C/r‘ which is obtained through quantum mechanical calculations. Dispersion forces as implied by the above equation are long-renge 47 attractive forces. These forces are always present between two bodies possessing dipole moments. van der Iaels forces are made up of dispersion. induction and orientation forces. with the dispersion forces contributing most except in the case of very polar molecules where the orientation energy dominates. Hydrocarbon tails in the membrane interact mainly through van der Heels and steric forces. The van der Vaels forces between the tails favor close packing of the tails. Mandhmnfm The combined effect of all the forces in a given system will be to drive the system to its minimum free energy state. The force involved could be divided into two categories. Long-renge and short-range. In lipid structures. such as liposues and bicmembrenes. it is the short-range interfaciel forces that play dominant'roles. This is a reflection of the "soft" structure of lipid molecules which makes them very susceptable to any shape charges induced by short-range interfaciel forces. This is exactly the main reason for biophysical systems being so sensitive to any charges in the ionic strength or pH of the aqueous medium. 48 In summary. hydrOphobic interactions are the major driving force for the formation of lipid structures such as micelles and bileyers. These interactions play an important role in the folding of proteins in aqueous medium. Credit is due to favorable electrostatic and hydrogenrbonding interactions between heed groups and water molecules for the spontaneous formation of lipid bilayers in water. LMM The discussion presented in this chapter has revealed the complexity of the biological membranes both in terms of their properties and behavior. This is reflected in the experimental and analytical difficulties associated with studies of such systems. For example for any thermodynamic analysis the system must be clearly defined. The model systems are desirable and advantageous on the basis that it allows one to design and construct a structure in vitro with precisely known parameters which mimics the real systems behavior in vivo. The control over parameters of the model system is then possible where it may not be accessible with a reel membrane system. Study of known processes and properties which are associated with the reel system of the model will contribute considereble insight to the basic understanding of the real membrane system. However. one should 49 always here in mind that results obtained from such well-defined and controlled model studies must be interpreted in light of the reel system. To account for all the different types of lipids and proteins in the membrane in a membrane model system at this point is not possible. The problem is further complicated as all biological membranes have different components in their inner and outer surfaces and each surface has a different enzymatic activity. However. the major parameters of interest concerning this work appear to be independent of the fine structure of the membrane to a certain degree. Fur exemple. single component lipid vesicles which are commonlly referred to as liposomes mimic the low temperature behevior observed in living cells remarkably well and are widely used as a very useful model cyst- [94.95]. The current model for the gross organization of biomembrenes is the conceptual view of the fluid mosaic model proposed by Singer and Nicolson (1972). This model basically is a refined version of several earlier models. Gorter and Grendel in.1925 were the first to put forth the lipid bileyer picture as the basic structure of bin-branea D7]. The bileyer picture was accepted and retained by the subsequent models as an integral part of the membrane [98-100]. Development of the black lipid membranes commonly referred to as BLIa was perhaps the most important step in the development of the fluid mosaic model. luller et al (1962) 50 developed a method to form a thin membrane of a lipid mixture. BLIs have been extensively studied and have provided significant insight into the way the real membranes behave. However. these studies have concentrated mostly on the permeability and electrical properties. The reader is referred to an excellent reference by H.T.Tien for further details [102]. The essence of this model is that the membrane is a two-dimentional fluid of oriented lipids in which globular proteins are inserted. Proteins if not restricted by special interactions may pass from one side of the lipid matrix to the other. Proteins and lipids are also capable of rotational and lateral diffusion. In fact proteins are found loosely bounded to the inside or outside of the membrane as well as imbedded in the bilayer. This is a reflection of the role played by specific proteins such as transport. communication. and energy transduction. Therefore. proteins localized on the external side of the membrane allow communication with the environment. Accordingly. membrane protein involved in interecelluler activities should be located within or on the inner surface. This model does not account for interactions between lipid and proteins. where as. there is experimental evidence indicating significant association of proteins with lipids in the bilayer structure all pointing to existence of mutual interactions between proteins and lipids [103-105]. Proteins classified as "integral" or "intrinsic" interact extensively with _the hydrocarbon chains of membrane lipids. Furthermore. proteins 51 classified as "peripheral" or ”extrinsic" are bound to membranes vie electrostatic and hydrogen-bond interactions. again emphasising the interdependence of lipid-protein interaction. CHAPTER III OSUTIC B-AVIOR OF THE CELL Iater is the solvent vital for the structure and function of living organism regardless of their morphological complexity. The functional and structural as well as the morphological properties of the living cell are very sensitive to changes in the water content. The thermodynamic process of self-assembly discussed in the previous chapter is a dramatic example of the role of water in living cells. It is then not surprising that the most important environmental alteration of the cell system is directly associated with the state and amount of water. Here we will discuss the osmotic behavior of the cell in response to freezing and thawing damage as it relates to solvent water in such a system. Removal of water as ice during freezing processes of cell suspensions results in a decrease in the liquid volume of the system [23]. For a system consisting of a cell suspension the most important consequence of freezing. as it relates to the biochemical and biophysical as well as thermodynemic state of the system. is the accompanying increase in the solute concentration of the system. The removal of water during a freezing process is 52 53 therefore manifested in the perturbation of the osmotic equilibrium between the cell and its environment. Once the concentration of the suspending medium is increased above the physiological isotonic level and the cell is exposed to hypertonic conditions the cell will experience dehydration and volumetric reduction. These effects are collectively referred to here as osmotic stress. The osmotic stress and the molecular changes produced by high electrolyte concentrations may either result in an irreversible injury or leave the cell vulnerable to any further alteration of the system. This vulnerability for the cell system undergoing the cryopreservetion process could manifest itself in the thawing stage when the cell experiences further osmotic disequilibrium. It is then clear that the decrease of temperature during freezing and its increase during thawing result in an osmotic stress. This is a reflection of the fact that the damage caused by dehydration and high salt concentration in the absence of low temperature resembles the freezing damage [32]. In fact the major determining factor of the cell survival during suboptimal cooling is believed to be the direct result of the hypertonic exposure and the concomittent pressure gradient build up across the membrane as a consequence of the decrease of temperature [106]. Ihen the chemical equilibrium between the cell and its 54 environment is altered as a result of freezing. the chenical potential of the water across the menbrane will be altered. The living cell osmotically responds to such a perturbation by a change in volume. The osmotic behavior of the cell plays an important role concerning the site and extent of injury experienced by the cell exposed to osmotic stress conditions. Cells during a cryopreservetion process experience concentrations different from isotonic and these concentration differences result in a change in volume [23]. However. it is known that shrinkage of the cell is more injurious than the absolute increase in solute concentration [106-108]. This is directly reflected in a hypothesis proposed by Neryman and Iilliams which states: freezing injury is due to the alterations to the plasma membrane as a result of stress imposed by cell water loss [109-111]. The relation between cell injury and osmotic shrinkage in general and the relation between cell water content and osmotic pressure of the surrounding medium in particular are primary motivations to study the osmotic properties and behavior of the cell under different conditions. The physiochemical principles responsible for observed osmotic properties as a result of exposure to "severe" environments are not well understood at this point. his makes a thermodynamic analysis of the osmotic properties more appealing as such analysis will be based on well-defined and preceisly controlled parameters such as 55 t-perature and concentration. It should be noted here that the idea of the minimum cell volume is related to the cell injury is losing support (for other hypothesis regarding this matter refer to chapter 2 and 8). A. mmmmm he overall concept of the extent of involvement and amount of water in living systems have been recognized for many years. However. questions concerning the state and amount of water associated with membranes ruains unresolved. his is an added difficulty to any thermodynamic analysis of the membrane. Such a quantitative study has to deal with this prole at the outset where the system and environsnt are to be defined. he observation has been made that the red cell does not behave as an ideal o-ometer and that a portion of the cell water does not can to be affected by the change in the enviromental conditions. his has led to the belief that part of the cell water (called ”bound water") is associated with the membrane and has a structure and dynamic properties different than bulk water. his is a direct result of proximity and interaction of water molecules with the protein and lipid molecules residing at the membrane. In fact it is known that the bound water is associated 56 with the proteins and phospholipids at the menbrane. Existence of water with properties different from that of free solution would have great consequences concerning the transport across the membrane and the thermodynamic treatment of membrane system. Peter is a polar molecule which acts as an inert solvent in all living systems. Rolecules comprising the biomembrane are not soluble in water (negligible solubility of approximately 10" molecules for each water molecule [72]) and as was discussed in chapter 2 possess a dual nature as one part is attracted to water (hydrophilic) and the other is expelled from it (hydrophobic). In fact this dual nature is responsible for the self assembly of structures comprised by such molecules. Peter has a complex structure where individual molecules are linked to each other by hydrogen bonds which are known to be effected by the introduction of non-polar molecules. due to the hydrophobic effect [73,112]. Frank and Evans measured a negative entropy change when non-polar molecules where transfercd into water [731. The explanation for such energetically favorable process is given as follows. The water molecules at the surface of the cavity created by a non polar solute must be capable of rearranging themselves in order to regenerate the broken hydrogen bonds (in fact. where the enthalpy change is negative they may be slightly stronger than before). but in doing so they create a higher degree of local order than exists in pure liquid water. thereby producing a decrease in entropy 57 [73]. It has also been shown that the r-oval of bound water requires high energies (comparable to the binding energy in solid phase) which is a direct manifestation of the negative entropy of formation of such bonds [66.$.ll3]. lost of our knowledge on the amount and state of water in living systems is due to celorimetric. X-ray. and nuclear magnetic resonance (NR) studies. where the red cell has been the most widely used biological system for such studies [64.65.68]. hose studies have measured the amount of bound water to be 20h-405 (by weight) of the hydrated membrene (25-70 gm 3.0/100 .- dry membranes). According to X-ray diffraction and differential scanning calorimetry studies 20% hydration is required for membrane integrity [64] and phospholipid-cholestrol mixing [68]. his means the water is a major constituent of the bicmembranc. he aboundenco of water in the mubrane syst- is revealed when the 208-405 estimate of the water content is translated into the mole fraction. Ass-ing typical molecular weights of 100.000 for protein and 700 for lipids gives better than (10:1) mole ratio of water “the membrane. Rater content of base red blood cell is reported to be .68gm water/gm cells [114]. he NI studies on the state of membrane bound water suggest a more tightly bound water celled irrotetionelly bound water [Q]. his membrane bound weter characteristically has a more ice-like 58 behevior. Beats of binding of the irrotetionelly bound water has been measured and are similar to or greater than the heats of binding of water in ice [66]. The amount of tightly bound water for the red cell ghost membrane is 4$iof the dry weight which is believed to be closely associated with protein molecules [118]. At this point we will briefly discuss the role of membrane associated water in a more general format. As discussed in the foregoing section. the most important role of water is the consequence of its unique structure which is manifested in the inherent tendency of hydrocarbons to aggregate in the water environsnt. NI studies have shown that the dynamic molecular structure of the bound water is modified and is more ice-like. The modified molecular configuration seems to result in an increase in the diffusion across the membrane [115]. his is attributed to the fact that the free energy of bonding between water and water (when bounded to membrane) is very compatible with the free energy of attraction between water and nonelectrolytea in water. According to Horowitz and Fenichel hydrogen 'bonding by nonelectrolytea in water competes with water-water bonds which results in a local structure disorder and when the molecular structure of water is disrupted diffusion proceeds at faster rate [116]. It has also been pointed out that hydrogen bond formation leads to intramoleouler attractions which increase the intramoleouler spacing which is manifested in a decrease in the S9 density of hydrogen bonding molecules [117]. 8.911911921211151 An outstanding characteristic of the cell membrane is the discriminating nature which enables it to maintain meny substances at different concentrations across it. This enables the cell to regulate the movement of matter across the membrane i.e..mombrenes are permeable only to certain substances. Ihen a solution is sepereted by such a membrane. if the concentration of the non-permeable solute is different on the two sides. the solvent will tend to be drawn toward the higher concentration. Then what is called the "osmotic pressure" of the solution is the excess pressure which must be applied to the solution in order to prevent the mov-ent of solvent across the membrane. he osmotic pressure is therefore to be regarded as a thermodynamic property of the solution. Therefore in order to define the thermodynamic equilibrium conditions in living cells the first step is to consider and understand the principles and meaning of osmotic pressure in such systems. The movement of matter across the cell membrane is termed collectively as ”transport" or "osmosis". The thermodynamic quantity used to describe the transport phenomenon is the chemical 60 potential .u. which is an intensive system property analogous to temperature and pressure. For equilibrium it is required that the chemical potential of the solvent (water) must be equal on two sides of the semi-permeable menbrane. Ihen the solute concentration is increased. for example in the process of freezing. the chemical potential of the solvent is decreased and as a result the solvent is driven from higher chemical potential region across the nembrane to re-esteblish equilibrium. If the osmotic pressure of the solution of a. system at pressure. p. and temperature. ’1‘. due to a semipermeable membrene separating two phases (1) and (2) is a. then the osmotic equilibrium condition in term of the solvent (water) is panama.) - fitter.) [3.11 where K is the mole fraction of the solute. Now a is defined as Mums) - u'trm + RTlnX [3.2] where a. is the chemical potential for pure solvent. Note that in Equation 3.2 ideal solution behavior is assumed. Equation 3.1 could then be written in the form mus...) + ems. - ...