Enthalpy–entropy compensation phenomena in water solutions of proteins and small molecules: A ubiquitous properly of water

This article presents evidence for the existence of a specific linear relationship between the entropy change and the enthalpy change in a variety of processes of small solutes in water solution. The processes include solvation of ions and nonelectrolytes, hydrolysis, oxidation–reduction, ionization of weak electrolytes, and quenching of indole fluorescence among others. The values of the proportionality constant, called the compensation temperature, lie in a relatively narrow range, from about 250 to 315 °K, for all these processes. Such behavior can be a consequence of experimental errors but for a number of the processes the precision of the data is sufficient to show that the enthalpy–entropy compensation pattern is real. It is tentatively concluded that the pattern is real, very common and a consequence of the properties of liquid water as a solvent regardless of the solutes and the solute processes studied. As such the phenomenon requires that theoretical treatments of solute processes in water be expanded by inclusion of a specific treatment of the characteristic of water responsible for compensation behavior. The possible bases of the effect are proposed to be temperature‐independent heat‐capacity changes and/or shifts in concentrations of the two phenomenologically significant species of water. The relationship of these alternatives to the two‐state process of water suggested by spectroscopic and relaxation studies is examined. The existence of a similar and probably identical relationship between enthalpy and entropy change in a variety of protein reactions suggests that liquid water plays a direct role in many protein processes and may be a common participant in the physiological function of proteins. It is proposed that the linear enthalpy–entropy relationship be used as a diagnostic test for the participation of water in protein processes. On this basis the catalytic processes of chymotrypsin and acetylcholinesterase are dominated by the properties of bulk water. The binding of oxygen by hemoglobin may fall in the same category. Similarities and differences in the behavior of small‐solute and protein processes are examined to show how they may be related. No positive conclusions are established, but it is possible that protein processes are coupled to water via expansions and contractions of the protein and that in general the special pattern of enthalpy–entropy compensation is a consequent of the properties of water which require that expansions and contractions of solutes effect changes in the free volume of the nearby liquid water. It is shown that proteins can be expected to respond to changes in nearby water and interfacial free energy by expansions and contractions. Such responses may explain a variety of currently unexplained characteristics of protein solutions. More generally, the enthalpy–entropy compensation pattern appears to be the thermodynamic manifestation of “structure making” and “structure breaking,” operationally defined terms much used in discussions of water solutions. If so, the compensation pattern is ubiquitous and requires re‐examination of a large body of molecular interpretations derived from quantitative studies of processes in water. Theories of processes in water may have to be expanded to accommodate this aspect of water behavior.

[1]  T. Iizuka,et al.  Analysis of a thermal equilibrium phenomenon between high-spin and low-spin states of ferrimyoglobin azide. , 1968, Biochimica et biophysica acta.

[2]  I. Wadsö,et al.  Heats of Ionization of Some Alkylammonium and Hydroxyalkylammonium Compounds. , 1968 .

[3]  J. Glasel 17O Nuclear Magnetic Relaxation in a Protein–Water System , 1968, Nature.

[4]  F. Millero,et al.  Thermochemical Investigations of the Water-Ethanol and Water-Methanol Solvent Systems. I. Heats of Mixing, Heats of Solution, and Heats of Ionization of Water , 1966 .

[5]  R. Biltonen,et al.  Studies of the chymotrypsinogen family of proteins. VI. Characterization of the conformational variation of chymotrypsin. , 1969, Journal of the American Chemical Society.

[6]  M. F. Polglase,et al.  Solubilities and Structures in Aqueous Aliphatic Hydrocarbon Solutions , 1952 .

[7]  V. Madison,et al.  Studies of the chymotrypsinogen family. 3. The optical rotatory dispersion of alpha-chymotrypsin. , 1965, Proceedings of the National Academy of Sciences of the United States of America.

[8]  F. Millero,et al.  Isothermal compressibility of water at various temperatures , 1969 .

[9]  G. Loglio,et al.  Anomalies in the Thermal Properties of Water , 1969, Nature.

[10]  B. Belleau WATER AS THE DETERMINANT OF THERMODYNAMIC TRANSITIONS IN THE INTERACTION OF ALIPHATIC CHAINS WITH ACETYLCHOLINESTERASE AND THE CHOLINERGIC RECEPTORS * , 1967 .

[11]  W. P. Bryan,et al.  Hydrogen--deuterium exchange of bovine plasma albumin. , 1969, Biochemistry.

[12]  J. Glasel Magnetic Relaxation Studies of Protein Solvation , 1968, Nature.

[13]  S. Malik,et al.  Nonpolar Group Participation in the Denaturation of Proteins by Urea and Guanidinium Salts. Model Compound Studies , 1964 .

[14]  W. Drost-Hansen Thermal anomalies in aqueous systems: manifestations of interfacial phenomena? , 1968 .

[15]  P. A. Egelstaff Neutron scattering studies of liquid diffusion , 1962 .

[16]  S. Edelstein,et al.  The simultaneous determination of partial specific volumes and molecular weights with microgram quantities. , 1967, The Journal of biological chemistry.

[17]  S. Ohnishi,et al.  Spin-labeled hemoglobin crystals. , 1966, Proceedings of the National Academy of Sciences of the United States of America.

