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Department of Life Sciences and Chemistry, Roskilde University, Roskilde, Denmark
Correspondence: Address reprint requests to Peter Westh, P.O. Box 260, Roskilde University, Building 18.1, DK-4000 Roskilde, Denmark. Tel.: +45-4674-2879; Fax: +45-4674-3011; E-mail: pwesth{at}ruc.dk or westh{at}virgil.ruc.dk
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODS AND MATERIALSRESULTS AND DATA TREATMENTDISCUSSIONAPPENDIXACKNOWLEDGEMENTSREFERENCES |
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µ1, for systems of unilamellar vesicles of DMPC in aqueous glycerol. It is found that µ1 decreases linearly with the glycerol concentration with a slope of -0.14 ± 0.014 per molal. This implies that glycerol is preferentially excluded from the membrane-solvent interface. Calorimetric investigations of the same systems showed that the glycerol-DMPC interactions are weakly endothermic, and the temperature of the main phase transition increases slightly (0.16°C per molal) with the glycerol concentration. The results are discussed with respect to a molecular picture which takes into account both the partitioning of glycerol into the membrane and the preferential exclusion from the hydration layer, and it is concluded that the latter effect contributes about four times stronger than the former to the net interaction. |
INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODS AND MATERIALSRESULTS AND DATA TREATMENTDISCUSSIONAPPENDIXACKNOWLEDGEMENTSREFERENCES |
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; Yancey et al., 1982). At severe stress levels, such as (partially) frozen or profoundly dehydrated states, where metabolism is strongly reduced (Storey and Storey, 1988) glycerol serves as a protectant, which is thought to stabilize native configurations in the macromolecules and thus enhance survival upon the return to normal conditions (compare to Anchordoguy et al., 1987; Carpenter et al., 1990). Some in vivo examples of pronounced glycerol synthesis include overwintering insects (Lee, 1991; Ramløv, 2000) and salt-stressed algae and yeasts (Hochachka and Somero, 1984; Andreishcheva and Zvyagilskaya, 1999). The protective and regulatory properties of glycerol also make it an interesting compound in biotechnology, where it is used both in vitro (e.g., at lyophilization and low temperature preservation protocols) and in vivo (Restrepo and Balish, 2000; Wagner, 1999).
The main effect of glycerol as a compatible solute is the retention of liquid water brought about by its colligative effect on the aqueous bulk. However, understanding of the particular compatibility of glycerol and related compounds requires detailed insight into their interactions with biopolymers. Such knowledge will not only elucidate stress adaptation on the molecular level, but also pave the way for a rational application in the formulation of biotechnological products. One access to information of this type is the thermodynamic characterization of the interaction, and this approach has already been extensively utilized for model systems comprising soluble proteins. Indeed, the thermodynamic interpretation of protein-compatible solute (or protectant) relationships forms the basis for the current understanding of the underlying mechanisms (Somero and Yancey, 1997; Timasheff, 1998; Courtenay et al., 2000). More specifically, it has been shown that the affinity of the protein surface for water is higher than that for glycerol, and hence that the solvent adjacent to the protein is enriched in water (or depleted for glycerol) compared to the bulk. This condition of so-called preferential hydration (or preferential exclusion of glycerol) has been demonstrated for several compatible solutes and protectants, and the extent of the preferential interaction is considered a key parameter for understanding their effects.
Despite the success within compatible solute-protein studies, preferential interactions parameters have not been directly measured for lipid membrane systems. However, the approach has been discussed (Epan and Bryszewska, 1988; Wolfe and Bryant, 1999), and may be of particular relevance in discussions of stabilizing mechanisms in severely stressed cells. Thus, the cellular membrane is thought to be the most susceptible site of damage during exposure to freezing or dehydration, and several mechanisms of membrane injury, including leakage, fusion, and phase separations, has been put forward (Anchordoguy et al., 1987; Crowe et al., 1990). In some cases, naturally occurring protectants such as glycerol have been shown to counteract such changes in model systems of phospholipid membranes (Anchordoguy et al., 1987; Crowe et al., 1990; Loomis, 1991), and Crowe, Crowe, and co-workers (Crowe and Crowe, 1991; Crowe et al., 1993) have suggested that the effects of polyhydroxy compounds may be directly related to a preferential hydration of the membrane–solvent interface.