‘,(r.r) + anus. [3.3] 61 The Gibbs-Duhem equation gives Jar + ;dP - 211%. - o [3.41 Ihere 3 and 3 are the partial molar entropy and .volume respectively. Equation 3.4 at constant temperature gives du' - v'dP [3.5] 'hOtO V. is the partial molar volume of the solvent in the solution. Integrating Equation 3.5 for a pressure increase equal to a we have fl:(T.P*n) - u:(T.P) - I ;'dP ' '.s [3.61 Now assuming incompressible solution Equation 3.3 becomes 3,. + nuns. - ins.) - o '5. - drama.) [3.11 Equation 3.7 with the dilute assumption can be simplified as fo1lows 62 =n,‘-"-n ln(K‘/X,) - lnlq/(n-ngll - -ln(1 - ugln‘) ’ 'nI/n. where n: is the solute mole number and n1is the solvent mole number and n:(53: ....uu . TJ®L «mezzo P c 2:... .-.. ...u H- _ - . _ 8:39. . _ 8:33 _ a: 52 _ _ j :3 _ _ :23... . Sn: 8 was“: . . I I I - ..... 4 was r w P _ . r h _ _ - - _t h. _ _ 385.: u I" IIIIIIII “I u I I u “ 8:8... a _ _ 8:53 . _ no: F J Pl’l .II I II II Ii ll- . v :3 «.3582 ..2 :25 8:332... — , gunning» AL =3 2:2: 3.38: 20.843 ...-2489 78 circuit. 3) a temperature control system designed to maintain the system at the desired temperatures. 'The fluid delivery system delivers the proper ratios of the cell suspension and the desired saline solution to be mixed and delivered into the observation chamber. To insure proper mixing the solutions are passed through a mixing chamber before reaching the observation chamber. The theory of the operation of the experimental apparatus is described as follows: Intact red cell suspensions scatter and absorb light very effectively which is reflected in the creamy appearance of such a suspension. Once the oxygen-binding protein hemoglobin leaks out of the cell (which for an individual cell is known to be an all or none event. and the cells are so called hemolysed) the cell suspension appears bright red and transmits the light very effectively. Therefore. provided that one can achieve instantaneous mixing of the lytic agent and the red cells without subjecting the cells to a mechanical stress. the transmitted or scattered light intensity once calibrated should provide a measure of the extent of hemoglobin release and consequently the extent of the hemolysis in the population. That is. provided that the light intensity is calibrated as a function of the extent of hemolysis. one can obtain the hemolysis time 79 history from the light intensity measuruents. At this point we should point out that. as was discussed earlier in chapter 3. the cell responds to a concentration gradient across its membrane osmotically by changing its water content and therefore its volume. In the present work the lytic agent is hypertonic sodium chloride solution. so that when the cell is introduced to such a condition it will lose its water content and subsequently shriek before becoming hemolysod. The reduction in the individual cell volume is concurrent with the reduction of the total cross-sectional area of the light attenuating sites. This at first may seem to result in an increase in the detected light intensity. however. as they shrink the red blood cells become spherical. absorb and scatter the light more effectively than when in the normal state. In fact the amount of the light absorbed by a suspension of cells in the spherical configuration is up to 2.5 times that of the suspension of normal rod cello (biccncave shepes). Therefore monitoring the light intensity one observes an initial drop which is a function of the tonicity of the sodium chloride solution. The cell volume effect on the system response will be further discussed in Chapter 5. 31mm 80 The major components comprising the experimentl apparatus are: the fluid delivery system: the optical system: the mixing system: and the thermal control system. These are described in detail in this section. The fluid delivery system shown in Figure 4.1 constitutes a major component of the system and consists of: (i) The reacting solutions reservoir (ii) Tic drive syringes (iii) A solenoid-activated drive bar connected to the plungora (iv) The mixing unit (v) The optical chamber (vi) Solenoid valves The drive syringes are connected to the packed red cell reservoir of desired hematocrit level and to the reservoir of reacting sodium chloride solution of known tonicity respectively. The solution reservoirs are housed in a plexiglass block and the syringes are connected to the block through a uni-axial three-way valve. 81 '10? VIII o O o O SIDE VIE' Figure 4.2: Top and Side Views of the Solutions Reservior. 82 Top and side views of the plexiglass block are presented in Figure 4.2. The drive syringes are 10cc and lcc Hamilton syringes with Luer tips and the plunger tips are teflon coated to create a biologically-inert environment. The plungers are coupled through a solenoid-activated drive bar which provides equal stroke lengths for both syringes. The subsequent volume ratio of fluid delivered from the two syringes is calculated to be 9 .67:1. he drive her is driven by pressurized air and is usually operated at 30-40 psig which is activated by a solenoid valve. The drive syringes are connected through the three-way valve to a mixing unit with tygon tubing. The mixing unit is an important part of the stop flow system and plays a significant role in terms of the reproducibility of the data. It is responsible for providing a homogeneous mixture of the test solution and the cells. The design of the mixing unit is such that it would provide a turbulent flow and therefore effective mixing. A design criteria is that the mixing process must not introduce any mechanical damage or stress to the cells. This criteria in turn dictates the flow characteristics and therefore the driving pressure. To create turbulence and hence enhance the mixing of packed cells and the saline solution. the solutions are introduced into the mixing unit at90 degrees. he mixing chamber is shown sch-etically in 83 Figure 4.3. The mixed solution after mixing is delivered to the optical chamber which is a vertically held glass column with OD=6mm. and ID-4mm and length of 10cm. The column is held in the vertical position and is made long enough so that the cell sedimentation effects are negligible. That is considering that the red cell sedimentation velocity is on the order of .5cm/hr. it will not effect the measurements with duration periods of 5-10 minutes. A major source of error concerning the stop flow system is associated with the mechanism of stopping the flow. Once the drive bar is activated it will provide a time dependent force to drive the fluids. The flow velocity may or may not reach a steady value during the delivery period and this may cause significant error in measured hemolysis. This means one needs to use a sophisticated mechanism to stop the flow without creating unwanted transients. In the present system an effective shut-off mechanism is used which insures the instantaneous halt of the mixed fluid in the optical column at zero time with minimal transients. The shut-off mechanism is presented schematically in Figure 4.4. An on and off trigger is mounted on the drive her support. The location is chosen such that the drive bar reaches the trigger before it begins the deceleration. assuring a very steady flow at l V ///¢ "7. / J ////// g ‘— mar SQUTION 86 the instant of shut-off. he trigger is connected to two solenoid valves positioned at the two ends of the observation column. he two solenoids then shut-off at the same time. thereby bisecting a column of the flow at an instant of time. he mechenism works as folows: he solenoid at the exhaust and of the optical column is a two-port valve while the solenoid at the upstream end. right after the observation chamber. is a three-port valve. he three-way solenoid valve is used to direct the flow from the observation chamber into a collecting beaker which allows the drive has to come to the resting position without creating a pressure build up due to the trapping the flow in the observation column. Both solenoids are chosen as 12 volt D.C. powered valves to avoid any noise commonly associated with A.C. units. he synchronized valve shut-off mechanism eliminates probl-s such as back flow and the pressure build up and the subsequent jet flows associated with other stoppage mechanisms. Besides eliminating the for-entioeed flow artifacts. it also precisely marks the experimental zero time and enhances the reproducibilty of the delivered mixture ratio. 3.1mm he optical system is shown in Figure 4.1 and consists of: 87 (i) The light source (ii) Voltege regulated D.C. power supply (iii) Photocell and amplifier circuit The light source is a 6 volt microscope illuminator tungsten bulb and is powered by a voltage regulated D.C. power supply. Tb eliminate contact resistance effects associated with ordinary spring loaded electrical contacts. the leads from the power supply are directly soldered to the bulb. A.Zeiss universal microscope light housing equipped with a variable diaphragm is used to hold the bulb. The light is directed through a hole bored in a solid brass cylinder. which is used to hold the observation chamber and also acts as the heat reservoir for the thermal control system. he light after passing through the observation column falls directly incident on the photocell. The photocell voltage output is amplified and is then recorded by a strip chart recorder. The amplified photocell voltage output for the normal saline solution used as a standard is chosen to be 10 volts which is achieved for every experimentel run by adjusting the light source intensity level by regulating the power supply voltage. The typical value obtained for the intact cell suspension of about 4% hematocrit at isotonic condition is about 65mv and the output voltage for a totally hemolyaed cell suspension is about 5 volts. This means 88 that for early times the error associated with the drift of the incident intensity from the nominal value is very small (less than .58). The overall photocell output drift is less than 58>over the period of 2 hours. Considering the 5-10 minutes duration period for each experimental run the photocell output drift is less than 18. In fact because of the logarithmic behavoir of the photocell response and the normalization procedure the error at later times due to the light intensity drift is also very small. numeral- The mixing system shown in Figure 4.3 plays a very important role concerning the overall performance of the stop flow system. The mixing chamber is made from clear plexiglass and the test solution inlet is at 90 degrees with respect to the packed cell solution inlet. The flow rate through the mixing unit and therefore the extent of the turbulence created in the unit is a direct function of the driving pressure. This implies that the higher the flow rate. the more effective is the mixing. However. the process of determining the optimal operating flow rate is not so simple. This is due to the compliance of the tygon tubings and the drive mechanism in general and the demeging effect of shear stress on the cells caused by such a turbulent mixing in particular. The shear stresses introduced in the mixing process 89 could result in an over estimation of the actual damage due to the reacting agent. This matter is discussed in Chapter VI. 51mm To obtain the hemolysis kinetics at temperatures different than rot. temperature. the stop flow system is equipped with a thermal system which consists of: (i) A heat exchanger unit associated with the test solution (ii) A heat exchanger unit associated with the observation chamber (iii) Tumperature sensors and coolant circulator To quantify and account for the effect of the low temperatures on the kinetics of red blood cell hemolysis the intention of this research has been to compare the room temperature responses to those at the subaero temperature experienced by a cell in a cryopreservetion process. However. to avoid ice formation in the present experimental system.tho extent to which the temperature of the system could be lowered is 90 limited. The lowest tenporature which could be achieved without freezing the sample is about -10 degrees centigrede at a sodium concentration of 4m. Another important factor concerning the design of the thermal control system was that the blood cells should be kept at ambient temperature until they are subject to mixing with the lytic agent. Therefore the syringe and the reservoir containing the packed cells are not included in the temperature control design of the system and are kept at room temperature. The effective mixing ratio for the stop flow system is about 10:1. hence the error introduced due to the temperature discrepancy of the mixing fluids is very small (1 C for about 20 seconds for the lowest temperature considered here). The zero time temperature of the mixture was recorded to be up to 258 higher than the desired temperature. however. the temperature reaches the desired value within 2-4 seconds depending on.the final temperature desired. To cool the test solution a heat exchanger unit was constructed around the syringe containing the test solution. The lines connecting the test solution to the mixing chamber are well insulated to keep all parts of the system with the exception of parts containing packed cells at the desired temperature. To assure that the observation chamber remains at constant temperature throughout the experiment and the fluid delivered to 91 the column could reach the desired temperature in a short time. the observation column is located inside a solid brass housing. The brass housing is cooled by passing coolant through copper tubes located on either side of the glass column. This provides a heat reservoir with very large thermal mass and hence a very stable and uniform temperature distribution across the observation chamber. The two heat exchanger units are coupled and the cooling is provided by a coolant circulator. The temperature of the components of the system are measured by two thermocouples. A thermocouple is located in the observation chamber close to observation site and another is placed at the teat syringe well. The coolant flows through the system for at least 2 hours before each experiment where the temperature of the coolant circulator is adjusted to reach the desired temperature. CHAPTER V OPERATIONAL CHflACTERISTICS AND CALIBRATION OF THE STDPrFLOI SISTEI The experimental aspect of the present research concerned the design and development of an improved stop-flow system with the potential for measuring destruction dynamics of the red blood, cell. The system theory of operation and major components comprising the experimental aparatus were discussed in chapter 4. This chapter is concerned with the operational characteristics and calibration of the experimental system. First. the general characteristics of the stop-flow system such as the transient response and cell volume effects on the system output will be discussed. Second. the calibration procedures are discussed and the results are presented. Finally. the effect of cell number density on the calibration protocol and measured kinetic data will be discussed. LMW The experimental aspect of the present work involved the 92 93 design and development of a systen capable of introducing desired step changes in the concentration of the extracellular medium at controlled temperatures in the range of -10'c to goal g..p.rgtu;. (about 23'C). Although the original design of the experimental system was straightforward. obtaining quality data proved to be very difficult. lany modifications and refinements of the initial design were required to realize a system with the desired characteristics. such as complete mixing and negligible flow effects. essential for the integrity of the present effort. The problems were effectively dealt with and corrections were made which are discussed in chapter 6. Here we will discuss the general characteristics and response of the refined version of the system used to obtain the reported hemolysis kinetics data. The system behavior operated at room temperature differed somewhat from that at lower temperatures. The major difference was that it required an initial period of one hour for the system components to reach the isothermal condition at the desired sub-atmospheric temperatures. The compressed-air pressure required to drive the plunger was about 20 psi at -5'c gogpgggd to 40 psi required when operated at room temperature. This is due to the difference in the coefficient of thermal expansion of glass and aluminum. The glass syringe expands more than. the aluminum plunger. creating smoother and a less tight fit. The warmup time required for the light source and the photocell and operational 94 amplifier circuit to reach steady state was about 15 minutes. However. the system was allowed one hour to warnup. The mixing ratio of the blood and test solution delivered to the observation chamber is pressure dependent and the highest blood/test solution ratio was obtained at 30 psi at room temperature. The smell syringe (containing the packed cell solution) and the large syringe (containing the test solution) had .455 cm and 1.415 cm radii respectively. Therefore. the theoretical ratio of the test solution volume with respect to packed cell solution volume (er)‘ 1' calculated ‘0 50 9-5731- Nevertheless the actual mixture ratio delivered to the observation column was measured to be somewhat less than this. For example for a packed cell solution of 558 hematocrit the delivered hematocrit was 48 at room temperature. The pressure dependence of the delivered hematocrit is presented in Figure 5.1. It should be noted here that the normalized hemolysis kinetic measurements were insensitive to the mixture ratio. i.e. the delivered hematocrit. he percent hemolysis data are obtained at 48 nuinal huetoorit and the corresponding photocell is measured to be about 65 mv at isotonic condition. The light intensity was adjusted to 10 volts for the observation column containing the sodium chloride osmalality equal to that of the test solution before each run. The system output PRINT IEIATOO IT 95 PACKED (ILLS AT 558 BC! MATURE I 23 C 0 U -4- i ‘ H 20 40 5° HBSURE (psi ) Figure 5.1: Percent H-atccrit Delivered to the Observation Ch-ber as a Function of Plunger Pressure. 