Interpretations of data in the extensive literature on the unfolding of proteins in aqueous solut... more Interpretations of data in the extensive literature on the unfolding of proteins in aqueous solution follow a variety of methods involving assumptions leading to estimates of thermodynamic quantities associated with the unfolding transition. Inconsistencies and thermodynamic errors in these methods are identified. Estimates of standard molar free energies and enthalpies of unfolding using incompletely defined equilibrium constants and the van't Hoff relation are unsound, and typically contradict model-free interpretation of the data. A widely used routine for estimating the change in heat capacity associated with unfolding based on changes in the unfolding temperature and enthalpy co-induced by addition of denaturant or protective additives is thermodynamically incorrect by neglect of the Phase Rule. Many models and simulations predicting thermodynamic measures of unfolding are presently making comparisons with insecure quantities derived by incorrect thermodynamic analyses of experimental data. Analysis of unfolding via the Gibbs-Duhem equation with the correct Phase Rule constraints avoids the assumptions associated with incomplete equilibrium constants and misuse of the van't Hoff relation, and applies equally to positive, negative, sitewise or diffuse solute binding to the protein. The method gives the necessary relations between the thermodynamic parameters for thermal and isothermal unfolding and is developed for the case of two-state unfolding. The differences in binding of denaturants or stabilizers to the folded and unfolded forms of the protein are identified as major determinants of the unfolding process. The Phase Rule requires the temperature and enthalpy of unfolding to depend generally on the protein concentration. The available evidence bears out this expectation for thermal unfolding, indicating that protein-protein interactions influence folding. A parallel dependence of the denaturant concentrations for isothermal unfolding on the protein concentration is anticipated. The degree of unfolding as measured by UV, CD, fluorescence and other non-calorimetric methods may not show the same temperature and concentration ranges for unfolding among themselves or as compared to DSC or isothermal calorimetry. Such disparities indicate distinct stages in unfolding detectable by particular methods.
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1978
A general thermodynamic treatment of electrical condensers is presented which avoids the use of t... more A general thermodynamic treatment of electrical condensers is presented which avoids the use of thermodynamically ill defined electrostatic quantities and concepts, and which does not neglect surface effects at the condenser plates. The following conclusions emerge. (1) For multicomponent bulk dielectrics, equations similar in form to those obtained previously by Koenig and Frank are derived describing field fractionation etc. (2) The derivations make clear the thermodynamic status of commonly employed electrostatic quantities, including the capacity. (3) Surface effects at the condenser plates are an important aspect of the properties of condensers. (4) By use of an intrinsically reasonable non thermodynamic assumption an expression in terms of well defined physical quantities is derived for the effect of dielectric composition on the inner potential difference between a metal and a multicomponent dielectric in contact with the metal. This leads to an expression for the absolute in...
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1971
Previous studies of the effect of monolayers on the electrical potential difference across polar ... more Previous studies of the effect of monolayers on the electrical potential difference across polar oil/water interfaces have produced only conflicting data about the existence, magnitude and stability of the so-called adsorption or surface potentials (∆ V ). It is now shown that, with carefully defined experiments, remarkably stable values for ∆ V can often be obtained whose rates of decay are so slow that ∆ V -surface density isotherms similar to those established for air/water or non-polar oil/water interfaces can be obtained. The rapid decays found previously are attributed to inadequate electrical or surface chemical controls.
