Freezing, drying and/or vitrification of membrane-solute-water systems.

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1 Thi material ha been publihed in Cryobiology, 39, , the only definitive repoitory of the content that ha certified and accepted after peer revie. Copyright and all right therein are retained by the Academic Pre. Thi material may not be copied or repoted ithout explicit permiion. Copyright 1999 Academic Pre. IDEAL (International Digital Electronic Acce Library) i at 1 Freezing, drying and/or vitrification of membrane-olute-ater ytem. Joe Wolfe 1 and Gary Bryant 2 1 School of Phyic 2 Department of Applied Phyic The Univerity of Ne South Wale RMIT Univerity Sydney J.Wolfe@un.edu.au Melbourne Gary.Bryant@rmit.edu.au Abtract Membrane are often damaged by freezing and/or dehydration, and thi damage may be reduced by olute. In many cae, thee phenomena can be explained by the phyical behaviour of membraneolute-ater ytem. Both olute and membrane reduce the freezing temperature of ater, although their effect are not imply additive. The dehydration of membrane induce large mechanical tree in the membrane. Thee tree produce a range of phyical deformation and change in the phae behaviour. Thee membrane tree and train are in general reduced by omotic effect, and poibly other effect of olute provided of coure that the olute can approach the membrane in quetion. Membrane tree may alo be affected by vitrification here thi occur beteen membrane. Many of the difference among the effect of different olute can be explained by the difference in the cytallization, vitrification, volumetric, partitioning and permeability propertie of the olute. Key ord Cryobiology, anhydrobiology, hydration force, dehydration, vitrification, membrane, phae behaviour, gel-fluid tranition, lipid. Introduction Membrane are often damaged during the proce of freezing and thaing, or during deiccation and rehydration. Indeed rupture of the plama membrane i one of the mot commonly ued indicator of cell death. Freezing may alo impair activity in biological membrane. Variou olute limit thi damage, both in living organim and in model ytem (Steponku, 1984; Leopold, 1986; Anchodorguy et al, 1987; Hincha, 1989; Sun et al, 1996; Shakir and Santariu, 1995; Croe et al., 1997; Ring and Dank, 1998; Sampedro et al, 1998) and thee olute are accumulated by ome freezing-tolerant and deiccation tolerant pecie (Lee, 1989; Ring, 1980; Roja et al, 1986; Walyk et al, 1988; Koter and Lynch, 1992). In thi paper e analye the interaction of membrane ith ater and olute at freezing temperature and/or lo hydration. We alo conider briefly the hydration of macromolecule in freezing olution. Thi paper extend a previou analyi of thi topic by the ame author (Bryant and Wolfe, 1992), in the light of reearch in the lat everal year, over hich time coniderable progre ha been made in undertanding the effect of olute on membrane hydration and interaction, and on the effect of vitrification. The approach taken i to give phyical explanation and illutration in the text, ith the mathematical and formal thermodynamical detail relegated to appendice. The firt half of the paper concentrate mainly on the phyical principle involved and the econd half on the effect of olute on membrane propertie at freezing temperature.

2 2 In dicuing olute, e can looely divide them into three broad categorie: alt (mall, charged), ugar and other medium ized related molecule (uually uncharged), and macromolecule. Some of the effect e dicu apply to all olute type (e.g. they all occupy volume). Other may differ among group (e.g. macromolecule are le likely to permeate membrane and to partition into lamellar phae). Mot of our dicuion concern ugar and macromolecule, and the electrical effect of ionic olute are dicued here only briefly. The cooling of cell can be divided into lo and fat cooling by comparing the time for thermal and hydraulic equilibrium. The cooling rate that mark thi diviion varie coniderably among cell of different type and ize. In the natural environment, cooling rate are lo and o the ditribution of ater often ha the time to approach equilibrium. In thi paper e conider procee and phenomena that are relevant mainly to lo cooling. Extracellular freezing uually occur before intracellular freezing (dicued later). The formation of extracellular ice concentrate the extracellular olute. Thi elevate the extracellular omotic preure and thu caue ater to leave the cell omotically. Water content of order 10% or le are poible. Thu lo freezing and deiccation in an atmophere ith lo humidity have many feature in common. In ome cae, equilibrium thermodynamic allo the calculation of the mechanical tree to hich membrane are expoed and the ay in hich olute affect thee. We hall therefore begin by conidering the equilibrium thermodynamic of olution, of membrane-ater phae, and membrane-olute-ater phae. For implicity e hall dicu lipid bilayer membrane, although e anticipate that much of the dicuion ill be applicable to other hydrophilic membrane a ell. Non-equilibrium effect, epecially vitrification, are dicued later. From model and theorie to living cell Experimental invetigation of thee thermodynamic and mechanical effect have often been conducted on model ytem compriing only everal different chemical component, but in hich the compoition i both knon and controlled. Thi alo facilitate theoretical analyi. Much of thi revie concern uch imple ytem. Caution hould of coure be exercied hen comparing phenomena in a lamellar phae of lipid membrane or a regular hexagonal array of macromolecule ith thoe occurring in biological cell. Neverthele, in the cae of freezing-induced dehydration, the analogy i relatively trong. When the ater content of a cell fall to ay 10 or 20%, all of the non-aqueou component are cruhed very cloe together. Electron micrograph of uch freeze dehydrated cell ho tack of membrane hich cloely reemble lamellar phae, and ometime hexagonal II phae (Gordon-Kamm and Steponku, 1984; Steponku, 1993; Steponku et al., 1993, Uemura et al., 1995). (It i alo likely that a cell ith 10% ater content alo contain region of cloely packed macromolecule, although thi ould be harder to recognize in electron microcopy.) Further, electron microcopy of freeze-dehydrated cell ho ome intereting topological feature that are correlated ith damage (Steponku and Webb, 1992; Fujikaa, 1995). Thee feature, hich e dicu in more detail later, are found in the membrane-rich region or here membrane are cloe together. In ome cae the region appear to lack intra-membrane particle and o may be plauibly modelled by tack of bilayer in a lamellar phae. Macromolecule are often excluded from dehydrated lamellar phae (Li et al, 1982; Bryant and Wolfe, 1989) o it i reaonable to expect that a dehydrated cell contain membrane-rich domain and macromolecule-rich domain. Moreover, many of the thermodynamic and mechanical effect dicued in thi paper ould be expected in any ytem compriing nanometer-ized hydrophilic object in aqueou olution. A e hall ho (Appendix 4), different geometrie give imilar equation, differing chiefly in numerical factor. The complicated geometrie and uually unknon compoition of cell component mean that, hile quantitative etimate may be difficult, the qualitative behaviour hould be imilar. The la of thermal phyic and thoe of Neton may be difficult to apply quantitatively to cell, but there i no reaon to expect that they are violated. Phae equilibria of ater, olute, membrane combination It i orth revieing freezing and the effect of olute on freezing, o that e can compare thi ith the effect of membrane.