To address this experimentally we have utilized a recently developed vapor pressure instrument (Andersen et al., 2002), along with more established calorimetric techniques, to the study of preferential interactions of glycerol and unilamellar vesicles of dimyristoyl phosphatidylcholine (DMPC). The former equipment is capable of resolving lipid-induced changes well below 0.01% of the total vapor pressure, and thus to quantify preferential interactions with satisfactory precision. The results show that in glycerol solutions of a few mol (kg water)-1, DMPC membranes are indeed preferentially hydrated, and that the extent of the preferential hydration, when normalized with respect to the solvent accessible surface area, is about twice that typically observed for globular proteins. Moreover, the glycerol–DMPC interaction is weakly endothermic. Together with available structural data, these observations can be rationalized with respect to a molecular picture, which combines the preferential interactions at the membrane–solvent interface and partitioning of glycerol into the membrane.
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METHODS AND MATERIALS |
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TOPABSTRACTINTRODUCTIONMETHODS AND MATERIALSRESULTS AND DATA TREATMENTDISCUSSIONAPPENDIXACKNOWLEDGEMENTSREFERENCES |
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). The concentration of the extruded vesicle suspension (5–6% w/w) was determined gravimetrically. To minimize errors from evaporative loss during the weighing procedure, the mass of 60 µl aliquots was recorded over a 2-min time span, and the (linear) mass versus time course extrapolated to the time of sample application. The SD on parallel determinations was 0.05% w/w. Glycerol (>99.5%) was purchased from Merck (Darmstadt, Germany).
Vapor pressure measurements
The net (free energy) effect of glycerol-DMPC interactions was measured in homemade vapor-pressure equipment, which has recently been described in detail (Andersen et al., 2002). In this setup, the vapor pressure difference between a cell and a reference is determined with high resolution (0.5 µbar at best). The principle of the current measurements is to quantify the pressure difference, 
P, in a situation where the glycerol concentration (in moles per kg water) is exactly the same in cell and reference, whereas DMPC vesicles are present only in the cell. Since water is the only compound with a detectable vapor pressure, P will reflect the effect of the vesicles on the chemical potential of water (the difference in chemical potential of water arising from the presence of the vesicles is RT ln[(Pref + P)/Pref], where Pref is the vapor pressure of the reference, and R and T are respectively the gas constant and the absolute temperature). The significance of P may be explained in terms of the osmotic pressure of the bulk solution. Thus, addition of DMPC may change the osmotic pressure of the bulk remote from the vesicles in one of two ways. If glycerol accumulates preferentially near the vesicles, then the osmotic pressure in the bulk solution falls. In this case, the bulk solution in the DMPC suspension will have an osmotic pressure lower (or a water vapor pressure higher) than that of the equilibrated reference without DMPC. If glycerol is preferentially excluded, as reported here, then the bulk solution has a higher osmotic pressure (i.e., lower vapor pressure) than does the reference solution.
Solutions for the cell (DMPC–glycerol–water) and reference (glycerol–water) were prepared gravimetrically and 
4-ml weighed aliquots were transferred to the vapor pressure equipment so that the amounts of glycerol and water in the cell and reference were approximately equal. The cell and reference were hermetically sealed and after removal of atmospheric air by repeated exposures to a previously evacuated 0.5-L flask (Andersen et al., 2002) and adjustment of the water content to yield equal glycerol:water mole ratios, P and Pref were recorded until a constant (equilibrium) value was obtained. Details of the relevant procedures are described elsewhere (Andersen et al., 2002).