[18]  J. Wyman,et al.  The problem of the heme interactions in hemoglobin and the basis of the bohr effect , 1951 .

[19]  Henry Eyring,et al.  Conformation Changes of Proteins , 1954 .

[20]  Frank J. Millero,et al.  Viscosity of water at various temperatures , 1969 .

[21]  D. D. Eley On the solubility of gases. Part I.—The inert gases in water , 1939 .

[22]  Walter Kauzmann,et al.  The Structure and Properties of Water , 1969 .

[23]  H. Berendsen,et al.  HYDRATION STRUCTURE OF FIBROUS MACROMOLECULES , 1965 .

[24]  J. Jortner,et al.  SOLVENT EFFECTS ON THE PHOTOCHEMISTRY OF THE IODIDE ION , 1963 .

[25]  J. Burke,et al.  Solvent Effects in Organic Chemistry. V. Molecules, Ions, and Transition States in Aqueous Ethanol1 , 1965 .

[26]  M. Polanyi,et al.  Further considerations on the thermodynamics of chemical equilibria and reaction rates , 1936 .

[27]  F. Pohl Einfache Temperatursprung‐Methode im Sekundenbis Stundenbereich und die reversible Denaturierung von Chymotrypsin , 1968 .

[28]  G. Stein,et al.  The Formation of Solvated Electrons in the Photochemistry of the Phenolate Ion in Aqueous Solutions , 1963 .

[29]  K. Laidler Thermodynamics of ionization processes in aqueous solution. Part 1.—General theory of substituent effects , 1959 .

[30]  M. L. Bender,et al.  MECHANISM OF ACTION OF PROTEOLYTIC ENZYMES. , 1965, Annual review of biochemistry.

[31]  J. Greyson,et al.  Water structure in solutions of the sodium salts of some aliphatic acids , 1970 .

[32]  Rudolph A. Marcus,et al.  On the Theory of Electron-Transfer Reactions. VI. Unified Treatment for Homogeneous and Electrode Reactions , 1965 .

[33]  M. Perutz,et al.  Structure Of Hæemoglobin: A Three-Dimensional Fourier Synthesis of Reduced Human Haemoglobin at 5.5 Å Resolution , 1963, Nature.

[34]  E. Grunwald,et al.  Relative Strength of Picric, Acetic, and Trichloroacetic Acids in Various Environments. Dispersion Effects in Acid-Base Equilibria , 1964 .

[35]  M. A. Lauffer Polymerization--depolymerization of tobacco mosaic virus protein. V. Osmotic pressure theory for hydrated proteins. , 1966, Biochemistry.

[36]  P. Rüetschi The Relation between Frequency Factor and Activation Energy (Compensation Law) , 1958 .

[37]  P. George,et al.  A spectrophotometric study of ionizations in methaemoglobin. , 1953, The Biochemical journal.

[38]  W. Drost-Hansen The Structure of Water and Water—Solute Interactions , 1967 .

[39]  Rudolph A. Marcus,et al.  On the theory of oxidation—Reduction reactions involving electron transfer. V. Comparison and properties of electrochemical and chemical rate constants , 1963 .

[40]  H. F. Fisher An upper limit to the amount of hydration of a protein molecule. A corollary to the "limiting law of protein structure". , 1965, Biochimica et biophysica acta.

[41]  R. Biltonen,et al.  Validity of the “two‐state” hypothesis for conformational transitions of proteins , 1966, Biopolymers.

[42]  W. H. Orttung Plausible Interpretation of the Bohr Effect in Haemoglobin , 1968, Nature.

[43]  Corwin Hansch,et al.  α-Chymotrypsin: A Case Study of Substituent Constants and Regression Analysis in Enzymic Structure—Activity Relationships , 1970 .

[44]  M. Mandel,et al.  The Conformational Transition of Poly(methacrylic acid) in Solution , 1967 .

[45]  J. Glasel A study of water in biological systems by O-17 magnetic resonance spectroscopy. II. Relaxation phenomena in pure water. , 1967, Proceedings of the National Academy of Sciences of the United States of America.

[46]  N. Pace,et al.  Thermodynamics of the unfolding of beta-lactoglobulin A in aqueous urea solutions between 5 and 55 degrees. , 1968, Biochemistry.

[47]  L. Rossi-Bernardi,et al.  The carbamate reaction of carbon dioxide with glycyl-glycine , 1966, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[48]  B. Hofstee Specificity of esterases. IV. Behavior of horse liver esterase towards a homologous series of n-fatty acid esters. , 1954, The Journal of biological chemistry.

[49]  R. Lumry,et al.  THE REVERSIBLE THERMAL DENATURATION OF CHYMOTRYPSINOGEN.1 I. EXPERIMENTAL CHARACTERIZATION , 1963 .

[50]  M. Perutz,et al.  Molecular Pathology of Human Haemoglobin , 1968, Nature.

[51]  J. Pople,et al.  Molecular association in liquids II. A theory of the structure of water , 1951, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[52]  L. Storey Ultrasonic Absorption in Mixtures of Ethyl Alcohol and Water , 1952 .

