  The tunable design of protein redox potentials promises to open a range of
applications in biotechnology and catalysis. Here we introduce a method to
calculate redox potential changes by combining fluctuation relations with
molecular dynamics simulations. It involves the simulation of reduced and
oxidized states, followed by the instantaneous conversion between them. Energy
differences introduced by the perturbations are obtained using the Kubo-Onsager
approach. Using a detailed fluctuation relation coupled with Bayesian
inference, these are post-processed into estimates for the redox potentials in
an efficient manner. This new method, denoted MD+CB, is tested on a de novo
four-helix bundle heme protein (the m4D2 `maquette') and five designed mutants,
including some mutants characterized experimentally in this work. The MD+CB
approach is found to perform reliably, giving redox potential shifts with
reasonably good correlation (0.85) to the experimental values for the mutants.
The MD+CB approach also compares well with redox potential shift predictions
using a continuum electrostatic method. The estimation method employed within
the MD+CB approach is straightforwardly transferable to standard equilibrium MD
simulations, and holds promise for redox protein engineering and design
applications.

Biological Physics;Statistical Mechanics;Computational Physics