The effects of osmotic and hydrostatic pressures on macromolecular systems

Biochimica et Biophysica Acta 1595 (2002) 30^47 www.bba-direct.com

Review

The e¡ects of osmotic and hydrostatic pressures on macromolecular systems Jack A. Kornblatt *, M. Judith Kornblatt Enzyme Research Group, Department of Biology, Concordia University, 1455 de Maisonneuve, Montreal, QC, Canada H3G 1M8 Received 24 July 2001; received in revised form 17 October 2001; accepted 18 October 2001

Abstract Osmotic pressure and hydrostatic pressure can be used effectively to probe the behavior of biologically important macromolecules and their complexes. Using the two techniques requires a theoretical framework as well as knowledge of the more common pitfalls. Both are discussed in this review in the context of several examples. ß 2002 Elsevier Science B.V. All rights reserved. Keywords: Protein hydration; Hydrostatic pressure; Osmotic pressure

1. Introduction It is somewhat ironic that two of the earlier quantitative studies on enzymes and proteins involved manipulation of water, although the importance of that factor was not recognized at the time. Michaelis and Menten [1] worked initially with the enzyme invertase. Bridgman [2] worked with ovalbumin. The former showed that the hydrolysis of sucrose could be accounted for by rate laws that ignored the concentration of water; at 54 ‘M’ in their solutions, it Abbreviations: op, osmotic pressure; hp, hydrostatic pressure; T state, the taut conformer of hemoglobin: it has a low a⁄nity for O2 ; R state, the relaxed conformer of hemoglobin: it has a high a⁄nity for O2 ; K2 L2 , KL, K, L, the hemoglobin tetramer, dimer and individual subunits; P450camo;os , substrate free and substrate bound forms of cytochrome P540; cytox, cytochrome c oxidase from ox heart; cyt c, cytochrome c; cyt, cytochrome; DPG, diphosphoglyceric acid; DOPC, dioleyl phosphatidylcholine * Corresponding author. Fax: +1-514-848-2881. E-mail address: [email protected] (J.A. Kornblatt).

was e¡ectively constant. The latter showed that the application of high hydrostatic pressure (hp) would denature ovalbumin. Many years later, we accept that hp acts at the level of driving a system from a lower density to a higher density; Bridgman’s phenomenon results from water at pressure forcing the hydration of a protein’s buried surface. This exposure of new surface may lead to aggregation. We have, at the same time, been slow to recognize that if we change the activity of water, increase the osmotic pressure (op), such as Michaelis and Menten did, we can alter the way enzymes behave. Increasing op drives a system from the more hydrated state to the less hydrated according to the number of soluteinaccessible waters that connect the two states. The e¡ects of hp and op on nucleic acids, proteins, enzymes and their assemblies are mainly mediated through the e¡ects of water on those systems. Accordingly, this review deals with water e¡ects on systems and what can be learned about them using hp and op as tools. The two pressures are two of the three parameters that can be varied in a thermody-

0167-4838 / 02 / $ ^ see front matter ß 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 4 8 3 8 ( 0 1 ) 0 0 3 3 3 - 8

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namic treatment; we have now and then considered the third parameter, T, when it is logical to do so. Some of the conclusions discussed here will sound quite familiar since they have been expressed in other reviews [3^8]. If water, studied by the application of op and hp, is the real subject of this review, what roles does it play in the lives of enzymes, other proteins and other macromolecular systems? The two most familiar roles are those of solvent and substrate/product. More than 99% of the known biological macromolecules function in an aqueous environment. More than 90% of the known enzymes and ribozymes have water as either a substrate or as a product. Other roles for water include the following. It will ¢ll voids when it is energetically favorable to do so [9]. It stabilizes conformations and facilitates the interconversions between conformations. It facilitates binding between distant groups thereby functioning as a molecular bridge. Water modulates midpoint potentials, ionization potentials, pKs, and binding coe⁄cients. It acts as a molecular wire to transmit protons from one site to another. Lastly, water can act as a bulk carrier for protons, other ions, uncharged molecules, etc. These points are important in that the application of our two pressures is going to in£uence all of them. Even when we are careful, the fact that they are sensitive to changing water activities will confuse the interpretation of results. For the analysis of how hp and op can give us information about the e¡ects of water on our macromolecular systems we will try to restrict ourselves to ‘simple’ but real cases; complex cases, enzyme aging or whole cell studies have been recently reviewed [10,11]. The simple cases fall into two categories. 1. Equilibria between two states of a macromolecule in solution in which temperature, hp or op is varied. This constitutes the vast majority of cases. We will also consider equilibria in which hp and temperature, or hp and op, or temperature and op are varied two at a time. This approach has been pro¢tably used by several groups; the original data should be consulted [12^15]. In principle, all three parameters could be varied. There are no data on biological systems here but there are

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indications as to how they might behave based on non-biological systems [16]. 2. Kinetics in which hp or op changes the overall rate by changing the rates of speci¢c steps in the reaction.