[53]  D. Shiao,et al.  Calorimetric investigations of the binding of inhibitors to alpha-chymotrypsin. I. The enthalpy of dilution of alpha-chymotrypsin and of proflavin, and the enthalpy of binding of indole, N-acetyl-D-tryptophan, and proflavin to alpha-chymotrypsin. , 1969, Biochemistry.

[54]  H. Scheraga,et al.  THE STRUCTURE OF WATER AND HYDROPHOBIC BONDING IN PROTEINS. III. THE THERMODYNAMIC PROPERTIES OF HYDROPHOBIC BONDS IN PROTEINS1,2 , 1962 .

[55]  K. Laidler,et al.  The influence of pH and inhibitors on the kinetics of enzyme reactions involving two intermediates , 1967 .

[56]  A. E. Martin,et al.  Investigations of infra-red spectra (2.5—7.5µ). Absorption of water , 1940, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[57]  C. Hansch,et al.  THE USE OF SUBSTITUENT CONSTANTS AND REGRESSION ANALYSIS IN THE STUDY OF ENZYMATIC REACTION MECHANISMS. , 1965, Journal of the American Chemical Society.

[58]  L. Hepler Partial Molal Volumes of Aqueous Ions , 1957 .

[59]  R. Lumry,et al.  Studies of the chymotrypsinogen family of proteins. IX. Steady-state kinetics of the chymotryptic hydrolysis of N-acetyl-L-tryptophan ethyl ester at pH 8.0. , 1970, Journal of the American Chemical Society.

[60]  Herman J. C. Berendsen,et al.  Nuclear magnetic resonance study of collagen hydration , 1962 .

[61]  Goro Wada A Simplified Model for the Structure of Water , 1961 .

[62]  H. E. Cox XVI.—The influence of the solvent on the temperature-coefficient of certain reactions. A test of the radiation hypothesis , 1921 .

[63]  S. Umeda,et al.  Effects of Nonelectrolytes on the Temperature of the Maximum Density of Water. I. Alcohols , 1962 .

[64]  F. Richards STRUCTURE OF PROTEINS. , 1963, Annual review of biochemistry.

[65]  C. J. Burton A Study of Ultrasonic Velocity and Absorption in Liquid Mixtures , 1948 .

[66]  J. Jarzynski,et al.  Structural relaxation in water , 1968 .

[67]  J. F. Foster,et al.  The microheterogeneity of plasma albumins. IV. Evidence from reversible denaturation that three-dimensional folding is not responsible for microheterogeneity. , 1968, Biochemistry.

[68]  S. Freed,et al.  Enzymatic reactions below 0° of α-chymotrypsin in methanol-water solvents , 1964 .

[69]  T. Inagami,et al.  Participation of an acidic group in the chymotrypsin catalysis. , 1969, Journal of biochemistry.

[70]  L. Brooker,et al.  Color and Constitution. XIII.1 Merocyanines as Solvent Property Indicators2 , 1965 .

[71]  Solubility and Thermodynamics of Solution of Argon in Mixtures of H2O and D2O , 1966 .

[72]  J. Weinberg,et al.  Nuclear Magnetic Resonance Studies of Living Muscle , 1965, Science.

[73]  J. Hermans,et al.  Reactivity of the individual tyrosine side chains of myoglobin toward iodination. , 1967, Archives of biochemistry and biophysics.

[74]  R. Verrall,et al.  Vacuum‐Ultraviolet Study of Liquid H2O and D2O , 1969 .

[75]  R. E. Marsh,et al.  The Structure of Chlorine Hydrate. , 1952, Proceedings of the National Academy of Sciences of the United States of America.

[76]  L. J. Bellamy,et al.  A simple relationship between the infra-red stretching frequencies and the hydrogen bond distances in crystals , 1969 .

[77]  D. D. Eley The structure of water in aqueous solutions , 1944 .

[78]  F. Franks,et al.  Accurate evaluation of partial molar properties , 1962 .

[79]  H. Eyring,et al.  Significant structure theory of liquids , 1963 .

[80]  J. Butler The energy and entropy of hydration of organic compounds , 1937 .

[81]  W. Person,et al.  Spectroscopic study of the ethanol-iodine complex , 1969 .

[82]  J. W. Chase,et al.  Structural effects on the enthalpy and entropy of diluted of aqueous solutions of the quaternary ammonium halides at 25.degree. , 1967 .

[83]  D. Phillips,et al.  THE HEN EGG-WHITE LYSOZYME MOLECULE , 1967 .

[84]  L. Pauling A molecular theory of general anesthesia. , 1961, Science.

[85]  M. Jhon,et al.  SIGNIFICANT-STRUCTURE THEORY APPLIED TO WATER AND HEAVY WATER , 1966 .

[86]  J. Brandts The Thermodynamics of Protein Denaturation. II. A Model of Reversible Denaturation and Interpretations Regarding the Stability of Chymotrypsinogen , 1964 .

[87]  J. Burke,et al.  The Importance of Ground State Solvation in the Solvolysis of t-Butyl Chloride , 1963 .

