Fluctuation relations to calculate protein redox potentials from molecular dynamics simulations

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.