We start by considering two relatively simple and well de¢ned cases ^ the phospholipid bilayer and hemoglobin. 1.1. The in£uence of temperature, hp and op on the behavior of multilamellar phospholipid bilayers These are multiple bilayers stacked parallel to each other and separated by layers of water, in much the way that the myelin sheath is composed. There is a wealth of information on the e¡ects of temperature on the liquid-crystalline, gel transition of phospholipid bilayers [17]. Increasing temperature causes the bilayer lipids to go from the ordered gel state with the hydrocarbon chains crystallized, to the less ordered liquid crystalline state as the hydrocarbon chains disorder and melt. From the structural point of view this means that as temperature increases the fatty acid chains become disordered and are able to sweep out a volume that is larger than the volume swept out in the gel phase. The phosphoderivative head groups have greater mobility in the latter state. With increasing T, the hydrocarbon chains of bilayers melt at Tc , and thin as T increases further. The inter bilayer or polar group layer between hydrocarbon regions of opposing bilayers can be hydrated to a limited extent if the lipids have no net electric charge. There are about 32 waters per DOPC head group in DOPC membranes at saturation [18^ 20]. Using the op stress approach, one can reduce the activity of water under tightly controlled conditions. With increasing op, water is removed osmotically, forcing/pushing bilayers together. This results in a strong mutual repulsion. The bilayers thicken, molecular area decreases and the dipoles (of the head groups) become more perpendicular to the plane of the bilayer. Tc increases. Others have found that the application of hp to phosphatidyl choline multilayer membranes causes (1) a linear increase in Tc along with an interdigitation of acyl chains from apposing lea£ets [21], (2) a

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tilting of the head groups [22] and (3) increases in the bilayer thickness and separation of the liquid crystal to gel transition from the gel to ordered crystalline phase transition [23,24]. In other words, op can cause membrane thickening in some species of phospholipids while hp can cause a similar net result in other phospholipid species. If we belabor this example of phospholipids and bilayers, it is because one starts with the preconceived idea that bilayers should be relatively easy to analyze. One also often starts with the preconceived idea that op and hp should have opposite e¡ects on the system. The above points out one signi¢cant fact: temperature, op and hp perturbations yield unexpected results because they do not interrogate the same end states. Phospholipid bilayers can exist in more than two states; one is not dealing with a simple two-state equilibrium. 1.2. The in£uence of temperature, hp and op on the oxygen binding capacity of hemoglobin The e¡ects of temperature on the equilibrium shown below were studied well before the era of X-ray crystallography and the Monod^Wyman^ Changeux model of cooperative interactions [25]. ðT stateÞ Hb þ 4O2 3½Hb 4O2 Š ðR stateÞ Temperature increases in£uence this reaction by lowering the a⁄nity of Hb for oxygen. The p50 , the partial pressure of oxygen required to bring about 50% saturation of Hb, increases as temperature increases. vGo changes because reactions are governed either by an enthalpy term, vHo , or by an entropy term, TvSo . Perutz [26] pointed out, based on his crystal structure, that T state hemoglobin contained many salt bridges that were not present in the R state protein. These would have to be broken in order for the T to R transition to take place. Breaking them required heat; the T state of Hb is stabilized by an enthalpy term. hp should also act to break these salt bridges, thereby favoring the T to R transition, whereas op should act to strengthen their interactions. Furthermore, to go from the T to R state requires deprotonating Hb at some of those same residues as well as releasing bound Cl3 . Protons and the organophosphates stabilize the fully deoxygenated T state of Hb. A thorough analysis of the

energetics of hemoglobin binding oxygen showed that the above reaction was really a simpli¢cation of reality [27]. The binding reaction was better described by the equation: ðT stateÞ ½Hb; Cl3 ; DPG23 ; Hþ Š þ 4O2 3½Hb4O2 Š þ Hþ ; DPG32 þ Cl3 ðR stateÞ in which oxygen bound to hemoglobin in four discrete steps. vH and TvS for the individual binding reactions were determined under several conditions [27]. Imai showed several salient features of the reaction. vH and TvS appeared to vary widely for the individual steps in oxygen binding; once the contributions for ion binding and protonation were subtracted, vH and TvS for the actual binding of oxygen were more or less the same for the individual steps. The variation in the two terms resulted and results from the binding of other substances during the binding of oxygen and the T to R transition that accompanies the oxygenation. With so many di¡erent things binding or released, with the known large conformational change that takes place, it should go without saying that hp should have major e¡ects on the oxygen binding curve of hemoglobin and the associated T to R conformational change. The e¡ects of hp on the above equilibrium can be easily summed up. When the various contributions to the equilibrium are examined there is general agreement that hp does not in£uence the T to R transition [28^30]. hp has either a small or no discernible in£uence on the equilibrium [31,32]. The volume change for the system must be close to zero. There is a small in£uence of pressure on the spin state of the hemes but this does not appear until pressures above 400 MPa [28,33]. One place where pressure does have an in£uence is on the overall equilibrium K2 L2 3KL3K+L [34]. hp drives the equilibrium in the direction of free monomers. Accordingly, if there is a signi¢cant concentration of dimer in a sample, hp will displace the overall equilibrium away from the native tetramer. The hemoglobin story has always been interesting but it became more so when the three dimensional structures of both R and T state hemoglobins were established. The two structures clearly demonstrated the conformational di¡erences between the two states but they also showed that the oxygenated R state

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contained about 60 waters ‘tightly’ associated with it. This motivated Colombo et al. [35^37] to ask whether the excess waters were a necessary part of the structure of oxygenated hemoglobin. The waters turned out to be an obligatory component of oxygenated hemoglobin. The approach used relied on lowering the activity of water with cosolvents; the log of the binding constant, p50 , was then shown to vary as the op and as [Cl31 ]. Applying the Wyman linkage relationships [38], the authors showed that concomitant with the binding of four oxygens, approximately 60 waters were also bound as the hemoglobin molecule went from T state to R state. In the absence of anions, only 25 additional waters bound to hemoglobin as it bound oxygen [39]. From hindsight, this means that the equilibrium written above should really be written ðT stateÞ ½Hb:Cl31 Hþ DPG23 Š þ 4O2 þ 60H2 O3 ½Hb4O2 60H2 OŠ þ Hþ þ DPG32 þ Cl31 ðR stateÞ or ðT stateÞ ½Hb; Hþ ; DPG23 Š þ 4O2 þ 25H2 O3 ½Hb4O2 25H2 OŠ þ Hþ þ DPG32 Š ðR stateÞ The Colombo experiments were performed at concentrations of Hb between 15 WM (4 heme tetramer) and 45 WM, concentrations where signi¢cant fractions of dimer were, in the past, thought to have been present [27]. More recent data [40,41] indicate that the Kd for the transition varies between 0.2 WM and 1 WM depending on [salt], pH, and temperature; the fraction dimer present is small but signi¢cant at the lower concentrations. In the unlikely case that the dimer/tetramer equilibrium is contributing to the change in water binding that accompanies oxygen binding and the T to R transition, the analysis would become quite complicated. The di¡erences between the four above equations point out another unexpected feature. Release of chloride from bound Hb should result in water binding to the chloride. Electrostriction of the chloride does not result in the disappearance of 35 waters. This means that there must be another form of hemoglobin; the above authors refer to this as P state hemoglobin. We have referred to the case of hemo-

