Temperature-Accelerated Sampling and Amplified Collective Motion with Adiabatic Reweighting to Obtain Canonical Distributions and Ensemble Averages.

Abstract

In molecular simulations, accelerated sampling can be achieved efficiently by raising the temperature of a small number of coordinates. For collective coordinates, the temperature-accelerated molecular dynamics method or TAMD has been previously proposed, in which the system is extended by introducing virtual variables that are coupled to these coordinates and simulated at higher temperatures (Maragliano, L.; Vanden-Eijnden, E. Chem. Phys. Lett.2005, 426, 168-175). In such accelerated simulations, steady state or equilibrium distributions may exist but deviate from the canonical Boltzmann one. We show that by assuming adiabatic decoupling between the subsystems simulated at different temperatures, correct canonical distributions and ensemble averages can be obtained through reweighting. The method makes use of the low-dimensional free energy surfaces that are estimated as Gaussian mixture probability densities through maximum likelihood and expectation maximization. Previously, we proposed the amplified collective motion method or ACM. The method employs the coarse-grained elastic network model or ANM to extract collective coordinates for accelerated sampling. Here, we combine the ideas of ACM and of TAMD to develop a general technique that can achieve canonical sampling through reweighting under the adiabatic approximation. To test the validity and accuracy of adiabatic reweighting, first we consider a single n-butane molecule in a canonical stochastic heat bath. Then, we use explicitly solvated alanine dipeptide and GB1 peptide as model systems to demonstrate the proposed approaches. With alanine dipeptide, it is shown that sampling can be accelerated by more than an order of magnitude with TAMD while correct distributions and canonical ensemble averages can be recovered, necessarily through adiabatic reweighting. For the GB1 peptide, the conformational distribution sampled by ACM-TAMD, after adiabatic reweighting, suggested that a normal simulation suffered significantly from insufficient sampling and that the reweighted ACM-TAMD distribution may present significant improvements over the normal simulation in representing the local conformational ensemble around the folded structure of GB1.