Computer Simulations of the Temperature Dependence of Enzyme Reactions

Abstract

In this review we discuss the development of methodology for calculating the temperature dependence and thermodynamic activation parameters for chemical reactions in solution and in enzymes, from computer simulations. We outline how this is done by combining the empirical valence bond method with molecular dynamics free energy simulations. In favorable cases it turns out that such simulations can even capture temperature optima for the catalytic rate. The approach turns out be very useful both for addressing questions regarding the roles of enthalpic and entropic effects in specific enzymes and also for attacking evolutionary problems regarding enzyme adaptation to different temperature regimes. In the latter case, we focus on cold-adaptation of enzymes from psychrophilic species and show how computer simulations have revealed the basic mechanisms behind such adaptation. Understanding these mechanisms also opens up the possibility of designing the temperature dependence, and we highlight a recent example of this.

Figure 1

(a) The rearrangement of chorismate to prephenate catalyzed by the chorismate mutase. (b) Calculated reaction free energy profiles for uncatalyzed reaction in water (red) and for the B. subtilis chorismate mutase catalyzed reaction (blue) at 25 °C. The generalized reaction coordinate Δε is the energy gap between the two diabatic potentials for reactant and product.^, (c) Computed Arrhenius plots for the two reactions from MD/EVB simulations at six temperatures.

Figure 2

(a) Optimized transition-state structure for the reference reaction in water from DFT calculations (atoms marked with asterisks were fixed). (b) Calculated reaction free energy profiles for the reference reaction in water (red) and the reaction catalyzed by the cold-adapted α-amylase AHA (blue).

Figure 3

Three different ways in which an enzyme (enz) could reduce the entropy penalty compared to the uncatalyzed water reaction (wat). (a) If the entropy penalty of the uncatalyzed water reaction () is dominated by reorientation of the substrates, then the enzyme could pay the penalty already when binding them in a reactive orientation ( and ). (b) If is dominated by reorientation of water molecules, then the enzyme could bind the substrates in a preorganized active site that does not need reorientation of the protein dipoles (). (c) If the uncatalyzed reaction has similarly small charge separation in the reactant and transition states, then the enzyme could yield a favorable activation entropy by stabilizing a more polar reactant state, causing a relaxation of the aligned protein dipoles in the transition state ().

Figure 4

(a) Illustration of how an unfolding equilibrium naturally leads to a rate optimum with T_opt close to T_m. (b) Illustration of how the temperature dependence of a hypothetical reaction with a free energy barrier of 15 kcal/mol at 25° is altered when enthalpy contribution is changed from 20 kcal/mol (red curve) to 10 kcal/mol (blue curve), with an opposing change in entropy contribution of 10 kcal/mol.

Figure 5

(a) Calculated Arrhenius plots for arctic salmon (blue) and bovine (red) trypsins. (b) Illustration of the concept of a softer protein potential in cold-adapted enzymes. The effective potential for displacing the protein coordinates from their reactant minimum to that of the TS is characterized by a smaller force constant than in the warm-active enzyme. (c) Calculated backbone RMSF averaged per residue for salmon (blue) and bovine (red) trypsins. (d) Calculated backbone RMSF averaged per residue for salmon (blue) and porcine (red) elastases. Mutated loops are indicated.

Figure 6

(a) Calculated Arrhenius plots for the reactions catalyzed by the α-amylases AHA (blue/green) and PPA (red). (b) Calculated T-dependence of the relative rate constants k_cat for AHA (blue) and PPA (red). (c) Average MD structures of active (ES) inactive (ES′) reactant states in AHA with H-bonds between Asp264 and the substrate indicated.

Figure 7

Calculated probability densities for the Asp264-substrate distance as a function of temperature for the (a) cold-adapted AHA and (b) warm-active PPA α-amylases. (c) Calculated average backbone RMSF per residue in the reactant state at 298 K for sequence region comprising the β7-α7 loop for AHA (blue) and PPA (red). PPA numbering is used due to sequence insertions.

Figure 8

(a) Free energy diagram for the AHA reaction in the temperature range 283 K (blue) to 323 K (red). (b) Temperature dependence of the apparent activation enthalpy and entropy contributions obtained from the scheme of eq 3. (c) The corresponding activation heat capacity as a function of temperature.

Figure 9

(a) View of the loop region following the universally conserved His-Asp motif in AHA (cyan/blue) and PPA (yellow/red). The catalytic residues Asp174 and Glu200 are also shown. (b) Mutated residues in the chimeric variants that interact with the β7-α7 loop.