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globin binding oxygen and water as elegant; it also points out the same trap as the phospholipid bilayers pointed out. Increasing hp and op experiments drive systems in the direction of increased density and decreased water associations. If our probes are not speci¢c for our end points, it is possible to interrogate di¡erent end points without being aware of doing so. In such cases, the thermodynamic conclusions are not valid. If biochemical conclusions or physiological conclusions are based on invalid thermodynamic conclusions, they too cannot be valid. What do we vary in hp and op experiments? In an hp experiment we measure changes in equilibria (or rates) as we vary hp. We analyze those changes in terms of changes in volume or changes in density between two states of a system. In an hp experiment we equate those two states of the system with two states of a macromolecule or macromolecular interaction. This is convenient but it is not strictly true. The change in the macromolecule is only a portion of the overall change exhibited by the system. In an op experiment we measure changes in equilibria (or rates) as we vary water activity (op). We analyze those changes in terms of the number of solute-inaccessible waters that must change to go between two states of a system. In this instance, the equations that relate the chemical potential of water to the chemical potential of the macromolecule are exact and require no assumptions other than everything else is kept constant. If this were true in hp experiments and op experiments, there would be few problems with the interpretation of results. However, most often, the data from either type of experiment are open to other interpretations. The most important things to keep in mind are the following. hp acts at the level of density. Atoms are not compressible. Voids can be compressed. Solvent water contains ‘void’ space compared to the space the actual atoms occupy but protein interiors also contain void space [3]. Solvent can solvate a macromolecular surface where it may occupy less volume (where its density may be increased) but where it may also occupy more volume [42]. Where the void space of a protein interior can be reversibly compressed without disrupting the total energetics of folded state, hp will compress those spaces. op acts at the level of number of waters. Comparing two solute-inaccessible com-

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partments, it is unimportant whether the waters occupy more or less space in the comparison. What is important is that the numbers of waters in the two are di¡erent. This means that predicting whether hp will force a system into one particular direction is not possible without prior knowledge of the densities of the components. It also means that predicting whether op will force a system into one particular direction is not possible without prior knowledge of the required hydration states of the components. Crystal structures and NMR structures may be useful in rationalizing the experimental results of the two kinds of pressure but are only useful for prediction ‘after the fact’. What things interfere with our interpretation of pressure data? What kinds of things can be varied in a biochemical experiment and what other things do we vary when we change them? The traditional enzymologist varies [x], pH, T, I and measures a response. In cryoenzymology, for instance, one lowers T while trying to keep other things ‘under control’. We include the quotation marks because you cannot change T and not change a large number of other factors at the same time. They are linked. Changing T for instance changes the dielectric coef¢cient of the solution. If we try to correct for this (using graded concentrations of zwitterions for example) we then have other additions that must be corrected for. Is it important to keep the dielectric coe⁄cient constant? The answer is: ‘It all depends’ [43]. If one is measuring the equilibrium between two states, denatured and native, the stability of the two states is a function of the sum total of the forces acting on the molecule. If there are non-neutralized charges in the interior of a macromolecule, those charges act to destabilize it. The destabilization energy scales as E s ¼ q2 =2Drs

ð1Þ

where q is the charge, D the dielectric coe⁄cient in the vicinity of the charge, and rs the radius over which the charge is distributed. Increasing T causes D of the solvent to decrease and D of the protein interior to decrease. The net change in stability is, in part, a re£ection of the di¡erence in D internal vs. external.

What else changes? The addition of high salt to a solution exerts an op but it also disorders solvent such that the solvent looks as though it is under high hp [44]. From the point of view of a macromolecule in solution, this means that the addition of salt increases the op of the solution ^ it decreases the chemical potential of water ^ but it also provides a milieu in which the remaining water looks like water at hp. This means that bifurcated hydrogen bonds are introduced where they did not previously exist. We have spent a substantial amount of e¡ort to persuade readers that op and hp experiments must be planned and interpreted with caution. Moreover, the cautions that we suggest should be viewed in addition to, rather than instead of, those of other authors [6^8,45]. This does not mean that hp and op experiments should not be done. What tools does one need to plan and execute an experiment using op as a perturbant? One needs four equations and a practical framework. The four equations are: dðRTlnK M Þ ¼ ðv NV 0 ÞdðopÞ

ð2Þ

where KM is the equilibrium coe⁄cient for the two states of the macromolecule, vN is the number of solute-inaccessible waters associated with one of the states that are absent in the other state, V0 is the partial molar volume of water and op is determined from op ¼ ðRT=V 0 ÞlnX H2 O

ð3Þ

X, the mole fraction, is most easily obtained from either the Handbook of Chemistry and Physics or from one of two WEB sites (http://aqueous.labs. brocku.ca/os¢le.html; http://dir.nichd.nih.gov/Lpsb/ docs/osmdata/osmdata.html). The left side of Eq. 3 is the familiar expression for the free energy of a system, in this case, the chemical potential. Inspection of Eq. 3 indicates that the right side of Eq. 3 is also an energy term. We plot RTlnKM vs op. The slope of the resulting straight line is equal to the di¡erence in the number of solute inaccessible waters associated with the two forms of the macromolecule. To carry out an op vs temperature experiment requires knowing that vCp , the heat capacity of the protein, does not vary as a function of the op per-

