HEAT CAPACITY IN PROTEINS
Annual review of physical chemistry (Print)
Key Words hydrophobic effect, entropy-enthalpy compensation, protein stability, protein hydration ■ Abstract Heat capacity (Cp) is one of several major thermodynamic quantities commonly measured in proteins. With more than half a dozen definitions, it is the hardest of these quantities to understand in physical terms, but the richest in insight. There are many ramifications of observed Cp changes: The sign distinguishes apolar from polar solvation. It imparts a temperature (T) dependence to
... ) dependence to entropy and enthalpy that may change their signs and which of them dominate. Protein unfolding usually has a positive Cp, producing a maximum in stability and sometimes cold denaturation. There are two heat capacity contributions, from hydration and protein-protein interactions; which dominates in folding and binding is an open question. Theoretical work to date has dealt mostly with the hydration term and can account, at least semiquantitatively, for the major Cp-related features: the positive and negative Cp of hydration for apolar and polar groups, respectively; the convergence of apolar group hydration entropy at T ≈ 112 • C; the decrease in apolar hydration Cp with increasing T; and the T-maximum in protein stability and cold denaturation. 0066-426X/05/0505-0521$20.00 521 Annu. Rev. Phys. Chem. 2005.56:521-548. Downloaded from www.annualreviews.org by University of California -San Francisco UCSF on 10/13/14. For personal use only. 522 PRABHU SHARP changes. With these tools at the disposal of biophysicists and biochemists, the output of heat capacity data on proteins has steadily increased. Most heat capacity data are collected at constant pressure, yielding Cp. Constant volume heat capacity (Cv) data are much rarer in the protein field. In addition, at 1 Atm PV (P = Pressure, V = Volume) changes in protein reactions are usually very small compared with kT (thermal energy, where k is the Boltzmann constant, and T the absolute temperature). In this review, we refer almost exclusively to Cp and for brevity use enthalpy (H) and mean energy (E) interchangeably. Cp is one of the five major thermodynamic quantities commonly tabulated in biophysical studies on proteins; the others are Gibbs free energy (G), enthalpy, entropy (S), and volume. Of course, these data are not an end in themselves, but they are measured with the aim of providing physical, mechanistic, even atomiclevel insight into how proteins fold, how they are stabilized, and how they function. In some respects, which we outline below, Cp is both the richest potential source of this insight and the hardest of the five thermodynamic quantities to understand in physical terms. Volume is by definition a physical quantity and straightforward to understand, although there are some subtleties in defining the volume of a protein in solution. Enthalpy is a direct measure of heat or energy, whereas entropy quantifies the "disorder" or number of configurations available to the system. Free energy has a direct relationship to a primary observable, the equilibrium constant K, through G = −kT ln K, which describes the balance between enthalpy and entropy. In our experience, however, heat capacity is less intuitively understood. Why should one protein or protein state be able to absorb more heat than another for the same increase in T? What is the physical origin of Cp differences? In this review, we first provide a short theoretical overview of heat capacity and then discuss some theoretical and experimental papers. Our goal is not to be exhaustive either in the theoretical overview or in the literature review, but rather to provide, through some background and simple models, physical intuition about Cp that can be used to parse experimental measurements; to indicate the many potential ramifications of Cp changes observed in the literature; and to focus on some experimental and theoretical studies that, in our view, elucidate physical origins and fundamental aspects of heat capacity changes in proteins. Space limitations preclude discussion of many studies of particular protein systems and tabulations of heat capacity data. Furthermore, our focus is on physical aspects rather than on applications.