3 3 Freezing point depreion due to olute. Freezing repreent a balance beteen the loer enthalpy of the olid phae and the higher entropy of the liquid phae 1. An equilibrium phae tranition occur at a temperature T here T S = L here L i the latent heat of fuion and S i the change in entropy at fuion. The preence of olute in liquid ater increae the entropy of the ater molecule. When ice form, it crytalline tructure exclude almot all olute, o that ice i an almot pure, ingle component phae. A a reult, the entropy of the ice i almot unchanged by the preence of olute in an ice-olution ample. On the other ide of the equation, the preence of olute make little difference to the latent heat of fuion. In the preence of olute, S i larger o the equilibrium freezing temperature T i loer. (Some of the thermodynamic for thi ection i developed in Appendix 1.) Thi familiar reult commonly called freezing point depreion i uually plotted a freezing temperature T v olute concentration C (Fig 1a). For the purpoe of comparion ith membrane hydration and for cryobiology, hoever, it i helpful to conider T a the independent variable. It i alo helpful for the comparion to repreent the compoition of the olution a the hydration of the olute, i.e. the mole ratio of ater to olute, rather than the concentration. Thi i hon in Fig 1b. At lo (olute) concentration, the hydration of the olute i approximately proportional to the reciprocal of the concentration, o the nearly linear region in Fig 1a approximate a hyperbola in Fig 1b. The data in Fig 1a are tandard data for ucroe (Weat, 1990). The olid line in 1b ho the behaviour of a hypothetical ample hoe total compoition ha 80 ater molecule for each ucroe molecule. Thi compoition ha a freezing point of about 1.5 C o, above thi temperature, the ample i a ingle, homogeneou olution phae. Thi i indicated by the horizontal line. At loer temperature, the equilibrium condition for thi ample comprie a pure ice phae in equilibrium ith a olution hoe compoition i given by the curve. Thi olution phae contain all of the olute and a quantity of liquid ater, hich decreae a the temperature fall. Sample ith different total compoition ould be repreented by different horizontal line above freezing, but all follo the ame curve belo freezing. Freezing point depreion due to membrane. A tandard ay of repreenting the colligative or hydration propertie of a lamellar phae i a plot of the inter-lamellar force per unit area a a function of hydration or inter-lamellar pacing (Fig 1c). We return to thi repreentation later but, for the purpoe of thi comparion, e hall firt conider the hydration of a lipid lamellar phae a a function of temperature (1d). At high hydration (more than about thirty ater per lipid) and above freezing temperature, lipid-ater upenion eparate into to different phae: a lamellar phae ith about thirty ater per lipid, and a bulk phae of nearly pure ater. At loer hydration and/or freezing temperature, hoever, there i no exce ater phae: jut a ingle lamellar phae. When a highly hydrated ample i frozen, the bulk ater freeze and the lamellar phae begin to dehydrate, o it i ufficient here to conider lo hydration phae. Nuclear magnetic reonance (NMR) can be ued to meaure the amount of liquid ater preent a a function of temperature (Yan et al, 1993). Fig 1d ho the equilibrium hydration of lamellar phae of DOPC at freezing temperature. The data in 1d are for three ample having different total compoition: thee compoition are each hon by point on a horizontal line. (Thee point are meaured above the equilibrium freezing temperature for each ample.) Belo thee temperature, ice and ater coexit. The NMR ignal from the liquid ater give information about the ize and geometry of the contributing volume. Thee ignal indicate that the ater lie beteen the lamellæ and i in a condition imilar to that of ater in lamellar phae at lo hydration hen no ice i preent. There are everal other reaon to believe that the ice form a eparate, macrocopic phae and that there i no ice in the narro pace beteen adjacent pair of lamellæ. Firt, at any given freezing temperature, there i a minimum ize for ice crytal belo hich they are untable ith repect to ater and there i inufficient pace for table ice beteen lamellæ at the average eparation (ee Appendix 2). Second, the hydration curve for ample ith different initial hydration uperpoe very cloely in Fig 1d, hich ugget that the thee lamellar phae have the ame compoition at the ame freezing temperature. Finally, the curve in Fig 1d cloely reemble the hydration behaviour of lamellar phae in the abence of ice, a 1 Liquid ater ha a higher internal energy (U) than doe ice: the latent heat of fuion (L) i jut the difference in internal energy per unit ma. But liquid ater alo ha higher entropy (S) than doe ice, becaue it molecule can tranlate and rotate more freely. The entropy i more important at high temperature: expreion for the Gibb and Helmholtz free energie include the term U TS.

4 meaured in divere ay, a e hall ee next. Thi behaviour i uually repreented in a rather different form, a hon in 1c, in hich a repulive force per unit area i meaured a a function of the hydration or the inter-lamellar eparation. 4 freezing temperature/ C a F / MPa y/nm c C/kmol.m ater per lipid ater per olute b ice ater per lipid d ice freezing point depreion/k freezing point depreion/k Figure 1. (a) ho the equilibrium freezing temperature a a function of concentration for a olution of ucroe (Weat, 1990). In (b), the ame data are plotted to ho the compoition of an unfrozen ucroe olution (expreed a the mole ratio olvent:olute) a a function of temperature. (The to unhaded point in (a) are omitted in (b).) The olid line repreent the ater:ucroe ratio in a ample hoe total compoition ha a mole ratio of 80:1. Such a ample i a ingle, homogeneou phae above about 1.5 C. Belo that temperature, ice and olution coexit, a hon by the cartoon inet, in hich repreent a olute molecule and hite repreent ater. In (c), the hydration propertie of a DOPC lamellar phae are hon a the inter-lamellar force per unit area a a function of mole ratio ater:lipid or inter-lamellar eparation y (Yoon et al, 1998). On thi emi-log plot, the data are approximately linear, uggeting an exponential force la at mall inter-lamellar eparation. The hydration behaviour of mot lipid are qualitatively imilar (though quantitatively different), o one ould expect qualitatively imilar reult from other lipid that did not undergo a phae tranition in the temperature range invetigated. The data in (c) are the ame a thoe alo plotted in (d). Here they are plotted a the compoition of a lamellar phae of DOPC:D 2 O a a function of temperature. At ufficiently lo temperature, an ice phae coexit ith the dehydrated lamellar phae, a hon in the cartoon inet, in hich haded bar repreent the bilayer. At higher temperature, there i no ice and, for any given ample, the hydration doe not change ith temperature. The different ymbol repreent ample ith three different total compoition: mole ratio 30 ( ), 25 ( ) and 17.7 ( ). For both olution and lamellar phae, upercooling i poible. For the ample hoe equilibrium behaviour i hon by the olid line in (b) and (d), upercooling i repreented by the dahed horizontal line to the left of the equilibrium curve. Hydration and hydration force When urface in ater are brought to cloe eparation (a fe tenth of a nanometer), a very large repulive force, called the hydration force, i meaured. Hydration force have been invetigated uing a number of different and complementary method. The origin of the hydration force i till not unanimouly accepted. Some reearcher attribute it to normal motion of the urface, either individual

5 molecular motion or urface undulation (Iraelachvili and Wennertröm, 1996). A more idely held vie i that it i due to ordering of ater at the urface, hich propagate out from the urface ith decreaing trength (Kjellander and Marc elja, 1985a,b). For the purpoe of thi dicuion, the nature of the force i not of fundamental concern (but ee the dicuion by Bryant and Wolfe, 1992). 5 Force-eparation curve beteen bilayer and other urface may be meaured directly uing a technique developed by Iraelachvili and co-orker (Iraelachvili and Adam, 1978; Horn, 1984; Helm et al, 1989). In the Surface force apparatu (SFA) the deflection of a calibrated pring meaure the force and ophiticated optical interference method are ued to meaure the change in eparation of the atomically mooth urface upon hich the lamellæ are depoited (Fig 2a). In the Omotic Stre Technique (OST) of Rand, Paregian and colleague (LeNeveu et al, 1976; Rand and Paregian, 1989), the force beteen bilayer i determined thermodynamically by equilibrating the ater in the phae to be tudied ith a reference aqueou phae. Depending on the range of hydration to be tudied one of three method i ued to control the chemical potential of the reference phae. For modet dehydration, preure i applied hydraulically through a membrane. For moderate dehydration large molecular eight polymer are introduced into the lipid/ater mixture. A thee do not permeate the membrane, they remain in a eparate ater-polmer phae, thu dehydrating the membrane. For mot moderate to evere dehydration, a erie of aturated olution i ued to control the vapour preure, hich i ued to control the hydration of lipid-ater ample. Each lamellar phae ample i equilibrated ith an unaturated ater vapour, hich in turn i equilibrated ith one of a erie of reference olution (Fig 2b). The chemical potential of ater (µ) i knon for each of the reference olution, and at equilibrium it equal the chemical potential of ater in the lamellar phae. In a olution, µ i loer than it i in a pure ater phae at zero preure becaue of the omotic effect of the olute, hich loer the entropy of the ater. The ater beteen the lamellæ contain no olute, but it chemical potential can be loered by loering the hydrotatic preure in thi region, o a negative preure or uction i developed in the inter-lamellar ater. For mechanical equilibrium, the magnitude of the uction equal the repulive force per unit area beteen the lamellæ. A the lamellæ approach cloer, the repulive force can be very large (ten of MPa) and it require ucceively loer chemical potential of ater to dra ater out of the inter-lamellar region 2. The repeat pacing and the eparation may be meaured by X-ray diffraction to give force-ditance curve. At cloe approach, the hydration force dominate other force (the attractive van der Waal interaction, electrotatic interaction) and the force depend approximately exponentially on eparation, ith a characteritic length of about 0.2 nm, a hon in Fig 1c. The to method (Fig 2a and 2b) are quite different and the contraint upon the bilayer are different. Neverthele, the force curve meaured are qualitatively imilar, and may be quantitatively reconciled (Horn et al, 1988). In a variant on thi method, the hydration, rather than the eparation, i meaured by eighing the ample (Marh, 1989) to give force-hydration relation. Knoledge of the bilayer geometry and mechanical propertie allo comparion of force-ditance and forcehydration curve (Appendix 3). Hydration force behaviour can alo be tudied uing freezing, a i hon in Fig 2c (henceforth Freezing Stre Technique or FST). Conider firt the cae hen there are no olute preent. When a lamellar phae equilibrate ith a macrocopic phae of pure ice, the chemical potential of the ice depend on it temperature in fact it decreae approximately linearly ith temperature. A the temperature fall, the chemical potential of the inter-lamellar ater alo fall, again by upporting an increaingly negative hydrotatic preure. Again the magnitude of thi uction mut equal the repulive force per unit area, and o the force beteen the lamellæ may be calculated directly from the temperature (Appendix 1). The hydration may be meaured directly by NMR, a decribed above, to give force-hydration relation. Fig 1c ho the data from Fig 1d replotted in thi ay. Thee meaurement alo give an approximately exponential force la ith parameter imilar to thoe determined by the to other method (Yoon et al, 1998). We note in paing that the OST ha alo been applied to determine force-eparation relation for other geometrie. Paregian et al (1986) have meaured the hydration repulion and other force in 2 Depite thee very large uction, cavitation i highly improbable. Thi i becaue the urface are very hydrophilic and the eparation are maller than the critical diameter for cavitation (Appendix 2).