96 voltages normalized with respect to the isotonic saline solution output for different levels of sodium chloride concentration is plotted in Figure 5.2. he data indicates that the measurements are quite independent of the salt concentration in the observation chamber . he normalized photocell output behaves very linearly with respect to normalized lamp voltage independent of whether the observation chamber is filled with cells or normal saline solutions. he data is shown in Figure 5.3 which indicates. although the magnitudes of the photocell output are different for the two cases. the normalized voltages are quite the same. his implies that the systems response is independent of the content of the observation column. meumm he stop-flow system transient response is related directly through the calibration curve to the h-olysis of the blood cell suspension in the observation chuber. In order to relate the photocell voltage output to percent hemolysis the data is normalized with respect to the initial or zero-time response of the system for a given experimental conditions. Specifically the zero-time response corresponds to the condition of 08 h-olysis and the minimum volume state. hat is the initial response of 97 ... Tl W's. s. molarity Figure 5.2: Normalized Photocell Voltage as a Function of NaCl Iolarity in Absence of Blood “NJ. I '00 v), 98 *- O V... - 14.0: v 1 .9 .. ’ V... - 65.40 v .0 , 9 O .7 - 6. .. r .3 >3 5 r- 3 Q o V'..x I 2.66 v 09 .3 I- o V' 2 48 v . - ... .0 O .l r 0 1* L L J L 1 4 1 1 or; O .l .3 .5 .7 9 vlamp/V'max Figure 5.3: Normalized Photocell Output as a Function of Normalized Lamp Voltage for Optical Chuber Filled with. Normal Saline and Blood at 48 H-atocrit . 99 such a system is a very important factor in concern with the reliability of the normalized data. There exists an unexpected initial transient response associated with every measurement. The voltage output systematically behaves as shown in Figure 5.4. i.e. the zero-time response is a few percent different from the ideal case. This behavior is likely due to the orientation of the red cells in the direction of the flow as suggested by the results of the following experiments. The initial transient period is associated with some type of flow relaxation. The average relaxation time for 10:1 mixing is measured to be 6.52 seconds on the average. where normal saline solution is mixed with packed cells with resultant hematocrit at 48. The following experiments were conducted to explain the characteristics of the relaxation period. In order to eliminate other possible sources of problems which might contribute to the observed behavior such as improper mixing. the syringe containing the packed cells is replaced by a syringe identical to the one used for the test solution thereby producing a 1:1 mixing ratio. i) 168 hematocrit blood is mixed with an equal volume of normal saline solution and the average time required for the photocell output to reach the steady state value is measured to be 7.40 seconds. ii) 88 hematocrit blood is mixed with equal volume of the moment venue (mv) 100 3 $— t 48 Hustocrit Coll Suspension at Isotonic g_ i Condition hired with Equal Vol-e of Her» tical Suspension. ' (- ' L1 1 . [— . lg. " _ . l- .. i _. _ - ' - -... “'ME 0 r _L I ......... ...!“ ..‘. ,' .... ..- .' I -- -- q a _+ - . --ms mo m - a e-m. ... .o .- ... . e - -..—.— > ‘- ..§-__...... . o u - . -- . e u --—a- --.~. g pom—_- ] ‘ i . —— 4 J a .F .. a.-. -on—o-n-o— .— e m --.- e-—m o c—tbom-o-u e .-. ---O- L‘" as.- ...- -e~ - -L . l ‘ J l o. L— ’m.‘ 8-“ .. ...-en— .. . - ‘—o e . ‘ I o-‘—o-‘-o—-Iol ‘Pf—I- bra-Ta— . l Figure 5 TI! (25 cm/ min) .4: he Initial Transient. Effect of Cell Orientation. 101 identical suspension and the average relaxation time is measured to be 6.33 seconds. iii) l68»hematocrit blood is mixed with equal volume of 2m saline solution and the average time required for the photocell output to reach the minimum value is measured to be 3.65 seconds. The results of the above experiments clearly indicate that for the cells suspended in normal saline solution the relaxation time is longer than when suspended in lm saline solution. The following argument is given in an attempt to explain the observed results above. The cells introduced into the 1 molel saline solution almost instantaneously (in 250mseo) reach the minimum volume state and assume spherical geometry hence there is no preferential orientation and consequently a relatively short relaxation period. Vhere cells suspended in isotonic sodium chloride solution have normal biccncave goaetry and therefore could be preferentially oriented and subsequently have a longer relaxation period. Although the initial transients. could not be completely accounted for on the basis of the foregiven argument as there are other possibilities such as incomplete mixing. However. based on the relaxation times obtained for different conditions the major contributing factor is due to the orientation of the cells in the direction of the flow. 102 2.... mmmmmmmm Vhen cells are exposed to tonicity levels of salt different than the physiological isotonic level they experience osmotic stress. he tolerance level of cells to such osmotic stress depends on the amount of stress and the exposure time. Once the tolerable level of perturbation is exceeded the cells are damaged. he cell o-otic characteristics allow transport across the membrane and therefore a volume change proceeds the cell damage. In the case of hypertonic exposure of the red blood cell. a minimum volue state is reached before h-olysis. hen the equilibrium of the cell syst- is perturbed by imposing a concentration gradient across the membrane. the difference in the chemical potential of water across the cell acts as a driving force for the flow of water across the membrane. he induced flux of water will persist until the cell system reaches a state of onetic equilibrium with the environment. In this research we are concerned with exposure of the human red blood cells to hypertonic conditions. consequently the induced driving force results in an outward water transport across the plasma membrane. he loss of cell water content results in a decrease of the cell volume referred to as the shrinkage of the cell. he cell shrinkage. when exposed to exceedingly increesing hypertonic 103 sodium chloride solution: continues up to a concentration of .8 molel. Increasing the salt concentration beyond .8 does not result in further shrinkage and the so called the Iinimum Volume State (IVS) is reached. The minimum volume state proceeds the hemolysis under such conditions. The water transport across the plasma membrane is a very rapid process. and consequently the characteristic time associated with it is very small (~25O msec) compared to h-olysis kinetic characteristic times (~ seconds to minutes) [114,137-139]. That is. relative to the time frame of this work, the minimum volume state is realized instantaneously. It should be pointed out here that. the argument given above only holds for a single cell and the cell population seems to reach the minimum volume state in a finite time. Inferred from the time required for the photocell output voltage to reach its minimum value. the time required for a given cell population to reach the IVS depends on the level of perturbation and ranges between about 1 sec for 4 molel and about 7 seconds for 1 molel salt concentration. The photocell output at W8 is used for normalization of the h-olysis date. To quantify the IVS and therefore obtain the corresponding photocell output. the following experiments were designed and carried out. 104 Cell suspension of 558 h-atocrit was prepared following the standard procedure outlined in chapter 6. he suspension was the exposed to different concentrations of sodium chloride ranging from .075m to 2.5m. he experiments were carried out at rot- temperature and the usual procedure was followed to obtain the stripchart traces of the photocell output. he photocell output traces were examined and minimum photocell responses corresponding to the quasi-steady state values were tabulated as a function of the extracellular salt solution molality (Table 5.1). he photocell voltage for a cell concentration of 48 h-atocrit and known sodium chloride concentrations normalized with respect to the photocell voltage corresponding to 48 hematocrit in normal saline are plotted as a function of the oamolality of the extracellular solution in Figure 5.5. From Figure 5.5 the minimum volume is achieved for hypertonic Nacl concentration of greater than or equal to about .6m (between 0.5-1.0m). hese results verify the earlier finding that the human red cells subject to hypertonic osmotic shock undergo a dr-atic volume reduction of about 608 before lysing [114]. hese results also suggest that the initial photocell output for Nacl solutions of concentration greater than .6m should be the same for a given cell concentration. he results shown in Figure 5.5 are in excellent agre-ent with the results obtained by Farrant et al [114] concerning the cell volume estimation based on the amount of 105 TABLE 5.1 Normal ized Photocell Voltage at 48 Hematocrit mm; .075 .150 .250 .500 1.000 1.500 2.000 2.500 as a Function of Neil Nblality W Ms. 134.53 3 23.76 1.99 1 .35 67.50 1 42.05 :0; 3.17 .62 :1; .05 33.12 1', 2.77 .49 1: .04 29.30 3 2.23 .43 1 .03 29.16 1 2.16 .43 j: .03 28.55 i 2.30 .42 z .03 28.139 3 2.25 .43 z .03 106 |.O _. rsorouc .9 — v... - 67.50 a .7 0. '1' .— ’8 b .5 - L I _ w 1? Y .3 '- .2 - | L. 0 l 1 1 1 1 O 5 IO l.5 20 25 “BIT! Figure 5.5: Normalised Photocell Voltage as a Function of NaCT molarity (at 48 I-atocrit). 107 coll wator loaa duo to inoroaood oauolality of tho oxtracollular aolution. n. Salihrssisc 21 sh: Exassa Tho goal of tho proaont work is to obtain dyuanic coll roaponaoa duo to hyportonic porturbation in tho tom: of ho-olyaia porcout hiatory for tho dowolopuont of a thorlodyuanic nodol for tho coll dootruction. Tb tranator tho hinotic data tron tho photocoll voltago hiatory protocol to tho doairod for. of porcout houolyaia aa a function of oxpoouro tino. calibration of tho qyataa io roquirod. That ia. a calibration oarvo ia noodod to intorprot tho photoooll output woltago in tor-a of porcoat inducod houclyaia duo to a known atop ohangoa in tho ortracollular concontration of Nacl. Tho rational for tho intorprotatioa of tho ohotocoll voltago hiatcry ia aa followo. Tho inoidont light ia partially abaorbod and. patially ocattorod by tho rod blood coll auaponaion in tho obaorvation cola-n. In fact colla aro vary ottoctiwo aitoa for light attonuation in both tho acattoring and abaorption nodoa. Ihon colla aro porturbod thoy go through ahapo changoa and it tho porturbotion lovol ia in oxcoaa of that which tho call can auatain it will lyao and looo ita houoglobin oontont. Tho da-agod oolla 108 booolo loaa opaqua and noro tranaparont. Ac tho colla in tho obaorvation chanbor aro honolyaod tho anount of light that roachoa tho photoooll incroaaoa which in diroctly rofloctod in an incrcaac in tho ayaton voltago output. Tho incroaao in tho anount of light trananittod can thou bo rooordcd and intorprotod to infor tho tino courao of tho rod ooll hanolyaia kinotica. To obtain data at a giwon honatocrit lowol froo of poaaiblo orrora aaaociatod with difforonco in tho initial roapoao duo to diacropancy in tho doliworod niniug ratio tron run to run. wo nood to nonitor tho nixing ratio. Tb inior tho porcont honatocrit dolivorod to tho oboorvation colunu and thoroforo nouitor tho nining ratio a calibration protocol in tho torn of photocoll output on a function of porcont honatocrit in noodod. LmflmmniM£ WWW To quantify‘ tho photocoll output on a function of tho poroontago of oolla lyaod. tho following procoduro waa onployod. A coll ouaponaion ct dcairod porcont honatocrit waa proparod following tho uaual proooduro oxplainod for coll handling in ohaptor 6. A portion of tho coll auaponoion waa totally hanolyrod by rapid froozing via auhnoraion in liquid nitrogon and thou 109 thawod by warning undor running tab wator at 30—40'c, 151. atop waa ropoatod onco and than tho auoponaion waa chockod by tho atandard clinical cyannothonoglobin apoctrophotonotric tochniquo. and 100i honolyaia waa vorifiod. Tho rcnaining portion of tho auoponaion waa alao chockod by apoctrophotonotor and won vorifiod to bo 1005 intact. Tho optical chanbor wan tillod with iaotouio aodiun chlorido solution and tho light intonaity lovol waa adjuatod for 10w photocoll output. Tho output waa vorifiod to bo atablo for at loaat 30 ninutoa. Dittoront lovola of hanolyain waa thou ‘obtainod by niring propor portiona of totally honolyrod and intact auaponoiona. Thoao auoponaiona at ditioront known honolyaia lowola woro than nanually inJoctod into tho optical chanbor and tho rooulting photocoll output woro rocordod aa atripchart tracoa. A atoady atato waa alwaya roachod within 5 aooonda. Tho ordor of doliworod porcont honolyoia waa alwaya in tho aano diroction. i.o.. oithor incroaoing or docroaaing. and tho ayaton waa rinood with nonal aalino botwoon oach run at loaat twico and tho 10w photocoll output wan voriiiod. Tho ordor of tho onporinont waa than roworaod.i.o. if for oranplo tho porcont hanclyaia doliworod to tho chanbor won at firot tron high to low porcont o1 hanolyaio. in tho aooond run uaing tho aano batch tho ordor waa awitchod and tho nixturoa woro doliworod in incroaoing ordor of porcont honolyoia. An orcollont corroapondonoo waa obaorvod botwoon two auna. 110 In ordor to olininato uncontrollablo paranotora involvod. ouch aa donor'a ago or no: and variation in proparation routino. tho calibration orporinont waa ropoatod nany tinoa (22) with difforont batchoa of colla ovor a poriod of 6 nontha. Tho calibration protocola woro obtainod at 4% and 8% hunatocrit and tho data aro tabulatod along with tho aaaociatod otandard doviationa in Tablo 5.2. Tho photocoll voltagoa nornalirod with roapoct to tho 05 honolyaia output aro plottod voraua ldifl/loo and aro proaontod in Figuro 5.6. Tho loaat aquaro fit of tho data yiolda with r‘ - .9997 Tho an calibration curvo in not a function of tonporaturo and fl). .xp.gi..nt DOIIOIIOd ‘t -5'C ptOdIIOOd VII". 'ithill 4‘ Of tho onoo tabulatod in Tablo 5.2. Tho photocoll output on diacuaaod oarlior in vary aonaitivo to tho coll donaity. Tho coll donaity lovol (5 hnnatocrit) offoct in of concorn on tho iflCT dolivorod to tho obaorvation chanbor ia a function of aovoral paranotora ouch an driving proaauro and packod coll donaity. This at firat nay noon to bo a oouroo of orror. howovor. tho calibration curvo at 8% honatoorit waa 3 00 05 10 15 20 30 40 50 60 70 80 90 TABLE 5.2 Calibration of Percent Hanolyaio aa a Function of Normal ined Photocell Voltage W M W 04.530 1 10 00.015 1 1.100 1.054 1 .017 12 75.455 1 2.041 1.109 1 .044 10 79.704 1 2.071 1.210 1 .012 12 09.013 1 3.150 1.192 1 .049 10 109.772 1 3.117 1.701 1 .040 10 130.733 1 5.092 2.119 1 .000 10 179.935 1 5.400 2.700 1 .005 20 240.100 1 0.041 3.045 1 .137 10 305.300 1 20.275 5.002 1 .314 17 045.401 1 49.172 10.002 1 .702 13 1420.904 1 105.351 22.020 1 2.502 10 112 practically identical with the one obtained at 45 henatocrit. Thia notion in further aupported by the excellent agroenent of roanlta obtained here with the calibration protocol reported by Papanok uaing a conplotoly different orperinontal not up at 10% henatoorit [137]. Thin inpliea that the calibration protocol reported hero in a univeraal one. independent of the ayaten paranetora. and that the kinetic data will not be affected by a few percent deviation of the delivered honatocrit fron the noninal level of 4b. The calibration protocol preaentod in Figure 5.6 in obtained for the unhonolyned portion of the auapenaion at iaotonic oonditiona. However. the unhenolynod cella in a hypertonic condition are at IVS. To account for any differencea which nay influence the interpretation of the raw data. the following erperinent it carried out. To arrive at calibration protocol at IVS. the cell auapeneion at.4$ hnnatocrit i0 adJuatod to .6n aodiun chloride concentration. Thia concentration level aeaurea the IVS without introducing neaanrablo. if any. anount of hnnohyoia for the duration of the erperinent. A portion of the cell auapeneion in totally henolyned following the freeze thaw cycle on before. The intact portion wae kept iaotonic and the Nacl concentration wao elevated at .6n right before the injection into the obaorvation chanber. Following the 113 procedure diacuaaed earlier. a new not of data was obtained. The conperieon of the data in nude through Figure 5.6. which ahowa an excellent corroapondonoo. In aunnary the calibration haa been ahown to be independent of henatocrit (over the range 3 to 10%); independent of t-perature (over the ranege -5 to 25 .C) and independent of extracellular o-olality (over the range 0.15 to 0.6n). Thua the calibration curve in applied to oxperinenta 1.0 to 4.0n over a tenperature range of -10 to 25'b. ammummmmmnsmmu 21121914312111“ The ayaten noninal nixing ratio of 10:1 in not exactly reproduced for every experinent. If the cell denaity preoent in the light path in the oboervation chanber i0 altered. a different anount of light will reach the photocell and the nyotena output will be altered. That in the abeoluto nagnitudea of the photocoll output for identical experinental rune could be different due to the difference in delivered percent henatocrit. In order to nonitor the percent honatocrit delivered to the oboervation chanber we need to calibrate the photocell output uith reapect to the percent henatocrit. It ahould be pointed out here that thin v - 1.014(1-511/1001'1 .42 r’ - .9997 CELLS AT'IINIIDI1VOLUIB 81113.. l-l'llfllT mule/100 b: l vt/ V0011 Figure 5.6: Calibration Curve for the Doterninntion of Percent lnnolyoio an a Function of Nornalired Photocell Voltage. 