To evaluate preferential interactions as a function of the glycerol concentration, P and Pref were measured after sequential removals of controlled amounts of water vapor from the cell and reference. The gas phase (P, V, T) quantification of the removed water was precise to within 0.05%, and thus allowed to keep a strict balance of the cell and reference composition. The three experimental trials involved respectively seven, eleven, and nine such removals, which totaled 70% of the water originally loaded. For all trials, the initial DMPC concentration was 
70 mmol DMPC (kg water)-1 although the initial glycerol concentration ranged from 0.22 to 1.18 mol glycerol (kg water)-1. The DMPC concentration at the end of the trials was 2-300 mmol (kg water)-1, which translates into 180–280 water molecules per lipid (i.e., much more than the 20–30 water molecules required for the hydration of DMPC). The data allowed calculation of preferential interaction data (see below) in the 0.3–3 mol glycerol (kg water)-1 concentration range. The experimental reproducibility was found to be ±4 µbar, and the temperature was 30°C.
To investigate the temperature dependence of glycerol-DMPC interactions, and elucidate possible effects of the gel-to-fluid phase transition at 24°C, P, and Pref were recorded as a function of temperature for some samples (about every third). Hence, after the pressure measurement at 30°C, the sample was taken through heating and/or cooling scans at 1°C/h during continuous monitoring of P and Pref.
Calorimetry
The transfer enthalpy of DMPC vesicles from water to water–glycerol mixtures was measured by a four-step procedure (Westh and Koga, 1997), which has recently been adapted to vesicle systems (Trandum et al., 1999, 2000). Data at 30°C and 40°C were retrieved with a MSC-ITC calorimeter (Microcal, Amherst, MA).
The effect of glycerol on the main transition temperature of unilamellar vesicles was measured in an MC2 differential scanning calorimeter (Microcal). Samples of DMPC vesicles (5 mmol (kg water)-1) in glycerol solutions ranging from 0 to 2.5 mol (kg water)-1 were prepared volumetrically from a freshly extruded vesicle suspension (80 mmol (kg water)-1) and a 30% w/w glycerol stock solution. The glycerol–DMPC–water mixtures were equilibrated for 24 h and then analyzed in the scanning calorimeter (heating from 10 to 40°C at 60°C/h).
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RESULTS AND DATA TREATMENT |
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TOPABSTRACTINTRODUCTIONMETHODS AND MATERIALSRESULTS AND DATA TREATMENTDISCUSSIONAPPENDIXACKNOWLEDGEMENTSREFERENCES |
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Raw data from the vapor pressure measurements showing the cell-reference pressure difference, P, as a function of the glycerol concentration, m3, in moles (kg water)-1, is illustrated in Fig. 1. It appears that P attains small negative values under the investigated conditions. This implies that the presence of DMPC vesicles in the cell acts to decrease the chemical potential of water, or, in the language used for protein–cosolvent interactions, that DMPC is preferentially hydrated in mixed glycerol–water solvents. Due to parallel variations in m2 and m3, dictated by the experimental procedure, different data points in Fig. 1 are not immediately comparable. To get the data on a common footing, it was interpreted along the lines of the theory of preferential binding (Casassa and Eisenberg, 1968; Timasheff, 1998; Courtenay et al., 2000). Inasmuch as in this work we monitor the chemical potential of water, the so-called isoosmotic preferential binding parameter µ1
 | (1) |
; Courtenay et al., 2000; Anderson et al., 2002). Here, we only emphasize that µ1 signifies the (positive or negative) number of glycerol (3) molecules needed to reestablish the chemical potential of water upon the addition of one DMPC (2) molecule. Thus, positive values of µ1 indicate that the affinity of the membrane for glycerol is higher than for water and vice versa. To numerically evaluate the derivative in Eq. 1, the data in Fig. 1 has to be combined with the measurement of the vapor pressure of the reference, Pref. Since the cell-reference pressure difference is P, and the slope dPref/dm3 is known, the change in glycerol concentration m3 required to balance out (small values of) P (i.e., to bring the chemical potential of water in the cell to the level of the reference) is