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turbant. The basic experiment is to measure KM as a function of op at a ¢xed temperature and to extrapolate the data to ¢nd the op at which vG = 0. This experiment is then repeated at a number of di¡erent temperatures. One then plots T vs. op at vG = 0 to yield a curve in much the same way that one handles hp vs. temperature data [12]. For this curve,

D T=D ðopÞ ¼ ðv NV 0 Þðv So þ v C p ððT3T o Þ=T o ÞÞ31 ð4Þ

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the op are acting only at the level of the activity of water and not by some direct interaction between macromolecule and perturbant. Op e¡ects should be invoked because most other considerations do not explain a set of data. The reader is directed to [7,8] in order to obtain a full appreciation for the problems that arise during analysis and the level of friction those problems can generate. 1.4. The application of op to perturb equilibria

To carry out an op vs. hp experiment requires knowing that compressibility does not vary as a function of the osmotic perturbant. The basic design is the same except that we vary op at constant hp. In this case we plot hp and op at vG = 0 to yield the curve. The equation is similar to Eq. 4:

D ðhpÞ=D ðopÞ ¼ ðv NV0 Þðv Vo þ v L ððhp3hpo Þ=hpo ÞÞ31

The past 10 years has seen a large number of papers in which equilibria have been studied as a function of cosolvent activity. We have chosen a very few selected case studies based on our familiarity with those; we apologize to the authors of other studies whose work has not been included here. The omission carries no judgement with it.

ð5Þ

In an op vs. temperature experiment or an op vs. hp experiment, the instantaneous slope (Eqs. 4 and 5) gives information on vN, vSo , and vCp or on vN, vVo and vL. The complete derivations of Eqs. 2^5 are given in the Appendix. The above analyses are what we, as physical biochemists, should be trying to achieve. As will be evident in the remaining sections of this article, in practice, hp and op have not been used to their full potential. 1.3. Practice Traps to avoid. Eqs. 2^5 are totally general and rigorous. Using them to carry out an analysis requires some caution. All calculations must be based on activities and only activities. The use of molar or molal concentrations leads to false conclusions except in the case of very dilute solutions. Since we work at high op, we are not working in the very dilute regime. Calculating the chemical potential of the macromolecule usually requires that you know that there are only two end states in question. It requires that the population of intermediates between those states is small. Finally it requires that the materials used to alter

2. The case of cytochrome P450cam Cytochrome P450cam is a heme containing enzyme from Pseudomonas putida which catalyzes the hydroxylation of camphor in an ordered reaction as shown in Fig. 1. The enzyme has been studied since the late 1950s [46^49]. The individual steps leading to the conversion of camphor to 5-exo-hydroxycamphor are shown in Fig. 1. There is little formation of the dead-end product cytochrome P420 during steady state turnover. There is little electron transfer from reduced putidaredoxin (Pdr ) in the absence of bound camphor which means that there is little accumulation of activated oxygen products during steady state turnover. P450cam is a well designed enzyme. From the point of view of op studies, the following points should be kept in mind. (i) The crystal structures of P450o and P450os were established many years ago and are shown in Fig. 2 [50,51]. The pocket of P450o is large, consists of a hydrophobic surface and is ¢lled with about six water molecules; the sixth ligand to the oxidized iron is probably a water molecule. The substrate pocket of P450os is ¢lled with a well ordered camphor molecule; it displaces the waters including that which is ligated to the iron in P450o . The entire cat-

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Fig. 1. Cytochrome P450 converts camphor to 5-exo-hydroxycamphor. The enzyme, cytochrome P450, is represented as P450. P420 is a non-native form which is enzymatically inactive. The enzyme form with camphor bound is P450os , in which ‘o’ means oxidized and ‘s’ means that camphor is bound. Putidaredoxin reduces the enzyme to P450rs in which ‘r’ means reduced. O2 binds and forms P450os O2 . The ¢nal electron transfer step comes when the second molecule of putidaredoxin binds.

alytic pathway at atomic resolution has been recently elucidated and summarized [52]. (ii) P450o contains low-spin iron whereas it is highspin in P450os . The iron of P450 undergoes a spin transition [53,54] which is associated with substrate binding [55^57]. The spin transition is susceptible to hp [58,59]. Starting with P450os , hp drives the complex low-spin and drives the camphor from and water into the pocket [60]. In addition to hp, KCl, temperature and cosolvents also in£uence the equilibrium between the two spin states [49]. (iii) Qualitatively, the e¡ects of T, hp and op on the spin equilibrium of P450 are consistent. Higher temperatures promote the high spin, camphor containing form. hp promotes expulsion of the camphor from the pocket, op promotes its retention. Quantitatively the situation is somewhat more complex. The volume change for hp expulsion of camphor from the P450 pocket is about 30 ml/mol [61]. This number is (1) consistent with 6^7 water molecules if one assumes that the density of water in the P450 pocket is about 25% greater than that of bulk water [62] and (2) satisfying when one considers that there are about six waters in the pocket of P450o . However, this number increases to 17 waters if one assumes only a 10% di¡erence in water density [63]. A second problem arises when one considers the op data. Di Primo et al. showed that the volume change for the spin transition is about 350 ml/mol [61]. In an op

experiment volume and number are related by the partial molar volume of water which means that this corresponds to about 20 waters. Clearly, the waters probed by op include too many to be associated with just the camphor pocket. Is this really surprising? Of course not! We perturb the equilibrium with cosolvents or other compounds that change the activity of water; in the best of cases, such as the Di Primo studies, it is reasonably clear that the osmotic perturbants are only in£uencing water activity and are not binding to the protein. Nonetheless, in this system there are waters associated with the P450 equilibrium other than just those in the heme/camphor pocket. Amongst those are the waters that hydrate the released camphor. Until such time as we have a complete picture of the hydration states of all the components of the system, we prefer to take a cautious attitude. All the data point to about 20 osmotically sensitive waters being involved in the spin equilibrium. Thermodynamics cannot tell us where these waters are. (iv) The spin equilibrium is not the only aspect of the P450 cycle (Fig. 1) that is sensitive to op. The binding of putidaredoxin, the reducing substrate, to the P450 is also perturbed by op [64,65]. The e¡ects of temperature on this system were the ¢rst indication that waters might mediate the binding. When two solvated molecules bind with a resulting dehydration of their surfaces, there is a large gain in en-

