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• W2014001433 abstract "The sulfated glycosaminoglycan heparin is an important anticoagulant, widely used to treat and to prevent arterial thrombosis. Heparin triggers conformational changes in, and the functional activation of, the serine proteinase inhibitor antithrombin. We investigated water-transfer reactions during the activation process to explore the possibility that functional interaction between antithrombin and sulfated glycosaminoglycans can be regulated by osmotic potentials. Volume of water transferred upon heparin binding was measured from differences in free energy change, Δ(ΔG), with osmotic stress, π. Osmotic stress was induced with chemically inert probes that are geometrically excluded from the water-permeable spaces of antithrombin and from intermolecular spaces formed during the association reaction. The free energy change, ΔG, for the antithrombin/heparin interaction was calculated from the dissociation constant, determined by functional titrations of heparin with antithrombin at fixed concentrations of the coagulation protease factor Xa. The effect of osmotic stress was independent of the chemical nature of osmotic probes but correlated with their radius up to radius >17 Å. In mixtures including a large and a small probe, the effect of the large probe was not modified by the small probe added at a large molar excess. With an osmotic probe of 4-Å radius, the Δ(ΔG)/π slope corresponds to a transfer of 119 ± 25 water molecules to bulk solution on formation of the complex. Analytical characterization of water-permeable volumes in x-ray-derived bound and free antithrombin structures revealed complex surfaces with smaller hydration volumes in the bound relative to the free conformation. The residue distribution in, and atomic composition of, the pockets containing atoms from residues implicated in heparin binding were distinct in the bound versus free conformer. The results demonstrate that the heparin/antithrombin interaction is linked to net water transfer and, therefore, can be regulated in biological gels by osmotic potentials. The sulfated glycosaminoglycan heparin is an important anticoagulant, widely used to treat and to prevent arterial thrombosis. Heparin triggers conformational changes in, and the functional activation of, the serine proteinase inhibitor antithrombin. We investigated water-transfer reactions during the activation process to explore the possibility that functional interaction between antithrombin and sulfated glycosaminoglycans can be regulated by osmotic potentials. Volume of water transferred upon heparin binding was measured from differences in free energy change, Δ(ΔG), with osmotic stress, π. Osmotic stress was induced with chemically inert probes that are geometrically excluded from the water-permeable spaces of antithrombin and from intermolecular spaces formed during the association reaction. The free energy change, ΔG, for the antithrombin/heparin interaction was calculated from the dissociation constant, determined by functional titrations of heparin with antithrombin at fixed concentrations of the coagulation protease factor Xa. The effect of osmotic stress was independent of the chemical nature of osmotic probes but correlated with their radius up to radius >17 Å. In mixtures including a large and a small probe, the effect of the large probe was not modified by the small probe added at a large molar excess. With an osmotic probe of 4-Å radius, the Δ(ΔG)/π slope corresponds to a transfer of 119 ± 25 water molecules to bulk solution on formation of the complex. Analytical characterization of water-permeable volumes in x-ray-derived bound and free antithrombin structures revealed complex surfaces with smaller hydration