The dependence of enzyme activity on temperature: determination and validation of parameters

Abstract

Traditionally, the dependence of enzyme activity on temperature has been described by a model consisting of two processes: the catalytic reaction defined by DeltaG(Dagger)(cat), and irreversible inactivation defined by DeltaG(Dagger)(inact). However, such a model does not account for the observed temperature-dependent behaviour of enzymes, and a new model has been developed and validated. This model (the Equilibrium Model) describes a new mechanism by which enzymes lose activity at high temperatures, by including an inactive form of the enzyme (E(inact)) that is in reversible equilibrium with the active form (E(act)); it is the inactive form that undergoes irreversible thermal inactivation to the thermally denatured state. This equilibrium is described by an equilibrium constant whose temperature-dependence is characterized in terms of the enthalpy of the equilibrium, DeltaH(eq), and a new thermal parameter, T(eq), which is the temperature at which the concentrations of E(act) and E(inact) are equal; T(eq) may therefore be regarded as the thermal equivalent of K(m). Characterization of an enzyme with respect to its temperature-dependent behaviour must therefore include a determination of these intrinsic properties. The Equilibrium Model has major implications for enzymology, biotechnology and understanding the evolution of enzymes. The present study presents a new direct data-fitting method based on fitting progress curves directly to the Equilibrium Model, and assesses the robustness of this procedure and the effect of assay data on the accurate determination of T(eq) and its associated parameters. It also describes simpler experimental methods for their determination than have been previously available, including those required for the application of the Equilibrium Model to non-ideal enzyme reactions.

Figure 1. The temperature-dependence of enzyme activity

(A) Experimental data for alkaline phosphatase. The enzyme was assayed as described by Peterson et al. [2], and the data were smoothed as described here in the Experimental section; the data are plotted as rate (μM·s⁻¹) against temperature (K) against time during assay (s). (B) The result of fitting the experimental data for alkaline phosphatase to the Equilibrium Model. Parameter values derived from this fitting are: ΔG‡_cat, 57 kJ·mol⁻¹; ΔG‡_inact, 97 kJ·mol⁻¹; ΔH_eq, 86 kJ·mol⁻¹; T_eq, 333 K [2]. (C) The result of running a simulation of the Classical Model using the values of ΔG‡_cat and ΔG‡_inact derived from the fitting described above. The experimental data itself cannot be fitted to the Classical Model.

Figure 2. The effect of temperature on the initial (zero-time) rate of reaction of acid phosphatase

Acid phosphatase was assayed continuously as described by Peterson et al. [2]. For each triplicate progress curve, the initial rate of reaction was determined using the linear search function in the programme, Vision32™. The data are plotted as rate (μM·s⁻¹) against temperature (K).

Figure 3. Data sampling requirements: the effect of data points beyond T_opt

Acid phosphatase was assayed as described by Peterson et al. [2]. Temperature points above the T_opt (see Figure 2) were sequentially truncated from the complete data set to determine the influence of data points above the T_opt on the final parameter values. Illustrated here are the results plotted as rate (μM·s⁻¹) against temperature (K) against time (s) for the fit of acid phosphatase data to the Equilibrium Model using (A) the full data set, (B) the data set excluding the last data point, (C) the data set excluding the last two data points, and (D) the data set excluding the last three data points.