Recovering biological electron transfer reaction parameters from multiple protein film voltammetric techniques informed by Bayesian inference

Abstract

Deciphering the mechanism, kinetics and energetics of biological electron-transfer reactions requires a robust, rapid and reproducible protein-film voltammetry information recovery process. Here we describe a semi-automated computational approach for inferring the chemical reaction parameters for a simple protein system, a bacterial cytochrome domain from Cellvibrio japonicus that displays reversible one-electron Fe2+/3+ redox chemistry. Despite the relative simplicity of the experimental system, developing a robust data analysis approach to find the global optimum in 13-dimensional parameter space is a challenging task because the Faradaic-to-background current ratio in such experiments is often low. We describe how a multiple-technique approach, whereby data from three voltammetry techniques (direct-current, pure sinusoidal and Fourier transform alternating current voltammetry) is combined, ultimately enables the automatic extraction of both (i) quantitative “best-fit” redox reaction parameter point values that are robust across multiple experiments performed on different protein-electrode films, and (ii) a statistical description of parameter correlation relationships, along with uncertainty in the individual parameter values, obtained using Bayesian inference. It is the latter achievement which is particularly important as it represents a method for visualising the possible limitations in the mathematical model of the experimental system. Our multi-voltammetry analysis approach enables such powerful insight because of the complementarity between the information content, simulation-speed and parameter sensitivity of the current–time data generated by the different techniques, illustrating the value of adding purely sinusoidal voltammetry to the bioelectrochemistry measurement toolkit.