6 hexagonal array of DNA. In principle the OST and the FST may be ued to determine forcehydration relation for a variety of ultratructural element, provided that their geometrie are knon. 6 b mica ilayer light unaturated vapour pring to pectrometer Force meaured directly µ = µ(rh) reference olution Fig 2. Meauring lipid hydration and inter-lamellar force. In the Surface Force Apparatu (a), the interlamellar force i meaured directly and change in the eparation of the upporting urface are meaured optically. In the Omotic Stre Technique (b), the force i determined from the equilibrium of the interlamellar ater, a vapour phae and a aturated olution. The inter-lamellar eparation i determined from X-ray diffraction or the hydration i determined gravimetrically. In the Freezing Stre Technique (c), the force i determined from the equilibrium of the unfrozen inter-lamellar ater ith ice at knon temperature. The inter-lamellar ater content i determined from it NMR ignal. a'< a a F F y uction F' > F F' > F y' < y ce µ = µ(τ) Fig 3. y i the eparation beteen the denity eighted lipid-ater interface and a i the area per lipid in (one ide of) the lamella. The volume of ater per lipid i ay/2. Removal of ater from the inter-lamellar layer could produce reduction in either a or y. If the lamellæ ere infinitely rigid, only y ould be reduced by a reduction in ater volume. If the hydration repulion ere an infinite tep function, then only a ould be reduced. In practice, both are reduced (Appendix 3). Reduction in y are balanced by an increaingly large hydration repulion beteen the lamellæ. Reduction in a produce increaingly large lateral compreive tre in the lamellæ. In the abence of olute, the inter-lamellar layer i expected to remain fluid at quite lo temperature and eparation. Conider the force acting in the lamellar phae. In the direction normal to the bilayer, the uction in thi layer i balanced by the hydration repulion. In the lateral direction, it act to compre the lamellæ and produce a compreive tre 3 in them 4 (Wolfe, 1987). Thi i illutrated in Figure 3. Note that thi lateral tre can be produced by deiccation in equilibrium ith an unaturated atmophere (cf Fig 2b) or by freezing induced dehydration (cf Fig 2c). Conequently, much of the folloing dicuion ha relevance to both cryobiology and anhydrobiology. Stree and train in membrane Thee intra-membrane tree produce everal train and other repone: geometrical train, topological train, thermotropic change and pontaneou demixing. They are illutrated in Fig 4. Some of thee have been aociated ith membrane damage in freezing or dehydration of living cell or model ytem. 3 In thi paper, "tre" i ued in it trict phyical ene: a force per unit area. "Strain" mean a deformation produced by the tre. The ord "tre" and "train" are often ued metaphorically in cryobiology. 4 The compreive tre could be conidered a a force per unit area acting at a point in any urface perpendicular to it plane. Integrating thi three dimenional tre acro the membrane thickne give a lateral force per unit length hich e call lateral preure or lateral tre π.

7 7 The geometric train of a membrane i the implet. If a membrane at initially high hydration (Fig 4a) i dehydrated (Fig 4b), a compreive lateral tre i aociated ith a reduction in area per molecule. For mall change, the to are proportional and the contant of proportionality i called the area elatic modulu. Thi ha been meaured for lipid bilayer, and for animal and plant membrane uing micropipette apiration (Mitchion and Sann, 1954; Wolfe and Steponku, 1983; Evan and Needham, 1987). Becaue the lamellæ have very lo volumetric compreibilitie, a fractional reduction in area i aociated ith a nearly equal fractional increae in thickne. Thi ha been meaured by X-ray diffraction (Li et al, 1982). The mot noticeable effect of lateral tre i on the gel-fluid (alo knon a gel-liquid crytal) tranition in a planar bilayer (4c). Dehydration elevate the tranition temperature for lipid-ater phae a much a 40 C above the exce ater tranition temperature To. Thi effect ha been oberved by many invetigator for a ide range of lipid (e.g. Croe et al. 1988; Tvetkov et al., 1989; Koter et al. 1994; and reference contained in thee paper). The effect i readily explained in term of a to dimenional verion of the Clauiu-Clapeyron effect (Bryant and Wolfe, 1992). When the bilayer goe from gel to fluid, it area in the plane increae by an amount a per molecule. In a dehydrated phae, thi occur againt a lateral preure π in the bilayer, or π/2 in each monolayer, o it incur an extra energy cot of π a/2. Thi make the gel phae more table ith repect to the fluid, and o the tranition temperature i elevated. The to dimenional verion of the Clauiu- Clapeyron equation may be ritten: T = T o a 2L π (1) here T i the increae in the tranition temperature due to a lateral tre π, L i the latent heat of the tranition, and a = (a f a g ) i the difference in molecular area beteen the gel (g) and fluid (f) phae. Thu the tranition temperature T o i increaed in proportion to the lateral preure applied, at leat for mall applied tree. Taking value (for DPPC) of L ~ J.molecule 1 and a ~ 0.15 nm 2, the tranition temperature i elevated by ~ 0.5 K for each mn.m 1 of applied lateral tre 5. (For membrane under a tenile tre, Eqn (1) give the depreion of the tranition temperature. Tenile tree are poible hen a vitrified inter-lamellar olution upport the compreive tre, a e hall dicu later.) Another deformation produced by lateral tree i lateral demixing in membrane of more than one component. If a membrane include component that differ ufficiently greatly in their hydration interaction, then in ome region of the hydration-temperature phae diagram, they eparate into to fluid phae ith different compoition (Bryant and Wolfe, 1989). Thi ha been oberved in to component lipid bilayer (Bryant et al, 1992; Webb et al, 1993) (Fig 4d). It can alo explain the excluion of protein from area of fluid moaic membrane under uitable condition (Fig 4e), although other explanation are alo poible. The poible ignificance of thi demixing i dicued belo. Apart from the geometric deformation hon in Fig 4b,c and d, there i another ay in hich the aqueou volume can be reduced: via a dicontinuou change in the hape of the interface. Hexagonal II phae (invere hexagonal phae) have tube of ater urrounded by lipid, a hon in Fig 4f. For invere cubic phae, approximately pherical volume of ater are urrounded by lipid 6. The geometry of thee invere phae i ill uited to perform the role of emipermeable eparation, hich i an important function of membrane, and o it i not urpriing that obervation of thee phae, or ultratructural feature reembling them, ha been aociated ith damage at lo hydration (Gordon-Kamm and Steponku, 1984; Steponku, 1993; Steponku et al., 1993, Uemura et al., 1995). Several further topological change have alo been reported in plant cell membrane that are brought cloely together during freezing, and thee have been related to freezing damage (Steponku and Webb, 1992; Fujikaa, 1995). 5 Phae diagram in term of T, π, and compoition are given by Guldbrand et al (1982) and Marcelja and Wolfe (1979).(46) and (18). 6 In ome cae, membrane urface may have a pontaneou curvature and thi tranition may alo loer the mechanical energy. Thi i analyed by Kirk et al, 1984 and Gruner et al, 1985.

8 a t y t'>t y'<y a'<a 8 a - fluid (high hydration) b - fluid (lo hydration) c - gel e - lipid-protein eparation d - fluid-fluid eparation f - invere hexagonal phae Fig 4. The train produced by dehydration-induced tree. (a) ho a lamellar fluid phae (Lα) at high hydration. (b) ho the geometric train produced at loer ater content. The average area per lipid a and the inter-lamellar eparation y are decreaed, hile the lamellar thickne t of the bilayer i increaed. At loer ater content, increaed lateral tre (ee text) can produce the tranition to the gel phae (Lβ (ith traight chain) or Lβ' (ith chain at a fixed angle, a hon)). In the gel phae a'<a, t'>t and y'<y. Dehydration tre produce thi tranition at elevated temperature (equation 1). In figure 4d the haded circle repreent the lipid pecie ith the greater hydration, and the unhaded circle repreent the lipid ith the loer hydration. At high hydration the to lipid form a ingle mixed phae (4d, upper figure), but a hydration i reduced, they eparate into to eparate phae. The lipid ith the greater hydration i preferentially equetered in domain ith relatively high hydration (4d, bottom right), hile the le trongy hydrating lipid are concentrated in domain ith loer hydration (4d bottom left)(,(e) large hydrophilic molecule, uch a intrinic membrane protein (circle in thi diagram), have a larger hydration interaction and can therefore be demixed by dehydration tree (loer diagram). (f) ho a topological repone to tre. At very lo hydration the lipid may undergo a tranition to the hexagonal II phae (HII), hich conit of mall cylinder of ater urrounded by lipid. At the top of the diagram, lipid are repreented by the haded area and ater by the unhaded. The hexagon are the repeat unit of the tructure. In the loer part of the diagram, individual lipid molecule are repreented.