[88]  George F. Foy Engineering plastics and their commercial development : a symposium co-sponsored by the Division of Chemical Marketing and Economics and the Division of Polymer Chemistry at the 157th meeting of the American Chemical Society, Minneapolis, Minn., April, 15-16, 1969 , 1969 .

[89]  Henry S. Frank,et al.  Free Volume and Entropy in Condensed Systems III. Entropy in Binary Liquid Mixtures; Partial Molal Entropy in Dilute Solutions; Structure and Thermodynamics in Aqueous Electrolytes , 1945 .

[90]  R. Wildnauer,et al.  A hydrocarbon-water model for the formation of the enzyme-inhibitor complex in the case of alpha-chymotrypsin. , 1966, Biochemistry.

[91]  G. Choppin,et al.  Near‐Infrared Studies of the Structure of Water. I. Pure Water , 1963 .

[92]  B. Jacobson On the Interpretation of Dielectric Constants of Aqueous Macromolecular Solutions. Hydration of Macromolecules , 1955 .

[93]  J. F. Foster,et al.  THE MICROHETEROGENEITY OF PLASMA ALBUMINS. I. CRITICAL EVIDENCE FOR AND DESCRIPTION OF THE MICROHETEROGENEITY MODEL. , 1965, The Journal of biological chemistry.

[94]  J. Hyne,et al.  Enthalpy and entropy of activation for benzyl chloride solvolysis in various alcohol–water solvent mixtures , 1968 .

[95]  Jen-Tsi Yang,et al.  Dilatometric and refractometric studies of the helix—coil transition of poly‐L‐glutamic acid in aqueous solution , 1963 .

[96]  G. Royer,et al.  A common size parameter for hydrophobic binding of inhibitors by α-Chymotrypsin, alkylated α-Chymotrypsin, and yeast alcohol dehydrogenase☆ , 1968 .

[97]  W. H. Orttung Proton binding and dipole moment of hemoglobin. Refined calculations. , 1970, Biochemistry.

[98]  R. Parsons Hydrogen-Bonded Solvent Systems , 1969 .

[99]  Mrevlishvili Gm,et al.  HYDRATION OF MACROMOLECULES IN THE NATIVE AND DENATURED STATES , 1967 .

[100]  G. Hammes,et al.  Mechanism of Enzyme Catalysis , 1964, Nature.

[101]  G. Schwert,et al.  THE REVERSIBLE HEAT DENATURATION OF CHYMOTRYPSINOGEN , 1951, The Journal of general physiology.

[102]  E. Antonini,et al.  Oxygen Equilibrium of Myoglobin from Thunnus thynnus , 1960, Nature.

[103]  A. Fainberg,et al.  Correlation of Solvolysis Rates. IV.1 Solvent Effects on Enthalpy and Entropy of Activation for Solvolysis of t-Butyl Chloride2 , 1957 .

[104]  P. F. Low Physical Chemistry of Clay-Water Interaction , 1961 .

[105]  H. Vogel,et al.  Temperature of compensation: significance for virus in- activation. , 1969, Proceedings of the National Academy of Sciences of the United States of America.

[106]  L. Grossweiner,et al.  Optical generation of hydrated electrons from aromatic compounds. II. , 1966, Journal of the American Chemical Society.

[107]  M. Walker,et al.  Exciplex Studies. II. Indole and Indole Derivatives , 1967 .

[108]  M. Symons,et al.  Solvation spectra. Part 1.—The effect of environmental changes upon the ultra-violet absorption of solvated iodide ions , 1958 .

[109]  S. Abdulnur,et al.  HYDROPHOBIC STACKING OF BASES AND THE SOLVENT DENATURATION OF DNA * , 1964 .

[110]  J. Sturtevant,et al.  THE MECHANISM OF CHYMOTRYPSIN-CATALYZED REACTIONS. , 1956, Proceedings of the National Academy of Sciences of the United States of America.

[111]  J. Zung,et al.  Cluster Structure of the Anomalous Liquid Water , 1969, Nature.

[112]  R. Lumry,et al.  Studies of heme-proteins , 1967 .

[113]  J. R. Abrams,et al.  Some Kinetic Considerations of the Thermal Decomposition of Benzenediazonium Chloride in Various Solvents , 1941 .

[114]  M. L. Bender,et al.  Kinetic Evidence for the Formation of Acyl-Enzyme Intermediates in the -Chymotrypsin-Catalyzed Hydrolyses of Specific Substrates , 1964 .

[115]  E. Itagaki,et al.  Studies on Cytochrome b562 of Escherichia coli I. PURIFICATION AND CRYSTALLIZATION OF CYTOCHROME b562 , 1966 .

[116]  T. Litovitz,et al.  Two‐State Theory of the Structure of Water , 1965 .

[117]  G. Walrafen,et al.  Raman Spectral Studies of Water Structure , 1964 .

[118]  Q. Gibson,et al.  The reaction of methemoglobin with some ligands. , 1969, The Journal of biological chemistry.

[119]  D. Waddington,et al.  Analysis of sound velocities in aqueous mixtures in terms of excess isentropic compressibilities , 1970 .

[120]  G. Walrafen,et al.  Raman Spectral Studies of the Effects of Temperature on Water and Electrolyte Solutions , 1966 .