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Fig. 2. The crystal structure of cytochrome P450. (A) P450os is shown looking into the camphor pocket at the camphor (PDB2CPP). The amino acids are blue, heme is green and the camphor is shown in red. The camphor does not quite ¢ll the pocket. (B) P450o is shown looking into the same camphor pocket; in this case camphor is not present but has been replaced by about six, well ordered water molecules, shown in yellow ((PDB1PHC). Note that this view is similar to but not exactly the same as that in A.

tropy by the system. Water at the macromolecular surface is more ordered than bulk and its release into the bulk phase must be accompanied by a large gain in entropy. The converse is true. If there is a large decrease in entropy on binding of two macromolecules, there must be net amounts of solvent taken up from the bulk. In the case of some ferridoxin type associations, the reactions are entropy driven [66]. In the case of P450 and putidaredoxin, the binding is enthalpy driven [67]. When the complex was subjected to osmotic stress, it was found that binding was weakened as though there were waters sequestered at the interface which were necessary for binding [64,65]. The crystal structure of a related complex, the P450 BM-3/P450 reductase, shows waters sequestered at the interface [68]. The numbers of

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waters associated with the P450cam/putidaredoxin case are large: 25 waters in the physiologically relevant case between the oxidized P450 and the reduced putidaredoxin; 13 waters between the non-physiologically relevant partners, oxidized P450 and the oxidized putidaredoxin [65]. (v) To summarize what we know about P450cam: Temperature studies indicated that there was an hydration di¡erence between the camphor containing protein and the ligand free species. This was reinforced by hp studies which showed that expulsion of camphor from the P450 pocket was probably accompanied by water entry. The crystal structures of the ligated and unligated forms substantiated this deduction. The waters associated with the P450 pocket can be perturbed osmotically but additional waters associated with the system are also perturbed. The interfacial area between putidaredoxin and P450 probably contains water. Lastly, the numbers of waters in the physiologically relevant and irrelevant complexes di¡er. We have mastered the art of applying the three thermodynamic perturbants to the cytochrome P450cam; in retrospect we can rationalize their signi¢cance even if we have di⁄culty with absolute numbers.

3. The case of cytochrome c oxidase Cytox (cytochrome c oxidase) is the terminal electron transfer component of the mitochondrial electron transport chain. It is an integral membrane protein that can be solubilized with detergents. It consists of four redox centers: two hemes as cytochromes a and a3 , CuA and CuB. It has been crystallized and the crystal structure determined [69,70]. The reactions catalyzed by the protein are shown below. Reduced cyt c (cytochrome c) must bind transiently to cytox, it must transfer an electron and then dissociate from the complex; this cycle must be repeated four times in order for oxygen to be reduced. The binding and electron transfer reactions occur on the cytosolic side of the mitochondrion; oxygen reduction occurs towards the inner space of the organelle. Four protons are consumed inside the mitochondrion to form water; at the same time, four protons are transferred against the electrochemical gradient from inside to outside the mitochondrion.

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4 cyt cðIIÞ þ O2 þ 4Hþ þ 4 Hþ 34 cyt cðIIIÞþ 2H 2 O þ 4 H þ The protein has been extensively studied since the 1950s and the studies reviewed on a regular basis. A reasonably current view of the inner workings of electron transfer, proton transfer and oxygen reduction can be found in two recent references [71,72]. There have been innumerable temperature studies on the oxidase. Most have been carried out at low temperature in order to establish the electron transfer path from reduced cytox to oxygen. None to the best of our knowledge allows for the decoupling of individual electron transfer steps, proton transfer steps or cyt c binding and release. Cytox has been the subject of several pressure studies. The fully oxidized protein shows a small spin change when subjected to hp; the volume change is similar to those found in other heme containing proteins [73]. Similarly, the totally reduced protein is impervious to hp [74]. During catalytic turnover, the situation changes and the protein becomes highly sensitive to pressure. A block in electron transfer is introduced between cytochrome a and cytochrome a3 for which the volume change is about 80 ml/mol [74]. This was postulated to be too large a volume change to be associated with anything other than solvent movements into and out of the cytox during turnover. Osmotic perturbation of cytox showed that the two static forms of the protein were relatively impervious to op but that the enzyme during turnover was quite sensitive to inhibition by op. The response to op was consistent with a catalytic cycle in which about 10 waters must enter and leave the molecule with each turnover [75]. Other techniques have indicated that the actual number of waters that must enter and leave during catalysis range from about 4 to 10 [76^78]. At ¢rst glance, it is surprising that op and hp both inhibit the activity of the enzyme. However, an enzyme during turnover is quite di¡erent from a system in equilibrium. If, during turnover, there is a step which involves an increase in the number of water molecules associated with the protein, then there must be a later step in which those water molecules are lost from the protein. Thus the catalytic cycle would include steps that would be inhibited by op (and acti-