9 In biological membrane, mot of the lipid are trongly hydrating lipid that do not readily undergo tranition to non-bilayer phae. Hoever, ome membrane component are le trongly hydrating. Even relatively mall fraction of the eakly hydrating pecie may hoever be important, becaue the fluid-fluid demixing that reult from dehydration tree (dicued above ee figure 4d) produce domain rich in the lo hydrating component. Thee domain may then undergo a tranition to a hexagonal II phae (figure 4f). The demixing may thu be an intermediate tage prior to formation of damaging invere phae (Bryant and Wolfe, 1989, Bryant et al 1992, Webb et al., 1993, 1995). 9 Effect of olute Solute partitioning. Membrane are poorly permeable to many olute, epecially hen the olute molecule are large. It follo that olute may not alay equilibrate beteen phae, and that the compoition of the phae of a ample ith a particular overall compoition may depend on the hitory of it preparation. A a imple example, conider a upenion of multi-lamellar 7 veicle in pure ater, in the preence of exce ater. Water permeate eaily and o the lamellæ approach full hydration. No add to the ample a non-permeating non-ionic olute. It i ditributed (at leat initially) in the bulk ater phae. The omotic preure of the bulk olution no dehydrate the multi-lamellar veicle. The extent of the dehydration i determined by the repulive force beteen the lamellæ. The greater the olute concentration in the bulk, the greater the inter-membrane repulion and o the greater the intramembrane tre. In thi cae e ould expect lateral compreion of the membrane, elevation of the membrane liquid crytal-gel tranition temperature (T m ) and perhap other train if the bulk olution ere ufficiently concentrated. Compare thi ample ith one of the ame overall compoition, but in hich the olute partition beteen the bulk and inter-lamellar ater (by one of the mean dicued belo), until both olute and ater reach equilibrium. Here there i no omotic preure difference, little or no dehydration of the lamellar phae and little or no lateral tre. Non-pecific olute effect ould produce little or no change in T m at temperature above the freezing temperature of the olution. Freezing the ample further complicate the picture becaue it change the olution compoition, and can do o quite rapidly. Yoon et al (1998) reported experiment that compared lipid:ugar:ater ample having imilar lipid:ugar ratio, but different level of initial hydration. When thee ere frozen, the lamellar phae a dehydrated and the ater equilibrated beteen that phae and a bulk olution phae. The number of olute in the lamellar phae a higher in ample hoe initial hydration a lo, imply becaue there a no (or le) exce olution. A a reult, the ample ith lo initial hydration produced lamellar phae ith higher hydration at a given freezing temperature. Fig 5 illutrate thi point for a hypothetical olute to hich the membrane i completely impermeable. In cae a, anhydrou lipid are hydrated ith a relatively mall amount of a highly concentrated olution. Thi i likely to produce a lamellar phae ith a highly concentrated olution in the inter-lamellar pace. It i poible that there i alo a macrocopic olution phae hoe concentration i not necearily the ame a that of the the inter-lamellar olution. In cae b, the ame amount of anhydrou lipid i hydrated by adding a large volume of dilute olution, hich contain (for the purpoe of thi illutration) the ame amount of olute. Thi ill form a lamellar phae ith a dilute inter-lamellar olution and a large volume of bulk olution. The econd ample i then either frozen or dehydrated in an unaturated atmophere until (let u uppoe) it ha the ame total ater content a the firt ample. If the olute fail to permeate the membrane, then the final reult may be that the econd ample comprie a lamellar phae containing le olute (and alo le ater) than the firt ample, and a larger bulk volume of concentrated olution. If the dehydration ere ufficient, it might alo contain crytal of the olute. A range of procedure may be applied to the econd ample to increae the olute content of the inter-lamellar olution: repeated centrifugation ith regular alternation of the orientation of the ample, repeated cycle of freezing and thaing, and 7 A omehat imilar reult may occur ith unilamellar veicle. If the veicle radiu i much greater than the membrane thickne, adding an impermeant olute to the upending medium ill caue the veicle to collape until the membrane eparation i determined by the hydration force. At lo hydration, region of flattened veicle may reemble and repond like lamellar phae.

10 the elape of time (eek or more P. Rand, peronal communication). Neverthele, it ould be unie to aume that, even after thi treatment, the compoition of the inter-lamellar phae and the bulk phae ere the ame. Firt, the olute may till not have reached equilibrium beteen the to phae. Second, the equilibrium may not correpond to equal concentration. Some olute may be preferentially ditributed into the lamellar phae, other excluded from it. The purpoe of thi illutration i to arn that ample preparation and hitory mut be conidered in any comparion of data, and that the compoition of the lamellar phae component of a lipid-olute-ater ample i not readily determined from the total compoition of the ample. 10 a no exce volume arge exce olume Unhydrated lipid Unhydrated lipid Volume of ice or removed ater Fig 5. The effect of different initial hydration on olute reditribution. (a) ho a ample, hich i hydrated from the dry tate ith a mall volume of a concentrated olution of olute. There i no exce ater, and o the olute and ater are all or nearly all in the inter-lamellar region (auming no olute crytallization). (b) ho lipid being hydrated from the dry tate ith the ame ratio of olute to lipid, but enough ater to create a ubtantial exce volume. Upon removing ome of the ater, o that the total ater volume i the ame a in (a), many of the olute concentrate outide the lamellar region. Both the number of olute per lipid in beteen the membrane, and the inter-lamellar eparation y, are loer in cae (b) than (a). NMR of the olute or the ater can be ued to determine the ditribution (Yoon et al, 1998). Specific v non-pecific effect. Solute affect the hydration of membrane, hydration force, membrane-membrane interaction and intra-membrane tree in a number of ay. The interaction of olute ith ater and ith membrane may be pecific to particular olute. There are alo, hoever, ome important effect that are non-pecific, in the ene that any olute (or any olute of imilar ize) ould have a imilar effect. Omotic effect. All olute have an omotic effect: they increae the entropy and loer the chemical potential of the ater in hich they are diolved. Conider firt a lamellar phae containing no olute, in equilibrium ith ice at 1 C. The ice and the lamellar phae compete for ater, ith the reult that the preure in the inter-lamellar ater i 1.2 MPa and o the inter-lamellar repulion i 1.2 MN.m 2 (Appendix 1). Typically thi give rie to a lateral tre in the lamellæ of order 1 mn.m 1, although the value depend on the type of lipid. No conider a ytem ith olute in the interlamellar fluid. Ice at 1 C can equilibrate ith a olution having zero hydrotatic preure and a olute concentration of about 500 mol.m 3 (for a non-diociating olute). One might expect that a olute concentration of thi order in the inter-lamellar ater ould reduce the uction, the intermembrane repulion and the lateral tre to zero, and increae the inter-lamellar eparation. In practice, the omotic effect of inter-lamellar olute i a little more complicated for everal reaon (Yoon et al, 1998). The ize of olute molecule i not negligible in comparion ith the interlamellar eparation, o the excluded volume near the interface mut be conidered. Due to thi effect, a olute ha a greater omotic effect in a confined pace than it ould in bulk olution, and the effect increae omehat for large olute. There may alo be variation in olute ditribution ithin the inter-lamellar layer due to interaction beteen the olute and the lamellæ. In hort, the purely omotic effect of the preence of olute in a fluid inter-lamellar layer i to increae the hydration, to decreae the intra-membrane tre and thu to reduce the dehydration induced increae in the gelfluid tranition temperature, but the effect i omehat le than predicted by the implet model.

