Multidimensional Replica Exchange Simulations for Efficient Constant pH and Redox Potential Molecular Dynamics

Efficient computational methods that are capable of supporting experimental measures obtained at constant values of pH and redox potential are important tools as they serve to, among other things, provide additional atomic level information that cannot be obtained experimentally. Replica Exchange is an enhanced sampling technique that allows converged results to be obtained faster in comparison to regular molecular dynamics simulations. In this work we report the implementation, also available with GPU-accelerated code, of pH and redox potential (E) as options for multidimensional REMD simulations in AMBER. Previous publications have only reported multidimensional REMD simulations with the temperature and Hamiltonian dimensions. In this work results are shown for N-acetylmicroperoxidase-8 (NAcMP8) axially attached to a histidine peptide. This is a small system that contains only a single heme group. We compare results from E,pH-REMD, E,T-REMD, and E,T,pH-REMD to one-dimensional REMD simulations and to simulations without REMD. We show that two-dimensional REMD simulations improve sampling convergence in comparison to one-dimensional REMD simulations and that three-dimensional REMD further improves convergence in comparison to two-dimensional REMD simulations. Also, our computational benchmarks show that our multidimensional REMD calculations have a small and bearable computational performance, essentially the same as one-dimensional REMD. However, multidimensional REMD makes use of a significantly higher number of replicas because the number of replicas scales geometrically with the number of dimensions; therefore, more computational resources are required. In addition to the pH dependence on standard redox potential values and the redox potential dependence on p K_a values, we also investigate the influence of the temperature in our results. We observe an agreement between our computational results and purely theoretical predictions.