Abstract
Enzymes in biology’s energy chains operate with low energy input distributed through multiple electron transfer steps between protein active sites. The general challenge of biological design is how to lower the activation barrier without sacrificing a large negative reaction free energy. We show that this goal is achieved through a large polarizability of the active site. It is polarized by allowing a large number of excited states, which are populated quantum mechanically by electrostatic fluctuations of the protein and hydration water shells. This perspective is achieved by extensive mixed quantum mechanical/molecular dynamics simulations of the half reaction of reduction of cytochrome c. The barrier for electron transfer is consistently lowered by increasing the number of excited states included in the Hamiltonian of the active site diagonalized along the classical trajectory. We suggest that molecular polarizability, in addition to much studied electrostatics of permanent charges, is a key parameter to consider in order to understand how enzymes work.
Highlights
Enzymes in biology’s energy chains operate with low energy input distributed through multiple electron transfer steps between protein active sites
We introduce the ability of the electronic density of the heme in cytochrome c to redistribute in response to a thermal fluctuation of the bath
The choice of the level of QM calculations is dictated by the physics of the problem and, to a large degree, by the time-scale required to capture the essential collective modes of the thermal bath contributing to the activation barrier[45]
Summary
As more elastic modes enter the observation window (the length of the simulation trajectory), the reorganization energy grows nearly continuously through the range of time-scales up to tens of microseconds currently reached by simulations[32] Given these constraints imposed by the physics of the problem, a QM algorithm needs to capture the entire range of thermal motions sampled by classical simulations. X = EgOx − EgRed. The limit of classical simulations is obtained by representing the quantum center by a set of atomic charges coupled to the bath through the corresponding electrostatic potentials φα (Fig. 1C). The non-polarizable active site corresponds to ξ = 0 when coupling between the quantum states is turned off Even in this limit, the algorithms of calculating X are still somewhat different in the quantum and classical cases since we use an expansion of the potential in the quantum Hamiltonian in equation (6), in contrast to a full set of atomic charges in the classical.
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