volumes in the bound relative to the free conformation. The residue distribution in, and atomic composition of, the pockets containing atoms from residues implicated in heparin binding were distinct in the bound versus free conformer. The results demonstrate that the heparin/antithrombin interaction is linked to net water transfer and, therefore, can be regulated in biological gels by osmotic potentials. glycosaminoglycan polyethylene glycol osmotic stress factor Xa heparin antithrombin bound free Protein Data Bank atmosphere(s) Antithrombin is one of the more important inhibitors of blood coagulation proteinases. Deficiencies in antithrombin, either acquired or congenital, are associated with thrombosis. The inhibitory activity of antithrombin is markedly increased by binding with charged glycosaminoglycans (GAGs)1present on the vascular wall and extravascular spaces (1Jordan R.E. Oosta G.M. Gardner W.T. Rosenberg R.D. J. Biol. Chem. 1980; 255: 10081-10900Abstract Full Text PDF PubMed Google Scholar, 2Gettins P.G.W. Patston P.A. Olson S.T. Serpins: Structure, Function and Biology. R. G. Landes, Austin, TX1996Google Scholar, 3Carrell R.W. Evans D.L. Stein P. Nature. 1991; 353: 576-579Crossref PubMed Scopus (271) Google Scholar, 4Lane D.A. Olds R.R. Thein S.L. Blood Coagul. Fibrinolysis. 1992; 3: 315-341Crossref PubMed Scopus (53) Google Scholar, 5Stratikos E. Gettins P.G. Proc. Natl. Acad. Sci. U. S. A. 1999; 96: 4808-4813Crossref PubMed Scopus (218) Google Scholar, 6Lawrence D.A. Nat. Struct. Biol. 1997; 4: 339-341Crossref PubMed Scopus (50) Google Scholar, 7Huntington J.A. Olson S.T. Fan B. Gettins P.G. Biochemistry. 1996; 35: 8495-8503Crossref PubMed Scopus (126) Google Scholar, 8Desai U.R. Petitout M. Bjork I. Olson S. Biochemistry. 1998; 37: 13033-13041Crossref PubMed Scopus (66) Google Scholar). Among GAGs, the heparan sulfates are the most effective antithrombin activators. Stereospecific requirements for maximal inhibitory activity have been ascribed to a pentasaccharide sequence containing four sulfate groups on glucosamine residues and two carboxylates on uronic acid residues (9Rosenberg R.D. Lam L. Proc. Natl. Acad. Sci. U. S. A. 1979; 76: 1218-1222Crossref PubMed Scopus (232) Google Scholar, 10Lindahl U. Backstrom G. Thunberg L. Leder I.G. Proc. Natl. Acad. Sci. U. S. A. 1980; 77: 6551-6555Crossref PubMed Scopus (419) Google Scholar). Commercial preparations of heparin used routinely as anticoagulants are enriched with these highly charged sequences as compared with heparan chains that are isolated from the vasculature (11Parthasarathy N. Goldberg I.J. Silvaram P. Mulloy B. Frory D.M. Wagner W.D. J. Biol. Chem. 1994; 269: 22391-22396Abstract Full Text PDF PubMed Google Scholar). In vivo, natural antithrombin ligand(s) are part of complex biopolymer gels and subjected to hydration and dehydration osmotic forces (12Tanaka T. Sci. Am. 1980; 244: 110-123Google Scholar) in the extracellular matrix. The possible effect of osmotic forces on the functional interactions of GAGs remains essentially unexplored. In the present study, we examine the effect of osmotic forces on the heparin/antithrombin interaction. Antithrombin is a prototype metastable protein, and its activation by heparin appears to result from the release of several structural constraints (6Lawrence D.A. Nat. Struct. Biol. 1997; 4: 339-341Crossref PubMed Scopus (50) Google Scholar, 7Huntington J.A. Olson S.T. Fan B. Gettins P.G. Biochemistry. 1996; 35: 8495-8503Crossref PubMed Scopus (126) Google Scholar, 13Futamura A. Gettins P.G. J. Biol. Chem. 2000; 275: 4092-4098Abstract Full Text Full Text PDF PubMed Scopus (30) Google Scholar, 14Beauchamp N.J. Pike R.N. Daly M. Butler L. Makris M. Dafforn T.R. Zhou A. Fitton H.L. Preston F.E. Peake I.R. Carrell R.W. Blood. 