'The Line Correaponda to the Leaat Square Pit of Data Obtainodfor Cello at lactonic Condition. 115 is only a precautionary noeauro and a few percent variation in the delivered percent henatocrit to the observation chanber is not expected to alter the results. This waa acconplished as follows. A cell suspension of relatively high volune fraction of cells of about 80% was prepared as explained earlier. Proper portions of the packed cell and the isotonic aodiun chloride were nixed to obtain desired levela of‘SflCT. The nixtures were then nanually injected into the observation chnnber and the voltage output of the syston at different cell density levels were recorded. The results are tabulated in Table 5.3 and the nornalixed photocell voltage with respect to the 10 volts reference for nornal saline is plotted as a function of hflCT in Figure 5.7. The range of presented data is II~8i1 BCT as the noninal desired cell nunber density delivered to the optical chnnber was typically 45 for this work. The least square fit of the data yields V - 475.171(iflCT)“(-1.452) with r‘ - .9995 There exists an excellent agrennont between the results presented in Figure 5.7 and results obtained by Papanek [137]. The data for the range of 3-lOb nor are in agreenent to within 4‘. Calibration of Photocell Voltage as a Function of m a: W 110.111.11.11. 1 459.33 3 3.49 3 2 178.47 1, 5.51 9 3 98.42 _4; 3.98 9 4 64.74 1 1.84 8 5 45.05 1 1.00 0 6 35.51 1: 1.48 8 7 27.36 3 1.77 8 8 22.89 1 1.75 9 9 l9.” 3 2.23 4 10 16.82 i 2.10 4 I IOOP _ L - L d P d I 1; b - \ 0 I I > 30 - - v - 475.1711ummum'1-432 20 1- ‘ .. r - .9995 91mm '0 1 1 1 1 1 L 1 I 2 3 .4 10 mar nmmarr Figure 5.1: Nornalired Photocell Voltage aa a Function of luatocrit. 118 The excellent correspondence of the data obtained independently by two observers using systens with different characteristics suggest the universality of the nornalired 1801' calibration protocol. CHAPTER VI EXPERIENTAL $060088 10! DETERIINING MYSIS KINETICS A. mmmmm Fresh blood collected the sane day was obtained courtesy of the Lansing Anerican led Cross in EDTA tubee. The blood is stored at 4 degrees centigrede until the tine of use. Blood not used within 48 houra of collection was not used to obtain hunolysis kinetic data. Blood older than 2 days was used for percent henolysis calibration protocol and for acne control oxperinenta. The blood was first centrifuged at 1104.. while in the BETA tubes. for 3 ninutes and the supernatant fluid waa aspirated after the cells had settled. The packed blood was then transferred into larger disposable plactic test tubea and diluted three fold by the addition of nornal saline after allowing 30 ninutes for the cells to warn up to rou tenperature. The test tubes were sealed In paraffin paper and gently shaken several tines to assure oonplete auapeneion of the packed blood. The sanple waa then centrifuged as before for 5 ninutes and the aupernatant fluid was aspirated. This procedure (so called "washing") was repeated once nore and 119 120 the cell count (henatocrit) obtained was neasurod to be about 80 percent on the average. The henatocrit of the sanple is neasurod through standard clinical procedure. The packed cells were then diluted by the addition of the proper anount of nornal saline to obtain a washed cell suspension of 55 percent henatocrit. The choice of 55$ is due to the fact that the noninal 4% henatocrit is obtained when a packed coll solution at 558 henatocrit is nixed with the test solution through the stop flow systen. The percent henatocrit of the sanple was neasurod after dilution and the deviation fron the noninal value of 55% was about 58. This introduces 0.681uncortainty in the noninal henatocrit of the nixed suspension delivered to the observation chanber. This conpared to the uncertainties of henatocrit associated with the fluid delivery nechanisn is extr-ely snall. Iashed cells if not used within 4 hours were discarded. To prepare a totally henolysed blood suspension. used to obtain a percent henolysis calibration protocol. blood was washed and prepared as above. The sanple was then innersod in liquid nitrogen for“ 30 ninutes to assure deep freezing of the entire blood sanple. The sanple was then thawed by placing it under running tap water at 30—40 degrees centigrede. This procedure of freoxe-thawing was repeated once and total henolysis of the prepared sanple was verified'using the spectronic 20 before use. 121 5.. mmmwummmm mmmmumw Wumm The experinental procedure for deternining henolysis kinetics of hunan red blood cells at a given tenperature due to different hypertonic concentrations of extracellular electrolyte (aodiun chloride) solution will be discussed here. L mmnmw The voltage supply-to the solenoid valvee. light source. and the photocell circuit were turned on and the electronics were allowed to warn up for 50 ninutes. The drive ayatnn and the triggering nechanisn were checked and the preasure of the supplied air was adjusted for annoth drive of the plungers. After fluahing the systen with nornal saline. the observation colunn.was filled with the desired hypertonic aodiun chloride solution. The strip chart recorder was turned on and the proper voltage scale was set. The power supplied to the light source was adjusted such that the voltage output was 10 volts with isotonic saline in oboervation 122 chanber. This voltage level waa verified to be stable to within 2‘ for at least 30 ninutes. The packed blood cell and test solution roserviora were filled with the blood sanple prepared at 55% hnnatocrit and the hypertonic aodiun chloride solution of interest respectively. The stop flow systen was then prined following the procedure explained in chapter 5. by several injections. The drive nechanian was checked once again for optinnn nixing. Once the systen was verified to be operating properly the drive nechanian was triggered and the photocell voltage output was recorded for about 5 ninutes. In the neantine while the optical chanber renained undisturbed and iaolated frcn the rest of the systen. the drive ayriuges were reloaded for the next run. Nornally 5 to 6 runs for the sane conditions were perforned to aasuro reproducibility. Upon conpletion of datd collecting for a given level of hypertonic saline solution. the reservior and the syringe containing the teat solution were enptied and rinsed with the saline solution to be filled next. After flushing the entire systen with the hypertonic aolutiou at a concentration different frcn the previous experinent. the photocell output was adjusted to 10 volts for the new test solution. Following a procedure identical to that nentioned above a new set of strip chart traces corroaponding to the sanple behavior at the new aaline concentration was obtained. 123 The hypertonic electrolyte concentration was increased by 0.5n. each tine and the range of concentration fron 2n to 4n was covered. The rational for the chosen concentration range is as follows. Although the red cell becones spherical and reaches nininun volune state. and therfore experiences danaging stress. when exposed to saline concentration as low as .8n. the kinetics at concentrations less than about l.5n are extrenely slow and undetectable on the tine scale of the present work. Concerning the upper linit of the concentration range. the naxinu attainable aodiun chloride concentration is 5.2n. Furthernore at 4n concentration the kinetics are very fast where about 90‘ h-olysis is induced in the course of the experinent (about 5 ninutes). L. WMHWW 'hen h-olysis kinetics at t-peratures other than the anbient tenperature are desired the experinental procedure for nost parts is the sane as that explained above. Hence we will only point out the differences between the two cases here. It should be noted that the packed cells are naintained at anbient t-perature for the entire course of the experinent and are only exposed to low tenperatures beginning at the instant of nixing. Before the electronics are turned on the thernal syst- consisting of two coupled heat exchangers is hooked up to the coolant 124 circulator. The coolant flow rate is set at a pro-established level and tenperatures at several locations including the observation ch-ber are nonitored. The systen is allowed 2 hours to reach the desired equilibriun tenperature and then the electronics are turned on. After each run the syringes are reloaded as before. however at this point the test solution is at a tenperature higher than the desired tenperature. Hence. the test solution is allowed 15 ninutos to reach the desired tenperature before another run is attenpted. Once the data are collected for a given tenperature at a given concentration . the saline concentration was increased by .5n (procedure explained earlier) while the tenperature was kept the sane. When all the concentration range was covered the t-poraturo was changed to a new value by appropriately changing the coolant taperature and flow rate if necessary; At this point the cyst. was allowed 1 hour to reach the new tenperature before further oxperinenta are carried out. ‘lhornal equilibriun was verified by nonitoring tenperatures of the test aolutiou and observati on ch-ber. The t-peratures considered for this work were -5.0.5.10.. and 25 degrees centigrede. The rational for the chosen tenperatures 125 is as follows. The henolysis kinetics are found to be quite insensitive to an absolute tenperature drop between 25 and 10 degrees centigrade. This behavior has also been observed with respect to hypertonic cryohenolyaia [20-22]. The lower linit of the tenperature range is due to the fact that the saline solution at 2n concentration would begin to freeze at about -7 degrees centigrede. The raw data recorded by the atrip chart recorder were in the forn of photocell voltage traces. The procedure for nornalising and converting the photocell voltages so that the henolysis kinetics were obtained will be diacussed in chapter 7. LMW The systen was proven to be quite insensitive to uncertaintities aasociated with the delivered nixturo ratio and the light source intensity. However for purposes of reproducibility several control oxperinenta were perfcrned to assure cousistnnt behavior of the systen at different conditions. The reference photocell voltage with no cells in the observation chanber was always set at 10 volts for each aodiun chloride concentration level. This was acconplished through 126 adjusting the voltage supplied to the light source. This reference voltage value nust be atable for the duration of each experinental run of about 10 ninutos. However. since the reference voltage waa not nonitored during a 2 to 3 hour course of the entire experinent. the signal nust rennin stable for at least 3 hours. Iith the systen warned up. a drift of loss than 2% was observed for a period of 4 hours. Considering the fact that the nornalired voltages are very insensitive to the reference voltage. the electronics proved to be quite stable. The stability of the photocell signal checked at different tenperatures revealed sinilar results. The stability of the photocell voltage output wae also checked for the observation chanber filled with cells at isotonic condition an well as 1005 henolysed suspensions. The photocell output renained constant to within 25 for periods of 10 ninutos. At periods exceeding 20 ninutos sedinentation causes the photocell output to drop slightly and for longer periods of tine the sedinentation effect is reflected in an increase in the output voltage. Considering the 5 ninute duration of each experinental run the photocell voltage was considered to be free of artifact. either due to cell sedinentation or changes in the photocoll voltage. The reproducibility of the delivery systen was checked by 127 nixing the packed cells with isotonic saline. The delivered percent henatocrit at nuiual operating condition waa within .158 of tho noninal value of 48. This was verified at different t-peratures and aodiun chloride concentrations by virtue of the existece of a very reproducible xero tine response corresponding to 05 h-olysis frcn run to run at the sane conditions. meumnmmm MMnrmgfmidliam As was discussed earlier the criteria for the injection flow rate were unifornity and reproducibility of the delivered nixturo of packed cells and the test solution into the observation chanber. Since the packed cells are delivered through large- tubings (6nn I.D.) at low flow rates (about 5 cn’lcec) it in unlikely to shear the cells at all. However. the turbulent nixing of the packed cells and the test solution in the nixing unit will introduce scne level of cheer. Tb inveatigate the possible shearing effect on the reported results. the following control oxperinenta were perforned. Following the atandard procedure outlined in Chapter 5 a sanple of 208 henatocrit blood was nixed with an identical aolutiou (20$ henatocrit blood) through the stop flow systen. The 128 nixed solutions were collected and the procedure. using the sane sanple solutions. were repeated several tines. The sanple was then collected and checked for percent henolysis. through spectronetric nothod and stop flow technique. with the result that no henolysis had occurred as a result of nixing. It in inportant to realize that this does not near that the nixing procedure does not introduce any shear effect. The result of the above experinout nerely suggests that an upper linit for the extent of the shear. That is we can only safely conclude that no henolysis will result frcn nixing under isotonic condition. In fact the red cells nay be aheared to an extent such that they becone abnornally vunerable when exposed to hypertonic solutions. To investigate such a poasibility the following experinent was carried out. The desired ratios of blood and hypertonic solutions were nixed. external to the stop flow in a beaker. The nixed solutions were then nanually delivered directly into the observation chanber with a ayringe and the systen's response was recorded for several perturbation levels for several exposure tines. These results along with results obtained for long exposure tines using the spectronetric nothod (sanple prepared as above) are tabulated in Table 6.1. Iol arity (n) 2.0 129 Table 6.1 Cupnrison of Percent H-olysia For Externally lixed and Ianually Injected led Blood Cells Iith the Onee lixed and Delivered “Drough the Stop-Flow Syst- prosure Tine(aec) 30 40 60 0.0 0.0 .8558 0.0 .2+.3 .7+.7 15.2+3.1 D.1+3.1 24.5+3.8 3.0 14 .54-1 .4 20.242 .1 25.744 .3 67.349 .7 75.6-09.6 80.4+8.2 4.0 71.5+8.8 3.4+8.1 85.1‘t6.‘ 0 :Innual inj ection “:8tcp flow 90 2.5+1.‘ 2.5+1.3 20.l+4.1 , .54-2.3 82 .3+7.9 88.2+5.0 150 6.5+]. .4 5.91.6 30.61?4.3 35 .244 .5 83.5+7.2 90.1+5.7 300 10.2+1.5 4‘ 9 .5+1 .6 12“ 35.7+4.7 6‘ 36 .9 4'2 .8 11” 86.5+6.7 5‘ 9 1 .4412 .8 12” 130 At a 2 nolar perturbation level the concluaion is that no shear effect is present as the nanually nixed results are statiatically speaking identical with ones nixed through the atop flow device. For 3 and 4 nolar perturbation levels the nanually nixed results are alightly lower. The largest diecropnncy. if there was one. appear in results for exposure tines of l ninuto and longer. Since the analysis concerning kinetics only involved initial response. i.e. percent henolysis for tines less than one ninuto. the apparent discrepancy would not affect the analysia. Furthernore all the results reported in Table 6.1 are statistically equivalent for the given level of perturbation and exposure tine. Finally the long exposure tine results show a reasonable correlation with the stop flow ayat- results (This will be discussed in Chapter VII). Therefore it is concluded that the shearing effect will only be appreciable and for that nutter it is neasurable only at long exposure tines. To further aubatanciate the above conclusion the kinetic neasur-ents were perforned at high injection pressures (high nechanical stress) for 3.0 and 4.0n NaCl concentrations at different t-peratures. These results are presented in Tables 6.2-6.5. The results show significant increase in the anount of h-olysia at high injection pressures (conparod to the noninal). H-olysis at ahort expoauro tines (conparod to the long exposure tines) are shown to be less sensitive to the injection pressure. Exposure Tine (sec) 10 15 20 25 30 40 60 120 180 240 300 131 TIILH 6.2 Percent Honolysis as a Function of Injection Preesure (3n NaCl at 88K) 60 (n-5) 0.33+0.57 3.00+0.00 8.73+2.55 10.00+3.73 23 .31+2.89 33.23+2.48 40.6o+2.65 48.4l+2.16 52.23+3.62 53.4543.67 55.21+5.44 Pressure.8n) the cell will lyse and lose its henoglobin content [32]. For a cell population this process is a tine dependent (kinetic) process. Ihen a population of red blood cells is nixed through the stopflow cysten the hynolyaia process is reflected in the increased intensity of light transnitted through the sanple. The change in the transnitted light intensity is detecdted and recorded as a voltage output history of a photocell detection circuit. An increase in the photocell output is therefore directly related to the red blood cell henolysis. It will be ahown that at a given tnnporature. the higher the perturbation level the faster the photocell output will increaae and coneequently the faster the henolyeis kinetics. Figure(7.l) represents a typical photocell voltage output due to 2n and 3n isothernal hypertonic atop changes of the extracellular solution It '5 0. Colin exposed to 2n concentration reach the nininun volune state in a finite tine. represented by the initial drop in 138 TI. (25 onlnin) Figure 7.1: Typical Photocell Vol tare Outputo Due to Ioothornal ' Stop flange of the Extracellular Concentration. 