11 The foregoing dicuion concern the omotic effect of olute hich have partitioned into the interlamellar pace. If olute are too large to partition into the interlamellar layer, or if the ample preparation and their impermeability ha kept the olute out of that pace, then their omotic effect are indirect. They can have an effect on hydration becaue they affect the chemical potential of ater, but thi i mot important at temperature above freeing. Conider, for example, a upenion of unilamellar veicle in pure ater, to hich i added a non-permeating olute. Firt conider temperature above freezing: Water leave the veicle, hich then hrink until further dehydration i prevented by the hydration force hen membrane are puhed cloe together. When the ater i at equilibrium, the omotic preure of the olution equal the uction in the interlamellar ater. In thi cae, the excluded olute produce an intra-membrane force and dehydration-induced intra-membrane tree at temperature above freezing. In the preence of ice, the behaviour of the lamellar phae i largely unaffected by the preence of thee olute, hich are equetered in a co-exiting concentrated olution phae. Effect on the hydration force. The preence of the olute (in high concentration) may be expected to affect the hydration force. Many reearcher believe the hydration force to be due to the non-random orientation of ater propagating from the interface (Kjellander and Marc elja, 1985a,b). Solute do not hydrogen bond in the ame geometry a ater, and the olute ha a different (uually loer) polariability. One might therefore expect all olute, at ufficiently high volume fraction, to reduce the hydration repulion and thu the intra-lamellar tre. At equal concentration, a olute ith a larger volume ould be expected to have a larger effect, all ele equal. Volumetric effect. The volume of olute (hen not negligible in comparion ith the volume of ater) itelf increae the volume of the inter-lamellar olution. If thi layer of olution ha negative preure, that uction no act on a greater thickne of olution, and thi increae the lateral tre. Except for large volume fraction, thi effect i relatively mall (Wolfe and Bryant, 1992). The molecular volume alo affect the teric interaction ith membrane, dicued belo. Finally, one of the mot important effect of molecular ize i that larger molecule are more likely to be excluded from the inter-lamellar layer. Interaction among olute, membrane and ater. After etimating and alloing for the omotic and volumetric effect, Yoon et al (1998) reported that the diaccharide ucroe and trehaloe, at concentration of everal kmol.m 3, reduced the hydration force beteen dioleylphophatidylcholine bilayer to a greater extent than did the maller olute orbitol and dimethylulphoxide. The effect of orbitol and dimethylulphoxide on the inter-lamellar repulion ere very imilar to hat thee author calculated from their omotic and volumetric effect. It hould be noted that, at high volume fraction of olute, the effect of olute make a bigger difference to a plot of force v eparation than it doe to a plot of force v hydration. Yoon et al made comparion in term of force-hydration curve. The larger effect of the larger olute ucroe and trehaloe might be becaue of their increaed perturbation of ater tructure: the volume fraction reached a high a 50% and one ould expect ubtantial diruption of the hydrogen bonding netork at thee concentration. An alternative explanation i that they are due to pecific effect of thee olute on the hydration force. Solute could affect hydration force either if they ere adorbed onto the membrane-ater interface, in hich cae they ould produce an interface ith an altered capacity to polarie ater and an altered urface mobility, or if they ere excluded from the interface and thu created a very high concentration miday beteen the lamellæ. The reult of Yoon et al (1998) and Pincet et al (1994) ere conitent ith the excluion, to a mall extent, of ugar from the region cloet to the bilayer urface. For all of the effect of olute dicued above, rather large concentration (everal kmol.m 3 or more) are required to produce ubtantial effect. For inter membrane ugar concentration of much le than 1 kmol.m 3, the effect on the hydration propertie and inter membrane force for mot freezing temperature i jut that predicted from the omotic effect (Yoon et al, 1998). The Surface Force Apparatu (SFA) i quite different from and complementary to the Omotic Stre Technique (OST) and the Freezing Stre Technique (FST) in that, in the SFA, meaurement are conducted in the preence of a large volume of exce olution. Conequently the SFA i unaffected by omotic force, except at very cloe eparation hen excluion effect may be 11

12 important. A a reult, the SFA i ell uited to examining the pecific effect of different olute. A limitation on the technique i that it i difficult to ue very large concentration of olute becaue, in order to compare ith control, the aqueou medium mut be replaced during an experiment. Pincet et al (1994) meaured the effect of dimethylulphoxide, orbitol and trehaloe on the force beteen dioleylphophatidylcholine (DOPC) bilayer. For the accharide, their tudy a limited to concentration of only 1.5 to 2 kmol.m 3. Their reult hoed little pecific difference among the olute. Their reult alo uggeted that, hen bilayer ere brought very cloe together in the preence of a reervoir of olution, orbitol and trehaloe ere, to ome extent, excluded from the region very near the membrane urface. Electrical interaction. The effect of ion on charged urface a firt tudied in colloid cience, and much of the theory of the interaction beteen colloidal urface (Verey and Overbeek, 1948) ha been carried over to analye force beteen membrane (ee alo Cevc, 1990 and Iraelachvili, 1991). Experimentally, the effect of ionic olute on intermembrane force ha been tudied in coniderable detail uing the SFA, and chiefly at concentration that are modet in comparion ith thoe found in freeze-dehydrated or deiccated cell. The mot pectacular effect are on charged membrane and they have a large proportional effect on the electric double layer force at moderate to high hydration (Marra and Iraelachvili, 1985). The effect of different ion upon the interaction beteen urface ith variou charge are varied and complicated, and are revieed by other. The effect of monovalent ion on the repulion beteen urface i uually to reduce it (Verey and Overbeek, 1948; Attard, 1996; Marc elja, 1997). The divalent ion Ca ++ may change the ign of electrotatic force beteen charged urface (Marc elja, 1992). Electrical force are potentially very important in determining the inter membrane pacing in highly hydrated ytem, and have been invoked to explain uch effect a the tacking and untacking of thylakoid membrane in fully hydrated chloroplat. Further, the interaction beteen ion and membrane are capable of producing repone that include demixing and change in the phae tranition temperature (Raudino et al, 1987; Tamura-Li et al, 1986). In membrane at lo hydration, hoever, cloe approach almot alay produce a very large repulive force, a dicued above, and thi paper i concerned primarily ith the effect of uch force, rather than a detailed dicuion of their origin. Compatible olute. All olute, hether ionic or non-ionic, loer the chemical potential of ater. Thu the purely omotic effect of inter-lamellar olute i to increae hydration and to reduce intra-membrane tree at any given freezing temperature. The effect of different olute on the activity of enzyme may hoever be quite different and ome olute are toxic in high concentration. At equilibrium, the effect of any one olute, at a given freezing temperature or chemical potential of ater, i to loer the concentration of the other by reducing the amount of ice preent. Compatible olute are thoe that can be accumulated in large concentration ith no deleteriou effect (Bron, 1976). The interaction beteen ion and enzyme affect the tate and activity of the enzyme, o one effect of compatible olute i that they reult in a reduction in the concentration of ionic olute (Mazur, 1963). To have uch an effect directly, the compatible olute mut partition into the olution in hich the enzyme i found. It i alo poible for non-permeating olute to have an effect by vitrification, hich hinder omotic equilibrium (thi i dicued belo). The effect of permeating and non-permeating non-ionic olute can therefore be rather different. Santariu and co-orker tudied the effect of complex media including both alt and nonionic olute on photoynthetic reaction in thylakoid membrane (Shakir and Santariu, 1995). They conclude that the colligative action of penetrating cryoprotectant i the primary mechanim for protection of the photoynthetic reaction in the thylakoid. We do not kno of any tudy of the effect of freezing induced tree in the thylakoid, and the extent to hich permeating olute reduce thee tree. Shakir and Santariu alo dicu poible interaction beteen olute and membrane. Freezing and vitrification of ater The normal fluid to olid phae tranition occur by a proce of nucleation and groth (e.g. Frank, 1982). Thi proce i the ame for any liquid, but here it ill be explained by the example of the ater-ice tranition. Conider undercooled ater at a temperature T, hich i a fe degree belo the equilibrium freezing point Tf. If the ater i pure and the volume mall, the ater can remain in thi non-equilibrium undercooled tate almot indefinitely. In order for freezing to occur, the ater molecule, hich are undergoing Bronian motion, mut pontaneouly adopt a 12