1998; 92: 2696-2706Crossref PubMed Google Scholar). Considerable evidence indicates that antithrombin undergoes sequential changes in conformation during functional interactions with heparin and its target proteinases (2Gettins P.G.W. Patston P.A. Olson S.T. Serpins: Structure, Function and Biology. R. G. Landes, Austin, TX1996Google Scholar, 3Carrell R.W. Evans D.L. Stein P. Nature. 1991; 353: 576-579Crossref PubMed Scopus (271) Google Scholar, 4Lane D.A. Olds R.R. Thein S.L. Blood Coagul. Fibrinolysis. 1992; 3: 315-341Crossref PubMed Scopus (53) Google Scholar). The conformational changes initiated by heparin propagate throughout the antithrombin structure in ways that are not completely understood. Kinetically, it has been shown that the antithrombin/heparin interaction is a two-step reaction with a strong electrostatic component. An initial, low affinity step equilibrates very rapidly and induces the conformational transitions leading to high affinity interactions (8Desai U.R. Petitout M. Bjork I. Olson S. Biochemistry. 1998; 37: 13033-13041Crossref PubMed Scopus (66) Google Scholar, 14Beauchamp N.J. Pike R.N. Daly M. Butler L. Makris M. Dafforn T.R. Zhou A. Fitton H.L. Preston F.E. Peake I.R. Carrell R.W. Blood. 1998; 92: 2696-2706Crossref PubMed Google Scholar). These antithrombin conformational transitions improve access of the reactive loop to the target proteinase's active site and are responsible for most of the ∼500-fold increase in antithrombin affinity for coagulation factor Xa (fXa) (1Jordan R.E. Oosta G.M. Gardner W.T. Rosenberg R.D. J. Biol. Chem. 1980; 255: 10081-10900Abstract Full Text PDF PubMed Google Scholar, 7Huntington J.A. Olson S.T. Fan B. Gettins P.G. Biochemistry. 1996; 35: 8495-8503Crossref PubMed Scopus (126) Google Scholar, 13Futamura A. Gettins P.G. J. Biol. Chem. 2000; 275: 4092-4098Abstract Full Text Full Text PDF PubMed Scopus (30) Google Scholar). The subsequent inhibition of fXa is also a two-step process (3Carrell R.W. Evans D.L. Stein P. Nature. 1991; 353: 576-579Crossref PubMed Scopus (271) Google Scholar, 5Stratikos E. Gettins P.G. Proc. Natl. Acad. Sci. U. S. A. 1999; 96: 4808-4813Crossref PubMed Scopus (218) Google Scholar, 6Lawrence D.A. Nat. Struct. Biol. 1997; 4: 339-341Crossref PubMed Scopus (50) Google Scholar, 7Huntington J.A. Olson S.T. Fan B. Gettins P.G. Biochemistry. 1996; 35: 8495-8503Crossref PubMed Scopus (126) Google Scholar, 8Desai U.R. Petitout M. Bjork I. Olson S. Biochemistry. 1998; 37: 13033-13041Crossref PubMed Scopus (66) Google Scholar,13Futamura A. Gettins P.G. J. Biol. Chem. 2000; 275: 4092-4098Abstract Full Text Full Text PDF PubMed Scopus (30) Google Scholar, 14Beauchamp N.J. Pike R.N. Daly M. Butler L. Makris M. Dafforn T.R. Zhou A. Fitton H.L. Preston F.E. Peake I.R. Carrell R.W. Blood. 1998; 92: 2696-2706Crossref PubMed Google Scholar, 15Ersdal-Badju E. Lu A. Zuo Y. Picard V. Bock S.C. J. Biol. Chem. 1997; 272: 19393-19403Abstract Full Text Full Text PDF PubMed Scopus (85) Google Scholar, 16Meagher J.L. Beechem J.M. Olson S.T. Gettins P.G. J. Biol. Chem. 1998; 273: 23283-23289Abstract Full Text Full Text PDF PubMed Scopus (51) Google Scholar, 17Craig P.A. Olson S.T. Shore J.D. J. Biol. Chem. 1989; 264: 5452-5461Abstract Full Text PDF PubMed Google Scholar, 18Olson S.T. Bjork I. Shore J.D. Methods Enzymol. 