[121]  J. Jortner,et al.  CAGE EFFECTS AND SCAVENGING MECHANISMS IN THE PHOTOCHEMISTRY OF THE IODIDE ION IN AQUEOUS SOLUTIONS , 1962 .

[122]  Irving M. Klotz,et al.  Near‐Infrared Spectra of H2O—D2O Solutions , 1966 .

[123]  W. L. Masterton Partial Molal Volumes of Hydrocarbons in Water Solution , 1954 .

[124]  J. Brandts THE NATURE OF THE COMPLEXITIES IN THE RIBONUCLEASE CONFORMATIONAL TRANSITION AND THE IMPLICATIONS REGARDING CLATHRATING. , 1965, Journal of the American Chemical Society.

[125]  K. Grjotheim,et al.  On the Correlation between Structure and Some Properties of Water. , 1954 .

[126]  D. Ritson,et al.  The Dielectric Properties of Water and Heavy Water , 1948 .

[127]  Djt Hill,et al.  The heats of solution of alcohols in water , 1969 .

[128]  A. Weller,et al.  Dipolar Nature of Molecular Complexes Formed in the Excited State , 1967 .

[129]  B. Hofstee Specificity of esterases. II. Behavior of pancreatic esterases I and II towards a homologous series of n-fatty acid esters. , 1952, The Journal of biological chemistry.

[130]  J. A. Rupley,et al.  Comparison of protein structure in the crystal and in solution. VI. Volume change in the crystallization of horse methemoglobin. , 1968, Journal of molecular biology.

[131]  J. Stern,et al.  Thermodynamics of aqueous mixtures of electrolytes and nonelectrolytes. VIII. Transfer of sodium chloride from water to aqueous urea at 25 , 1969 .

[132]  J. Jortner,et al.  On the Photochemistry of Aqueous Solutions of Chloride, Bromide, and Iodide Ions , 1964 .

[133]  W. Drost-Hansen THE EFFECTS ON BIOLOGIC SYSTEMS OF HIGHER‐ORDER PHASE TRANSITIONS IN WATER * , 1965 .

[134]  G. Walrafen,et al.  Raman Spectral Studies of the Effects of Temperature on Water Structure , 1967 .

[135]  F. Pohl Kinetics of reversible denaturation of trypsin in water and water--ethanol mixtures. , 1968, European journal of biochemistry.

[136]  H. Morimoto,et al.  EPR STUDIES ON SINGLE CRYSTALS OF MYOGLOBIN AND MYOGLOBIN FLUORIDE , 1967 .

[137]  H. Eyring,et al.  SIGNIFICANT LIQUID STRUCTURES, VI. THE VACANCY THEORY OF LIQUIDS. , 1961, Proceedings of the National Academy of Sciences of the United States of America.

[138]  P. Pl State and role of water in biological systems , 1958 .

[139]  S. Ogawa,et al.  Spin-label study of hemoglobin conformations in solution. , 1967, Proceedings of the National Academy of Sciences of the United States of America.

[140]  W. G. Miller,et al.  Cooperativity of the helix–random coil transition determined from hydrodynamic data , 1970, Biopolymers.

[141]  L. Hepler,et al.  THERMODYNAMICS OF IONIZATION OF AQUEOUS meta-CHLOROPHENOL , 1961 .

[142]  Saul G. Cohen,et al.  Active Site of α-Chymotrypsin Activation by Association-Desolvation , 1970 .

[143]  D. Ives,et al.  Structure and properties of water , 1968 .

[144]  A. Otis,et al.  The determination of the individual equilibrium constants of the four intermediate reactions between oxygen and sheep haemoglobin , 1955, Proceedings of the Royal Society of London. Series B - Biological Sciences.

[145]  W. Luck,et al.  Die Temperaturabhängigkeit der D2O- und HOD-Spektren im nahen IR bis in überkritische Bereiche , 1969 .

[146]  I. M. Klotz Protein hydration and behavior; many aspects of protein behavior can be interpreted in terms of frozen water of hydration. , 1958, Science.

[147]  J. E. LEFFLEKR,et al.  Concerning the Isokinetic Relationship , 1965, Nature.

[148]  M. Magat Raman spectra and the constitution of liquids , 1937 .

[149]  T. Fife,et al.  Steric effects in the deacylation of acyl-chymotrypsins. , 1967, Biochemistry.

[150]  P. Flory,et al.  Random coil configurations of polypeptide copolymers , 1967 .

[151]  A. Ben-Naim Solubility and thermodynamics of solution of argon in water-methanol system , 1967 .

[152]  J E Leffler,et al.  Parameters for the Description of Transition States. , 1953, Science.

[153]  I. M. Klotz,et al.  Hydrogen Bonds between Model Peptide Groups in Solution , 1962 .

[154]  R. Marcus Exchange reactions and electron transfer reactions including isotopic exchange. Theory of oxidation-reduction reactions involving electron transfer. Part 4.—A statistical-mechanical basis for treating contributions from solvent, ligands, and inert salt , 1960 .

[155]  R. Mcgregor,et al.  On the Enthalpy–Entropy Relationship , 1966, Nature.

