Biomedical subjects
Publications and source records attributed to J A Schellman.
Molecular concepts have been gradually incorporated into chemical thermodynamics. This is done by applying standard thermodynamics manipulations to systems which are restricted by the assumption of a specific molecular model or mechanism. Here we trace the development of this procedure and its applications from Avogadro's hypothesis to modern work on site-directed mutagenesis.
The Carlsberg Laboratory in Copenhagen has had a long tradition of outstanding science. At the time covered by this discussion, Kjeldahl, Sørensen, and Linderstrøm-Lang had been consecutive directors of the Chemical Laboratory for 83 years. Lang's inspired leadership began in the 1930s with a number of innovations (study of metabolism in single cells, titrations in non-aqueous solvents, relation of proteolysis to structure) but it was not until the early 1950s that Denmark had sufficiently recovered from the war for the laboratory to enter world science again. During World War II, Lang had been active in the Danish resistance movement. After the war, a number of major advances were being made that would revolutionize the field of protein chemistry (Pauling and Corey's H-bonded structures, Sanger's sequencing techniques, chromatography, Watson and Crick structures, modern instrumentation). The time for the new field of the physical biochemistry of proteins had arrived. Lang, with his broad experience, adventurous spirit, and genius for innovation, created an environment that was ideal for the convergence of these disconnected advances into a uniform science. The emphasis was to be on quantitative measurements on proteins in solution with interpretations based on molecular structures. During an all-too-brief period of time, Lang's laboratory attracted a large fraction of those who were destined to be the leaders of the next generation of protein chemists. At this time, the Carlsberg Laboratory was probably the most scientifically exciting environment for a protein chemist. The methods developed at that time-hydrogen exchange, limited proteolysis, optical rotatory dispersion, volume changes accompanying protein reactions, automatic titrations-are still all in common use and many of the visitors to the laboratory in that period and their students are still playing major roles in protein research. Lang's other qualities should not be ignored. He was not only a great scientist but also a musician, raconteur, artist, and an exceptionally warm and compassionate human being.
Changes in free energy are normally used to track the effect of temperature on the stability of proteins and hydrophobic interactions. Use of this procedure on the aqueous solubility of hydrocarbons, a standard representation of the hydrophobic effect, leads to the conclusion that the hydrophobic effect increases in strength as the temperature is raised to approximately 140 degrees C. Acceptance of this interpretation leads to a number of far-reaching conclusions that are at variance with the original conception of the hydrophobic effect and add considerably to the complexity of interpretation. There are two legitimate thermodynamic functions that can be used to look at stability as a function of temperature: the standard Gibbs free energy change, deltaG degrees, and deltaG degrees/T. The latter is proportional to the log of the equilibrium constant and is sometimes called the Massieu-Planck function. Arguments are presented for using deltaG degrees/T rather than deltaG degrees for variations in stability with temperature. This makes a considerable difference in the interpretation of the hydrophobic interaction, but makes little change in the stability profile of proteins. Protein unfolding and the aqueous solubility of benzene are given as examples. The contrast between protein unfolding and the hydration of nonpolar molecules provides a rough estimate of the contribution of other factors that stabilize and destabilize protein structure.
G. Makhatadze and P. Privalov [J. Mol. Biol., 226 (1995) 491] have recently measured the enthalpy of transfer of three proteins into urea and guanidinium chloride solutions as a function of concentration and temperature. The present paper applies the solvent-exchange model [J.A. Schellman, Biopolymers, (1994)] to the data and compares it with the binding model utilized in the original publication. Both calculations assume identical binding sites. It is found that the data may be fit tolerably well using either procedure, but that the parameters describing the binding vary considerably. Consideration of the transfer properties of amino acid moieties and small peptides leads to the conclusion that solvation sites are heterogeneous and that the quantities determined by both methods are statistical averages. The parameters describe an identical-site system that has (approximately) the same properties as the real heterogeneous system. The results have mainly heuristic and mechanistic value. One quantity determined with these simplified isotherms, sigma kj delta hj, is a property of the real system and can serve as a measure of a thermal binding capacity for a protein. The appendices contain a resume of the solution theory required for the exchange model of solvation as well as the development of a number of empirical equations for the thermodynamic properties of urea and guanidinium chloride solutions.
