Pressure Dependence of Protein Electron Transfer Reactions: Theory and Simulation

Pressure dependence of protein electron transfer rate constant is discussed. The rate constant is given as a
product of two factors; electronic factor (electron tunneling matrix) and nuclear factor (Franck−Condon factor).
Pressure affects the rate through both of these two factors. We analyzed effects of pressure on these two
factors individually. The pressure dependence of the electronic factor is discussed by considering the dependence
of through-space gaps in the tunneling pathway model. The effect of pressure on the nuclear factor is discussed
in terms of the Marcus expression of the Franck−Condon factor and the pressure dependence of the two
parameters, reorganization energy λ and reaction free energy ΔG, in it. We show that the dependence of λ is
generally smaller than that of ΔG. To obtain a more quantitative picture, we carry out an analysis of pressure
dependence of through-space gaps and ΔG by normal mode simulation on cytochrome c. In light of the
results of these analyses, some experimental results in literature on pressure effects are discussed to identify
their relative causes.