[156]  J. W. Stout,et al.  Heat capacities from 11 to 305 degrees K and entropies of hydrated and anhydrous bovine zinc insulin and bovine chymotrypsinogen A. Entropy change for formation of peptide bonds. , 1969, The Journal of biological chemistry.

[157]  L. Hepler,et al.  THERMODYNAMIC THEORY OF ACID DISSOCIATION OF METHYL SUBSTITUTED PHENOLS IN AQUEOUS SOLUTION , 1961 .

[158]  L. Kaminsky,et al.  Effects of organic solvents on cytochrome c , 1969, FEBS letters.

[159]  俊治 片山 メタノール-水, イソプロパノール-水系の混合熱, 液熱容量およびエンタルピー , 1962 .

[160]  A. Quist,et al.  Pauling's Model and the Thermodynamic Properties of Water , 1961 .

[161]  M. Symons,et al.  The effect of environmental changes upon the ultra-violet absorption spectra of solvated anions , 1957 .

[162]  K. T. Leffek,et al.  Studies on the decomposition of tetra-alkylammonium salts in solution. Part II. Dependence of the activation parameters on the structure of the substrate , 1969 .

[163]  M. A. Lauffer,et al.  Pollymerization–Depolymerizatic Tobacco Mosaic Virus Protein , 1958, Nature.

[164]  W. Wen,et al.  Thermodynamics of hydrocarbon gases in aqueous tetraalkylammonium salt solutions , 1970 .

[165]  Charles E. Skinner,et al.  Kinetics of the formation of the trans-dibromotetracyanoplatinate(IV) ion , 1969 .

[166]  F. Warth,et al.  CLXXIV.—The affinity constants of aniline and its derivatives , 1904 .

[167]  N. Hush,et al.  Adiabatic theory of outer sphere electron-transfer reactions in solution , 1961 .

[168]  J. Brandts,et al.  Thermodynamics of protein denaturation. Effect of pressu on the denaturation of ribonuclease A. , 1970, Biochemistry.

[169]  J. Brandts,et al.  Thermodynamics of protein denaturation. III. Denaturation of ribonuclease in water and in aqueous urea and aqueous ethanol mixtures , 1967 .

[170]  J. Leffler,et al.  The Role of the Solvent in Radical Decomposition Reactions: Phenylazotriphenylmethane , 1954 .

[171]  R. Lumry,et al.  A Kinetic Study of the Imidazole Grouips of Chymotrypsinogen, Chymotrypsin, and Some Derivatives, Using the Temperature-Jump Method , 1964 .

[172]  R. Lipnick,et al.  Lifetimes of amine-water and amine-alcohol hydrogen-bonded complexes in hydroxylic solvents. Role of London dispersion forces in solvation , 1969 .

[173]  W. Wynne-Jones,et al.  The thermodynamics of acid-base equilibria , 1939 .

[174]  S. Miller A theory of gaseous anesthetics. , 1961, Proceedings of the National Academy of Sciences of the United States of America.

[175]  H. Vogel,et al.  Water adsorption and dielectric properties of lyophilized hemoglobin. , 1968, The Journal of physical chemistry.

[176]  F. Richards,et al.  Some Studies of Protein Crystals in a Variety of Different Media1 , 1956 .

[177]  Felix Franks,et al.  Structural Approach to the Solvent Power of Water for Hydrocarbons; Urea as a Structure Breaker , 1968 .

[178]  H. A. Resing Nuclear magnetic resonance relaxation of molecules adsorbed on surfaces , 1968 .

[179]  C. Hansch,et al.  The linear free-energy relationship between partition coefficients and the binding and conformational perturbation of macromolecules by small organic compounds. , 1968, Biochemistry.

[180]  J. Leffler The Interpretation of Enthalpy and Entropy Data , 1966 .

[181]  H. Scheraga,et al.  Structure of Water and Hydrophobic Bonding in Proteins. IV. The Thermodynamic Properties of Liquid Deuterium Oxide , 1964 .

[182]  S. D. Hamann,et al.  The chemical effects of pressure. Part 1 , 1953 .

[183]  C. Cori,et al.  Effects of substrates and a substrate analog on the binding of 5'-adenylic acid to muscle phosphorylase a. , 1967, Biochemistry.

[184]  Rudolph A. Marcus,et al.  On the Theory of Oxidation‐Reduction Reactions Involving Electron Transfer. I , 1956 .

[185]  O. Exner On the enthalpy-entropy-relationship , 1964 .

[186]  A. Ben-Naim,et al.  Solubility and thermodynamics of solution of argon in water + ethanol system , 1964 .

[187]  A. Ben-Naim On the Origin of the Stabilization of the Structure of Water by Nonelectrolytes , 1965 .

[188]  D. Koshland Application of a Theory of Enzyme Specificity to Protein Synthesis. , 1958, Proceedings of the National Academy of Sciences of the United States of America.

[189]  D. Hornig,et al.  Raman Intensities of HDO and Structure in Liquid Water , 1965 .

[190]  D. Hornig,et al.  Raman Spectra of Water in Concentrated Ionic Solutions , 1967 .

[191]  T. A. Ford,et al.  INFRARED SPECTRUM AND STRUCTURE OF LIQUID WATER , 1966 .