1993; 222: 525-559Crossref PubMed Scopus (269) Google Scholar), with an initial fast equilibrating step to form a ternary complex, followed by a slower, first-order reaction resulting in heparin release and formation of an essentially irreversible antithrombin-fXa complex. Proteinase inhibition and heparin release are linked to reinsertion of antithrombin's reactive loop into a β-sheet structure in the protein's core and translocation of the proteinase from its initial low affinity interaction site in the exposed reactive loop to the other end of the antithrombin molecule (5Stratikos E. Gettins P.G. Proc. Natl. Acad. Sci. U. S. A. 1999; 96: 4808-4813Crossref PubMed Scopus (218) Google Scholar, 6Lawrence D.A. Nat. Struct. Biol. 1997; 4: 339-341Crossref PubMed Scopus (50) Google Scholar). Previous studies using the osmotic stress (OS) technique indicated that the first-order reaction leading to irreversible antithrombin-fXa complex formation is linked to net water transfer from the reactants to bulk solution (19Liang J. McGee M.P. Biophys. J. 1998; 75: 573-582Abstract Full Text Full Text PDF PubMed Scopus (9) Google Scholar). The possibility that hydration water is transferred during heparin-induced conformational transitions has not been investigated before. The theoretical basis of the OS technique has been described and validated in detail (20Colombo M.F. Rau D.C. Parsegian V.A. Science. 1992; 256: 655-659Crossref PubMed Scopus (332) Google Scholar, 21Rand R.P. Science. 1992; 256: 618Crossref PubMed Scopus (77) Google Scholar, 22Colombo M.C. Bonilla-Rodriguez G.O. J. Biol. Chem. 1996; 271: 4895-4899Abstract Full Text Full Text PDF PubMed Scopus (46) Google Scholar, 23Douzou P. Proc. Natl. Acad. Sci. U. S. A. 1994; 91: 1657-1661Crossref PubMed Scopus (19) Google Scholar, 24McGee M.P. Teushler H. J. Biol. Chem. 1995; 270: 15170-15174Abstract Full Text Full Text PDF PubMed Scopus (11) Google Scholar, 25Parsegian V.A. Rand R.P. Rau D.C. Methods Enzymol. 1995; 259: 43-94Crossref PubMed Scopus (375) Google Scholar, 26Dzingeleski G.D. Wolfenden R. Biochemistry. 1993; 32: 9143-9147Crossref PubMed Scopus (41) Google Scholar) and revised recently (27Parsegian V.A. Rand R.P. Rau D.C. Proc. Natl. Acad. Sci. U. S. A. 2000; 97: 3987-3992Crossref PubMed Scopus (429) Google Scholar). Osmotic stress gives a direct thermodynamic measure of hydration. Many functional reactions of complex proteins like antithrombin are associated with conformational transitions that drastically alter the magnitude and distribution of their water-permeable spaces (19Liang J. McGee M.P. Biophys. J. 1998; 75: 573-582Abstract Full Text Full Text PDF PubMed Scopus (9) Google Scholar, 20Colombo M.F. Rau D.C. Parsegian V.A. Science. 1992; 256: 655-659Crossref PubMed Scopus (332) Google Scholar, 21Rand R.P. Science. 1992; 256: 618Crossref PubMed Scopus (77) Google Scholar, 22Colombo M.C. Bonilla-Rodriguez G.O. J. Biol. Chem. 1996; 271: 4895-4899Abstract Full Text Full Text PDF PubMed Scopus (46) Google Scholar, 23Douzou P. Proc. Natl. Acad. Sci. U. S. A. 1994; 91: 1657-1661Crossref PubMed Scopus (19) Google Scholar, 24McGee M.P. Teushler H. J. Biol. Chem. 1995; 270: 15170-15174Abstract Full Text Full Text PDF PubMed Scopus (11) Google Scholar, 25Parsegian V.A. Rand R.P. Rau D.C. Methods Enzymol. 1995; 259: 43-94Crossref PubMed Scopus (375) Google Scholar, 26Dzingeleski G.D. Wolfenden R. Biochemistry. 1993; 32: 9143-9147Crossref PubMed Scopus (41) Google Scholar). During these transitions, the change in free energy has a component corresponding to the work of water transfer. When the transition proceed in the presence of cosolutes that are excluded from the water-permeable spaces, the difference in water activity between the excluded spaces and bulk solution favor water transfer to bulk solution. The sensitivity of the free energy change, (ΔG), to water activity is a measure of the volume of water transferred during the transition and reflects differences in hydration between initial and final states. In the present work, OS is used with functional titrations to analyze antithrombin activation by heparin. Results show net water transfer from reactants to bulk on formation of the heparin-antithrombin complex and imply that functional GAG interactions are susceptible to osmotic regulation in vivo. The dissociation constant of the heparin/antithrombin interaction was determined from functional titrations under different osmotic stress conditions. The effect of osmotic stress on binding parameters was analyzed on the basis of the previously validated (18Olson S.T. Bjork I. Shore J.D. Methods Enzymol. 