139 output voltage whereas at the 3n concentration level the cells reach nininun volune state inatantaneously conpnred to the oxperinental tine scale. To translate the raw data in the forn of photocell voltage as a function of exposure tine into the desired henolysis kinetics data the following procedure is enployed. The photocell voltage at any instant of tine is nornalized with respect to the output voltage corresponding to the initial nininun volune. 051 henolysis voltage level. The calibration curve (Figure 5.6) in then used to transforn the nornalized voltages to percent henolysis. The henolyais kinetic data are obtained for hypertonic sodiun chloride concentrations of 2.5. 3.0. 3.5. and 4.0n at roon tenperature(25C). 10.5.0. and -5C. The result in the torn of percent henolysis as a function of exposure tine for the above oanotic perturbation levels at different tenperatures are presented graphically in Figures 7.2-7.6. As evident fron these results the h-olyais kinetics at a given tenperature are a function of the osnotic perturbation level as well as the exposure tine. For exanple the results show that for an exposure tine of 30 8000143 4t 25 C, while the 2n perturbation level produces no neasurable henolysis. about 50% of the cell papulation is henolysed at the 4n level. Furthernore. the henolysis kinetics are quite rapid at short tines and as a larger portion of the population is henolysed the rate of the henolysis reaction procesa HEMOLYSIS 1110 MATURE - .8! 2.5 2.0 10 fliii ++4L++H+uf 00 EXPOSURE TIME [sec] Figure 7.2: Percent l-clysis as a Function of Exposure Tine. HEMOLYSIS 141 MATURE II 283E . o ”3.0 . 2.5 10m 1” EXPOSURE TIME [sec] Figure 7.3: Percent l-olyaia no a Function of Exposure Tine. 10’ HEMOLYSIS 142 MATURE I 278 ° : 2-3": - 3.5m ' . .. ’ + 1% l—H—HL EXPOSURE TIME [sec] Figure 7.4: Percent l-olysia aa a Function of Expoeure Tine. HEMOLYSIS . - ° ; :—: .asm 4.0m. . ' a 3.0 2.5 ”2.0 .. at +1 ++H+£ 143 MATURE - 275E 1 i E EXPOSURE TIME [sec] Figure 7.5:, Percent I-olyaia as a Function of Exposure Tine. ' HEMOLYSIS 144 TEIPERATURE - 2688 16 +% 44 -- 1 EXPOSURE TIME [see] Figure 7.6: Percent l-olysia as a Function of Exposure Tine. fii—H-H'u‘ 145 in the population shown a considerable decreaae. This general pattern is observed for all the tenperatures studied. Au inportant observation is that even though the level of henolysia at a given tenperature and tine is higher for a higher aaline concentration. nevertheless the rate of henolysis reaction does not follow this trend. Aa a specific exanple. at relatively large tines the reaction rate in quite slow for the 4n perturbation level. whereaa the reaction rate at the 2n level is quite rapid. So far we have referred to henolysis rate in the sane nanner no reaction rate is connonly addressed. this natter will be discussed in chapter 9 . However. an attenpt is nade here to define the henolysis rate for the present data. Io define the rate of percent henolysia RPH as RPH - dun/ct [7.1] - f(tine) As pointed out earlier it is evident fron results presented in figures (7.2- 7.6) that HPH is a tine dependent quantity. The tine dependency in very pronounced for short tines and for long tines it approaches zero. In terns of the kinetics of the henolysis reaction this inpliea that a kinetic analysis should enphasise short exposure tine data as the long tine data containa very little kinetic infornation since the syaten reaches 146 equilibriun. That is for a given NaCl concentration and isothernal tenperature the danage process characteristically proceeda rapidly for early tines and it in followed by a relatively abrupt transition to a considerably lower rate. 1 This in especially pronounced at NaCl concentration greater than 2.5n. In this work the ahort tine exposure data will be analysed in terns of reaction rate theory. At ahort tines (less than 60 seconds) without loss of generality the ln(HI) is assuned to be a linear function of ln(tine). Furthornore the linear dependency in only applied between two consecutive data points. Therefore for a given interval of tine we have ln(H5) - Alnt + lnB IR - 3.11 17.21 where t in tine and A and H are constants. The values of A for different sodiun chloride concentrationa for various tine intervals at given touperaturea are tabulated in Table 7.1. The calculated A values clearly dononstrate strong tine and concentration as well as tenperature dependency. Graphically speaking A represents the local slope of the henolysis versus expoauro tine curve at an instant of tine. For ahort exposure tines the curvature of the curve is not pronounced and to a good approxination for anall intervals it can be assuned to be linear 147 an..— ntv.~ ~3N.v .5n..— tan.— o-.~ non.- no..~ v—o.~ «anon th.~ nus.— nn°.~ On..- vav.~ can _ueu u4q uINMI. njunuu. v~n0~ can.o oun.o nu~40 v.0.N canon nun.o von0o N5n.¢ 00.0u vonoo two-e an... canon non.~ nu..- 000 Q—n0n v.9.n an..— 000 000 .000 vouofl _Nqu «4N .uqu add .uuuu 001 an..— hn~.u nu..e 010 noc.u nun.— man.- 000 sun.o onn.— van.— 000 000 nun0N .ooh.u 000 000 nh~0~ b...— 101 000 «noon ovuou «is «in N¢u dad oun.n «nu.— ‘-- --- --- --- N4~ no..~ uuuon ban.- .vuou a...~ oou.u 0.90N h...n .un.n ono.~ «coon oucou 000 so~.~ on..— 000 «on.» Gnu.N .qqu .ucu ucv .uaqu nun.u no..o nooon anoou no... on... nen.u ouv.N 000 uoaou osn0~ 000 ..n.N onuon 000 nan.v an... Chloe atlas onlnu “noes Gala— mule— Aduuuu —a>ueon— QIFP enlev 0’00n enlnN nuleu anon- n~00~ _q4u .ueu d4« .1144uuua 32:3..— olfl. ocean-=0 com “(on a It cen—g :5. —.u ndnsr _eauean— 1:. 148 (locally). again justifying the assuned functional forn of H5 given in Equation 7.2. Eaaed on the calculated A valuea the rate of percent henolysis RPH is obtained for exposure tines of 40 and 60 seconds. The HPH data are tabulated in Thble 7.2 and are repreaented graphically in Figure 7.7. It ahould be noted that to obtain HPH values at a given tine. concentration 0. and tenperature T3 the following equation derived fron Equation 7.1 is enployed; RPH(t.c.T) - H5(t.c.T)‘A(t.c.T)/t [7.3] The results show that. except for the care of 2.5n concentration whore RPH is decroaaed by decreasing tenperature. decreasing tenperature fron anbient to 100 results in a sharp increase in the RPH. Decreasing tenperature further does not noon to have a aignificant effect on HPH for the 4n concentration. An interesting point in that except for the cases of 4n and 2.5n concentrationa the naxinun RPH occurs at 10 C, 11.: 1. 1101.1313. tenperature beyond 100 in general seens to result in a decrease in RPH at the given tines. The general pattern observed in Figure 7.7 can be deceiving as to arrive at rates at an instant of tine the h-olysis kinetics are asauned to have the sane characteristic tines associated with then. This in fact is not the case. that is the characteristic tine associated with henolyaia kinetica at a 149 TIILE 7.2 Rate of Percent I-huelyais at 40 and 00 Seconda 412:. _12c_ .43. .103...“ 40 60 40 60 40 60 40 60 40 60 1.154 1.107 1.037 0.965 1.197 1.252 0.958 0.794 0.343 0.245 0.912 1.159 0.682 0.763 0.858 1.016 1.045 1.093 0.247 0.325 0.232 0.247 0.213 0.308 0.167 0.202 0.335 0.472 0.298 0.252 0 '0‘. 0.. .0. ... ... ... ... 0.. o . 1‘, .0 1,, m 7.3 Initial Hunlyaia Rate (Sloan) .513. _12:_ _12:_ .1112. ELI-n. 1.510 1.280 1.100 1.440 4.030 0.650 0.670 0.950 1.030 1.770 0.350 0.280 0.250 0.250 0.870 0.031 0.046 0.060 0.080 0.180 268 273 278 283 298 EMT 38.31.1818 “I! ma HINDI! IOO - O ' \ 4.0. NaCl :— \ O O/. ' ° 3.5: mm 20 - ‘ 3.0. NaCl IO - 3 _ I l l l l 1 1 150 3.2 3.3 3.4 3.5 3.6. 3.7 111' (mu-t) FIG!!! 1.1: Initial l-olyaia lata at 40 and 60 Saaoada. 151 givon condition ia function of tonporaturo. In othor oorda tho tranaition of tho honolyaia proooaa from rapid to aloo ia a function of t-poraturo aa voll aa NaCl conoontration. For onanplo. at 2.5- tho honolyaia roaotion ia dolayod by about ono ninuto for calla at 0C conparod to tho rou tonporaturo roaponao. 'l'horoforo tho ohaorvod drop in [PB for -SC ia laraly duo to tho dolayod roaponao of tho calla. ‘l‘o nako thia inportant point cloar ono can oonparo tho honolyaia kinotica at a givon aodiun chlorido ooncontration lovol aa a function of tonporaturo. For thia tho h-olyaia roaponaoa of tho colla at aivon concontrationa aro plottod for difforont tuporaturoa in Figuroa 7.8-7.12. Tho firat and porhapa tho noat inportant ohaorvation ia that tho ainplo nonotonioally incroaoing honolyaia aa a function of concontration trond ohaorvod for aodiun chlorido concontration dooa not hold truo for tho tonporaturo. For inatanoo for tho caao of 3- NaCl oonoontration. whilo tho kinotic roaction ia dolayod for about 10-15 aooonda it 5 0 conparod to tho othor tonporaturoa atudiod horo. tho final lovol of h-olyaia ia in fact highor for 5 0 aa oonparod to 25 0. 'Ihia inplioa that tho inatant of tino at which aignificant honolyaia occura ia a function of taporaturo. In othor uorda. tho oxporinontally noaaurod roro roaotion tino dooa not coincido uith tho aoro nixing tino. Bouovor tho roaction rato at a aivon t-poraturo night ho rapid onough to ovoroono thia ahift or dolay of noaaurahlo honolyaia aa ia tho caao for tho HEMOLYSIS 152 2 .6I mu to +# %+—H+Hsa 1r +£+++HJ EXPOSURE TIME [sec] Iiauro 7.8: Porcont I-olyaio aa a Function of Bapoauro Tino. HEMOLYSIS 153 2.5. NaC1 . ° / 25C : . O ./ . o o 5 OC IO ' . ’ ..5 “ k + H—s—Hw EXPOSURE TIME [sec] Figuro 1.9; Porcont l-olyaia aa a Function of Expoanro ‘l'ino. HEMOLYSIS 154 3.0- mt: . g g n ++0WJ EXPOSURE TIME [sec] Iinro 7.10: Porcoat I-olyaia aa a l'unction of Inpoaaro ‘l'ino. HEMOLYSIS . +t; 155 3.5. NaCI I—I—H—R. + + i H-Hrw EXPOSURE TIME [sec] limo 7.11: Iorcoat l-olyaia aa a Function of lapoanro Tho. HEMOLYSIS " . ‘ * .. 1" EXPOSURE TIME [sec] linro 7.12: Poroont l-clyaia aa a Function of Inpoanro Tino. 157 abowo onanpl o. Tb ovorcono tho difficulty duo to tho difforonoo in charactoriatioa of tho kinotic roaponao of tho coll ayaton at difforont tonporaturoa. wo will not fix tho tino at which tho roaction rato ia noaaurod for all tnnporaturoa and conoontration lovola. Spocifically. tho tino at which tho roaction rato ia noaaurod at a aivon tnnporaturo will bo dotorninod indopondontly for oach caao. Tb obtain thia charactoriatic honolyaia roaction rato. horoaftor roforrod to aa tho initial rato of porcont honolyaia IIPB. tho initial portion of oach honolyaia curvo ia approxinatod aa a atraight lino. flonco tho alopo of tho oarly portion of tho honolyaia hiatory roproaonta tho initial rato of porcont hnnolyaia for a givon condition (tnnporaturo and concontration). In ahort tho tinoa at which IRPB ia ovaluatod for oach caao doponda on tho ooncontration lovol and tho abaoluto t-poraturo of tho oxporinont. tho initial huolyaia ratoa for conditiona conaidorod horo aro tabulatod in Tabla 7.3 and aro roproaontod graphically in Figuro 7.13. ‘l'ho initial huolyaia rato at tonporaturoa 298! and .273! aa a function of aodiun ohlorido nolarity aro plottod in Figuro 7.14. Ihia figuro oloarly ahowa tho offoct of roduood tonporaturo in auhatantially docroaain; tho initial honolyaia rato. 158 298 278 273 268K i F T F 100 L : 4.0n NaCl 1. a I— D g .. 3.5 E 30 - L! g 20 b 3.0n Nam S 3 l O *- = I E _ , ill. I- 6 r- E 3 P'- 2 F- 2.5 l I J l 1 1 l 3.3 3.5 3.7 1111mm“) Figuro 7.13: Initial l-olyoia Iato at Difforont NaCl Conoontrationa. 159 PERMIT INITIAL mums urn/sumac N mamas-21 3x I L l 2.0 25 3.0 3.5 4.0 0 NaCl 01.11111 Figuro 7.14: Porcont Initial l-olyaia lato Voraua NaCl Iolarity at 38K and 2732. 160 An inportant offoct of tonporaturo in dolaying tho honolyaio hinotioa ia rovoalod in Figuro 7.15 whoro tho honolyaia kinotica at rocn tonporaturo for NaCl concontrationa of 2.5n and 3.5n aro oonparod with that of 2.5n and 4n at aub-anbiont tonporaturoa. It ahowa tho striking offoct. that for loworod tonporaturo tho ortont of danago for ahort tinoa ia lowor owon for highor NaCl ooncontration lovol. Tho porcont honolyaia at nolaritioa of 2.5 and 3 for oxpoauro tinoa of 1 and 3 ninutoa aa a function of tonporaturo aro plottod in Figuro 7.16. Ihoao roaulta ahow that tho dopondonoo of tho abaoluto anount of danago at 2.5n NaCl conoontration aa a function of tonporaturo for 1 and 3 ninuto oxpoauro tinoa aro quito ainilar. It alao cloarly ahowa a oonplicatod tonporaturo offoct on honolyaia at a 3n conoontration. For 1 ninuto oxpoauro tino tho honolyaia lovol ia docroaaod by docroaaing tonporaturo. flowovor for tho 3 ninuto oxpoauro tino docroaaing tho tonporaturo oithor haa no offoct (at tonporaturoa 0 and 5 0) or n..gt1v. offoct at tonporaturoa (-5 and 10 0) on aurvival of ltho colla orpoaod to 3n NaCl. mam Fran tho data proaontod in thia ohaptor concorning tho offoct 161 . o o 0 o o 4.0. ('5t) ° . , . . . . 3.5. (st) . . g ‘ o (D o 2; . . ' o‘. O *. 2 " I” I . I 1 . 2 o 2.0. (250) 2.5n (00) a :5 'ri-H-Hre EXPOSURE TIME [sec] Figuro 7.13: Conparioon of linolyoia Kinotica at Soloctod ‘l'uporaturoa and Concontrationa of NaCl. 162 4O 3O '- 0 2.5n (l nin) O 2.5n (3 nin) 20 D 3.0n (1 nin) moor: Imnu 0 3.0n (3 nil) l L O 5 O 5 IO IS 20 25 mmuuaa (e, Figaro 7.16: Porcont l-olyaia for Bnpoaaro ‘l’inoa of 1 and 3 Iinntoa aa a Function of ‘l'uporaturo. 163 of abaoluto tonporaturo on tho rato of tho danago procoaa. tho following concluaiona can bo nado: 1) Tho appoaranco (noaaurablo oocuranco) of danago ia dolayod for aub-nnbiont tonporaturoa at all conoontrationa. Ihia offoct . ia noro pronounood at NaCI oonoontrationa of 2 and 2.5n. Tho charactoriatio dolay tino aaaociatod with thia offoct is about 3.5 ninutoa for a 2n NaCl conoontration and about 1 ninuto for tho 2.3n caao. It ia on tho ordor of aooonda for highor concontrationa. 2) At ahort tinoa tho doatruotivo honolyaia roaction procooda at faator ratoa at rocn tonporaturo oonparod to lowor tonporaturoa. This bohavior ia noro dranatic at tho NaCl conoontration of 2.5n whoro tho initial honolyaia rato it .18 porcont por aooond at rocn tonporaturo oonparod to .031 porcont por aooond at -5 0 3) For oanotic porturbationa of Zn and 2.5n. tho nininal anount of danago ia inducod whon tho onporinontal tonporaturo in 0 6. 4) For oanotic porturbation lowola groator than 2.5n tho nininal total danago for tho courao of tho orporinonta (about 6 ninutoa) oocura at tho iaothornal tonporaturo of 25 C. 164 5) Charactoriatically tho rato of tho danago prooooa ia rapid at ahort tinoa conparod to that at long tinoa for all t-poraturoa and oonoontrationa. 6) ‘l'ho tranaition of tho rato of roaction frcn rapid to alow takoa a fairly ahort tino. particularly at NaCl oonoontrationa groator than 2.5n. at rou tonporaturo conparod to tho roaponaoa at aubanbiont t-poraturoa. 'lhat in tho tranaition and thoroforo ourvaturoa at thoao inatanta aro aharpor at rou tonporaturo than at lowor t-poraturoa. ‘lho naxinun lovol of danago ia roachod in 45 aooonda for 4n concontration conparod to 5 ninutoa roquirod for Zn oonoontration. 7) At aub-anbiont tonporaturoa conparod to rocn tonporaturo tho danago proooaa prooooda at fairly highor ratoa for rolativoly long tinoa. ‘Ihat ia. tho tranaition fron initial rapid ratoa to final alow ratoa aro anoothor and dolayod. 'lhia dolay in tho tranaition acoounta for highor final danago lovola at low tonporaturoa for NaCl oonoontrationa groator than 2.5n. 8) For 3.5n and 4n NaCl concontrationa tho danago hinotica and ontont of danago for tho oxporinontal oxpoanro tinoa obaorvod aro inaonaitivo to ohangoa in aub-anbiont tonporaturoa. 9) For oanotic porturbation lovola of 2 and 2.5n loworing tho 165 abaoluto t-poraturo roaulta in roduction of tho anount of danago for tino poriod of up to 4 ninutoa. nat ia tho rod colla aro ablo to auatain tho oanotic atroaa for longor tinoa at lowor tuporatur oa. 10) Tho largoat offoct of roduood tonporaturo ia obaorvod whon tho iaothornal t-poraturo ia droppod fron 25 C to 10 C, A furthor docroaao of tonporaturo haa oonparativoly Ioaa aignificant offoct on aurvival. For onanplo. at 3 and 3.5n NaCl concontrationa no approoiablo difforonoo in danago oniata botwoon dnta at 0 e and 5 0. mumwmmmm A najor goal of tho proaont work waa to gonorato a roliablo data baao for hyportonic honolyaia hinotioa at rou tonporaturo aa woll aa aub-anbiont tonporaturoa. ‘Iho inoidonoo of roportod hnolyaia data in kinotio forn for tho rod ooll danago. procoao aa obtainod by proaont roaoaroh haa boon raro and for noat caaoa unroliablo. In thia aootion wo intond to juatify tho proaont offort both in light of ita noooaaity and roliability. 