[192]  J. A. Rupley,et al.  Studies on the enzymic activity of lysozyme, 3. The binding of saccharides. , 1967, Proceedings of the National Academy of Sciences of the United States of America.

[193]  L. Hepler Effects of Substituents on Acidities of Organic Acids in Water: Thermodynamic Theory of the Hammett Equation , 1963 .

[194]  W. H. Orttung Anisotropy of proton fluctuations and the Kerr effect of protein solutions. Theoretical considerations. , 1968, The Journal of physical chemistry.

[195]  J. Kendrew,et al.  Structure of Deoxymyoglobin : A Crystallographic Study , 1966, Nature.

[196]  M. Perutz The first Sir Hans Krebs lecture. X-ray analysis, structure and function of enzymes. , 1969, European journal of biochemistry.

[197]  D. Doherty,et al.  THERMODYNAMIC STUDY OF SOME ENZYME-INHIBITOR COMPLEXES OF CHYMOTRYPSIN. II , 1953 .

[198]  J. Kirkwood,et al.  Theory of Solutions of Molecules Containing Widely Separated Charges with Special Application to Zwitterions , 1934 .

[199]  J. Hyne,et al.  ON THE PRESSURE DEPENDENCE OF REACTION RATES , 1966 .

[200]  M. A. Lauffer POLYMERIZATION-DEPOLYMERIZATION OF TOBACCO MOSAIC VIRUS PROTEIN. II. THEORY OF PROTEIN HYDRATION. , 1964, Biochemistry.

[201]  M. Perutz,et al.  The structure of haemoglobin. IX. A three-dimensional Fourier synthesis at 5.5 Å resolution: description of the structure , 1962, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[202]  T. Ackermann Physico-Chemical Processes in Mixed Aqueous Solvents , 1969 .

[203]  H. Mcconnell,et al.  Spin-labeled hemoglobin. , 1966, Proceedings of the National Academy of Sciences of the United States of America.

[204]  H. Eyring,et al.  The Application of the Theory of Absolute Reacton Rates to Proteins. , 1939 .

[205]  G. Walrafen Raman Spectral Studies of the Effects of Electrolytes on Water , 1962 .

[206]  J. Butler,et al.  The entropy of solution , 1938 .

[207]  D. Doherty,et al.  Thermodynamic Study of an Enzyme—Substrate Complex of Chymotrypsin. I1,2 , 1952 .

[208]  W. Jencks Catalysis in chemistry and enzymology , 1969 .

[209]  A. S. Brill,et al.  Spectral studies of iron coordination in hemeprotein complexes: difference spectroscopy below 250 millimicrons. , 1968, Biophysical journal.

[210]  D. Eatough,et al.  Computer evaluation of entropy titration data. Calorimetric determination of log .beta.i, .DELTA.Hi.degree., and .DELTA.Si.degree. values for the silver(I)- and copper(II)-pyridine systems , 1968 .

[211]  E. C. Baughan Electrostatic Effects on Ionization Constants , 1939 .

[212]  W. Good,et al.  The kinetics of malonamide-induced haemolysis of mammalian erythrocytes. II. The Eyring activation parameters. , 1968, Biochimica et biophysica acta.

[213]  H. Schwan,et al.  Further observations on the electrical properties of hemoglobin-bound water. , 1969, The Journal of physical chemistry.

[214]  L. Hammett,et al.  Physical organic chemistry , 1940 .

[215]  O. Exner Concerning the Isokinetic Relationship , 1964, Nature.

[216]  L. Henderson The fitness of the environment , 1913 .

[217]  B. Nichols,et al.  Evidence for the Existence of a Minimum of Two Phases of Ordered Water in Skeletal Muscle , 1969, Nature.

[218]  P. George,et al.  The ionization of acidic metmyoglobin. , 1952, The Biochemical journal.

[219]  K. Miller,et al.  Solutions of inert gases in water , 1968 .

[220]  B. Belleau,et al.  A biophysical basis of ligand-induced activation of excitable membranes and associated enzymes. A thermodynamic study using acetylcholinesterase as a model receptor. , 1968, Canadian journal of biochemistry.

[221]  F. Cennamo,et al.  On the X-ray diffraction in water-dioxane and water-ethyl alcohol mixtures , 1959 .

[222]  D. Ives,et al.  The structural properties of alcohol–water mixtures , 1966 .

[223]  B. Hofstee Fatty acid esters as substrates for trypsin and chymotrypsin. , 1957, Biochimica et biophysica acta.

[224]  F. Teale,et al.  The ultraviolet fluorescence of proteins in neutral solution. , 1960, The Biochemical journal.

[225]  Henry S. Frank,et al.  Ion-solvent interaction. Structural aspects of ion-solvent interaction in aqueous solutions: a suggested picture of water structure , 1957 .

[226]  H. Eyring,et al.  Application of Significant Structure Theory to Water1 , 1964 .

[227]  F. Long,et al.  Entropies of Activation and Mechanisms of Reactions in Solution , 1963 .

[228]  U. Schindewolf Formation and Properties of Solvated Electrons , 1968 .

[229]  L. J. Bellamy,et al.  The significance of infra-red frequency shifts in relation to hydrogen bond strengths , 1969 .