Journal of the Chemical Society, Faraday Transactions 1: Physical Chemistry in Condensed Phases, 1982
Isotherms of surface pressure (π) against area per molecule (A) are reported for a homologous ser... more Isotherms of surface pressure (π) against area per molecule (A) are reported for a homologous series of pure synthetic saturated 1,2-di-acyl glycerophosphocholines (lecithins)(C14 to C22) spread at n-heptane/aqueous electrolyte interfaces. The lecithins show second-order phase transitions which for a given temperature move to higher π and lower A as the chain length is decreased until for di-C12 lecithin no phase transition can be distinguished.The calculations of Clapeyron heats in Part 1 are extended to the new data using a single value of the reference area for the solid state for all temperatures and chain lengths. These heats vary with chain length and decrease linearly with temperature. The high heat capacity calculated in Part 1 for di-C18 lecithin at low temperatures is shown to be an artefact. Entropies of compression have been calculated from the free energies obtained by integrating the full isotherms between a reference area in the expanded region above any phase transition and another area in the solid-condensed region. These entropies vary linearly with chain length, having a slope given by the configurational entropy term R ln 3 per methylene group, where R is the gas constant. The entropy change for each phospholipid is approximately 2(n–1)R ln 3, where n is the chain length. This finding, taken together with a comparison of the heats of the monolayer phase transitions with the calorimetric heats of melting of phospholipid chains, and with related published data on the heats of fusion and the heats of solution of the alkanes, suggests that the chains of the phospholipids are fully flexible at low monolayer densities and very restricted on the condensed side of the phase transitions.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1977
An explicit thermodynamic analysis of the Volta effect for a system including adsorbed films or s... more An explicit thermodynamic analysis of the Volta effect for a system including adsorbed films or spread monolayers is presented in terms of surface variables. From an appropriate fundamental equation, Maxwell relations are obtained describing the effect of an applied electric field on some of the parameters characterizing surface films. It is shown that the assumptions of Bridgman, Kelvin & Lorentz (B.K.L.) concerning the properties of the Volta and compensation potentials are strictly incorrect, but that in many cases of practical interest the errors introduced by these assumptions are negligible, and lie well within current experimental accuracy. Measurable effects associated with the breakdown of the B.K.L. assumptions are predicted at high fields corresponding to phenomena such as field desorption. New experiments are suggested by the demonstration that in the transition region of a two dimensional first-order phase change, the B.K.L. assumptions can break down significantly when...
As indicated by Gibbs and made explicit by Guggenheim, the electrical potential difference betwee... more As indicated by Gibbs and made explicit by Guggenheim, the electrical potential difference between two regions of different chemical composition cannot be measured. The Gibbs-Guggenheim Principle restricts the use of classical electrostatics in electrochemical theories as thermodynamically unsound with some few approximate exceptions, notably for dilute electrolyte solutions and concomitant low potentials where the linear limit for the exponential of the relevant Boltzmann distribution applies. The Principle invalidates the widespread use of forms of the Poisson-Boltzmann equation which do not include the non-electrostatic components of the chemical potentials of the ions. From a thermodynamic analysis of the parallel plate electrical condenser, employing only measurable electrical quantities and taking into account the chemical potentials of the components of the dielectric and their adsorption at the surfaces of the condenser plates, an experimental procedure to provide exceptions to the Principle has been proposed. This procedure is now reconsidered and rejected. No other related experimental procedures circumvent the Principle. Widely-used theoretical descriptions of electrolyte solutions, charged surfaces and colloid dispersions which neglect the Principle are briefly discussed. MD methods avoid the limitations of the Poisson-Bolzmann equation. Theoretical models which include the non-electrostatic components of the inter-ion and ion-surface interactions in solutions and colloid systems assume the additivity of dispersion and electrostatic forces. An experimental procedure to test this assumption is identified from the thermodynamics of condensers at microscopic plate separations. The available experimental data from Kelvin probe studies are preliminary, but tend against additivity. A corollary to the Gibbs-Guggenheim Principle is enunciated, and the Principle is restated that for any charged species, neither the difference in electrostatic potential nor the sum of the differences in the non-electrostatic components of the thermodynamic potential difference between regions of different chemical compositions can be measured.
The lateral intermolecular forces between surfactant or lipid molecules in monolayers at interfac... more The lateral intermolecular forces between surfactant or lipid molecules in monolayers at interfaces are fundamental to understanding the phenomena of surface activity and the interactions of lipids in two-dimensional structures such as smectic phases and biomembranes. The classical approach to these forces is via the two-dimensional virial coefficients, which requires precise micromanometry on monolayer isotherms in the dilute gaseous region. Low pressure isotherms out to high surface areas in the two-dimensional gas range have been measured at 15, 25 and 30 degrees C for insoluble monolayers of n-pentadecanoic acid spread at the interface between water-vapour saturated air and a dilute aqueous solution of HCl. The data allow estimates of virial coefficients up to the third term. The second virial coefficients are compared with those predicted from a statistical mechanical model for monolayers of n-alkylcarboxylic acids treated as side-by-side parallel chains extended at the surface with the carboxyl head groups shielded in the water phase. The two sets coincide at approximately 26 degrees C, but the experimental estimates show a much larger dependence on temperature than the model predicts. Chain conformation effects, head group interactions and surface field polarization are discussed as possible temperature-dependent contributions to the lateral potentials of mean force.