vated by hp) and others which exhibit the opposite pattern. It is not surprising that the degree of solvation should change as macromolecules change conformations and oxidation states. What is surprising is that these changes should be obligatory in a macromolecule whose only roles are electron transfer and proton pumping. What is gratifying is that a water cycle should be predicted on the basis of osmotic perturbation studies and that 6 years later the X-ray crystal structure [69,70] should reveal a cluster of waters in the vestibule of the heme pocket of this protein. This cluster is perfectly positioned in the region where proton transfer is postulated to occur. We envisage a proton pump in which the hydrated proton is transferred across the molecule rather than a proton wire in which there is transient dehydration of each proton transferred. What is signi¢cant about the work on cytox is that osmotic perturbation predicted water involvement in electron and proton transfer and that this idea has subsequently been supported by several independent lines of evidence. The catalytic cycle of cytox relies on binding and release of cytochrome c. The equilibrium binding has been subjected to the same sort of scrutiny as the catalytic cycle. Early studies from the Margoliash laboratory [79] established quite clearly that the binding of cyt c to cytox involved a ring of positive charge on the cyt c molecule and that these charges interacted with negative charges on cytox. The ionic strength dependence of interaction indicated that about four charges on each protein should take part in binding. This should have meant that there would be a strong force favoring electrostriction of the individual charges when the complex was subjected to hp. The experimental results were somewhat surprising in that hp had little e¡ect on the interaction between cyt c and cytox, nor between cyt c and cytochrome c peroxidase. There was a substantial in£uence on the interaction between cyt c and cyt b5 [80^83] which had a volume change of about 50 ml/mol. The binding sites for cyt c on all three acceptor proteins were thought to be similar but hp results indicated that the b5 site di¡ered from the other two. Modeling had shown that the b5 , cyt c complex formed a tight ¢t with little space between the molecules. Osmotic perturbation of the cyt c/cyt ox and cyt c/cyt b5 complex showed entirely di¡erent

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results [84,85]. In the cyt c/cyt ox couple, op caused the interaction between the two proteins to weaken. In the cyt c/cyt b5 couple op caused the interaction between the two proteins to strengthen. This indicated that the interface between cyt c/cyt ox contained sequestered solvent and that forces that inhibited the sequestration of the solvent would

39

simultaneously inhibit binding. The data indicated that there was no such sequestration of solvent in the cyt c/b5 interface. When this work was published, 1993, the crystal structure of the cytochrome c peroxidase/cyt c complex had just been published [86] but details of the interaction site were not available. Since then the coordinates have been deposited and the interaction site shows that the contacts between the two partners are made, with few exceptions, through water bridges (Fig. 3). Once again the utility of the combined hp, op approach was to reveal details of the interaction site, details that were later con¢rmed by X-ray crystallography.

4. The case of enolase

Fig. 3. The crystal structure of the cytochrome c, cytochrome c peroxidase complex (PDB2PCC). (A) The complex as viewed from cytochrome c down onto the peroxidase. On the cytoî from the peroxichrome c, all atoms further away than 10 A dase have been removed so that one can see the broad outline of the interfacial region. The amino acids of the peroxidase are blue, those of cytochrome c are green. Heme is red and water is yellow. (B) The exact same view of the complex removing î those atoms of cytochrome c that are further away than 4 A from the peroxidase. The interfacial waters are clearly seen as well as a few atoms of cytochrome c that are within the restricted distance. There are more waters close to the peroxidase than there are atoms of cytochrome c.

Enolase catalyzes the interconversion of 2-phosphoglycerate and phosphoenolpyruvate. The yeast protein is a homodimer as are known mammalian enzymes with the exception of some brain forms. From the point of view of one surface recognizing another, of one surface making good contacts with another, this poses a problem. There are constraints operating on the structure of homodimeric enzymes that do not operate on heteropolymers. Under controlled conditions the dissociation of enolase into subunits is a reversible reaction in which intermediates do not accumulate. hp promotes dissociation [87,88] as would be predicted if the subunit surfaces which are buried in the dimer become hydrated upon dissociation. op promotes dimer formation [89]. The volume changes measured by op, hp and dilatometry are consistent (unpublished data). With yeast enolase, vV for dissociation, as measured by hp, is 3260 ml mol31 . The presence of osmolytes stabilizes the dimeric state and shifts the curve for dissociation to higher hydrostatic pressures. Osmolytes do not, however, change vV for dissociation. The op experiments yield a value of about 120 waters that bind to the protein upon dissociation. One hundred and twenty bound waters corresponds to the î 2 of surface. The published hydration of about 860 A î 2 of surX-ray structures report that almost 4000 A face are buried at the subunit interface [90,91]. This means that as much as 3/4 of the dimer interface should contain water molecules. The X-ray crystallographic structure of yeast eno-

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Fig. 4. The crystal structure of yeast enolase dimer (PDB1EBH). (A) The complex as viewed down one monomer onto the other. One subunit is blue, the other green. The waters seen in the complex are yellow. All atoms of the top subunit î from the bottom subunit have been removed further than 7.0 A such that some feel for the interfacial region can be obtained. (B) The exact same view of the complex removing all those î from the atoms of the top subunit that are more than 3.5 A bottom subunit. Note the large number of waters at the interface. Clearly, the water network covers less than 3/4 of the interface but it is still extensive.

