One of the critical variables that determine the rate of any reaction is temperature. For biological systems, the effects of temperature are convoluted with myriad (and often opposing) contributions from enzyme catalysis, protein stability, and temperature-dependent regulation, for example. We have coined the phrase "macromolecular rate theory (MMRT)" to describe the temperature dependence of enzyme-catalyzed rates independent of stability or regulatory processes. Central to MMRT is the observation that enzyme-catalyzed reactions occur with significant values of ΔCp(‡) that are in general negative. That is, the heat capacity (Cp) for the enzyme-substrate complex is generally larger than the Cp for the enzyme-transition state complex. Consistent with a classical description of enzyme catalysis, a negative value for ΔCp(‡) is the result of the enzyme binding relatively weakly to the substrate and very tightly to the transition state. This observation of negative ΔCp(‡) has important implications for the temperature dependence of enzyme-catalyzed rates. Here, we lay out the fundamentals of MMRT. We present a number of hypotheses that arise directly from MMRT including a theoretical justification for the large size of enzymes and the basis for their optimum temperatures. We rationalize the behavior of psychrophilic enzymes and describe a "psychrophilic trap" which places limits on the evolution of enzymes in low temperature environments. One of the defining characteristics of biology is catalysis of chemical reactions by enzymes, and enzymes drive much of metabolism. Therefore, we also expect to see characteristics of MMRT at the level of cells, whole organisms, and even ecosystems.

The increase in enzymatic rates with temperature up to an optimum temperature (Topt) is widely attributed to classical Arrhenius behavior, with the decrease in enzymatic rates above Topt ascribed to protein denaturation and/or aggregation. This account persists despite many investigators noting that denaturation is insufficient to explain the decline in enzymatic rates above Topt. Here we show that it is the change in heat capacity associated with enzyme catalysis (ΔC(‡)p) and its effect on the temperature dependence of ΔG(‡) that determines the temperature dependence of enzyme activity. Through mutagenesis, we demonstrate that the Topt of an enzyme is correlated with ΔC(‡)p and that changes to ΔC(‡)p are sufficient to change Topt without affecting the catalytic rate. Furthermore, using X-ray crystallography and molecular dynamics simulations we reveal the molecular details underpinning these changes in ΔC(‡)p. The influence of ΔC(‡)p on enzymatic rates has implications for the temperature dependence of biological rates from enzymes to ecosystems.

We have determined the pKA values of the 12 carboxyl residues in the native and denatured state of barnase by a combination of thermodynamic measurements on mutants of charged residues and NMR titration data. The pKA values of the 11 residues titrating under folding conditions (above pH 2.2) were determined by two-dimensional 1H NMR. The pKA value of the remaining residue, Asp 93 which forms a salt link with Arg 69 and titrates at much lower pH values, was determined by changes in the pH dependence of the stability of the protein upon mutation to Asn: pKAsp93A at low ionic strength (50 mM) and pKAsp93A at high ionic strength (600 mM). The overall titration of the native state is nonideal, and the protein retains fractionally ionized residues other than Asp 93 throughout the experimental pH range of 0.2-6.3. Protonation events taking place at pH values below 2 were further characterized by the pH dependence of the unfolding kinetics of wild-type and charge-mutant proteins. By comparing the observed pH dependence of the protein stability with that calculated from the pKA values for the native protein, we demonstrate that the pKA values of the denatured state are significantly lower than those reported for model compounds: the pKA values of the denatured state appear on average 0.4 units lower than previous estimates in the presence of chemical denaturant. The results have direct implications for calculations of the energetics of proton equilibria and suggest that the acid/thermally denatured state is not an extended coil where the residues are isolated from one another by the intervening solvent but is compact and involves intramolecular charge repulsion.

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