13 configuration that i "ice-like". The probability of thi happening to the entire ample at the ame time i vanihingly mall. Locally, hoever, mall cluter of molecule ith an ice-like tructure (called homogeneou nuclei) are continuouly forming and breaking up. If one of thee nuclei reache a critical ize (ee appendix 2), then it become energetically favourable for more ater molecule to gro on thi nucleu, and the ice ill propagate rapidly through the entire ample. Thi to tage proce i called nucleation and crytal groth. A cartoon of the nucleation proce i hon chematically in Fig. 6a. Each ater molecule (indicated by a ith an arro) undergoe Bronian motion ith a characteritic diffuion coefficient (the magnitude of that i indicated by the arro). The circle repreent the critical radiu for nucleation, and the ater molecule inide the radiu are, at thi naphot in time, arranged in a peudo regular ("ice-like") manner. If the regularity gro to be larger than the critical radiu, then the ample ill crytalie. Nucleation can alo proceed via heterogeneou nucleation, here the ater molecule near a urface (uch a the container all), or large particle in the olution (uch a dut, protein etc), act a a catalyt for the formation of ice nuclei (e.g. Frank, 1982). a - ater S S S S S S S S S b - ater + olute Fig. 6. A cartoon of the effect of olute on the nucleation proce. Water molecule and olute are repreented by the ymbol and repectively. The arro repreent diffuion, and the length of the arro indicate the peed of diffuion. The large circle repreent the critical nucleation radiu. (a) ho the ituation here only ater i preent. For a critical nucleu to form, the ater molecule in the volume repreented by the circle mut pontaneouly arrange themelve (through Bronian motion) into a regular ice-like tructure. If thi regular lattice i larger than the critical radiu, then the crytal ill gro. (b) ho the ame ituation in the preence of ome hypothetical olute (for a olute:ater molar ratio of 1:4). Firt, the olute increae the vicoity, o diffuion i reduced (indicated by the maller arro in (b) than (a)). Second, in order for a critical nucleu to form, a volume equal to or greater that the critical radiu mut be completely free of olute molecule. In the ituation hon in (b) thi i not the cae. A the concentration of olute increae, thi effect become even tronger, further reducing the chance of nucleation occurring. A the olute of interet are much larger than ater molecule, olute diffuion i much loer than ater diffuion, o no arro have been dran on the olute molecule. The probability of nucleation (i.e. the formation of nuclei larger than the critical volume) i proportional to ample volume 8, the amount of undercooling ( T = Tf T), and the vicoity of the liquid. A the liquid i cooled, the vicoity rie. If the liquid i cooled ufficiently quickly the vicoity may become o great that molecular rearrangement in the liquid become extremely lo or S S S 13 8 Thi i the primary reaon that freezing occur in the extracellular olution before it occur inide individual cell. A econd reaon i that the number of heterogeneou nucleation ite inide cell i exceedingly lo.

14 top. Nucleation and crytal groth ill be hindered, and the liquid ill be in a table nonequilibrium phae, hich i amorphou (i.e. it ha no long range order, like a liquid), but hich ha mechanical propertie like a olid. Such a phae i called a gla or vitrified olid, and the proce by hich it form i called vitrification. A olution i aid to be vitrified if it vicoity i greater than Pa. (Frank, 1982). For comparion the vicoity of ater i ~ 1 mpa. at 20 C. 14 Freezing and vitrification of aqueou olution In many ingle component ytem uch a ater, the rate of cooling mut be extremely high (> 10 7 K. -1 ) to achieve vitrification. Hoever, in ytem ith to or more component, vitrification i eaier to achieve. The addition of olute decreae the probability of nucleation and groth for to reaon. The firt effect i that the vicoity at any particular temperature (hon chematically in Figure 6b here the arro are horter than in figure 6a) i uually larger ith olute than ithout, implying that the motion and reorientation of the ater molecule into the ice tructure take longer. The higher vicoity therefore hinder both nucleation and groth. Second, becaue the olute are incompatible ith the ice tructure, the phyical preence of the olute hinder the formation of nuclei - an ice nucleu can form only if, at a particular time, a volume greater than or equal to the critical volume i free of olute molecule. At high concentration thi i unlikely (a hon in Figure 6b here the olute ithin the circle mean that an ice nucleu cannot form there at that point in time). The probability of nucleation occurring at any particular temperature i reduced ith increaing concentration. For both thee reaon, a the concentration of olute i increaed, the temperature Tg at hich vitrification ill occur increae, and the cooling rate needed to achieve vitrification i reduced 9. At ufficiently high concentration Tg may become larger than Tf, and ice cannot form. In the cae of diaccharide, concentration of 90% (by eight) are ufficiently high to vitrify under ambient condition. A familiar example of uch a ugar gla i toffee, hich e mention here becaue e hall oon dicu the mechanical propertie of ugar glae. Vitrification in membrane model and biological material Vitrification can occur in biological ytem at ambient temperature (deiccation) or ub zero temperature (cooling), and ha been uggeted a a mechanim for membrane protection during dehydration (e.g. Burke, 1986; Green and Angel, 1989). In both cae, if the vicoity rie to ~10 14 Pa. (caued by either higher concentration or loer temperature) then the olution i vitrified. In cell or lamellar phae at lo hydration, the vitrification ill occur here the ugar are located. If the ugar are beteen the membrane, then vitrification hould occur there. If the ugar are excluded from the region beteen the membrane, then vitrification may occur in extra-lamellar volume near the membrane, but not beteen them. The fact that membrane can be protected from dehydration by vitrification ugget that vitrification doe occur in the inter-lamellar pace, but the evidence i only circumtantial. It i poible that vitrification in volume outide the lamellae may provide protection from further dehydration if the membrane are completely encaed in the gla, though thi eem unlikely to be the cae in general (ee belo). If vitrification doe occur beteen the lamellae, there are a number of conequence. Firt, ordinary thermodynamic equilibrium cannot be aumed (though thermal equilibrium till applie). The force beteen the lamellae in a gla i unknon, but it i not needed - becaue the gla i olid it cannot be deformed to any ubtantial degree, o the inter-lamellar eparation y ill remain unchanged. Ho doe the preence of a gla protect membrane? It doe three thing: (i) once a gla ha formed, further dehydration ill be limited (i.e. loering the ub-zero temperature or the humidity ill have little effect on the intermembrane eparation). The membrane ill thu have an effective hydration higher than at equilibrium. (ii) Vitrification loer the probability of crytallization. When olute crytalie, they no longer loer the chemical potential of a olution and o further dehydration i poible. If hoever the olution tart to vitrify, thi limit the increae in the concentration of the unvitrified olution. Crytallization i therefore le likely and further dehydration doe not 9 At cooling rate ithin a couple of order of magnitude of 1 K. -1, the intracellular concentration i itelf a function of cooling rate, becaue cell dehydrate omotically in the preence of extracellular ice (Mazur, 1963).

15 necearily take place. (3) Finally, a gla may allo the membrane to remain in the fluid lamellar phae at hydration and temperature that normally ould lead to deleteriou phae tranition. Thi lat point i dicued in the folloing ection. Koter and co-orker (Koter et al., 1993; Koter et al., 1994) reported that, for POPC and mall olute, if the gla tranition temperature T g of the concentrated olution exceed the value of the gelfluid tranition temperature (T m ), then the gel-fluid tranition at lo hydration occur about 20 C belo the fully hydrated tranition temperature T o. They found imilar effect in other lipid, but the range of depreion of the gel-fluid tranition temperature varie beteen about 10 C and 60 C, depending on the lipid pecie (Koter and Anderon, 1995; Koter et al., unpublihed). Zhang (1998) and Zhang and Steponku (1995; 1996; m ubmitted) tudied a range of lipid and mall olute choen to give a ide range of T o and T g, and developed a model to undertand the proce. While they report that dehydration elevate the gel-fluid tranition temperature T m, they find that (mall) olute minimie thi increae only if T g i belo the fully hydrated tranition temperature T o (rather than T m ). When the tranition occur in a glay matrix (T g > T o ), the effect depend on the thermal hitory of the ample. If the lipid a in the fluid tate hen the inter-lamellar layer vitrified, T m i depreed (both for cooling and arming). If it a in the gel phae hen the gla a formed, T m i elevated above T o. Zhang and Steponku propoe that the glay matrix impede the conformational change aociated ith the lipid phae tranition. A gla can upport a ubtantial aniotropic tre. For a lamellar phae that a gel at vitrification, heating ould create compreive tre in the bilayer and tenile tre in the gla, and T m ould be elevated, according to Eqn (1). For a lamellar phae that a fluid at vitrification, cooling ould create tenile tre in the bilayer and compreive tre in the gla, and T m ould be depreed. I the gla matrix ufficiently rigid for thi model? The elatic propertie of a relevant ugar gla (a olution of ucroe:raffinoe 85:15 at a concentration of 90%) have recently been meaured (Martin and Bryant, in prep). The Young' modulu, Y, i about 20 GPa (compared to 9 GPa for ice). Uing the Clauiu-Clapeyron equation, an etimate of the compreive tre for a membrane 20 C belo it To can be made. Uing typical value (for DPPC) of L~ J.molecule -1, a~0.15 nm 2, and To = 42 C (Caffrey, 19????, Nagle et al, 1996), π/ T ~ 2 mnm -1 K -1. If the gla ere to upport the tre of a membrane don to 20 C belo To, thi ould correpond to a tre of ~40 mn.m -1. If thi tre ere upported over half the thickne of the inter-lamellar eparation (ay ~0.5 nm), thi ould lead to a tre of 80 MPa. For a gla ith Y = 20 GPa, thi correpond to a train in the gla of about 0.4%, hich i eaily upported. It eem reaonable to aume that Young' modulu ould not differ greatly beteen ugar glae compoed of different ugar, o the model ould predict that the depreion of the phae tranition temperature due olely to thi effect ould be independent of the type of ugar, a long a Tg i higher than Tm. The tudie of Koter and her colleague and thoe of Zhange and Steponku provide experimental confirmation of thi prediction. The magnitude of the effect varie ith lipid pecie, hoever, becaue of the variation in a and L among lipid. Figure 7 chematically ummarize the main non-pecific effect of olute on the gel fluid tranition temperature a a function of hydration. The bold line i for a lipid-ater ytem, here dehydration caue the tranition temperature to rie everal ten of degree above the exce ater tranition temperature T o. The full line ho the effect of the omotic and volumetric effect of mall, uncharged olute uch a ugar, hich reduce the membrane tre and hence the tranition temperature at any hydration. If vitrification occur at a particular hydration, then the tranition temperature ill fall by an amount in the range ~10 C to 60 C, depending on the lipid pecie (indicated by the filled circle in Fig 7), and then remain almot contant a any further dehydration ill be limited in extent and rather lo 10. Thi effect i mot likely due to the mechanical propertie of the gla, a it can upport an aniotropic tre, and can thu upport the membrane in the fluid tate at temperature here the gel tranition ould occur in the abence of a gla Diffuion i loed but not topped in vitrified material. Further, highly vicou ample may be inhomogeneou and not all region may vitrify at the ame time or temperature. Thu ome further dehydration may occur over period of eek (Steponku, peronal communication; Zhang and Steponku, 1995).