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A model for solvation in mixed solvents, which was developed for the free energy and preferential interaction [J. A. Schellman (1987), Biopolymers, Vol. 26, pp. 549-559; (1990), Biophysical Chemistry, Vol. 37, pp. 121-140; (1993), Biophysical Chemistry, Vol. 45, pp. 273-279], is extended in this paper to cover the thermal properties: enthalpy, entropy, and heat capacity. An important result is that the enthalpy of solvation H(ex)2 responds directly to the fraction of site occupation. This differs from the free energy G(ex)2 and preferential interaction gamma 32, which are measures of the excess binding above a random distribution of solvent molecules. In other words, the enthalpy is governed by K while G(ex)2 and gamma 32 are governed by (K-1) where K is the equilibrium constant on a mole fraction scale [Schellman (1987)]. The solvation heat capacity Cpex2 consists of two term: (1) the intrinsic heat capacity of species in solution with no change in composition, and (2) a term that accounts for the change in composition that accompanies solvent exchange. Binding to biological macromolecules is heterogeneous but experimentalists must use binding isotherms that assume the homogeneity of sites. Equations are developed for the interpretation of the experimental parameters (number of sites nexp, equilibrium constant Kexp, and enthalpy, delta hexp), when homogeneous formulas are applied to the heterogeneous case. It is shown that the experimental parameters for the occupation and enthalpy are simple functions of the moments of the distribution of equilibrium constants over the sites. In general, nexp is greater than the true number of sites and Kexp is greater than the average of the equilibrium constants. The free energy and preferential interaction can be fit to a homogeneous formula, but the parameters of the curve are not easily represented in terms of the moments of distributions over the sites. The strengths and deficiencies of this type of thermodynamic model are discussed.
The kinetics of unfolding and refolding of T4 lysozyme and nine of its mutants have been investigated as a function of guanidinium chloride concentration at 12 degrees C. All show simple two-state, first-order kinetics. Two types of mutants were studied: proline-alanine interchanges and substitutions at position 3 with side chains of varying hydrophobicity. Crystal structures are available for seven of the ten proteins. The effect of mutations on the folding kinetics is more pronounced and complex than on equilibrium thermodynamics. The proteins fall into two broad kinetic classes with one class rather close to the wild type. P86A is a mutant with marked changes in kinetics but only a very small change in stability. Since the 86 position is in the middle of an alpha-helix, the indications are that the helix containing an A residue is more stable in the transition state than one containing a P residue. The other mutants are more complicated, with the refolding and unfolding rates unequally affected by the mutations. On the basis of comparisons with other investigations, we conclude that the rate-determining step in the presence of guanidinium chloride is not the same as in aqueous solution and that it most likely precedes it. The indications are that we are studying the formation of a transition intermediate which is destabilized by the denaturant and which resembles the A intermediate of the framework or molten globule models for protein folding.
The standard view of alpha helix formation in water, based on helix propensities determined by the host-guest method, is that differences in helix propensity among the amino acids are small, except for proline, and that the average value of the helix propagation parameter s is near 1. A contradictory view of alpha helix formation in water is emerging from substitution experiments with short, unique-sequence peptides that contain only naturally occurring amino acids. Short peptides that contain only alanine and lysine, or alanine and glutamate, form surprisingly stable monomeric helices in water and substitution of a single alanine residue by another amino acid in these or related peptides produces a wide range of changes in helix content, depending on which amino acid is substituted for alanine. We show here that the ratio of the helix propensities of alanine to glycine is large, about 100, in substitution experiments with a 17-residue reference peptide containing alanine and lysine. The helix propensity is identified with s, the helix propagation parameter of the statistical mechanics model for alpha helix formation, and the results are interpreted by the Lifson-Roig theory. Single alanine----glycine substitutions have been made at a series of positions in individual peptides. The helix-destabilizing effect of an Ala----Gly substitution depends strongly on its position in the helix, as predicted by the Lifson-Roig theory if the ratio of s values for Ala:Gly is large.
The properties of a simple model for solvation in mixed solvents are explored in this paper. The model is based on the supposition that solvent replacement is a simple one-for-one substitution reaction at macromolecular sites which are independent of one another. This leads to a new form for the binding polynomial in which all terms are associated with ligand interchange rather than ligand addition. The principal solvent acts as one of the ligands. Thermodynamic analysis then shows that thermodynamic binding (i.e., selective interaction) depends on the properties of K'-1, whereas stoichiometric binding (site occupation) depends on K'. K' is a 'practical' interchange equilibrium constant given by (f3/f1)K, where K is the true equilibrium constant for the interchange of components 3 and 1 on the site and f3 and f4 denote their respective activity coefficients on the mole fraction scale. Values of K' less than unity lead to negative selective interaction. It is selective interaction and not occupation number which determines the thermodynamic effects of solvation. When K' greater than 100 on the mole fraction scale or K' greater than 2 on the molality scale (in water), the differences between stoichiometric binding and selective interaction become less than 1%. The theory of this paper is therefore necessary only for very weak binding constants. When K'-1 is small, large concentrations of the added solvent component are required to produce a thermodynamic effect. Under these circumstances the isotherms for the selective interaction and for the excess (or transfer) free energy are strongly dependent on the behavior of the activity coefficients of both solvent components. Two classes of behavior are described depending on whether the components display positive or negative deviations from Raoult's law. Examples which are discussed are aqueous solutions of urea and guanidinium chloride for positive deviations and of sucrose and glucose for negative deviations. Examination of the few studies which have been reported in the literature shows that most of the qualitative features of the stabilization of proteins by sugars and their destabilization by urea and guanidinium chloride are faithfully represented with the model. This includes maxima in the free energy of stabilization and destabilization, decreased and zero selective interaction at high concentrations, etc. These phenomena had no prior explanation. Deficiencies in the model as a representation of solvation in aqueous solution are discussed in the appendix.