lase is shown in Fig. 4 [92]. There is a rugged protein surface that has to make contact with an identical surface on the other monomer. The problem is how to maximize the good contacts and avoid creating large, potentially destabilizing voids. Evolution in the yeast enolase case has solved the problem by having a relatively small surface that makes good contacts on the two monomers and having an auxil-

iary surface that makes poorer contacts that are linked by water molecules. The interfacial waters are shown in Fig. 4. What is signi¢cant about these waters is that in some instances they make good contacts with monomer A, in other instances with monomer B and in some instances with other water molecules. They are far from the active site. These interfacial waters form a cushion ^ they take up space, improve van der Waals contacts and hydrogen bonding ^ that improves otherwise poor contacts; most signi¢cantly, the waters are probed by both hp and op. There is also a cleft between the two subunits that is ¢lled with water, including some waters su⁄ciently immobile to be seen in the X-ray structure. The measured volume changes and the e¡ects of both hp and op re£ect the net balance, upon dissociation, between buried surface that becomes hydrated and interfacial waters and inter-cleft waters that are liberated. Dissociation of enolase is promoted by removal of the bound Mgþþ . vV for dissociation of apo-enolase is only 3110 ml mol31 , much smaller than the 260 ml mol31 for Mg2þ -enolase [93]. This di¡erence in vV tells us that there must be a signi¢cant di¡erence between the two dimeric forms (apo vs. +Mg2þ ) or between the monomeric forms. In this case, it has been interpreted to mean that pressure dissociation involves loss of the bound Mg2þ and that Mg2þ monomers and apo-monomers do not have the same structure. The dissociation of one of the mammalian enolases (form QQ from rabbit) has also been studied. In this case, the rate of dissociation was measured as a function of hp and op [89]. Both pressures act primarily on the rate of dissociation; hp increases the rate and op decreases the rate. vVV , as measured by hp is negative, indicating that the transition state for dissociation is more hydrated than is the ground state.

5. The case of protein^nucleic acid interactions The speci¢cities of many nucleic acid^protein interactions are mediated by individual water molecules acting as bridges between the two macromolecular components of the system [94]. Does this water do anything?

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EcoRI is a restriction endonuclease from Escherichia coli. It binds to a well de¢ned sequential site (GAATTC) on DNA where it cleaves the DNA. High op causes the enzyme to bind to sites other than those for which it is speci¢c and introduce cleavage sites where they would not otherwise occur [95]; the simultaneous application of hp restored the lost speci¢city [96] to EcoRI. The compounds used as osmolytes in this and subsequent studies covered a wide range of characteristics. The loss of speci¢city correlated only with op and not with any other property of the solutions. As molecular biologists well know, the presence of osmolytes is not the only factor that can produce this altered speci¢city; cleavage at the alternate sites is promoted by changes in pH, ionic strength, or divalent cation concentration or identity. Changes in speci¢city produced this way were not reversed by hp. This suggests that there are multiple mechanisms for altering substrate speci¢city. The same conclusions applied to the endonucleases PvuII and BamHI but not to EcoRV [97]. The binding of this enzyme to non-speci¢c sites, the alternate site (TAATTC) and the cognate (speci¢c) site has been studied [95,98,99]. All three modes of binding involve loss of signi¢cant numbers of water molecules and therefore are all promoted by op. What is interesting here is that binding to the three sites involves loss of di¡erent amounts of water: 100 for the non-speci¢c site, 150 for the canonical site and 200 for the alternate site [99]. DNA and the protein, free in solution, would both be highly hydrated. The X-ray structure of the complex with the cognate DNA reveals an anhydrous DNA/ protein interface [100,101]. Both groups propose that upon forming the non-speci¢c complex, there is dehydration of both partners but retention of a full hydration layer at the interface. The binding at the alternate site is more di⁄cult to explain, since this structure releases about 50 more waters than does the canonical structure, yet both are catalytically competent. If the DNA/protein interface in the speci¢c complex is largely anhydrous, where are these 50 additional waters? Possible explanations include signi¢cant changes in the conformation or extent of local folding of the DNA or protein or both. The story becomes even more complicated when the catalytic activity is studied; op increases kcat at the alternate site but decreases kcat at the speci¢c site.

41

The opposite e¡ects may be the result of a change in the rate-limiting step of the reaction as one changes substrate. The obvious take-home message here is that understanding the e¡ects of hp or op on enzyme activity require being able to look at both binding and catalysis and knowing the identity of the slow steps in the reaction. op has been applied to other DNA binding proteins, often with similar results. The homeodomains ‘ultrabithorax’ and ‘deformed’ bind DNA with the release of water; the equilibrium positions are sensitive to applied op [102]. The gal repressor also brings about the release of water when it binds to its speci¢c sequence [103]. Transcription, the process by which DNA is copied into functional RNA, is a truly ‘messy’ biological system. It functions during the elongation process with a minimum of eight di¡erent components, of which the RNA polymerase and the DNA each contain multiple components. Erijman and Clegg [104] have subjected a transcribing system to high hp. The system stalls. The components do not dissociate; they simply stop doing what they were doing. When the pressure is released they resume doing what they were doing where they were doing it. Erijman and Clegg believe that the e¡ects of pressure here are the result of ‘a reduction of the partial speci¢c volume of the RNA polymerase’ thereby generating an enzyme which is too rigid to function. hp might also be interfering with hydration cycles as it does in the cytochrome c oxidase discussed above. Given that transcription involves bond making, unwinding and rewinding of a small segment of DNA and movement of the polymerase relative to the DNA and RNA, one can imagine that there may be multiple steps that involve water movement. Transcription is a prime candidate for systematic probing with op. It might help shed light on the process. Finally, the Silva group has looked at many DNA or RNA binding systems using hp as a probe. Often hp brings about denaturation or dissociation followed by denaturation of the binding protein. The nucleic acid displaces this protein equilibrium towards stability [105]. This system joins the list of those which might pro¢t from osmotic perturbation. We, along with numerous other authors, have used hp and op as probes of the thermodynamics of the macromolecular systems we study. The two ap-

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proaches are powerful in that they can tell us about the involvement of solvent in the catalytic working of proteins (and probably catalytic RNAs) and can tell us about the involvement of solvent at the interfaces between proteins, nucleic acids and phospholipids. The problem, as has been stated hundreds of times, is that thermodynamics does not give information on mechanism, on path, on structure. The e¡ects of hp on protein structures have been determined both by X-ray di¡raction [106,107] and by NMR [108]. The technical problems with hp and X-ray di¡raction are such that it is highly unlikely that it will ever be used for combined hp/op studies. This type of experiment should, however, be amenable to NMR. With NMR, we can obtain, in principle, both the total involvement of solvent in macromolecular interactions and where exactly the solvent is acting. Currently the laboratories of Akasaka and Markley and a few others are pursuing this approach [109^112,23, 24]. The rest of us would be well advised to join them.