1993; 222: 525-559Crossref PubMed Scopus (269) Google Scholar) kinetic scheme. AT+H↔KhAT·H+fXa↔KtH·AT­fXa→kAT­fXa+HREACTION1Kh is the equilibrium dissociation constant for the antithrombin/heparin interaction (AT·H).Kt is the dissociation constant for the ternary interaction between fXa and the AT·H complex, and k is the first-order rate constant for the stabilization of the inhibitory complex. The observed pseudo-first-order rate constant,kobs, is a hyperbolic function of the AT·H complex concentration.kobs=k[AT·H]/(Kt+[AT·H])Equation 1 The stabilization of the complex is closely linked to the release of heparin. Although the mechanism that links heparin dissociation to the first-order stabilizing step is not clear, detailed kinetic analyses indicate that dissociation occurs either simultaneously or in a faster, subsequent step (18Olson S.T. Bjork I. Shore J.D. Methods Enzymol. 1993; 222: 525-559Crossref PubMed Scopus (269) Google Scholar, 28Lee K.N. Im H. Kang S.W. Yu M.-H. J. Biol. Chem. 1998; 273: 2509-2513Abstract Full Text Full Text PDF PubMed Scopus (33) Google Scholar, 29Jin L. Abrahams J.P. Skinner R. Petitou M. Pike R.N. Carrell R.W. Proc. Natl. Acad. Sci. U. S. A. 1997; 94: 14683-14688Crossref PubMed Scopus (644) Google Scholar). Functional titration experiments were performed within a concentration range of antithrombin (20–450 nm), giving Kt [tmt] [AT·H] and kobs = k[AT·H]/Kt, and at fixed and low heparin (20 nm) and fXa (10 nm). Under these conditions, the change in kobs with antithrombin concentration reflects the concentration of AT·H and follows the saturation curve of heparin with antithrombin (18Olson S.T. Bjork I. Shore J.D. Methods Enzymol. 1993; 222: 525-559Crossref PubMed Scopus (269) Google Scholar) from which a functionally determined dissociation constant, Kd, can be determined. Antithrombin and heparin were equilibrated in Tris buffer, 25 mm, pH 7.2–7.4 at 25 °C, with NaCl at either 0.075 or 0.2 n. Osmotic stress was induced with the following chemically inert cosolutes: polyethylene glycol,Mr 300 or 8000 (PEG 300 or 8000); dextran,Mr 10,000; or polyvinylpyrrolidone,Mr 40,000. Standard and “stressed” solutions were identical in all components except for the added cosolute. The difference in osmotic pressure generated by the added cosolute was determined from empirical relationships derived by direct osmotic pressure measurements (24McGee M.P. Teushler H. J. Biol. Chem. 1995; 270: 15170-15174Abstract Full Text Full Text PDF PubMed Scopus (11) Google Scholar, 25Parsegian V.A. Rand R.P. Rau D.C. Methods Enzymol. 1995; 259: 43-94Crossref PubMed Scopus (375) Google Scholar). The change in [AT·H] with antithrombin was determined from the exponential rate,kobs, of fXa activity decay. The fXa activity was measured in six sequential samples withdrawn from reaction mixtures at 5–50-s intervals and diluted immediately in hexamethrine bromide (100 μg/ml). Residual protease activity was determined from the initial rate of substrate hydrolysis (methoxycarbonyl-d-cyclohexylglycylarginine-p-nitroanilide acetate), as described previously (32McGee M.P. Li L.C. J. Biol. Chem. 1991; 266: 8079-8085Abstract Full Text PDF PubMed Google Scholar). In reaction mixtures without heparin or without antithrombin, the fXa activity did not change significantly during the reaction time. The possible effect of OS on the [AT·H]/fXa stoichiometry and changes in proportions of antithrombin branching into the substrate pathway was also investigated. In these experiments, antithrombin and fXa were incubated at various molar ratios with heparin at fixed concentration. Reactions were followed under either standard or OS conditions until completion. The stoichiometry was calculated as the abscissa intercept of linear regression plots of residual proteinase activity versus the antithrombin/fXa ratio (18Olson S.T. Bjork I. Shore J.D. Methods Enzymol. 