Abstract
CoCo ("complementary coordinates") is a method for ensemble enrichment based on principal component analysis (PCA) that was developed originally for the investigation of NMR data. Here we investigate the potential of the CoCo method, in combination with molecular dynamics simulations (CoCo-MD), to be used more generally for the enhanced sampling of conformational space. Using the alanine penta-peptide as a model system, we find that an iterative workflow, interleaving short multiple-walker MD simulations with long-range jumps through conformational space informed by CoCo analysis, can increase the rate of sampling of conformational space up to 10 times for the same computational effort (total number of MD timesteps). Combined with the reservoir-REMD method, free energies can be readily calculated. An alternative, approximate but fast and practically useful, alternative approach to unbiasing CoCo-MD generated data is also described. Applied to cyclosporine A, we can achieve far greater conformational sampling than has been reported previously, using a fraction of the computational resource. Simulations of the maltose binding protein, begun from the "open" state, effectively sample the "closed" conformation associated with ligand binding. The PCA-based approach means that optimal collective variables to enhance sampling need not be defined in advance by the user but are identified automatically and are adaptive, responding to the characteristics of the developing ensemble. In addition, the approach does not require any adaptations to the associated MD code and is compatible with any conventional MD package.
Highlights
The procedure to correct, approximately, for the biased sampling produced by the CoCoMD method is as follows: 1. For each member of the ensemble, we obtain the coordinates in a principal component subspace, and the potential energy
If it has an energy that corresponds to a bin in the potential energy histogram that has a count less than the target value, the member is added to the new ensemble, and the population count in that bin is increased by one
The apparent 2D and 1D free energy surfaces from this biased sampling is shown in Figure S2e and S2f
Summary
; Output frequency and precision for .xtc file nstxout-compressed ; Separate tables between energy group pairs energygrp-table ; Pairs of energy groups for which all non-bonded interactions are excluded energygrp-excl b) Example MD input file for AMBER simulations: 10ns simulation of alanine pentapeptide &cntrl imin=0, ntx=1, ntpr=1000, ntwr=1000, ntwx=500, nstlim=5000000, dt=0.002, ntt=3, ig=-1, gamma_ln=5.0, ntc=2, ntf=2, ntb=2, cut=9.0, ntp=1, taup=2.0, &end c) Flowchart for the CoCo-MD method.
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