AbstractA methodology is proposed for calculating multidimensional free-energy landscapes of molecular systems, based on post-hoc analysis of multiple molecular dynamics trajectories wherein adaptive biases are used to enhance the sampling of different collective variables. In this approach, which we refer to as Weighted Force Analysis Method (WFAM), sampling and biasing forces from all trajectories are suitably re-weighted and combined so as to obtain unbiased estimates of the mean force across collective-variable space; multidimensional free-energy surfaces and minimum-energy pathways are then derived from integration of the mean forces through kinetic Monte Carlo simulations. Numerical tests for trajectories of butyramide generated with standard and concurrent metadynamics, biased to sample one and two dihedral angles, respectively, demonstrate the correctness of the method and show that calculated mean forces and free energies converge rapidly. Analysis of bias-exchange metadynamics simulations of dialanine, trialanine and the SH2-SH3 domain-tandem of the Abl kinase, using up to six collective-variables, further demonstrate this approach greatly facilitates calculating accurate multidimensional free-energy landscapes from different trajectories and time-dependent biases, outperforming other post-hoc unbiasing methods.
Path collective variables for exploring free energy landscapes of molecular transitions
