This paper explores the impact of pH on the mechanism of reversible disulfide bond (CysS-SCys) reductive breaking and oxidative formation in Escherichia coli hydrogenase maturation factor HypD, a protein which forms a highly stable adsorbed film on a graphite electrode. To achieve this, low frequency (8.96 Hz) Fourier transformed alternating current voltammetric (FTACV) experimental data was used in combination with modelling approaches based on Butler-Volmer theory with a dual polynomial capacitance model, utilizing an automated two-step fitting process conducted within a Bayesian framework. We previously showed that at pH 6.0 the protein data is best modelled by a redox reaction of two separate, stepwise one-electron, one-proton transfers with slightly “crossed” apparent reduction potentials that incorporate electron and proton transfer terms (Eapp20 > Eapp10). Remarkably, rather than collapsing to a concerted two-electron redox reaction at more extreme pH, the same two-stepwise one-electron transfer model with Eapp20 > Eapp10 continues to provide the best fit to FTACV data measured across a proton concentration range from pH 4.0 to pH 9.0. A similar, small level of crossover in reversible potentials is also displayed in overall two-electron transitions in other proteins and enzymes, and this provides access to a small but finite amount of the one electron reduced intermediate state.

Models of ionic currents or of the cardiac action potential (AP) are frequently calibrated by defining an error function that quantifies the mismatch between simulations and data, and using numerical optimisation to find the parameter values that minimise this function. Many optimisation algorithms assume knowledge of the derivatives of the error function with respect to the parameters, but for models formulated as differential equations these are typically unknown.In this study we extend our simulation tool, Myokit, with the capability to rapidly calculate derivatives of simulation output and couple it to our inference tool, PINTS, to calculate the derivatives of the error function. We measure the added overhead of the sensitivity calculations in a model of the ion current I Kr and in a model of a stem-cell AP. Next we compare the performance of a state-of-the art derivative-free optimiser with that of a popular derivativeusing method. For both problems, the derivative-based method requires fewer function evaluations, but this is offset by a significant increase in the computational cost of each evaluation. The derivative-free method is much faster for the I Kr case, while the derivative-using method outperforms on the AP case. However, the derivative-free method is more robust on both problems: providing the correct answer on a greater percentage of runs.