1993; 222: 525-559Crossref PubMed Scopus (269) Google Scholar). The quadratic form of the binding equation was fitted to data points (18Olson S.T. Bjork I. Shore J.D. Methods Enzymol. 1993; 222: 525-559Crossref PubMed Scopus (269) Google Scholar), using the computer program TableCurve (SAS Institute, Inc., Cary, NC), and linear regression analyses were performed with the computer program Stat-View (SAS Institute, Inc., Cary, NC.). Commercial-grade heparin with average molecular weight of ∼17,000 was purchased from Sigma. Fractionated heparin (molecular weight of 3000) and human antithrombin and factor Xa were purchased from Enzyme Research Laboratories. Experimentally, the possibility that a particular interaction is associated with net water transfer is determined from the difference in free energy change Δ(ΔG) with osmotic pressure. The direction of the water transfer is also deduced from the Δ(ΔG)/π slope. The slope is positive when transfer is from bulk to reactants. The slope is negative when transfer is from reactants to bulk. Changes in free energy are calculated from the binding parameters according to classical thermodynamic principles (33Glasstone S. Laidler K. Eyring H. The Theory of Rate Processes. McGraw-Hill Inc., New York1941Google Scholar). Osmotic stress theory (20Colombo M.F. Rau D.C. Parsegian V.A. Science. 1992; 256: 655-659Crossref PubMed Scopus (332) Google Scholar, 21Rand R.P. Science. 1992; 256: 618Crossref PubMed Scopus (77) Google Scholar, 22Colombo M.C. Bonilla-Rodriguez G.O. J. Biol. Chem. 1996; 271: 4895-4899Abstract Full Text Full Text PDF PubMed Scopus (46) Google Scholar, 23Douzou P. Proc. Natl. Acad. Sci. U. S. A. 1994; 91: 1657-1661Crossref PubMed Scopus (19) Google Scholar, 24McGee M.P. Teushler H. J. Biol. Chem. 1995; 270: 15170-15174Abstract Full Text Full Text PDF PubMed Scopus (11) Google Scholar, 25Parsegian V.A. Rand R.P. Rau D.C. Methods Enzymol. 1995; 259: 43-94Crossref PubMed Scopus (375) Google Scholar, 26Dzingeleski G.D. Wolfenden R. Biochemistry. 1993; 32: 9143-9147Crossref PubMed Scopus (41) Google Scholar, 27Parsegian V.A. Rand R.P. Rau D.C. Proc. Natl. Acad. Sci. U. S. A. 2000; 97: 3987-3992Crossref PubMed Scopus (429) Google Scholar) is derived from the theory of dilute solutions (34Wannier G.H. Statistical Physics. Dover Publications, New York1987: 336-383Google Scholar, 35Joos G. Freeman I.M. Theoretical Physics. Dover Publications, New York1986: 543-552Google Scholar), as it explains the indirect effects of cosolutes on macromolecules. It focuses on the role of hydration water in the region within and around a macromolecule from which cosolutes, but not water, are excluded. Detailed commentaries on various cosolute effects, such as crowding, preferential hydration, and binding, have been published (27Parsegian V.A. Rand R.P. Rau D.C. Proc. Natl. Acad. Sci. U. S. A. 2000; 97: 3987-3992Crossref PubMed Scopus (429) Google Scholar). Here we summarize the theory only in relation to the antithrombin activation experiments we present. To analyze the antithrombin transformation between an F (heparin-free) and an B (inhibitory, heparin-bound) state, the osmotic stress technique can give a thermodynamic measurement of the hydration volume difference. The free energy difference from F to B is the free energy difference, ΔG between the bound (GB) and unbound forms of antithrombin (Ga) and heparin (Gh).