Interpretations of data in the extensive literature on the unfolding of proteins in aqueous solut... more Interpretations of data in the extensive literature on the unfolding of proteins in aqueous solution follow a variety of methods involving assumptions leading to estimates of thermodynamic quantities associated with the unfolding transition. Inconsistencies and thermodynamic errors in these methods are identified. Estimates of standard molar free energies and enthalpies of unfolding using incompletely defined equilibrium constants and the van't Hoff relation are unsound, and typically contradict model-free interpretation of the data. A widely used routine for estimating the change in heat capacity associated with unfolding based on changes in the unfolding temperature and enthalpy co-induced by addition of denaturant or protective additives is thermodynamically incorrect by neglect of the Phase Rule. Many models and simulations predicting thermodynamic measures of unfolding are presently making comparisons with insecure quantities derived by incorrect thermodynamic analyses of experimental data. Analysis of unfolding via the Gibbs-Duhem equation with the correct Phase Rule constraints avoids the assumptions associated with incomplete equilibrium constants and misuse of the van't Hoff relation, and applies equally to positive, negative, sitewise or diffuse solute binding to the protein. The method gives the necessary relations between the thermodynamic parameters for thermal and isothermal unfolding and is developed for the case of two-state unfolding. The differences in binding of denaturants or stabilizers to the folded and unfolded forms of the protein are identified as major determinants of the unfolding process. The Phase Rule requires the temperature and enthalpy of unfolding to depend generally on the protein concentration. The available evidence bears out this expectation for thermal unfolding, indicating that protein-protein interactions influence folding. A parallel dependence of the denaturant concentrations for isothermal unfolding on the protein concentration is anticipated. The degree of unfolding as measured by UV, CD, fluorescence and other non-calorimetric methods may not show the same temperature and concentration ranges for unfolding among themselves or as compared to DSC or isothermal calorimetry. Such disparities indicate distinct stages in unfolding detectable by particular methods.
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1978
A general thermodynamic treatment of electrical condensers is presented which avoids the use of t... more A general thermodynamic treatment of electrical condensers is presented which avoids the use of thermodynamically ill defined electrostatic quantities and concepts, and which does not neglect surface effects at the condenser plates. The following conclusions emerge. (1) For multicomponent bulk dielectrics, equations similar in form to those obtained previously by Koenig and Frank are derived describing field fractionation etc. (2) The derivations make clear the thermodynamic status of commonly employed electrostatic quantities, including the capacity. (3) Surface effects at the condenser plates are an important aspect of the properties of condensers. (4) By use of an intrinsically reasonable non thermodynamic assumption an expression in terms of well defined physical quantities is derived for the effect of dielectric composition on the inner potential difference between a metal and a multicomponent dielectric in contact with the metal. This leads to an expression for the absolute in...
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1971
Previous studies of the effect of monolayers on the electrical potential difference across polar ... more Previous studies of the effect of monolayers on the electrical potential difference across polar oil/water interfaces have produced only conflicting data about the existence, magnitude and stability of the so-called adsorption or surface potentials (∆ V ). It is now shown that, with carefully defined experiments, remarkably stable values for ∆ V can often be obtained whose rates of decay are so slow that ∆ V -surface density isotherms similar to those established for air/water or non-polar oil/water interfaces can be obtained. The rapid decays found previously are attributed to inadequate electrical or surface chemical controls.
