Virtual states introduced for overcoming entropic barriers in conformational space

Free-energy landscape is an important quantity to study large-scale motions of a biomolecular system because it maps possible pathways for the motions. When the landscape consists of thermodynamically stable states (low-energy basins), which are connected by narrow conformational pathways (i.e., bottlenecks), the narrowness slows the inter-basin round trips in conformational sampling. This results in inaccuracy of free energies for the basins. This difficulty is not cleared out even when an enhanced conformational sampling is fairly performed along a reaction coordinate. In this study, to enhance the inter-basin round trips we introduced a virtual state that covers the narrow pathways. The probability distribution function for the virtual state was controlled based on detailed balance condition for the inter-state transitions (transitions between the real-state basins and the virtual state). To mimic the free-energy landscape of a real biological system, we introduced a simple model where a wall separates two basins and a narrow hole is pierced in the wall to connect the basins. The sampling was done based on Monte Carlo (MC). We examined several hole-sizes and inter-state transition probabilities. For a small hole-size, a small inter-state transition probability produced a sampling efficiency 100 times higher than a conventional MC does. This result goes against ones intuition, because one considers generally that the sampling efficiency increases with increasing the transition probability. The present method is readily applicable to enhanced conformational sampling such as multi-canonical or adaptive umbrella sampling, and extendable to molecular dynamics.