'lho apooific oarlior offorta wo intond to conparo our roaulta to aro duo to chrath and Jon [136.19]. 166 IcGrath has boon a pionoor in tho fiold of cryoprosorvation and tho nost conploto study of tho hyportonically inducod honolyaia kinotica of hunan rod blood coll populations to dato is duo to hin. n. usod a stop flow syaton sinilar to tho ono dovolopod for this work. Boforo attonpting to conparo tho kinotic roaulta wo nood to clarify an inportant point about tho calibration protocol usod to intorprot tho raw data in tho forn of tho photocoll voltagos to tho honolyaia forn proaontod horo. 'lho calibration protocols constituto tho nochanisn for transfornation of tho raw voltago historios into hnolyais kinotica and for this roaaon alono an orroronoua procoduro at this stago nakoa any furthor analyaia of tho roaulta noaninglosa. Duo to disagro-ont botwoon tho calibration curvo obtainod in tho prosont work and tho onoa uaod by IcGrath and Jon. tho first task is to justify tho validity of tho protocols roportod horo. n. conparison of tho honatocrit calibration curvo obtainod for tho proaont work with that roportod by othors is sunariaod in Figaro 7.17 [136,137.13]. All tho roaulta follow tho gonoral trond as V(phctoco11 voltago) ' a‘(porcont flaatocritfll whoro a and b aro constants. Fron Figuro 7.17 it is cloar that 167 IIIA‘IDQIT CALIBRATION GIVE IOO I r T l T l T _1 I: b—anar ‘ / I n 5. 933-1.57 ‘- FALLAII q - r - 415.1111-1-452 q a _ r - .9995 - u b - .L 5 , . z 30 I- -I 8 > 20 L IO 1 I 2 3 4 56‘769Io Pilaf nmman-x Figuro 7.17: Nornaliaod ictocoll Voltago as a Function of l-atocrit. 168 tho protocol duo to Papanok is statistically oquivalont to tho rosult roportod horo whilo tho othor two protocols diaagroo. Tho porcont honolyaia calibration curvos roportod by oarlior roaoarchors aro snnnariaod along with tho rosult obtainod horo in Figuro 7.18. Tho author boliovos this calibration protocol. nornaliaod photocoll output as a function of porcont honolyaia. ahould bo indopondont of tho oxporinontal ryatcn variablos such as light sourco and dotoction noohaninn. Tho oncollont agroonont botwoon tho roaulta of Papanak and tho prosont rosults ia thorofcro oxpoctod as tho two roaulta aro statiatically idontical. Bowovor tho roaulta obtainod by IcGrath and Jon dowiato sharply fron tho prosont roaulta. It is vory difficult to arrivo at tho sourco of thoso diacropancios. Nowortholosa. it aoons likoly to bo duo to tho aiao of tho boan width with rospoot to tho dianotor of tho obaorvation chanbor. Tho roaulta of porcont honolyaia kinotica at rocn tonporaturo obtainod horo aro conparod with that of othor inyostigators in Figuro 7.19.‘ Thoro appoars to bo considorablo disagrocnont botwoon tho prosont roaulta and roaulta roportod olaowhoro. It is boliovod that tho roots of tho apparont discroponcy lio in tho calibration protocols. An inportant obsorvation is that for tho rcsultod roportod by chrath tho initial huolyais ratoa aro indopondont of tino. A is oqual to 1 in Equation 7.2 for all 1 - illloo 169 -4 ' mum v - 1.014(1-sn/100r1-41 ,3 t r' - .9997 <— FAFANAI v - 1.04:1“)‘1-41 .0 \ r I I I I I I .9 '- °8 - locum - .7 - /- - .6 - u - .2 " 1m —" .l I L l I l l l I 2 3 4 5 6 7 B 9 Figuro 7.18: Ccnpariaon of Froaont l-olyaia Calibration Data with tho local to loportod by 0thora. IO 170 .nuOuomwuno>=H nosuo uo unmanom Aug: nuances unomoum mo conuunnaou uo~.n ounuqm con m2: 382%. onN I um=a unc‘ + NaCl whoro EEC. roprosonts a partially hanolysod EEC population. An inportant point to noto is that in tho analysis of tho honolyaia kinotica proaontod hora only tho initial portion of tho EEC rosponso will bo considorod. In such a syston, tho dogrco and rato of honolyaia dopands on tho tonicity (lovol of salt ooncontration) as woll as tho EEC ooncontration and tonporaturo [163]. Tho coll ooncontration dopondonoo is only significant at concontrations an ordor of nagnitudo largor than tho concontrations considorod in this work [163]. Concorning classical chanically roacting systons. thoro aro 204 gonorally two nain roasons for studying tho ratos of roactions. Tho first is tho prodiction of tho dopondoncy of tho rato of tho roacting nixturo on a nunbor cf controllablo factors such as prossuro and tonporaturo. This is of najor practical inportanco as it would onablo us to arrivo at an optinun rato for which tho roacting nixturo will nova to its oquilibriun stato. For instanco, frcn an industrial point of viow it is dosirablo for tho roactions to procood vary rapidly in ordor to savo tino and produco noro (savo nonoy). Frcn tho cryoprosorvation point of viow it is of utnost inportanco to acquiro a dotailod knowlodgo of tho tonporaturo dopondoncy of tho roacting nirturos nanoly sodiun chlorido and rod blood call. This knowlodgo could holp roduco tho unoortainty involvod in tho dosign of a working frooring protocol by gaining valuablo insight with rogard to froosing and thawing ratos. Tho roactions to procood vary rapidly in ordor to savo tino and produco noro (savo nonoy). Tho nochanisn is tho final goal of tho noro chanically criontod study. Ovor looking such olanontary and intornodiato roactions doos not offoct tho ganorality of our analysis. Tho rationalo for this is that for a sorios of consocutivo roactions tho ovorall rats is dotorninod by tho rato of passago of 205 activatod ccnploros (noloculos with onough onorgy to tako part in roaction) ovor tho highost onorgy barrior. Fran tho stand-point of tho thaory of abaoluto roaction ratos, it is sufficiont, providod that oquilibriun is ostablishod botwoon tho various intornodiato statos. to considor only tho oquilibriun botwoon tho initial stato and tho rato-dotornining activatod stato. Thorofcro all intornodiato statos can bo nogloctod [164]. mmmmm In chonical kinotica tho rato of roaction E at constant tonporaturo. basod on tho historic nass action rato law forn, is ccnvontionally proaontod as a function of tho conpcsiticn of tho syston in tho gonoral fcrn of E I f(anctants and products) - -d[A]/ct I f([A].[E].[C]....) [9.1] Ihoro A,D. and C. otc. aro roactants and products. Tho abovo oxprossion which givos tho rato of roaction E as a function of ccncontrations, is custcnarily roforrod to as tho "rato law" for tho roaction undor considoration. 206 Tho conploto nathunatical charactoristics and functional forn of tho rato law aro ofton vory oonplicatod. Eowovor, ono can ccnsidorably roduco tho conplority of tho rato law by propor choico of orporinontal conditions. Thorofcro, tho rato law alnost always roducos to tho fcrn I . [(THAI‘IBJYICJ‘ [9 .2] Ihoro I is scno coofficiont indopondont of ccncontrations. but usually dopondont on tho tonporaturo: it is callod tho rato coofficiont or tho rato constant. Tho statanont of tho rato law, givon tho conposition and tonporaturo of tho roacting nixturo and tho orporinontal valuo of tho rato constant I, pornits tho prodiction of tho rato. It also givos tho ordor of tho roaction whoro, tho ordor of a roacton is tho sun of powors to which tho ccncontrations of tho conpononts aro raisod in tho rato law. Tho rato law for tho syston cf (EEC + salt) takos tho fcrn a . -d[IBCJ/dt - unma‘mfilylcrl‘ [9 .3] All tho kinotic data aro gonoratod at noninal EEC ooncontration 207 lovol of 4% (Euatocrit) for difforont sodiun chlorido ccncontrations ranging frcn II to 4I. That is, roagonts [Na*] and [Cl’] aro in groat orcoss throughout tho courso of oach orporinont so that thoir ccncontrations ruain virtually constant. Thorofcro. tho rato law could now bo writton as I - Ipvr,[II.“J.[C1'J)[IIIIC]x I9 .4] whoro I, is a psuodo-roacticn rato ccnstant. I, - unlumflcrl'. Onco tho roaction rato for tho suggostod rato law is ovaluatod. tho nort task would bo that of dotornining how such ratos vary with tuporaturo and with tho dogroo of tonicity of tho suaponding nodia of tho rod blood calls. Tho kinotic data is in tho forn of a hanolysis tino history. thorofcro to rolato tho rato as dofinod in Equation9 .3 to porcont hanolysis wo can writo “nolysi s I SE - mosque]. - [mom/[use], [9.51 whoro [EEC]. and [EBCJt rofor to tho initial and instantanoous 208 intact EEC ccncontrations. Thus dlhfllldt I 10MIIRBC]. [9.6] solving Equation9 .6 for E wo havo n - [inch/mountain: Now Equation9 .4 could bo writton as II - rpm tu.*l.[c1"l.mcl,)mc1§ [9 .71 whoro I" - rpm, [II.*].[c1'J)IaIIc1,/100s - rmlut+lylc1’l'[u3c1,/1oos but fron Equation 9 .5 wo havo [IIIICIt - [use]. - [outrun/1001. Thorofcro Equation 9 .7 boconos I - l'punc]. - [willow/100$)" - r'plancn‘u - [Ml/100v.)x [9.8] - 209 Substituting for I frcn Equation9 .8 in Equation9 .6 wo havo dual/at - lOOhK'DIRBC]:-1(l - [cal/loos? [9.91 In tho abovo oquation, I" and [EEC]. aro constants for a givon orporinontal run bocauso T. [Na+], [Cl'], and [EEC]. r-nin unchangod for a givon onporinontal run, so Equation9 .9 could now bo writton as dual/at - r;(1 - [Tull/1001.)x [9.10] whoro x; - icosr'plaucll‘“ - rpmcl’,‘ To intograto Equation9 .10, writo: dun] I -d(1 - [“l/IOO‘MOO‘ I -dA(100$) whoro A is tho porcont rod blood coll survival. Than Equation 9 .10 boconos -dA/dt - K;A*I1oo 1"“ - -K;dt7100 I9 .12] 210 Nont, tho 1st and 2nd ordor honolysis roaction rato laws will bo discussod and tho rosults of oach rato law nodol will bo proaontod lator. Tho rationalo for not considoring tho roroth ordor roaction rato law lios in tho fact that tho kinotica of tho honolyaia procoss shows a strong ooncontration and tonporaturo dopondonoo. 11 El:£&.9!d££ 31121122 £311.L1! If rIl in tho difforontial rato law (Equation 9.12): i.o. tho forward roaction rato doponds only on tho ooncontration cf scno roactant A. Tho rato law is than A"dA - -l;dt/100 This intogratos to givo A IA.."“ [9 .13] whoro a c [pt/loo and A. . A(t.0) I 1 2]] This wall known rato law is cboyod in radioactivo docay of an unstablo nuclous and bactorial growth procossos. Now, if our syst- is to cboy tho 1st ordor rato law, a plot of ln[A] vs tino should givo a straight lino with slopo oqual to -K;/1oo, ‘11.. initial h-olysis data is fittod into tho abovo rolationship and tho ruto constant I; for givon t-poraturo and soluto ooncontration aro tabulatod in Tabla 9 .1. ho rosults show a good fit for this rato law with corrolations at difforont conditions ranging fron .9756 to .9991. Tho rato constant for a givon soluto ooncontration as a function of invorso tonporaturo is plottod in tho Appondir. his kind of plot could bo usod to infor tho nochanisn of tho huolysis procoss. 21 112231.9111r £1rs£isn.!ufr La! Tho rato law Equation9 .12 for v2 rosults in A"dA - -E;dt/100 which is tho sacond ordor rato law. This intogratos to givo A" - x;t/1oo + I? 9.141 Ihoro A. is tho constant of intogration and is ovaluatod by C(n) 2.5 3.0 3.5 4.0 212 TAM-89.1 loaction Iato Constant and Activation Enorgios For 1st and 2nd Ordor Ioaction Eato Laws 1st Ordor Eato Law rm I; MI" I" (lcallnolo) 88 0.190 18.43 .9830 283 0.064 18 .08 .9922 278 0.061 17 .78 .99 67 273 0.048 17.58 .9916 268 0.060 17 .13 .99 16 298 0.840 17.54 .9935 283 0.453 16.98 .9897 278 0 .234 17 .04 .99 73 273 0.261 16.66 .9991 268 0 .380 16 .14 .99 54 ”8 2.36 16.92 .9 775 283 1.840 16.19 .9932 278 0.881 16.30 .9860 273 1.086 15.89 .9975 268 1.268 15.50 .9945 298 4.90 16.50 .9810 283 3.80 15.78 .9820 278 2.23 15.3 .9 756 273 2 .41 15 .45 .99 40 268 2.65 15.11 .9865 2nd Ordor Into Law 9“ I, (soc“) 0.190 0.061 0.065 0.051 0.060 0.962 0.543 0.23 0.30 0.472 3.651 0.921 1.019 1.523 0.638 11.26 2.87 1 .80 2.57 2.43 M" 18.43 18.11 17.74 17.55 17.13 17.47 16.88 16.98 16.60 16.03 16.68 16.58 16.22 15.70 15.87 16.01 15.9 4 15.91 15.42 15.16 :8 .9962 .9994 .9964 .9967 .9908 .9855 .9805 .9953 .9987 .9933 .9943 .9807 .9 760 .9 643 .99 38 .9838 .9 623 .9623 9G6 .9630 213 100'131'8 that 4t tI0. 5'4” Equation9 .14 is tho intogratod rato law for a aooond-ordor roaction. Tho initial hanolysis data is fittod into tho abovo forn and tho rato constant I; for givon tonporaturo and soluto ooncontration aro tabulatod in Tablo 9 .1. Tho rosults show good fit with corrolations ranging frcn .9301 to .9994. Ccnparing tho rosults for first and socond ordor rato laws indicatos that tho dorivod rato constants aro not too nuch difforont to substantially offoct tho froo onorgy of activation. Thorofcro it is inpossiblo to chooso cno rato law ovor tho othor on this basis. Ecwovor, tho fact that tho 2.5n rosults aro vary closo for both rato laws can ba intorprotod to indicato that tho roaction procoss (tho danago nochanisn) is scnowhat difforont than thoso at highor soluto ooncontration lovols. Llama». Iochanisn in ch-istry is dofinod as, tho dotailod way through which tho roactants aro convortod into products. ho kinotic study fra a ch-istry point of viow is not conploto unloss tho study rovosls tho nochanisn of tho chonical roaction. Infornation about tho nochanisn is gainod frcn a dotailod knowlodgo about tho rato of roaction undor various tonporaturo. prossuro, and conposition conditions. This is why tho kinotic study in gonoral is vary oonplicatod and ofton controvorsial. Tho 214 rats at which oquilibriun is attainod and tho position of oquilibriun play inportant roloa in tho study of roactions. Changos of activation paranotors, froo onorgy AG‘, ontropy AS‘, and onthalpy AE’ can bo obtainod frcn tho oquilibriun roaction rato constant. Tho oquilibriun stato is gonorally indopondont of tho nochanisn, whoroas tho rato at which tho roaction procoods to tho oquilibriun stato doponds on tho nochanisn. L. Magma”; hmwmmnumsmgmm 11. mm Tho Arrhonius rato law narks tho origin of nodorn kinotic thoory. Iith vary fow oxcoptions tho rata of roaction docroasos onponontially with a docroaao in tonporaturo. Arrhonius [166] to account for tho tonporaturo dopondoncy of tho invorsion rats of sucroso. put forth tho idoa that tho variation of tho spooific rato or rato constant I of tho roaction with rospoot to tonporaturo is orprossod as: r - z .‘3.’“ [9.15] 215 whoro Z is tho "froquoncy factor" or pro-orponontial factor and E‘ is tho "onorgy of activation” or noro corroctly tho "orporinontal activation onorgy" of tho roaction. It is apparont frcn Equation 9.1 that by dotornining tho valuo of K at sovoral tonporaturos, . tho plot of log! vs 1/T will yiold tho activation onorgy frcn tho slopo of tho curvo and tho froquoncoy factor frcn tho intorcopt with tho In! axis. Th. 40‘1'4t103 030387: 3, . of tho roaction (chonical or physical) roprosonts tho onorgy that tho noloculo nust possos if it is to tako part in tho roaction (activatod stato). Tho dotornination of tho activation onorgy is an inportant objoctivo of any kinotic invostigation. Tho froquancy factor (sonotinos callod tho ”collision nunbor" or "collision froquoncy") 2, for a roaction which is tho consoquonco of tho collision of two noloculos nay bo rogardod as tho nunbor of collisions por aooond. Ihoro 0!P(’B.IET), is a noasuro oithor of tho probability of tho occurronco of tho activatod stato or a noasuro of tho fraction of tho total nunbor of noloculos which havo propor lovol ' of activation onorgy to tako part in tho roaction (fraction with 0‘038103 8304t0! th't 3‘). Tho froquoncy factor is usually found to dopond on tonporaturo, howovor, unloss tho tonporaturo rango is vory largo, tho tonporaturo offoct is alnost always nogligiblol164]. 216 Chanioal roactions dopond vory strongly on tonporaturo and nost aro found to follow tho Arrhonius rato law. Providod that tho tonporaturo rango is not largo, cortain physical procossos also follow tho Arrhonius rato law. Tho Arrhonius rato law Equation9.1 is justifiod on a thoorotical basis fron oithor collision thaory or tho thocry of abaoluto roaction ratos. Evan though tho fornor approach is intuitivoly noro appoaling tho lattor is noro ologant. Novortholass noithor thocry is ablo to prodict tho activation onorgy orcopt for vory sinplo casos. mmmmgm Tho oquilibriun constant 8‘ for a roacting systan(chanical or physical) is givon by I,“ ' ci/cs ' Na/Ns whoro 13, I Conccntration in activatod stato O 3 I Concontration in initial stato .F I No. of noloculos in activatod stato No. of noloculos in initial stato 217 ha aasunpticn that tho activatod conplox is in thornodynanic oquilibriun with tho roactants involvod in tho roaction allows cno to arrivo at thornodynanic paruotors of tho roaction by an oquilibriun thornodynanic analysis. Thorofcro, tho oquilibriun constant 1‘ nay bo orprossod in torns of tho standard froo onorgy of tho procoss or scnotinos callod Gibbs function of activation or sinply "froo onorgy of activation", AG’, by noans of tho faniliar thornodynanic oqua ti on (dof ini ti on) -A6‘ - Irma“ [9.16] Tho spocific roaction rato or noro gonorally tho rato constant K can bo shown to havo tho forn r - kTK‘lh [9 .17] whoro k is Boltsnann's constant and h is Plank's constant and it is asst-ad that tho rato constant is orprossod in torns of ccncontrations of tho roactants and products[167]. Equation 9 .17 is tho Eyring oquation for tho rato constant of a roaction. Introducing 1" frcn Equation9 .16, it follows that r - (Hintw‘m‘ [9 .18] 218 Sinco a Gibbs function is rolatod to tho ontropy and onthalpy by CIR-'18 this for constant tonporaturo procoss loads to tho introduction of tho ontropy of activation, AS“, and tho onthalpy of activation Al‘s mum-mt [9.13'1 Introduction of this onprassion into Equation 9 .4 loads to r - (tr/nI.