It is shown in the appendix that the derivatives of the excess free energy of a macromolecule in solution, with respect to the activities of other solution components, lead to fluctuation and linkage relations among these other components. Solution fluctuation theory is used, but it is specialized to the fluctuations and correlations associated with the presence of a macromolecule, and is developed with a modified ensemble. The relations of the appendix are used to analyze the interaction of two solution components, A and B, with the macromolecule and with one another. Three cases are considered: (1) A and B are ligands that bind stoichiometrically to the macromolecule. This case reduces to Wyman's binding polynomial analysis. (2) A and B are two substances at high concentration that interact selectively with the macromolecule. (3) A is a species that binds stoichiometrically to the macromolecule, while B is a component at high concentration that interacts weakly with the macromolecule.
The mutant protein I3C-C97/C54T of phage T4 lysozyme is free of sulfhydryl groups and has a genetically engineered disulfide bridge between positions 3 and 97 (Perry & Wetzel, 1986). This protein has a maximum stability at 12 degrees C in 3 M guanidinium chloride and undergoes reversible high- and low-temperature melting at 28 and -3 degrees C, respectively, in this medium. The free energy of stabilization of the protein has been studied over a range of temperature that includes both melting transitions. The stability curve fits a constant delta Cp model over the entire range, permitting an unusually complete determination of the thermodynamic parameters of the protein and demonstrating that the low-temperature unfolded form of the protein may be interpreted as an extrapolation with constant delta Cp of the high-temperature unfolded form. The free energy of unfolding is a linear function of guanidinium concentration within experimental error which permits a rough estimate of the stability of the protein at low temperatures and of the differential interaction of the unfolded protein with guanidinium chloride. These equilibrium studies provide a basis for the interpretation of the kinetic studies reported in the following paper.
A disulfide-bridged variant of bacteriophage T4 lysozyme has been found to undergo a low- as well as high-temperature unfolding transition in guanidinium chloride [see Chen and Schellman (1989)]. The kinetics for this process have been followed for several temperatures, a range of guanidinium chloride concentrations, and a number of values of pH. Microscopic rate constants for protein unfolding and refolding were extracted from these data to explore the nature of the cold unfolding transition. The data were interpreted using transition-state theory. It was found that the Arrhenius energy is temperature dependent. The transition state is characterized by (1) a high energy and low entropy compared to the native state, (2) a heat capacity which is closer to the native state than to the unfolded state, and (3) a low exposure to solvent compared to the unfolded state, as judged by its interaction with guanidinium chloride. With increasing concentration of guanidinium chloride, the low-temperature unfolding rate increases strongly, and the refolding rate decreases very strongly.
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The polyamines spermidine, spermine and putrescine are now known to induce tertiary collapse of DNA. In this collapsed state DNA assumes a compact toroidal conformation. However, the structural details of DNA in these compact particles and the forces that stabilize the collapsed state are not clear. We show here that the structural arrangement of DNA in this tertiary conformation is determined by the chemical structure of the agent used to collapse. We have used aliphatic triamines (NH+3--(CH2)3--NH+2--(CH2)n--NH+3 with n = 3, 4, 5 and 8) and diamines (NH+3--(CH2)x--NH+3 with x = 2, 3, 4 and 6) to collapse DNA. We find that the Bragg spacing and the calculated interhelical spacing for a hexagonal packing model vary systematically with the length of the methylene bridge. We also find that the ionic strength of the solution has no effect on the Bragg spacing. This observation suggests that the arrangement of DNA strands in the complexes is determined by the structure of the polycation, and argues against suggestions that the structure of the collapsed state is maintained by the balance of long-range electrostatic repulsive and attractive forces. Instead we propose that DNA helices form a hexagonal array with counterions in the interstices between the helices resulting in a stable three-dimensional phase with high structural order. Arguments are presented favoring such a model in terms of stabilizing and destabilizing thermodynamic forces.
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