16 T - To lipid + ater lipid + olute + ater Fig. 7. A chematic of the non-pecific effect of mall olute on the gel-fluid tranition temperature a a function of hydration. The y axi i T-T o, here T o i the tranition temperature in exce ater, indicated by the horizontal line. Value are approximate. The bold line ho T-T o a a function of hydration for a lipid-ater ytem. The full line i for a lipid-ater-hypothetical olute ytem, and illutrate the effect of the inter-lamellar olute reducing membrane tre and hence the tranition temperature. The filled circle indicate the tranition temperature if vitrification occur hile the lipid i in the fluid phae, a uggeted by Zhang and Steponku (1996) vitrified olution Hydration (%) Another effect of the preence of the gla phae, (and indeed highly vicou fluid that have not vitrified), i that the vicoity may hinder dynamic phae tranition. Thi i not important in the lo cooling rate in the natural environment, but it may have an important conequence in the laboratory. Rapid rate of temperature canning could lead to increaed hyterei becaue of the effect interlamellar vicoity may have on the time taken for the lipid to rearrange themelve beteen configuration. Glae and very vicou fluid alo reduce diffuion of olute. Zhang (1998) ha pointed out that thi may reduce the leakage of olute through membrane that otherie ould allo olute leakage at the phae tranition. Leakage of electrolyte and marker from dry lipoome ha been tudied extenively by Sun et al. (1994, 1996). Croe et al (1998), revieing thi ork, conclude that the rate of leakage drop coniderably belo the gla tranition, but doe not top completely until C belo the T g. To complication hould be mentioned. Firt, the gla tranition i a poorly defined, econd order tranition and the T g meaured by DSC i only one meaure of the gla tranition temperature, and there i diagreement among reearcher about ho to define it. Second, a the ample i cooled toard T g, diffuion lo dramatically, and local inhomogeneitie in concentration do not come to equilibrium. Conequently, ome area of the ample ill vitrify at loer temperature than other. It i therefore poible that the leakage meaured at temperature jut belo the ample average T g, a meaured by DSC, may occur in region of the ample that are not vitrified. Polymer v. mall olute The bulk of the dicuion o far ha concentrated on the effect of mall olute uch a diaccharide. Solution of larger molecule, uch a polymer, alo undergo vitrification during dehydration. In model ytem containing lipid, ater and polymer, large polymer molecule are often excluded from the lamellar phae at lo hydration and form eparate bulk phae in region outide the lamellar tructure (ee Fig 5). Thi partitioning i the bai of operation of one verion of the omotic tre technique (dicued above). Thu their direct omotic and volumetric effect on the membrane ill be mall. Beteen the bilayer ill be ater ith little or no macromolecular olute, and o the preence of large polymer ill have little direct effect on membrane tre, and hence little effect on membrane protection. When vitrification occur in a ytem of membrane-aterlarge polymer, it ill occur in the extra-lamellar volume. If the lamellar phae ha time to dehydrate, the preence of the polymer ill therefore have little direct effect on the freezing behaviour of the

17 lamellar phae 11. (Again, excluded olute do have an omotic effect at temperature above freezing, a dicued above.) Relatively mall polymer may partition into the inter-lamellar pace at high hydration. Whether on not they are excluded from a dehydrated lamellar phae depend upon the preparation and hitory of the ample. If uch molecule produce vitrification, the effect on membrane tranition ill depend on hether they are in the inter-lamellar phae or in a eparate bulk phae. The omotic preure of polymer at modet eight fraction i maller than that of the ame eight fraction of mall olute. Thu mall polymer ould be expected to have little effect on the membrane tranition temperature via the Clauiu-Clapeyron effect (equation 1). If they partition into the inter-lamellar olution and if they vitrify, then they could upport lateral compreive tree and might depre the membrane tranition temperature. In a recent revie, Croe et al. (1998) have examined the role of vitrification in protecting membrane and protein. They revie experimental ork, hich ho that, although dehydrated polymer uch a Dextran and hydroxyethyltarch (HES) vitrify at temperature ell above ambient, their ability to protect membrane and protein (at moderate cooling rate) i limited. They conclude from thi that vitrification alone i not ufficient to provide membrane protection, and appeal to pecific effect to olve the dilemma. The appeal to pecific effect i unneceary for the reaon explained above. The vitrified olution can only provide ubtantial protection to membrane if it occur beteen the bilayer. In the abence of any pecific effect, one ould expect the protective effect of carbohydrate to decreae ith increaing molecular ma above a certain ize, hich ould limit their partitioning into membrane phae, and limit their omotic effect (on an equal eight bai). Thi i hat i oberved (ee Croe et al 1998 and reference therein). Trehaloe v. other ugar What i pecial about trehaloe, that it protective effect eem to be ignificantly better than other imilar ugar uch a ucroe and raffinoe? Why are diaccharide better than monoaccharide? It i important to note the different phyical propertie of the variou ugar before appealing to pecific olute-membrane interaction. Firt, at any particular concentration, trehaloe ha a higher gla tranition temperature than mot other ugar. Second, highly concentrated trehaloe i le prone to crytalliation than many other ugar. Sucroe on the other hand crytalie readily at high concentration, although mall amount of raffinoe reduce the tendency of ucroe to crytalie (Koter, 1991), o ucroe:raffinoe mixture avoid crytallization and can vitrify. The accumulation of mall quantitie of raffinoe in ome tolerant pecie allo ucroe (rather than trehaloe) to play the role of vitrifier. It i poible that the mot important reaon trehaloe i conidered to be a better protectant at lo hydration i becaue it doe not crytalie readily, and becaue it ha a high gla tranition temperature. Koter and co-orker (Sommervold et al., 1995; Koter et al., 1996) hoed that the ability of ample to vitrify i important in reducing the incidence of olute crytallization during torage. Other biologically important propertie of trehaloe it lo reactivity and reducing poer and it high tability are cited by Ring and Dank (1998). Levine and Slade (1992) have ritten extenively on the non-pecific effect of trehaloe in dehydrated ytem. Macromolecule-olute-ater interaction Thi paper ha concentrated on membrane-olute-ater interaction. Some of the obervation ould be expected to apply to macromolecule-olute-ater interaction. Mot biological molecule are hydrophilic in their native tate and o one ould expect trong hydration repulion at cloe approach. Thee generate internal tree in the macromolecule (Appendix 4). The mechanical propertie of cro-linked polymer appear to influence their freezing behaviour (Murae et al, 1997), hich i conitent ith the uggetion that unfrozen ater under uction generate mechanical tree in the polymer. In ome geometrie, uch a long chain or flat heet, thee tree are aniotropic and thu give rie to geometrical deformation and tructural tranition (e.g. Paregian et al, 1986; Leiken et al, 1994). The non-pecific effect of olute on membrane-ater interaction ould therefore be expected to apply to macromolecule ater ytem that are dehydrated Note that the cryoprotective propertie of many polymer on ample frozen at very high cooling rate in the laboratory are due to different mechanim, and higher hydration are maintained hen vitrification occur (e.g. Sputtek et al., 1993; Körber et al., 1985; Takahahi et al.,1988; Macfarlane et al. 1990).