X ðD G=D ni ÞT;P dn

ðA1Þ

dG ¼ dE þ V dP þ PdV 3SdT3TdS

ðA2Þ

ðD G=D PÞT;n dP þ since

and dE ¼ TdS3PdV

ðA3Þ

substituting Eq. A3 into Eq. A2 yields dG ¼ V dP3SdT

ðA4Þ

and dG ¼ 3SdT þ V dP þ

X

W i dni

ðA5Þ

We can make the following simpli¢cations:at constant T X dG ¼ V dP þ W i dni ðA6Þ at constant P dG ¼ 3SdT þ

X

W i dni

ðA7Þ

at constant n Acknowledgements

dG ¼ V dP3SdT

We thank the Natural Science and Engineering Research Council of Canada for generous ¢nancial assistance. We owe a debt of gratitude to V.A. Parsegian, R.P. Rand, P. Nicholls, M.C. Marden and K. Heremans for trying to keep us honest. We extend apologies to all those many workers, not cited in this review, who have contributed to our knowledge of how op and hp might work. We note that the ¢nal word on the subject has not been spoken. Lastly, we wish to thank the editors of this volume for the invitation to be amongst the contributors.

ðA8Þ

The equations relating changes in hp and changes in temperature have recently been reiterated [12]. At constant T, P X dG ¼ W i dni ðA9Þ Eq. A9 can be simpli¢ed if we recall that X G¼ ni W i

ðA10Þ

therefore di¡erentiating gives X X dG ¼ ni d W i þ W i dni

ðA11Þ

Appendix. The theoretical ins and outs of op as a perturbant. The relations between op, temperature and hp

and setting Eq. A9 equal to Eq. A11 X X X dG ¼ W i dni ¼ ni d W i þ W i dni

ðA12Þ

A1. Theory

ergo X 0¼ ni d W i and nw d W w þ ns d W s ¼ 0

ðA13Þ

The relations between free energy, T, op, and hp are easily restated. dG ¼ ðD G=D TÞP;n dTþ

The utility of Eq. A13 is that it relates the chemical potential of water to the chemical potential of the macromolecule. If we change the chemical poten-

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43

tial of water, we necessarily change that of the macromolecule. The two are related by the ratio ns /nw or vN which is the number of waters that are associated with the macromolecule in one state that are not associated with it in the other state. In order to relate Eq. A13 to op, we need to be able to equate the chemical potential of water with the op.

knowing that compressibility does not vary as a function of the osmotic perturbant. In this case

d W w ¼ 3dðopÞ=V 0

D ðhpÞ=D ðopÞ ¼ ðv NV 0 Þ

ðA14Þ

where V0 is the partial molar volume of water. op is obtained from the mole fraction of water, X H2 O , op ¼ ðRT=V 0 ÞlnX H2 O

ðA15Þ

X is most easily obtained from either the Handbook of Chemistry and Physics or from one of two WEB sites (http://aqueous.labs.brocku.ca/os¢le. html; http://dir.nichd.nih.gov/Lpsb/docs/osmdata/ osmdata.html). Combining Eqs. A13^A15 we obtain dðRTlnK M Þ ¼ v VdðopÞ ¼ ðv N  V 0 ÞdðopÞ

ðA16Þ

where KM is the equilibrium coe⁄cient for the two states of the macromolecule, vV is the volume of water associated with one of the states that are absent in the other state, vN is the number of waters associated with the interconversion and op is the osmotic pressure. It is necessary to include the partial molar volume of water in Eq. A16 because of the nature of the derivation of Eq. A15. Eqs. A15 and A16 are the only two that are needed to carry out an op experiment. We plot RTlnKM vs. op and directly obtain the numbers of waters associated with the one equilibrium form that are not associated with the other. To carry out an op vs. temperature experiment requires knowing that vCp does not vary as a function of the op perturbant. If that is true, one plots T and op at vG = 0 to yield a curve in much the same way that one handles hp vs. temperature data [12]. For this curve,

v G ¼ v G o 3v S o ðT3T o Þ3v C p ðT3T o Þ2 =2T o þ ðv NV 0 Þðop3opo Þ

ðA17Þ

and

D T=D ðopÞ ¼ ðv NV 0 Þðv So þ v C p ððT3T o Þ=T o ÞÞ31 ðA18Þ To carry out an op vs. hp experiment requires

v G ¼ v Go þ v V o ðhp3hpo Þ þ v L =2ðhp3hpo Þ2 þ ðv NV 0 Þðop3opo Þ

ðA19Þ

and

ðv V o þ v L ððhp3hpo Þ=hpo ÞÞ31

ðA20Þ

In ideal cases the macromolecule is not readily compressible and Eq. A20 reduces to

D ðhpÞ=D ðopÞ ¼ v NV 0 =v V o

ðA21Þ

In an op vs. temperature experiment or an op vs. hp experiment, the instantaneous slope (Eq. A18 and A21) gives information on vN, vSo , and vCp or on vN, vVo and vL. The equation required to evaluate the simultaneous variation of T, op and hp is somewhat complex and because of its complexity we do not present it here. Su⁄ce it to say that it must contain at least 10 terms [113]. No one in biochemistry has yet approached the complete problem of how the free energy of the system varies as T, op and hp are varied.

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