Calculation of Heat Capacity Changes in Enzyme Catalysis and Ligand Binding

Abstract

It has been suggested that heat capacity changes in enzyme catalysis may be the underlying reason for temperature optima that are not related to unfolding of the enzyme. If this were to be a common phenomenon, it would have major implications for our interpretation of enzyme kinetics. In most cases, the support for the possible existence of a nonzero (negative) activation heat capacity, however, only relies on fitting such a kinetic model to experimental data. It is therefore of fundamental interest to try to use computer simulations to address this issue. One way is simply to calculate the temperature dependence of the activation free energy and determine whether the relationship is linear or not. An alternative approach is to calculate the absolute heat capacities of the reactant and transition states from plain molecular dynamics simulations using either the temperature derivative or fluctuation formula for the enthalpy. Here, we examine these different approaches for a designer enzyme with a temperature optimum that is not caused by unfolding. Benchmark calculations for the heat capacity of liquid water are first carried out using different thermostats. It is shown that the derivative formula for the heat capacity is generally the most robust and insensitive to the thermostat used and its parameters. The enzyme calculations using this method give results in agreement with direct calculations of activation free energies and show no sign of a negative activation heat capacity. We also provide a simple scheme for the calculation of binding heat capacity changes, which is of clear interest in ligand design, and demonstrate it for substrate binding to the designer enzyme. Neither in that case do the simulations predict any negative heat capacity change.

Figure 1

(a) Experimental k_cat versus temperature for the psychrophilic α-amylase, which was shown to be caused by an equilibrium with the inactive state ES′. This equilibrium is characterized by ΔH_eq(ES′ – ES) ∼ 30 kcal/mol and ΔS_eq(ES′ – ES) ∼ 0.11 kcal/mol/K and reflects breaking of an ionic interaction with the carbohydrate substrate at the T-optimum. The experimental data can also be fitted to eq 1, yielding a large negative ΔC_p^‡ = −0.98 kcal/mol/K, but such a model is incorrect in this case. (b) Experimental k_cat/K_M versus T for the Kemp eliminase. The ES′ state in the kinetic scheme was again identified by computer simulations. This data can be fitted either with a ΔC_p^‡ = −0.3 kcal/mol/K (relative to either ES, ES′, or E + S) or ΔC_p^bind = −0.3 kcal/mol/K or by all ΔC_p’s zero and a change of rate-limiting step from k₁ to k₃ at 35 °C.

Figure 2

Reaction scheme and calculated Arrhenius plot of ΔG^‡/T versus 1/T for the chemical step (k₃) in the 1A53-2.5 Kemp eliminase.

Figure 3

(a) Representative MD snapshots of the ES (yellow) and TS (cyan) structures used in the heat capacity calculations. Partially broken and formed bonds in the TS are denoted by dashed lines. (b) Model of the apo enzyme after 250 ps of MD equilibration, illustrating the entry of solvent replacing the substrate.

Figure 4

Plots of the average total energies (a) and total potential energies (b) for the reactant state (ES) and transition state (TS) from MD simulations.