Study of molecular processes through calculation of multidimensional free energy landscapes

The potential of mean force describing conformational changes of biomolecules is a central quantity for understanding the function of biomolecular systems. Calculating an energy landscape of a process that depends on three or more reaction coordinates requires extensive computational power, making some multi-dimensional calculations practically impossible. Here, I present an efficient automatized umbrella sampling strategy for calculating a multidimensional potential of mean force. The method progressively learns by itself, through a feedback mechanism, which regions of a multidimensional space are worth exploring and automatically generates a set of umbrella sampling windows that is adapted to the system. The self-learning adaptive umbrella sampling method is first explained with illustrative examples based on simplified reduced model systems and then applied to two nontrivial situations: the conformational equilibrium of the pentapeptide Met-enkephalin in solution and ion permeation in the KcsA potassium channel. With this method, it is demonstrated that a significant smaller number of umbrella windows needs to be employed to characterize the free energy landscape over the most relevant regions without any loss in accuracy.