[230]  M. L. Bender,et al.  The Current Status of the -Chymotrypsin Mechanism , 1964 .

[231]  J. Leffler,et al.  Solvent Effects in the Racemization of 2,2′-Dimethoxy-6,6′-Dicarboxy-biphenyl and its Derivatives , 1959 .

[232]  Thermodynamics of alpha-chymotrypsin-inhibitor complex formation. Effects of structural modification of the inhibitor. , 1969, The Journal of biological chemistry.

[233]  D. Hornig On the Spectrum and Structure of Water and Ionic Solutions , 1964 .

[234]  T. Ford,et al.  Hydrogen bonding in water and ice , 1968 .

[235]  John E. Leffler,et al.  THE ENTHALPY-ENTROPY RELATIONSHIP AND ITS IMPLICATIONS FOR ORGANIC CHEMISTRY , 1955 .

[236]  D. Shiao Calorimetric investigations of the binding of inhibitors to alpha-chymotrypsin. II. A systematic comparison of the thermodynamic functions of binding of a variety of inhibitors to alpha-chymotrypsin. , 1970, Biochemistry.

[237]  W. Jackson,et al.  Thermodynamics of protein denaturation. A calorimetric study of the reversible denaturation of chymotrypsinogen and conclusions regarding the accuracy of the two-state approximation. , 1970, Biochemistry.

[238]  Clinton D. Cook,et al.  Oxidation of Hindered Phenols. VII. Solvent Effects on the Disproportionation of Certain Phenoxy Radicals , 1959 .

[239]  Harold A. Scheraga,et al.  Structure of Water and Hydrophobic Bonding in Proteins. I. A Model for the Thermodynamic Properties of Liquid Water , 1962 .

[240]  L. Mazzarella,et al.  Structure and function of haemoglobin: IV. A three-dimensional Fourier synthesis of horse deoxyhaemoglobin at 5.5 Å resolution , 1967 .

[241]  M. Zinbo,et al.  Kinetic Studies on Gluc-amylase , 1966 .

[242]  T. A. Claxton,et al.  Thermal anomalies in the temperature dependence of the energy of the first absorption band maximum of iodide in water , 1967 .

[243]  E. Schrödinger What Is Life , 1946 .

[244]  R. Lumry,et al.  Studies of Rack Mechanisms in Heme-proteins. I. The Magnetic Susceptibility of Cytochrome c in Relation to Hydration , 1962 .

[245]  R. Aveyard,et al.  Calorimetric studies on n-aliphatic alcohol + water and n-aliphatic alcohol + water detergent systems , 1964 .

[246]  J. Hermans The Effect of Protein Denaturants on the Stability of the α Helix1 , 1966 .

[247]  C. Hansch,et al.  The role of hydrophobic bonding in the binding of organic compounds by bovine hemoglobin. , 1966, Biochemistry.

[248]  W. Kauzmann Some factors in the interpretation of protein denaturation. , 1959, Advances in protein chemistry.

[249]  C. Hansch,et al.  The effect of intramolecular bydrophobic bonding on partition coefficients , 1967 .

[250]  B. Jacobson Hydration Structure of Deoxyribonucleic Acid and its Physico-Chemical Properties , 1953, Nature.

[251]  Ikchoon Lee,et al.  The Initial-State Contribution to the Activation Volume for Benzyl Chloride Solvolysis , 1967 .

[252]  C. Tanford,et al.  Theory of Protein Titration Curves. I. General Equations for Impenetrable Spheres , 1957 .

[253]  J. D. Beck,et al.  Heat of dilution of some aqueous tetraalkylammonium fluorides , 1967 .

[254]  D. Irvine,et al.  Reactivity differences between haemoglobins I. The ionization of human methaemoglobins A, S and C , 1964, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[255]  L. Stryer,et al.  Kinetics of azide binding to normal and mutant ferrihemoglobins as evidence for subunit interaction. , 1968, Journal of molecular biology.

[256]  P. George,et al.  A MAGNETOCHEMICAL STUDY OF EQUILIBRIA BETWEEN HIGH AND LOW SPIN STATES OF METMYOGLOBIN COMPLEXES. , 1964, Biochemistry.

[257]  E. Arnett,et al.  Salt-Like Behavior of the t-Butyl Chloride Solvolysis Transition State1,2 , 1965 .

[258]  P. S. Lewis The Kinetics of Protein Denaturation: Part I. The Effect of Variation in the Hydrogen Ion Concentration on the Velocity of the Heat Denaturation of Oxyhaemoglobin. , 1926, The Biochemical journal.

[259]  M. Symons,et al.  Discontinuities in the Thermal Properties of Water and Aqueous Solutions , 1967, Nature.

[260]  J. Brandts The Thermodynamics of Protein Denaturation. I. The Denaturation of Chymotrypsinogen , 1964 .

[261]  T. H. Marshall,et al.  NH-proton exchange of purine in aqueous solution. Effect of molecular complexing on reaction rate , 1969 .

[262]  B. Derjaguin Effect of lyophile surfaces on the properties of boundary liquid films , 1966 .

[263]  W. Good A Biological Example of the Compensation Law , 1967, Nature.