 | (2) |
 | (3) |
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µ1 shows no systematic dependence on m2. Fig. 2 shows µ1, calculated according to Eq. 3, and plotted as a function of the glycerol concentration, m3. It appears that µ1 decreases approximately linearly with m3 with a slope of -0.14 ± 0.014 per molal. Hence, introduction of DMPC vesicles into a glycerol solution brings about a reduction in the water vapor pressure, which can be balanced out by the removal of (0.14 x m3) moles glycerol per mole DMPC added. This provides a measure of the free energy of glycerol–DMPC interactions, and to put this into more conventional units we used the relationship (Schellman, 1993; Poklar et al., 1996):
 | (4) |
Gtrans is the change in free energy upon transfer of DMPC vesicles from water to aqueous glycerol, A is the activity and µ3 is the preferential binding parameter at constant temperature, pressure, and chemical potential of glycerol. The measured values of µ1 were converted into µ3 as described by Courtenay et al. (2000), and it was found that the numerical difference between the two parameters was small (µ3 was 1–3% smaller). This similarity has been noted before (Schellman, 1993), and relationships between the preferential binding parameters has recently been discussed in detail (Anderson et al., 2002). Hence, µ1-values from Fig. 2 were directly introduced in Eq. 4 instead of µ3. The activities required in Eq. 4 were calculated using our recent data on binary aqueous glycerol (To et al., 1999). The transfer free energy, Gtrans, was estimated by numerical integration of Eq. 4, and plotted as a function of m3 in Fig. 3. This derivation of Gtrans is based on the general theory of preferential interactions. However, for the current system the same parameter can be estimated by an alternative, somewhat simpler approach briefly discussed in the Appendix.
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P for two samples is shown in Fig. 4 (open symbols, left ordinate). This figure also includes (solid lines, right ordinate) the vapor pressure lowering (compared to pure water) of the reference (P1* - Pref, where P1* is the vapor pressure of pure water). It appears that the two functions (P and P1* - Pref) are practically superimposed, or in other words, that during temperature scans, P is proportional to the vapor pressure lowering in the reference.
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Htrans < 0). This implies that membrane–glycerol interactions are enthalpically less favorable (i.e., higher energy) than water–DMPC interactions. Moreover, the interaction becomes progressively more endothermic as the glycerol content increases as signified by the positive curvature. The data in Fig. 5 does not identify any temperature dependence of Htrans, suggesting that the interaction does not bring about large changes in the heat capacity of the system.
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Strans = Htrans - Gtrans was calculated and illustrated, together with smooth curves of Gtrans and Htrans in Fig. 6. This figure, which provides an overview of the thermodynamics of DMPC–glycerol interactions at 30°C, shows that the unfavorable free energy of transfer is dominated by the enthalpic contribution.
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0.16°C/(mol (kg water)-1).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODS AND MATERIALSRESULTS AND DATA TREATMENTDISCUSSIONAPPENDIXACKNOWLEDGEMENTSREFERENCES |
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Gtrans, of transferring fluid-phase DMPC liposomes from water to aqueous glycerol is moderately positive and proportional to the glycerol concentration. Thus, there is no sign of binding, specific or nonspecific, of glycerol to this type of membrane. The analogous enthalpy transfer parameter, Htrans, is also positive over the investigated composition range, but shows an upward curvature. This endothermic nature of glycerol–DMPC interaction parallels that found for both the interaction of glycerol with a protein (Westh and Koga, 1997), and that of DMPC with other small alcohols (Trandum et al., 1999; 2000). However, the magnitude of the interaction enthalpy, specified by the slope of the curves in Fig. 5, is much smaller for the current system. The transfer entropy, illustrated as TStrans in Fig. 6, is numerically very small at the lower glycerol concentrations and becomes positive at higher m3.