ΔG=(Ga+Gh)−GBEquation 2 andΔG=−RT lnKEquation 3 K is a parameter measuring the ratio between the concentrations (or probabilities) of states F and B at equilibrium,R is the gas constant (1.987 cal/mol/degree), andT is the temperature (degrees Kelvin). The volume of water transfer is calculated from the equivalence: 1 atm × (volume of 1 mol of water) = 0.435 cal/mol. Thus, from the measured ratio Δ(ΔG)/π, (cal/mol/atm)/0.435 = mol H2O. In a multicomponent solution, such as those used to determine equilibrium parameters, the colligative properties, including the osmotic pressure, depend on the activity of all components. In our osmotic stress experiments, the activity of all components was held constant except for water and the inert cosolute used to induce osmotic stress. The composition of stressed and standard solutions was identical except for incremental additions of cosolute. The antithrombin and heparin molecules in the diluted solution used to measure equilibrium parameters are expected to influence the composition of the region of solution close to their surface, orsphere of influence (27Parsegian V.A. Rand R.P. Rau D.C. Proc. Natl. Acad. Sci. U. S. A. 2000; 97: 3987-3992Crossref PubMed Scopus (429) Google Scholar, 34Wannier G.H. Statistical Physics. Dover Publications, New York1987: 336-383Google Scholar, 35Joos G. Freeman I.M. Theoretical Physics. Dover Publications, New York1986: 543-552Google Scholar). Focusing on the inert cosolute and the water within the antithrombin's sphere of influence, the solution will have Nw, andNc, molecules of water and cosolute, respectively, whereas in regions outside the sphere of influence the solution will have nw andnc molecules, respectively. Obviously, the sphere of influence includes all geometrical spaces within and near antithrombin, from which the cosolute is sterically excluded. However, following thermodynamic reasoning, the size of the sphere of influence is of no importance, because the osmotic stress on the molecule depends on the disproportion of cosolute and water within and outside the sphere (25Parsegian V.A. Rand R.P. Rau D.C. Methods Enzymol. 1995; 259: 43-94Crossref PubMed Scopus (375) Google Scholar). The Gibbs-Duhem (34Wannier G.H. Statistical Physics. Dover Publications, New York1987: 336-383Google Scholar) equation links the changes in chemical potential,dμ, within the antithrombin sphere of influence,dμa=−Nwdμw−Ncdμc,Equation 4 and at solution regions outside the antithrombin's sphere of influence,nwdμw+ncdμc=0.Equation 5 These relations express the fact that the changes in cosolute, dμc, and water, dμw, chemical potentials are directly linked. The same arguments apply to the chemical potential of heparin. The change in water's chemical potential can also be expressed by considering the change in osmotic pressure induced by cosolute.dμw=−VwdπEquation 6 Vw is the molecular volume of water, and dπ is the change in osmotic pressure induced by changes in cosolute concentration (34Wannier G.H. Statistical Physics. Dover Publications, New York1987: 336-383Google Scholar, 35Joos G. Freeman I.M. Theoretical Physics. Dover Publications, New York1986: 543-552Google Scholar). The change in chemical potential is closely related to Gibbs free energy and can be defined as the Gibbs free energy per molecule. This definition of the free energy is frequently used in utilitarian forms of the Second Law equation, and its derivation is based on Euler identity for homogeneous functions (34Wannier G.H. Statistical Physics. Dover Publications, New York1987: 336-383Google Scholar). From Equations Equation 2, Equation 3, Equation 4, Equation 5, Equation 6 above, we obtain Equation 7.dΔG=−ΔNewdμwEquation 7 New is the excess (or deficit) amount of water in regions within, as compared with outside, antithrombin's sphere of influence (27Parsegian V.A. Rand R.P. Rau D.C. Proc. Natl. Acad. Sci. U. S. A. 2000; 97: 3987-3992Crossref PubMed Scopus (429) Google Scholar). If New differs in the F and B states, then the change in the equilibrium parameter upon incremental additions of cosolute measures the water molecules transferred in going between the F and B state, as shown in Equations 8and 9.