Free-energy landscapes and thermodynamic parameters of complex molecules from nonequilibrium simulation trajectories

Thermodynamic parameters such as free energies and heat capacities are important quantities for understanding processes involving structural transitions in complex molecules such as proteins. Computational investigations provide simulated data that can be used for calculating thermodynamic parameters. However, calculations give accurate results only if the simulations sample all of configuration space with the appropriate temperature-dependent Boltzmann equilibrium probabilities. For many systems, truly comprehensive sampling of configuration space is not computationally feasible. We present an approximation technique for the calculations that will give accurate values for thermodynamic parameters when the data is incomplete. Our work is applicable to systems in which there are two distinct, important regions of configuration space that must be sampled. Importantly, the results are also valid when the system is more complex than two-state systems. Transition pathways that involve intermediate configurations between two stable regions are allowed in this treatment, and therefore the results are valid for multistate systems.