18 by freezing or deiccation. We kno of no detailed analyi of the non-pecific effect of olute on uch tree but e preent a imple introduction in Appendix 4. The effect of divere olute in minimiing damage to biological macromolecule ha been idely reported. In the cae of enzyme, electrical interaction ith ion, and ion mediated interaction beteen macromolecule are obviouly important in maintaining activity. The colligative action of olute i alo acknoledged to be of coniderable importance. For thi reaon, e ugget that it may be contructive to examine the hydration interaction and mechanical tree produced by freezing or drying of aqueou macromolecular phae. A i the cae ith lamellar phae, vitrification of the aqueou phae ould reduce the extent of (further) mechanical tre in the macromolecule, and thi may be an important part of the contribution of cryoprotectant to the tabiliation of biological macromolecule. The ituation i hoever complicated by the different partitioning effect of different olute, their different effect on vitrification and their different pecific effect on enzyme activity (ee dicuion by Moreira et al, 1998; Santariu and Frank, 1998). In Appendix 4, e derive relation among the hydration interaction of macromolecule, their contribution to the freezing point depreion, and the intra-molecular tre. Croe et al. (1998) dicu the effect of vitrified olution on the tability of protein. They point out the vat difference beteen the tabilizing effect of mall olute and polymer in the vitrified tate, and they alo ugget that becaue protein themelve vitrify in the dry tate, but are not preerved, that vitrification i not ufficient to protect protein. Thi argument appear not to recognize the different behaviour found in three very different ituation: 1) Small olute can vitrify in the pace inide the protein tructure, and then maintain that tructure againt further dehydration. 2) Vitrification of polymer ill occur in the bulk, providing no direct protection to the membrane tructure 12. 3) When protein are dried, they immediately loe their tructure a the ater i removed. The protein gla i therefore made of protein that have already uffered ubtantial train. Thi contrat ith ultratructural element in an aqueou gla, here the latter upport the aniotropic tre and thu limit train in the hole phae. 18 Summary of the non-pecific effect of olute on membrane at lo hydration At full or high hydration, the hydration force i negligible and intra-membrane force are mall. At lo hydration, intermembrane force are dominated by the hydration repulion. According to the analyi preented here, the non-pecific effect of olute on membrane at lo hydration can be ummaried thu: 1) At lo or intermediate hydration, the omotic effect of the inter-lamellar olute reduce the tre on the membrane. In ufficient concentration, it may keep the gel-fluid tranition temperature near the value it ha in fully hydrated membrane. Thi effect i expected ith any olute (alt, ugar etc). 2) The olute ill have thee effect only if they remain beteen membrane. If the olute are excluded from the membrane region, then thee effect ill be ignificantly reduced. Solute that are completely excluded can, in ufficient concentration, dehydrate lamellar phae and elevate the gel-fluid tranition temperature via Eq. 1. 3) If the olute are relatively large (e.g. diaccharide), they ill have an additional volumetric effect, hich affect the tre decribed in Eq. (1). 4) The reduction of lateral tre by olute ill, all ele equal, reduce the tendency for freezing or dehydration to produce non-lamellar phae, uch a the hexagonal II phae. 5) A the olute are further concentrated by dehydration, further tre reducing effect ill occur only if the olute doe not crytalie. Some olute can be concentrated to very high level ithout crytalliation (e.g. trehaloe). Having mixture of olute alo inhibit crytalliation (e.g. ucroe/raffinoe mixture). 12 The preence of polymer can, hoever, affect the concentration of other maller olute, if preent, and the different olute concentration may affect protein tructure.

19 6) At very lo hydration, vitrification occur. Where the olution beteen fluid membrane i vitrified, it loer the intra-membrane tre and thi further loer the gel-fluid tranition temperature. Such vitrification ill uually maintain the membrane in the fluid phae, and top or everely lo any further dehydration. Converely, the vitrification of the olution beteen membrane in the gel phae ill uually elevate the gel-fluid tranition temperature. None of the effect lited above are pecific to any particular ugar or lipid they occur to varying degree for all lipid and mot olute, ith no pecific interaction required. In the cae of ugar, much of the reported difference in efficacy at protecting membrane during dehydration are primarily a conequence of their different phyical propertie different ize (volumetric effect), different olubilitie (crytalliation) and different gla tranition temperature. Thi doe not rule out the poibility of pecific effect, but much of the oberved behaviour of lipid-olute-ater ytem at lo hydration can be explained ithout them. Acknoledgement. We thank Peter Steponku, Karen Koter and an anonymou referee for helpful comment on an earlier draft of thi paper. Reference Anchodorguy T., A. Rudolph, J. Carpenter and Croe J. Mode of interaction of cryoprotectant ith membrane phopholipid during freezing. Cryobiology 24: (1987). Attard, P. Electrolyte and the electric double layer, in Advance in Chemical Phyic, XCII, Prigogine, I and Rice, S.A., ed., Wiley, pp (1996). Bron, A.D. Microbial ater tre. Bacteriol. Rev 40, (1976). Bryant G., Pope, J.M. and Wolfe, J. Lo hydration phae propertie of phopholipid mixture: evidence for dehydration-induced fluid-fluid eparation. Eur Biophy J., 21, (1992). Bryant, G. and Wolfe, J. Interfacial force in cryobiology and anhydrobiology. Cryo-Letter 13, (1992). Bryant, G., and Wolfe, J. Can hydration force induce lateral phae eparation in membrane? Eur. Biophy. J., 16, (1989). Burke, M.J. The glay tate and urvival of anhydrou biological ytem. In Membrane, Metabolim and Dry Organim (A.C. Leopold, ed.) Cornell, NY, (1986). Caffrey, M. "LIPIDAT> A Databae of Thermodynamic Data and Aociated Information on Lipid Meomorphic and Polymorphic Tranition." CRC Pre, Boca Raton, FL, Cevc, G. Membrane electrotatic, Biochim. Biophy. Acta 1031, (1990). Croe, J. H., Carpenter, J.F. and Croe, L.M. The role of vitrification in anhydrobioi. Ann. Rev. Phyiol. 60, , (1998). Croe, J. H., Oliver, A.E., Hoektra, F.A. and Croe, L.M. Stability of dry membrane by mixture hydroxyethyl tarch and glucoe: the role of vitrification. Cryobioloby 35, (1997). Croe, J.H., Croe, L.M., Carpenter, J.F., Rudolph, A.S., Witrom, C.A., Spargo, B.J. and Anchordoguy, T.J. Interaction of ugar ith membrane. Biochim. Biophy. Acta, 947, (1988). Evan, E.A. and Needham, D. Phyical propertie of urfactant bilayer membrane: thermal tranition, elaticity, rigidity, coheion and colloidal interaction. J Phy. Chem. 91, (1987). Frank, F. The propertie of aqueou olution at ubzero temperature. In: Water: A comprehenive treatie, Vol. 7, F. Frank (Ed). Plenum Pre, N.Y. (1982). Fujikaa, S. A freeze-fracture tudy deigned to clarify the mechanim of freezing nijury due to the freezing-induced cloe appoition of membrane in cortical parenchyma cell of mulberry. Cryobiology, 32, (1995). Gordon-Kamm, W.J. and Steponku, P.L.. Lamellar-to-hexagonal II phae tranition in the plama membrane of iolated protoplat after freeze-induced dehydration. Proc. Natl. Acad. Sci. U.S.A., 81, (1984). Green, J.L. and C.A. Angell. Phae relation and vitrification in accharide-ater olution and the trehaloe anomaly. J. Phy. Chem. 93: (1989). Gruner S.M., Culli, P.R. Hope, M.J. Tilcock, C.P.S. Lipid Polymorphim: The molecular bai of nonbilayer phae. Ann. Rev. Biophy. Biphy. Chem., 14, (1985). Guldbrand L., B. Jonon and H. Wennertrom, (1982). Hydration force and phae equilibria in the dipalmitoyl phophatidylcholine-ater ytem. J. Coll. Int. Sci., 89, Helm, C., Iraelachvili, J.N. and McGuiggan P. Molecular mechanim and force involved in the adheion and fuion of amphiphilic bilayer Science 246, (1989). Hincha, D.K. Lo concentration of trehaloe protect iolated thylakoid againt mechanical freeze-tha damage. Biochim. Biophy. Acta 987, (1989). Horn R.G. Direct meaurement of the force beteen to lipid bilayer and obervation of their fuion. Biochim.Biophy.Acta, 778, (1984). Horn R.G., J. Marra, V.A. Paregian and R.P. Rand. Comparion of force meaured beteen phophatidylcholine bilayer. Biophy. J., 54, (1988). Iraelachvili J.N. Intermolecular and Surface Force. Academic, Ne York (1991). 19

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