Journal of the Chemical Society, Faraday Transactions 1: Physical Chemistry in Condensed Phases, 1982
Isotherms of surface pressure (π) against area per molecule (A) are reported for a homologous ser... more Isotherms of surface pressure (π) against area per molecule (A) are reported for a homologous series of pure synthetic saturated 1,2-di-acyl glycerophosphocholines (lecithins)(C14 to C22) spread at n-heptane/aqueous electrolyte interfaces. The lecithins show second-order phase transitions which for a given temperature move to higher π and lower A as the chain length is decreased until for di-C12 lecithin no phase transition can be distinguished.The calculations of Clapeyron heats in Part 1 are extended to the new data using a single value of the reference area for the solid state for all temperatures and chain lengths. These heats vary with chain length and decrease linearly with temperature. The high heat capacity calculated in Part 1 for di-C18 lecithin at low temperatures is shown to be an artefact. Entropies of compression have been calculated from the free energies obtained by integrating the full isotherms between a reference area in the expanded region above any phase transition and another area in the solid-condensed region. These entropies vary linearly with chain length, having a slope given by the configurational entropy term R ln 3 per methylene group, where R is the gas constant. The entropy change for each phospholipid is approximately 2(n–1)R ln 3, where n is the chain length. This finding, taken together with a comparison of the heats of the monolayer phase transitions with the calorimetric heats of melting of phospholipid chains, and with related published data on the heats of fusion and the heats of solution of the alkanes, suggests that the chains of the phospholipids are fully flexible at low monolayer densities and very restricted on the condensed side of the phase transitions.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1977
An explicit thermodynamic analysis of the Volta effect for a system including adsorbed films or s... more An explicit thermodynamic analysis of the Volta effect for a system including adsorbed films or spread monolayers is presented in terms of surface variables. From an appropriate fundamental equation, Maxwell relations are obtained describing the effect of an applied electric field on some of the parameters characterizing surface films. It is shown that the assumptions of Bridgman, Kelvin & Lorentz (B.K.L.) concerning the properties of the Volta and compensation potentials are strictly incorrect, but that in many cases of practical interest the errors introduced by these assumptions are negligible, and lie well within current experimental accuracy. Measurable effects associated with the breakdown of the B.K.L. assumptions are predicted at high fields corresponding to phenomena such as field desorption. New experiments are suggested by the demonstration that in the transition region of a two dimensional first-order phase change, the B.K.L. assumptions can break down significantly when...
As indicated by Gibbs and made explicit by Guggenheim, the electrical potential difference betwee... more As indicated by Gibbs and made explicit by Guggenheim, the electrical potential difference between two regions of different chemical composition cannot be measured. The Gibbs-Guggenheim Principle restricts the use of classical electrostatics in electrochemical theories as thermodynamically unsound with some few approximate exceptions, notably for dilute electrolyte solutions and concomitant low potentials where the linear limit for the exponential of the relevant Boltzmann distribution applies. The Principle invalidates the widespread use of forms of the Poisson-Boltzmann equation which do not include the non-electrostatic components of the chemical potentials of the ions. From a thermodynamic analysis of the parallel plate electrical condenser, employing only measurable electrical quantities and taking into account the chemical potentials of the components of the dielectric and their adsorption at the surfaces of the condenser plates, an experimental procedure to provide exceptions to the Principle has been proposed. This procedure is now reconsidered and rejected. No other related experimental procedures circumvent the Principle. Widely-used theoretical descriptions of electrolyte solutions, charged surfaces and colloid dispersions which neglect the Principle are briefly discussed. MD methods avoid the limitations of the Poisson-Bolzmann equation. Theoretical models which include the non-electrostatic components of the inter-ion and ion-surface interactions in solutions and colloid systems assume the additivity of dispersion and electrostatic forces. An experimental procedure to test this assumption is identified from the thermodynamics of condensers at microscopic plate separations. The available experimental data from Kelvin probe studies are preliminary, but tend against additivity. A corollary to the Gibbs-Guggenheim Principle is enunciated, and the Principle is restated that for any charged species, neither the difference in electrostatic potential nor the sum of the differences in the non-electrostatic components of the thermodynamic potential difference between regions of different chemical compositions can be measured.
The lateral intermolecular forces between surfactant or lipid molecules in monolayers at interfac... more The lateral intermolecular forces between surfactant or lipid molecules in monolayers at interfaces are fundamental to understanding the phenomena of surface activity and the interactions of lipids in two-dimensional structures such as smectic phases and biomembranes. The classical approach to these forces is via the two-dimensional virial coefficients, which requires precise micromanometry on monolayer isotherms in the dilute gaseous region. Low pressure isotherms out to high surface areas in the two-dimensional gas range have been measured at 15, 25 and 30 degrees C for insoluble monolayers of n-pentadecanoic acid spread at the interface between water-vapour saturated air and a dilute aqueous solution of HCl. The data allow estimates of virial coefficients up to the third term. The second virial coefficients are compared with those predicted from a statistical mechanical model for monolayers of n-alkylcarboxylic acids treated as side-by-side parallel chains extended at the surface with the carboxyl head groups shielded in the water phase. The two sets coincide at approximately 26 degrees C, but the experimental estimates show a much larger dependence on temperature than the model predicts. Chain conformation effects, head group interactions and surface field polarization are discussed as possible temperature-dependent contributions to the lateral potentials of mean force.
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