Glycerol–DMPC interactions are only weakly dependent on temperature. This appears, for example, from the small values of Strans, which suggest that the net effect of the interaction is insensitive to temperature changes (dGtrans/dT = -Strans 0). This is further supported by the observation (Fig. 4) that P is practically proportional to the vapor pressure lowering P1* - Pref over the 10–40°C temperature range. Since P1* - Pref m3dPref/dm3 the proportionality of the two functions in Fig. 4 suggests that dPref/dm3 (and hence µ1; compare to Eq. 3) is temperature-independent. This is in strong contrast to the pronounced T-dependence observed for monohydric alcohols of the same size (Trandum et al., 1999; 2000).
Fig. 4 also shows that the change in µ1 at the gel-to-fluid phase transition is below the level of detection in the vapor pressure measurements (extrapolated curves from before and after the transition merge). A more sensitive test of the changes in preferential interaction around the phase transition is provided by the data in Fig. 7. Here it appears that the phase transition temperature, Tm, increases slightly with the glycerol concentration. An analogous, but stronger effect of glycerol has previously been observed for membranes of phosphatidylethanolamines (Sanderson et al., 1991; Williams et al., 1991; Koynova et al., 1997). Also, sugars and polyhydroxy alcohols other than glycerol, have been shown to bring about a pronounced increase in Tm for various phospholipid membranes (Koynova and Caffrey, 1998; Crowe and Crowe, 1991). The increase in Tm is consistent with negative values of µ1 (Fig. 2) inasmuch as preferentially excluded cosolvents tend to favor configurations with smaller surface area (e.g., see Crowe et al., 1993; Cevc, 1988); the lateral surface area of DPPC membranes increases by about a third upon the gel-to-fluid phase transition (Nagle and Tristram-Nagle, 2000).
Molecular picture of DMPC–glycerol interactions
The interaction of small organic compounds with lipid membranes is traditionally discussed on the basis of a model, which partitions the organic compound into two distinct states. One part is dissolved in the membrane whereas the rest is in aqueous solution in the bulk. This partitioning model is linked to macroscopic properties through the equilibrium (or partitioning) constant Kp = memm3 / bulkm3, where memm and bulkm specify respectively local concentrations in the membrane and aqueous bulk. If the two solutions are considered ideal, the concomitant standard free energy change for the water-membrane transfer of the solute is G° = -RTlnKp. For small values of Kp, this interpretation becomes questionable (Schellman, 1990, 1993; Westh and Trandum, 1999; Westh et al., 2001), and this limitation is readily illustrated by the present measurements. Thus, if the lipid takes up any glycerol, P should increase in response to the concomitant decrease in bulkm3. If no glycerol partitioned (Kp = 0) the partitioning picture would predict P = 0, but the negative P values (as those observed here) cannot be accounted for. The fact that glycerol readily permeates membranes (Efimov and Sharonov, 1985; Mitragotri et al., 1999) demonstrates its presence there, and precise isotope-label methods have quantified Kp for DMPC bilayers to be 0.06 (in molal units) at 30°C (Katz and Diamond, 1974). From this value, the number of membrane partitioned glycerol molecules, memn3, can be determined as (Westh et al., 2001):
 | (5) |
P in the 1–15 µbar range, or a constant (positive) contribution to µ1 of 0.040 per molal glycerol. This prediction is obviously in contrast to the observed slope of -0.14 ± 0.014 kg water (mol)-1 in Fig. 2. However, the discrepancy does not necessarily imply that the determination of either P or Kp is flawed. It merely stresses that the picture of the partitioning model is too crude to rationalize the free energy of membrane–glycerol interactions.
