Molecular Dynamics and Free Energy on Mandelate Racemase

In the current chapter we carry out molecular simulations to calculate the free energy profile corresponding to the mandelate racemization in Mandelate Racemase enzyme.

During the last years, there has been much effort towards the efficient calculation of free energy differences in condensed phase systems. Among the different possibilities, the so-called Potential of Mean Force (PMF) is the magnitude applied to enzymatic reactivity in order to elucidate the reaction mechanism and for predicting the rates of chemical processes. The PMF is obtained using molecular dynamics or Monte Carlo sampling methods, but many aspects in the simulation technique still require an improvement to avoid sources of error and to go beyond the qualitative results. For instance, an adequate potential energy is always required, the length of the sampling must be large enough to ensure an adequate exploration. In addition, the PMF must be performed along a distinguished coordinate (reaction coordinate) from reactant to product region, that must be known a priori and capable to adequately describe the reaction. The choice of the reaction coordinate will play a central role in the discussion of the present chapter.

We will calculate the PMF using the information about the racemization reaction acquired in the preceeding chapters by means of optimization methods. In particular, the reaction path obtained previously will be a helpful guide for obtaining the PMF, mainly in the crucial choice of an adequate distinguished reaction coordinate to be used in the PMF calculation.

From the chemical point of view, we will see the influence of the inclusion of temperature effects, and whether it makes the free energy profile very different from the potential energy profile or not. The PMF will be also obtained for the N197A mutant in order to explain the lower enzymatic activity observed in the mutagenesis experiment [223].

Many chemical steps in enzymatic reactions are proton transfers or nucleophilic substitutions. The geometrical reaction coordinate of these type of reactions can be well described by the difference between the bond breaking and bond forming distances $r_c=r_{form}-r_{break}$.

We saw that Mandelate Racemase enzyme catalyzes the mandelate substrate racemization through three different mechanisms. We found that the most favorable path is mechanism III which potential energy profile is depicted in figure 4.1. Unlike many other reactions, mechanism III cannot be described by a unique bond breaking / bond forming process. As we commented in the preceeding chapters, the central configuration inversion step is accompanied by two asynchronous proton transfers through the acid-base catalytic residues Lys166 and His297. We will see that the shallow minima, represented in figure 4.1 by Is and Ir, are not minima in the free energy profile computed in the present chapter. Therefore mechanism III might be seen as a concerted mechanism, although rather asynchronous, where there exist two proton transfers and a configuration inversion of the stereogenic center. In conclusion, in order to compute the PMF of this mechanism the geometrical reaction coordinate must describe the concerted process contemplating the different chemical changes already observed by optimization techniques.

Figure 4.1: Potential energy profile found for Mechanism III in the racemization of mandelate substrate by means of optimization methods