Study on the Application of the Combination of TMD Simulation and Umbrella Sampling in PMF Calculation for Molecular Conformational Transitions

Free energy calculations of the potential of mean force (PMF) based on the combination of targeted molecular dynamics (TMD) simulations and umbrella samplings as a function of physical coordinates have been applied to explore the detailed pathways and the corresponding free energy profiles for the conformational transition processes of the butane molecule and the 35-residue villin headpiece subdomain (HP35). The accurate PMF profiles for describing the dihedral rotation of butane under both coordinates of dihedral rotation and root mean square deviation (RMSD) variation were obtained based on the different umbrella samplings from the same TMD simulations. The initial structures for the umbrella samplings can be conveniently selected from the TMD trajectories. For the application of this computational method in the unfolding process of the HP35 protein, the PMF calculation along with the coordinate of the radius of gyration (Rg) presents the gradual increase of free energies by about 1 kcal/mol with the energy fluctuations. The feature of conformational transition for the unfolding process of the HP35 protein shows that the spherical structure extends and the middle α-helix unfolds firstly, followed by the unfolding of other α-helices. The computational method for the PMF calculations based on the combination of TMD simulations and umbrella samplings provided a valuable strategy in investigating detailed conformational transition pathways for other allosteric processes.