A more general approach to the interpretation of biopolymer interactions in mixed solvents is provided by the so-called local-bulk domain model (Record et al., 1998). In analogy with the partitioning model, the idea is to illustrate biopolymer–solvent interactions in terms of local variations in concentrations. Unlike the partitioning model, however, the latter is rigorously connected to the general thermodynamic theory of preferential interactions. The local-bulk domain model is devised for protein solutions, and inasmuch as the protein molecule is impenetrable to the solvent, it is intuitive to define the local domain as the hydration layer. For membrane systems, on the other hand, the definition of a local domain is somewhat more ambiguous inasmuch as changes in bulkm3 can be brought about by (at least) two mechanisms: i) the partitioning of glycerol (and water) into the membrane and ii) redistribution of the solvent constituents adjacent to the membrane surface. In the light of this, we suggest a modified model where the local domain consists of two zones, respectively lipid membrane and hydration layer, with distinct glycerol contents. This approach allows reconciliation of the shortcomings of the partitioning model discussed above, inasmuch as the amount of glycerol lost from the bulk can be counterweighted by its preferential exclusion from the membrane-solvent interface. Moreover, the approach is experimentally accessible inasmuch as the glycerol concentration of the two local zones can be derived through the combination of the data in Fig. 2 (elucidating differences between the bulk and the average of the two local zones), and memm3 (Eq. 5) giving the glycerol content of the membrane. Thus, the measured isoosmotic binding parameter is µ1/m3 = -0.14 kg water (mol)-1, and process i contributes +0.04 kg water (mol)-1. It follows that the preferential exclusion of glycerol in the hydration layer (ii) is µ1(ii)/m3 = -0.18 kg water (mol)-1. These numbers illustrate the important conclusion that the thermodynamics of glycerol–DMPC interactions are dominated by interfacial effects (ii), whereas glycerol partitioning (i) is less important.
A key relationship derived from the local-bulk domain model is (Record et al., 1998),
 | (6) |
µ1,µ3 is the preferential binding parameter measured by dialysis experiments, where both 1 and 3 are equilibrated over the membrane. Analogously to the treatment of Eq. 4 we find, based on the thermodynamic relationships of Courtenay et al. (2000), that this quantity is practically identical to µ1 under the conditions investigated here. Numerical utilization of Eq. 6 requires additional information. This could be an estimate of the amount, B1, of water involved in full hydration of DMPC, but a structurally more meaningful definition of a local domain comes from recent studies showing that at 30°C, seven to eight water molecules per lipid intercalate into the polar region of the fluctuating membrane interface (Balgavy et al., 2001; Nagle and Tristram-Nagle, 2000). If, based on this, we accept B1 = 7–8, Eq. 6 shows that B3 
0. This implies that the preferential interaction of glycerol and DMPC corresponds to a full exclusion of the cosolvent from water-filled defects in the polar region of DMPC membranes.
As discussed above preferential exclusion of glycerol has previously been observed for globular proteins, and it would be interesting to compare these data with the current measurements. To do so, µ1/m3 must be normalized with respect to the size of the biopolymer, for example by introducing the biopolymer-solvent interfacial area. For DMPC the lateral projected area is 59.6 Å2/molecule at 30°C (Balgavy et al., 2001), but the surface area accessible to the solvent is larger due to fluctuations and the protruding choline phosphate moiety. To estimate the solvent accessible surface area (ASA) we have recently applied the algorithm of Lee and Richards (1971) to simulated phospholipid membranes. For DPPC, we found an average ASA of 135 ± 15 Å2/molecule (at 52°C) equivalent to 2.2 times the projected area (Tuchsen et al., in preparation). If the same factor is valid for DMPC the ASA will be 131 Å2, and the normalized preferential exclusion of glycerol becomes 1.1 x 10-3 kg water (mol)-1Å-2. This normalized extent of preferential exclusion is two to three times that found for globular proteins. These latter values ranged from 2.9 x 10-4 Å-2 (kg water) mol-1 for ß-lactoglobulin, lysozyme, and RNaseA to 5.3 x 10-4 Å-2 (kg water) mol-1for chymotrypsinogen A (Courtenay et al., 2000).