-AI'"T.A3"‘ [9 .191 whoroAE‘ and AS'II aro gonorally roforrod to as tho "boat of activation" and "ontropy of activation" rospoctivoly. Equation 9.19 rosonblos tho Arrhonius oquation (Equation9 .15) orcopt that AE’ 49904" instoad 0! 3‘ and according to this oquation tho froquoncy factor is z - (kT/h)oAS*/n [9 .20] Frcn Equation9.20 it is apparont that a nogativo ontropy of activation rosults in a low froquoncy factor whilo apositivo ontropy of activation rosults in a high froquoncy factor. 219 At this point it is ossontial to discuss tho rospoctivo intordopondoncy of AG‘, AE‘, and AS‘ and thoir consoqucnt offoct on tho rato of a roaction. Ccnparing Equations 9 .17 and 9 .18 it is cloar that it is tho froo onorgy of activations AG‘ which is tho dotorninant of tho rato of tho roaction. his is ospocially inportant for roactions in liquids whoro largo valuas of AE‘ aro conponsatod by high valuas of TAS‘, whoroas in nany gas roactions, sinco tho ontropy of roaction doos not vary groatly, tho AE‘ nay appoar to play an inportant and dotorninistic rolo [167]. In gonoral, any factor docroaaing tho froo onorgy of activation AG" will rosult in incroasing tho rato. his fact is orplorod to advantago whoro cortain substancos, callod catalysts, aro -ployod to incroaso tho rato of tho roaction by loworing tho froo onorgy of activation. WWW An orporinontal activation onorgy can always bo attainod ovon whon tho rato coofficiont doos not follow tho Arrhonius rato law forn givon by Equation9 .15 through tho dofining statonont [166]: 3. - Irr'Iamr/a'r)v [9 .211 220 It is dosirablo to incorporato tho orporinontal activation snotty. E‘, into Equation9 .19 in placo of AE‘ as E. can bo found fra tho roaction rato constant. I. through Equation 9.21. Equation9 .17 nay bo writton as In: - Ink/h + lnT + Int [9.22] Ihoro upon difforontiation with rospoot to tonporaturo wo havo aux/or - 1/1‘ + curt/at [9 .23] but fru Equation 9 .21 aux/at - 8‘1“" [9 .24] also fru Equation 9 .16 wo havo curt/or - Act/31‘ - unnam’lar - AE‘IET' - As‘lar - (1/2)3AG‘"‘/3T [9.25] but sinco as" - OAG’VOT Equation 9 .25 boconos our/or - ant/31' I9 .26] Thorofcro with Equations 9 .24 and 9 .26, Equation 9 .22 boconos 221 B./ET‘ - 1/1' + An‘lnr' [9 .27] solving for E. givos B.-a'r+An" [9.28] Now introducing tho AH"I as givon by Equation 9.28 into Equation 9 .19 rosul ts I I (kT/h)o‘ .AS‘IE.-E.IET [9 .29] ha data fitting procoduro is discussod in dotail , in tho Appondir. ha in Figuros 7.2-7.6 woro fittod to produco tho roaction rato constants tabulatod in Tabla 1 and Tabla 2 in tho Appondir. hoso roaction rato constants aro than usod in Equations 9 .16 and 9 .26 to yiold AG"I and All' rospoctivoly. ho thornodynanic paranotors AG", AE", and AS“ along with tho roaction ruto constant 5 aro proaontod in Tablas 9 .1 and 9 .2. Frcn Tabla 9 .2 it is ovidont that AG‘ docroasos with rospoot to docroasing t-poraturo and incroasing osnotic ooncontration. A11 A8" valuas arcopt ono (boliovod to bo duo to an artifact) aro nogativo. ho Al"I valuas rango frcn positivo to nogativo but in nost casos aro positivo. Furthornoro tho rato constant [p incroasos with incroasing osnotic ooncontration. C(n) 2.5 3.0 3.5 ‘00 222 TABLE 9 .2 Activation Paranators For 1st and 2nd Ordor Iata Laws 1st Ordor :ato Law 2nd Ordor Eato Law rm 16‘ AS m w" 13‘ An‘ (loal/nolo) (lcal/nolo) (cal/nolo C) 88 18 .43 -23.33 10.78 18 .43 -21.33 12.07 283 18.08 -36.67 7.70 18 .11 -48.67 4.34 278 17 .70 ~50 .00 3 .88 17 . 74 -56 .00 2 .17 273 17.58 -65.00 -1.65 17.55 -61.00 .90 268 17.13 -90.00 -6 .99 17.13 44.00 -5.38 38 17.54 -37.33 6.41 17.47 -3 .33 5.75 283 16.98 -12.62 13.40 16.88 -9 .67 14.14 278 17 .04 -32 .00 8 .14 16.9 8 -28 .00 9 .20 273 16.66 -90.00 -7.91 16.60 '9 5.00 '9 .34 268 16 .14 -104 .00 -11 . 73 16 .03 -114 .00 -14 . 52 88 16.92 -48.67 2.42 18.68 -6.67 14.0 283 16.19 -13.33 2.42 16.58 -$ .34 5.45 278 16.30 -30.00 7.96 18.22 -88.00 -8.24 273 15.89 -80.00 -5.9 5 15.70 -35.00 6.15 268 15 .56 -78 .00 -5 .40 15 .8 7 34 .00 24 .9 8 88 16.50 -48 .00 2.20 16.01 -4.67 14.62 283 15.78 -23.00 9 .27 15.94 -5.33 14.43 278 15.3 -33.00 . 6.62 15.91 -52.00 1.45 273 15 .45 -68 .00 -3.11 15.42 -75.00 -5.06 268 15.11 -68 .00 ~3.11 15.16 -52.0 1.22 FREE 3430! OF ACTIVATION Mi" (logl/nola) 223 I8 - I7 - 16 - o T'EIPERATUIE - not I TEII’EIATUEE - an El manna: - 273: A TEIFEIATIIEE - 268! a 11mm“ - m ‘5 l l 2 3 4 NaCl “MEATION (I) Figuro9 .1: ho lolaticnshiphotwoon Froo Enorgy of Activation and NaCl Concontration for 1st ordor loacticn Iodol. 224 o 18 E E 1 5 b g 17 ‘3 3. 3 8 h 64 5 l6 . ~ ‘.’ i‘. o mums - bar 0 MAME - can u mama - 21:: A mucus - zosr . mmmuc - 2141! L 2 3 4 l NaCl Concontrati on (n) Figuro 9 .2: ho rolationship Dotwaon Froo Enorgy of Activation and NaCl Concontration for 2nd ordor loacticn Iodol. 225 ha froo onorgy of activation AG" for tho hyportonic h-olysis procoss has boon plottod in Figuros 9 .1 and9 .2 as a function of ontracollular sodiun chlorido ccncontration for difforont tonporaturos for 1st and 2nd ordor rato'laws rospoctivoly. ho data show slight daviation frcn a linoar rolationship. Sinco tho roaction rato will incroaso orpcnontially as tho froo onorgy of activation dorroasos (soo Equation 9 .18). tho nogativo slopos of thoso curvos indicato that an incroasingly hyportonic NaCl solution will groatly onhanco tho initial rato of tho dostructivo roaction procoss. ho rocn tonporaturo data is scnowhat loss offoctod by NaCl ccncontration as indicatod lg snallor alopo. ho lowost AG’ valuas aro rocordod for tho lowost t-poraturo atudiod, 268K, at a givon ooncontration of sodiun chlorido. ho roaction constant for tho h-olysis procoss, k , has boon plottod in Figuros 9 .3 and 9 .4 as a function of ortracollular NaCl ccncontration for difforont tonporaturos for 1st and 2nd ordor abaoluto rato laws rospoctivoly. ho data show that tho roaction constant I, incroasos with incroasing ccncontration for all tonporaturos. ho largost rato of incroaso is obsorvod for tonporaturos 298 and 2832. ha ccncontration dopondoncy of tho roaction constant is sinilar for tonporaturos bolow 278K. Lcworing tho sot point tonporaturo gonorally rosults in loworod roaction rato constant. hat is tho initial rato of tho 226 5 F O mucus - 29s: I mm“ - 233: g mmmn - 273: 'u" 4 -- A mmmn - rear ‘5 o manna: - 21a: 0 C I a 3 p I O 3 O 2 I: 2 - ‘ I C . fit I - O _ NaCl Concontrati on (n) Figuro 9 .3: Thu NaCl Concontration Dopondonco of Psoudo-Ioacticn constant 5; for 1st ordor loaction Iodol. beetle-Reection Content I 227 5 P O mum; - an: e MAN“ - 233: A manna - 213x ‘ ' c] mamas - 26:: o mama - 213x . 3 P I z I- e n - 0 e 1 O 0 Pi L 2 3 _4 Neel Cmenueuoe (I) Figure, .4: The Reel Ceeeeeneuon Dependence of Peeedo-leeetioe Content ‘; to: 2“ order Reection ledel. 228 destrnetion process is reduced w redncing tonperstnre. be 10"“ 5 vnines for 2.5- NnCI oocnrs nt 273! where (or higher NnCl ooncentrstions it occurs st 278K. At this point it is interesting to oonpnre the I, ..d AG‘ hehnviors hnsed on the shove ohservntions. ‘lhe to-perstnre st which I, is nininnl (278!) does not coincide with the tenperstnre corresponding to nsrinsl AG" vsines (88!). Further-ore. the tenperntnre st which AG‘ is nininnl (268!) does not correspond to nnrinsl 5 vslnes (38K). This indicntes s very oonplionted end strong tenperstnre dependency of the h-olysis process. The entropy of sctivntion As‘ hns been plotted on n function of the enthnlu of ectivetion Al“ for the 1st nnd 2nd order rnte lnws in Figures 9 .5 snd9 .6 respectively. he 1st order nnd 2nd order ectivetion peremeters show quite sinilsr spnn snd hehsvior. It is elso evident thnt grnphs of As‘ we Al' show psrnllel relstionship with o-otic concentretion. i.e.. the AS‘ end A? vslnes st s given NnCI concentrntion nre reinted hy the sinplo linesr eons tion ”harm [9.30] This is referred to ss s thernodynsnic conponsstion low [170]. 229 since ss is nppsrent fron Bqnntion 9 .19. vnrintion of one per-eter for ernnple AS‘ in the positive direction is oonpensnted for by vnrintion of All" in the negetive direction. In other words whntever the contrihntion of nny process or nechsnis- to ‘ AS‘. ennctly the snne contribution is oontnined in Al“. his in foot is the chief resson for the observed snnll vnrintion in AG‘ for different tenperstnres nnd concentretions. no t-perstnre “to-1]. is cnlled the conponsntion tenperntnre [170]. Bra the leest sonnre fit of the dntn presented in Fignres 9 .5 end! .6. the following resnlts nre ohtsined; 1st order rete lsw: 63‘ 3.635‘10"Al' - 60.064 H I 3 215.06 x 2nd order rete lsw: 3.644AIP - 60.440 Bi h I H I 6 214.43 1 Such slinesr relstionnhip between Ar nnd AS" hns been observed for severnl physicnl nnd ch-icnl processes [168-110]. 230 0 F f 0° -20 '- A0 P .. AB H .1 -40 __ 00 O 5 _. no g -60 u -so +- [P O 2.5- O 3.0- " 00 D 3.3- .100 #- A 4.0- (D L -120H— 1. I . L 1 __JJ -15 -10 -s 0 s 10 All" (ran/.616) Fignre9 .5: The Ielstionship Between the 1st Order Eyring Activetion Pnrsneters 48“ end Al“ for Byportonio NnCl-indnced lenolysis for 1st Order lesotion Iodol. 03‘ (csllnol e I) 231 20 0 _. .. O .20 - o b— O [J -40 — E ._ l§>’ 0<> -‘0 r- - o o 2.5- I: 40 _ O 3.0- 0 D 3.5- .. E] ‘5 4.0- O ~100 - —120 L I I 1 ' L—J -15 ~10 -3 0 5 10 60* (loci/loll) Figure 9 .6: The Relationship Between the 2nd Order Eyring Activetion Psrsneters AS“ nnd M“ for Hypertonio NsCl-induced lenolysis for 2nd Order lesction Iodol. 232 It hee been ergued thet this epperont lineer behevior is wholly ertifeetuel [171]. net is the lines: reletionship between A3‘ end Al'b of e reection is of no significence. However. the respective intercepts in Figures 9 .5 end 9 .6 ere significsnt. The AS‘ intercepts ere -60.064ce1ll end 40.440ce1/K for 1st end 2nd order rete lewe respectively. This intercept (i.e. b in Bountion9 .30) is celled the intrinsic entropy of ectivetion Mt, Substituting for 58" in Bountion9 .18' fro. Equetion 9 .30 we heve; AG“ - u‘u - 'r/ro) - m: [9.31] ForAr-O: - _ i W “3 . [9.321 Fro. the ebove equetion then. A6.”I the intrinsic ectivetion energy is tenpereture dependent end veries fru 16.10 to 17.90!oellnole'end 16.20 to 18.0110e1/nole for 1st end 2nd order rete lewe respectively. On the other hend fru Bountion9 .30 we heve; All‘ - Ar. + 'rcAs" [9.33] 233 where Al‘. - -b/e - 16.5213 [cel (let order rete lew) - 16.5867 lcel (2nd order rete lew) Substituting for All“ fro. Bountion9 .33 in Bquetion9 .18' we hevo.‘ 60" - u‘, + (1"3 - mm“ [9.34] For AS‘- 0. Mf-Al‘. Thet is when the entropy of ectivetion is equel to zero the free energy of ectivetion is equel to the intrinsic enthelpy of ectivetion. If we consider the Tom‘ in Bountion9 .33 to represent the structurel contribution to the enthelpy of ectivetion. it is evident fro. Bountion9 .34 thet the structurel contribution to the free energy is (To - 1)As‘. Since (T° - T) renges fro. ebout +8 to 44!. the structurel contribution to A0" is nuch -eller then thet of Al’. In fect this is the .ejor if not the only resson for the observed co.pensetion lew end therefore conperetively nell vnrintion of AG‘ velues (tebuleted in 'l'eble 9 .2). ‘lhis .eens AG" 234 is .ostly .ede up of the intrinsic enthelpy AI". es (To - ‘1')A8‘ renges fro. -1.41 to lsllcnl/nole end -1.43 to l.94lcel/.ole for 1st end 2nd order rete lews respectively. no structurel contribution. (‘1' - Tons", to A6‘ dogorven e. interpretetion. “his ter. in Bountion9.34 es discussed shove will chenge sign ee t-pereture is decreesed below To, net 1. 101’ tap-return 10“ “I“ To the structurel contribution is negetive (es ASWO) end for tenperetures greeter then ‘1'. the structurel contribution is positive. his in tons of AG‘ .eene thet it is less for t-peretures below To “9.3.4 to those .1: t-DOfltu'“ “31"! ”In To. i.e.. the energy berrier height is decreesed for te.peretures below To. however. the ebove ergunent does not necesserily .een thet the reection will proceed fester et lower taperetures. To cleer this very inportent point the following ergunent is presented. lhe behevior of the cell end therefore its fete depends prinerily on the enount of weter rushing in the cell.- In other worde. the rete of reection depends on the weter conductivity of the cell .e.brene. 'Ihe cell .e.brene per.eebility I, 1. t-pereture dependent end eccording to Jeoobs is given by the following generel for. (171]; I, - K'erplb(‘l'-'l'.l [9.35] 235 where T - 293x . b - .0323" end K‘ is the red blood cell no.brsno per.eebility st t-pcreture I“, end b is celled the per.eebility te.pereture coefficient [172]. Therefore we hsve; l,(1--290>/g(1-26s) - 2.65 net is the resistenoe of the cell .-brsne to trensport of weter ecross it is increesed by e fector of 2.65 for te.pereture 268! co.pered to 298‘. Since the dnnege is e function of weter rushing in the cell. the hinderence of weter trensport is directly responsible for the observed co.peretively slower kinetics st sub-snbient te.peretures. It is to sey thet the loss of cell weter end therefore denege is postponed st low te.peretur es. no ('1' - TOMS" vslues for different reection conditions ere tebulsted in Teble 9 .3 for 1st order rete lew. Concentretion (n) 2.5 3.0 3.5 4.0 236 IIILI!!.3 (T - 1;)A|‘(csl/.ole 0) 263 -.630 -.728 -.546 -.476 Ihnperstere(l) 273 273 233 -.130 .150 .293 -.130 -.096 .101 -.l6o .090 .107 -.136 -.099 .134 103 .303 .435 .633 .624 237 It is clesr fro. these dsts thet the tyrant “a...” for . given concentretion level by decreesing the te.pereture of the rescting nirture. no fsct thet the n-oricsl veins of Tc 4. close to the freezing point of weter is significent. uphesising the inportent role pleyed by weter in the reection process. Another inportent observetion is the ebrupt increese in the structurel contribution to the free energy of ectivetion st 298! co.pered to the veins st 233! for concentretions greeter then 2.5.. The positive vslues of (‘1' - TOMS‘ for te.peretures greeter then To is en indicetion of the extent of the disorder in the ectivetion stete. n. euthor believes it is st this disordered stege where .-brene .oleceles sre desorbed into weter. The thernodynenic properties for desorption of long chein hydrocsrbon .olecules shows thet the free energy of desorption is s positive quentity end increeses with chsin length [172). Furthornoro. where sneller .olecules gein entropy upon desorption into weter the entropy of desorption becc.es negetive for lerger .oleceles. “his is believed to be due to the orientstion end psrtiel i-obiliretion of the weter .olecules eround the hydrocsrbon chsins [173]. The dete represented in Figures 9 .5 end 9 .6 sre quelitetively in egreuent with the trends of the thernodynsnic properties of 238 the long ohein hydrocerbon desorption process. he negetive velues of ('I' - “rams“ in ‘l'sble9.3 for te.peretures below To represents the fect thet: even though the ectivetion process results in e .ore ordered stete. the structurel contribution to the free energy of ectivetion is negetive. Since the rete of the reection'is controlled by AG". this nesns thet st te.peretures below To a. reection "loony 1. higher. no euthor believes this is en indicetion of e brittle stete where the intersctions between .e.brene noloculos ere weekened end subsequently the .-brene is susceptible to denege. However. es nentioned eerlier. the weter conductivity of the cell .-brsne is drssticelly lowered st these t-perstures. ‘Iherefore the likelihood of the .-brene structure collepsing due to the substsntisl loss of weter in e short tine is considerebly reduced. The forgoing ergunent inplios s pertisl desorption of hydrocerbons or proteins fro. the .-brene into the equeous .ediu. According to Devis. end Hideel. s noler 43, group requires e A0 of +810 celories to pess into the equeous solution fro. the oil-weter interfece [172]. If the intrinsic free energy of ectivetion A?. (to: T'Tc or As’I-O) for the Ne01 induced he.olysis is co.pered to this figure of 810 cslories/nole. the 49113081.“. III-503' 01 '3, groups perticipeting in the ectivetion process is found to be 20. Considering the everege nunbor of «I, 239 groups per hydrocerbon noloculo of 28-48 [173]. it is clesr thet the derived nunbor Of 20 'Cl, groups indicstes thet the sctiveted co.pler or the trensition stete consists of e helf-desorbed hydrocerbon .olecule. no entropy lost by the equeous nedie per 4!, group i-ersion is ebout 5 cellnole I [173]. If the intrinsic entropy of ectivetion AS‘. is divided by the velue 5 cellnole I. then the epprorinete “lb“ 01 '5. groups involved in the sctiveted co.pler is found to be 12. Both estineted nunbor of «In, groups involved in the trensition stete indicete thet et this stete the noloculos ere still pertislly stteched to the .e.brene. Finelly. the present dste ere in egre-ont with the hyphothesis thet the ectivetion .echenis. for cell .e.brene densge due to hypertonic NeCl solution is s pertiel desorption of the .-brene co.ponents. CHAPTER! CONCLUSION AND SUGGESTIONS FOR FURTHER '08! Amount” The physioohuicel elteretion of cells es s result of freezing during e cryopreservetion protocol st sub-optinsl cooling retes is known to be due to the coupled effects of lowered te.pereture end the increesed solute concentretion. The living cell in the ebsence of protective egents is usuelly injured es s result of exposure to these thernel end ch-icel perturbetions which occur sinulteneously during froosing. An understending of the effect of these two nejor fectors is essentiel for the design of en optionsl freeze-thew protocol. no .ejor goels of this work were : 1) To develop en oxperinentel syste. end technique for ' s decoupled .eesure.ent of the enount of denege incurred due to e desired thernel end che.icsl elteretion of the cells. 