ΔNewFB=NewF−NewBEquation 8 andd(ΔGFB)/dπ=NewFBVwEquation 9 Therefore, the slope of the difference in free energy change (determined from changes in equilibrium constant) with osmotic pressure gives the amount of water transferred as reactants go from the F to the B state. On the basis of transition-state theory (33Glasstone S. Laidler K. Eyring H. The Theory of Rate Processes. McGraw-Hill Inc., New York1941Google Scholar), differences in the changes in free energy of activation with osmotic pressure can also be used to measure hydration volume changes. In this case, thermodynamic reasoning is applied to the formation of the activated complex, and the equilibrium considered is between the reactants and the activated complex. This activated complex corresponds to an intermediate transient conformation, the hydration of which is likely to differ from that of both the initial and final states. Therefore, it is not useful to correlate volumes with x-ray-derived structures, which are probably more closely related to the initial and final states. However, because rate measurements are much more sensitive than equilibrium constant determinations, the difference in the free energy of activation change is useful in detecting other possible secondary effects of cosolutes that are not osmotic. Water-permeable spaces excluded by the osmotic probes in antithrombin were analyzed from x-ray-derived structures of bound and free antithrombin using CAST software (36Liang J. Edelsbrunner H. Woodward C. Protein Sci. 1998; 7: 1884-1897Crossref PubMed Scopus (874) Google Scholar, 37Liang J. Edelsbrunner H. Fu P. Sudhakar P. Subramanian S. Proteins. 1998; 33: 1-29Crossref PubMed Scopus (278) Google Scholar). CAST is a unique computational method that provides comprehensive identification and accurate measurement of surface concavities of various shapes and geometries. It implements algorithms, developed using analytical computational geometry, and formalizes intuitive notions to classify concave regions into voids, pockets, and depressions. Briefly, voids are completely buried without access to the outside. Pockets are connected to the outside through a constricted mouth opening and mouth openings connecting the inside of a concave pocket with bulk solvent spaces are defined unambiguously using a triangulation procedure. All pockets and voids on a protein are identified and their metric properties, including both the pocket and mouth, determined analytically. The location of all pockets and voids, their atomic composition, volume, and the area of the mouths collectively describe the shape and specific physicochemical environment of a protein, providing a unique hydration fingerprint for each protein structure. Hydration fingerprints of antithrombin conformers were calculated from x-ray-derived atomic coordinates in the Brookhaven Protein Data Bank files 2ant (30Skin" @default.
• W2014001433 created "2016-06-24" @default.
• W2014001433 creator A5021819934 @default.
• W2014001433 creator A5091558783 @default.
• W2014001433 date "2001-12-01" @default.
• W2014001433 modified "2023-10-16" @default.
• W2014001433 title "Regulation of Glycosaminoglycan Function by Osmotic Potentials" @default.
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