Implications for biological membranes
A primary mechanism underlying the regulatory and protective functions of glycerol in vivo is its colligative effect on the aqueous bulk. Nevertheless, elucidation of glycerol–biopolymer interactions is imperative for the understanding of the exceptional lack of cellular perturbation caused by this solute, even at molar concentrations (Hochachka and Somero, 1984). For enzyme function, this noneffect has been directly related to the preferential exclusion of glycerol (Somero and Yancey, 1997), and the current results show that a comparable exclusion is observed for a phospholipid membrane. Moreover, the absence of conspicuous differences in the ASA-normalized preferential exclusion may suggest that glycerol will be rather uniformly distributed over lipid and protein domains of a biological membrane.
In addition to colligative effects, some reports have suggested stabilization by glycerol in severely stressed systems originating from its specific interaction with membranes (e.g., see Anchordoguy et al., 1987; Loomis, 1991; Ramløv, 2000), and this may also be related to the preferential interaction. Thus, Crowe, Crowe, and co-workers have proposed that the preferential exclusion from the membrane–solvent interface is a key factor underlying effects of polyhydroxy compounds on membranes (Crowe and Crowe, 1991; Crowe et al., 1993). The observation of preferential exclusion for a natural protectant calls for further elucidation of this mechanism for protective effects in vivo.
Closing remarks
Based on the current preferential interaction data and previously published structural information (Katz and Diamond, 1974; Balgavy et al., 2001) we suggest a simplified view in which glycerol–DMPC interactions are governed by two effects: membrane partitioning of glycerol and preferential exclusion of the solute from the membrane interface. These effects (denoted respectively i and ii) contribute to the net interaction with opposite signs, and their relative strength is 1:4 (ii being the stronger). This picture may be further investigated by considering the thermochemical data (this approach is generally more sensitive due to the pronounced enthalpy–entropy compensation, which is common to aqueous systems, and tends to make free energy measurements less conspicuous). Fig. 8 illustrates such an analysis where the experimental Htrans data (from Fig. 5) are compared with estimates of the enthalpic contribution of i (Htrans(i), dotted line) and ii (Htrans(ii), dashed line) as well as the sum of the two (solid line). The calculated values are based on the local changes in the solvent composition discussed above (Eqs. 5 and 6), and the heat of mixing of binary aqueous glycerol (To et al., 1999). This approach neglects the energetic contribution of direct glycerol–DMPC contacts, which is tantamount to the assumption that the membrane partitioned glycerol, memn3, has the same enthalpy as in the pure organic liquid. An analogous assumption has proven acceptable for several other small alcohols partitioned into DMPC membranes (Trandum et al., 1999; 2000). The reasonable coincidence of the calculated and measured values in Fig. 8 supports the suggested picture, and it is in accord with the absence of strong enthalpic effects of DMPC–glycerol contacts. In the light of this we suggest that dominant driving forces for processes i and ii are respectively the mixing entropy of dissolving glycerol in the membrane, and the steric exclusion of glycerol from packing defects in the fluctuating membrane interface.
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APPENDIX |
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µ1/m1)m3 0 in water-rich suspensions of DMPC (Andersen et al., 2002), allows a simpler access to the Gtrans. Thus, at equilibrium the perturbation induced by the lipid can be balanced out by a concentration change in the aqueous phase, m3, specified in Eq. 2. The concomitant change in free energy can be derived from the standard relationship G = 
miµi, and after normalization with respect to the amount of lipid, m2, Gtrans can be approximated
 | (A1) |
In Eq. A1, the activity coefficients at respectively m3 and m3 + m3 are assumed to be equal, and the amount of lipid transferred is accepted to be small enough to neglect the dependence of Gtrans on m2. Values of Gtrans calculated according to Eq. A1 were in accordance with those of Eq. 4, plotted in Fig. 3. However, the scatter of this approach (Eq. A1) is much larger due to the absence of the smoothening provided by the integration process in Eq. 4.
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ACKNOWLEDGEMENTS |
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The work was supported by the Carlsberg Foundation, the Novo-Nordisk Foundation, and the Danish National Research Foundation, through the establishment of the MEMPHYS Center for Biomembrane Physics.
Submitted on June 24, 2002; accepted for publication August 8, 2002.
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REFERENCES |
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