2) To generete e co.plete dete bese in the for. of h-olysis kinetics for the h-en red blood cell. 3) To enelyse the cell responses to inposod perturbetion in 240 241 terns of thernodynenic end kinotic principles. The outcone of e freeze-thew protocol greetly depends on the dynmnic events produced by the re.cvel of the syste. fro. its physiologicel equilibriu. stete. es the cell recovery is intinetely dependent on the cooling end werning retes. Unfortunetely infornstion on cell he.olysis hes either been of e stetic type or of e questioneble neture. However. it hes been cleerly shown thet in order to quentify the freezing injury due to the sinulteneous verietions of the te.pereture end concentretion. decoupled studies of these coupled fectors resulting in infornstion in the for. of he.olysis kinetics sre essentiel. To decouple the che.icel end thernel effects en inproved stop flow syste. equipped with te.pereture control with the potentiel for .eesure.ent of the red cell destruction dynnnics hes been designed end developed. The stop flow technique provides very rspid .iring end therefore the denege dynenics for short tines (order of seconds) ere obteined. This technique represents e definite edventege over the stenderd technique for henolysis .eesure.ent of the blood senple (on the order of severel ninutos). Even though the oxperinentsl principles of the stop flow technique were elreedy known. beceuse of the biologicel neture of the problon. severel vitel nodificetions were necessery in order- to obtein relieble results. The he.olysis rete dete for the hunen 242 red blood cell populetion induced by severel hypertonic sodiun chloride concentretions heve been obteined. Iith the eid of the thernel control cepebilities of the syste. the te.pereture dependence of the ch-icel perturbetion hes elso been studied for severel isothernel sub-snbient te.pereture conditions. The stop flow syste. proved to be cepeble of genereting the h-olysis dete in the desired rete fornet. However. it wes found thet extras cere in terns of e conplote understending of the opereting cherecteristics of the syste. is required. The results obteined here indicete thet the che.icel perturbetions (increesed selt concentretion) st e given isothernel condition were sinilsr et ell t-peretures. However. the thernel perturbetions et e given sodiun chloride concentretion level proved to indicete e te.pereture dependent process. For kinetic enelysis the h-olysis process is treeted es s che.ciel reection of the blood cell senple end sodiu. chloride. The te.pereture end the sodi- chloride concentretion dependence of the h-olysis kinetics is studied in terns of the let end 2nd order rete lew for short exposure tines. The retionel for this is thet the forwerd reection rete of the destructive huolysis process is cherecteristicelly very repid et short tines co.pered to thet et reletively long tines for ell te.peretures end concentretions. no thernodynenic ectivetion persneters. free energy of ectivetion. ectivetion enthelpy. end ectivetion entropy essocieted with these kinetics heve been enely sed. 243 Biologicel syste.s ere very sensitive to chenges in environ-ontel persneters such ss t-persture (resulting in so celled thernel shock) end electrolyte concentretion (resulting in so celled osnotic shook). Severel nechenisns for injury besed on the necroscopic enelysis of the physio-chenicel events essocieted with the thernel end osnotic shock heve been hypothesized by e nunbor of investigetcrs. Despite the diversity of the proposed nechenisns they inveriebly egree thet the he.olysis produced by either perturbetion nodes to ceuse duuege pri.erily et the .e.brene site. Specificelly evidence with respect to the loss of .e.brene conpononts induced by such environnentel elteretions is nounting. Therefore. in the present work. the thernodynenic ectivetion pere.eters essocieted with the he.olysis kinetic process heve been enelysed.’ It is shown thet the trends of the thernodynenic properties ere‘ in egreenent with thet of s desorbtion process involving long ohein hydrocerbons. The conclusions concerning the te.pereture effect on the h-olysis kinetics dete obteined here. ere presented. in chepter VII. Furthornoro e co.plete enelysis end conclusions regerding the derived thernodynenic ectivetion pere.eters ere presented in chepter n. In eddition. e co.plete discussion of the hypothesized .echenis. for celluler injury elong with e theoreticel ergunent in support of dissolution theory is presented in chepter VIII. Therefore in this section we would like to 244 consider sproposed nechenis. for the cell freezing injury in light of the present results end enelysis. Cells exposed to hypertonic solutions go through shepe chenges. The .e.brene becones distorted end the effective eree of the .e.brene decreeses while the volune re.eins constent. no fect thet red cells under stress beco.e sphericel during ouotic shrinkege inplios thet the intrecelluler .e.brene pressure should increese [1“.126.127.173-l75l. As pressure is releted to the nunbor density of .clecules et the .e.brene . the increesed .e.brene pressure results in .e.brene constituents beco.ing closely peoked (87]. The ven der Heels forces between the hydrocerbon teils fevor close pecking. On the other heed. the .utuel intersctions of the ionic or Zwitter-ionic poler heed groups do not fevor such close pecking. Now eccording to Hquetion 2.1. the concentretion of free ions et the .e.brene surfece should decreese i.e.. softening of the ice like structure of the hydretion shell. This nesns thet the .utuel intersctions between ions in the hydretion shell (bound weter) becones weeksr es s result. net is the shrinkege of the cell .e.brene produces e tendency for the bileyer constituents to leeve the plene of .e.brene. Since the lipid bileyer surfece in en equeous solution is nonhc.ogeneous. the tendency of the .e.brene surfece to expend will only be confined to certein lccel ”week" perts of the .e.brene. Therefore es s result of increesed pressure in the 245 .e.brene. the .e.brene conpononts ere forced out of the plene of the .e.brene. This could result in eveginetion end nicrovosicle fornetion which breek off fro. the .e.brene. This hypothesized behevior hes been observed in noncleyers (see Ref. [175] for review). Such vesicle releese fro. the cell .e.brene. either into the intrecelluler or extrecelluler co.pertnents hes been observed for erythrocytes end plsnt protoplests [45.46.130.174]. If such releese of .e.brene effective eree exceeds the criticel linit. the cell upon thewing. cen not return to its isotonic volune end therefore it .ey be lysod. Furthernore. if the osnotic stress is severe enough the loss of .e.brene eree could leed to e fornetion of holes in the .e.brene through which h-cglobin could be lost so thet the cell becones he.olysed. Evidence concerning the elteretion in the cytoskeleton network in red cell in response to hypertonic exposure hes been presented [45]. The .e.brene intersction with the spectrin-ectin cytoskeleton network hes been suggested to be responsible for the red cell (.e.brene) shepes end therefore lysis of the (cell [52-57]. This idee is definitely in line with the shove ergunent. Once the cell is shrunken to e criticel configurstion the cytoskeleton intersction with .e.brene noloculos will be greetly enhenced. The cytoskeleton network is .ede up of nuch lenger .olecules (proteins) co.pered to lipid .olecules et the .e.brene. Therefore. severel lipid .olecules could essociete with one 246 protein noloculo thereby. cresting e lccel necroscopic elteretion in the .e.brene. This egein could result in eveginetion end .icrovesicle fornetion. Horoske et sl. studied the effect of o-otic shrinkege on egg-lecithin liposmes. They found thet during o-otic shrinkege the vesicle r-eined or becene sphericel end their redii decreesed linesrly with tine. They reported fornetion of finger-like perturbenoes end deugther vesicles under osnotic shrinkege end concluded thet e loss of ective well eree tekes plece during the process. Since the liposo.es leck eny type of supporting skeletel network. one one not see-e thet the cytoskeletel network in for exenple blood cell .e.brene pleys the doninent role in h-olysis. The euthor believes thet the cytoskeleton pleys en inpcrtent role once the .e.brene is shrunken close to the criticel linit end the cell volune hes been considerebly reduced. In en effort to offer sue insight regerding the likely .echenis. end process of re-structuring of the .e.brene syste. es s result of extrecelluler perturbetions lending to denege. e hypotheticel 1““ will be given here. According to this .odel the ..brene syst- under osnotic stress is forced to go through s loss of .e.brene constituents to the ertre- end/or intrecelluler environnent. no loss of .olecules fro. the .e.brene is thought to stert st e structurelly week loci. Ioleceles ere releesed in the for. of nicelles end/or nicrovesicles. Here we will consider 247 the oese of hypertonic exposure. The euthor believes the releese of ..brene conpononts. eccording to our nodel. tekes plece in the following .enner; 1) Exposure to hypertonic solution results in increese in the .oleculer nunbor density. e direct consequence of intrecelluler pressure. This is envisioned es the .e.brene proceeding fro. stete A to stete H in Figure 10.1. Consequently the ice-like structure of the hydretion shell is softened. In other words. the concentretion of free icns et the .e.brene surfece decreeses. 2) In stete H es the noloculos begin to peck closer. the ven der Ieels intersctions between the hydrocerbon teils end ionic intersctions between the heed groups ere sltered. Due to the neture of these intersctions the hydrocerbon teils fevor close pecking. wherees the heed groups do not fevor close pecking. Therefore. the close pecking of .olecules in the plene of the .e.brene creetes en inbelence. This is conceptuelly reflected in stete C es kink forneticns on the n-brene surfece. 3) These structures ere finelly forced co.pletely out of the cell .e.brene. The re-strnctured .olecules .ey stey stteched to the nother cell or be releesed in the for. of nicelles or nicrovesicles. 249 The for-entioned procoss will el ter the .e.brene per.eebility to solutes. It will eventuelly result in fornetion of holes in the .e.brene lerge enough for the encepsuleted .olecules to leeve the cell end ceuse lysis. Concerning the low te.pereture preservetion. the euthor believes the .oleculer re-errengnent due to the externel perturbetions will be dresticelly eltered (unfevcreble) during cooling process of e frees-thew cycle. I; i!§§£flllflfl§.£9§ RUIZ!!! I!!! The inproved experinentel epperetus. nenely the stop-flow syste.. equipped with te.pereture control hes been developed end shown to be en excellent tool to neesure the destruction dynenics of the red blood cells over e wide renge of te.peretures. In the course of producing the thernel shock dete the te.pereture of the blood senple is dropped below the rca te.pereture velue in two to four seconds. It needs to be deternined whether or not the initiel te.pereture drop predisposes the cells to thernel stress severe enough to effect the kinetics st long exposure tines. To ecoe.plish this. the euthor suggests; 1) subject the cells to severel cycles of te.pereture drops (et cooling retes experienced by the cells during e typicle oxperinent) before the finel run. 2) initielly cool the blood cells to the sene tupereture es the test solution. Co.pering the dete presented in this work with those 250 obteined in 1 end 2 ebove should shed light on the question of the effect of initiel t-pereture drop on the he.olysis kinetics. It hes been ett-pted in this work to show thet the. sheer stress incurred during nixing does not effect the kinetics of denege process. An effort should be .ede to nessure end clessify the stress levels inposod on the red blood cells going through the nixing chenber. It is needed to exeggerete such e nechenicel stress in order to dotornine how this could effect the h-olysis kinetics et sub-optinel cooling retes. Another epproech would be to use less turbulent nixing sche.e where the nechenicel stress would be non-existent or nininel. end co.pere the results with the dete reported in this work. The long exposure tine h-olysis dete obteined here end elsewhere show fist e few percent of the cell populetion snstein severe hypertonic conditions for long periods of tine. This inplios the possibility fist in eny given populetion of the red blood cells there .ey exist e -ell populetion of "super" cells which ere r-erkebly different fro. fie "nornel" cells. A study of populetion-cherecteristic verience need to be underteken to deter-ine whether such super cells exist. For exenple. it is feesible to seperete these cells (if they exist) fro. others by he.olysing sey 90‘ of fie cells end through e proper technique r-oving the perturbing elaent (thernel end/or ch-icel). |\ 25] A..ejor contribution would require en effort concerning the deteiled .oleculer es well es etonic intersctions end .egnitude of forces involved in the .e.brene syste.. Such studies should bring ebout elegent stetisticel nechenics studies of the .e.brene syte. both et experinentel end theoreticel levels. An inpcrtent contribution would be to study the he.olysis kinetic process unploying conplotoly different oxperinentsl epproech. One such epproech would be through e photonetric study utilizing s diffusion chenber developed in this leboretory. For this the .ejor tesk is to errive et e celibretion technique. This could be eoccnplished through en inege enelysis technique. For exenple. the diffusion chenber could he used in conjunction with e light .icrcscope. The .icrcsccpe inege one then be digitized. Once e relieble correletion between the light intensity pessing through the cell (densged or heelthy) is esteblished. the he.olysis kinetic dete could be inferred st eny extrecelluler concentretion et eny desired te.pereture. Finelly. in order to fully understend the role of nonbrene constituents (lipids end proteins) in en equeous environ.ent in reletion to stebility of fie .e.brene syste.. e theoreticel kinetic nodel of the ectivetion process initieted here should be used es s sterting point. 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Therefore for e given tenpereture end NeCl concentretion severel initiel tine intervele were enenined (the tine intervels stert et zero second). The reection constent for the intervel with highest coefficient of deterninetion (r’) were then used to celculete the ectivetion pereneters. The rete constent end the coefficient of detemnibetion for different conditions ere tebuleted in Thble 1 (1st order reection rete lew) end Teble 2(2nd order reection rete lew). 267 T(K) 88 283 Exposure 60 90 180 240 Tine(see) A. 1.04 1.02 1.03 1.02 .19 .14 .07 .06 r .987 .954 .998 .992 “ND 38 Exposure 30 40 60 40 Tine(see) A; 1.13 1.11 1.05 1.05 K, .92 .84 .62 .31 r .995 .994 .963 .988 T(K) 38 283 Exposure 40 60 60 90 Tine(sec) A. 1.18 I.“ 1.25 1.27 x; 2.40 ms 1.19 1.“ r .978 .967 .981 .993 T(K) ’8 Exposure 25 30 40 60 Tine(see) A. 1.61 10" 1.33 1e1° x; 5.19 3.30 no 3.76 x .964 .979 .981 .933 A - A.EKP(-K;‘t/100) 268 TULEI 1st Order Hste Lew 120 1.03 .06 .999 1.07 .34 .9 88 1.0 .88 .9 83 2 .5- 278 130 180 240 180 1.03 1.03 1.03 1.03 .06 .06 .997 .999 3.0- 90 60 1.10 1.04 .45 .22 .990 .997 3.3- 278 60 90 1.14 1.20 1.10 1.31 .978 .981 4.03 .06 .99 7 278 90 1.03 .23 .99 7 1.14 .96 .993 1.31 4.10 .968 where .04 .996 120 1.06 .26 .994 90 1.42 3 .80 .9 82 A. 273 240 300 90 1.04 .05 .997 1.04 .03 .99 6 1.01 .03 .983 273 130 90 60 1.06 .26 .999 1.07 1.07 .35 .961 273 30 40 60 1.21 1 ..o .9 74 1.32 2.23 .9 76 1.13 .977 1 - W100 268 120 130 1.02 1 .02 .06 .07 .99 2 .9 83 268 90 120 I.“ I.“ .38 .38 .9. .99 3 268 90 120 1.24 1.23 1.31 1.27 .990 .993 1.63 1.48 3.01 2.65 .988 .987 T(K) .8 Exposure 60 90 150 Tine(sec) A. .961 .971 .973 r; .190 .160 .061 r .996 .985 999 T(K) '8 Exposure 40 60 40 Tine(see) A. .875 .927 .945 .96 .74 .33 r .996 .966 .986 T(K) ’8 Exposure 30 40 60 Tine(eee) A“ .630 .671 .810 K, 3.88 3.65 2.97 r .995 .994 .972 T(K) ’8 Exposure 40 60 90 Tine(see) A. -.013 .041 .34 s; 114 11.3 9 .61 r .963 .984 .974 180 240 971 .062 999 283 60 9 18 .43 .9 84 .920 0.. .986 20 .874 ..4 2.13 3.” 9. .907 973 .061 .999 9 0 .884 .34 981 283 40 .. 7 0.92 981 269 TAIL82 2nd Order Hete Lew 2 . 3- 278 130 180 240 .968 963 .063 .068 996 996 9. .063 996 3 .h 278 40 943 933 .23 .23 1.00 .998 .9. 996 3.3- 278 60 30 .830 .920 101‘ 00.1 .976 973 1.02 .9 76 4 .0- 278 20 30 .714 2.42 .9 43 .9 07 .821 1.20 1.80 99 7 9 62 1/ [HBC] - A. + 1;" 273 273 180 9 68 .047 99 3 120 928 .31 997 23 0.73 9 240 90 961 .032 993 60 927 9. 273 30 920 0.3 78 986 273 23 .803 ' 2.13 973 . 747 2.37 970 268 120 130 986 983 .977 .034 .060 .0. 998 991 981 268 90 120 130 903 ..3 .871 .44 .47 .32 986 993 9. 268 23 30 ..7 092 981 938 923 0.64 0.71 994 9. 268 90 120 130 -.64 7.83 9 72 ‘97 -93 8.87 8.80 981 990 270 4 L- 3 - 2 u— f‘ O 2 " 1. .. .1. en 5 : e 8 n .3 g .1 .3 — 3 3 .2 - NeCl Concentretion 92.5- 3.0- 0.1 - 3.5- 4.0- 0.05 ‘- 0.04 _ 0.03 1 L 1 I 3.3 3.4 3.5 3.6 3.7 3.8 1/1' (10%“) FIGDHE 1: Initiel Benolysis Hete et Different NeCl Concentretions.