Calculating Kinetic Rates and Membrane Permeability from Biased Simulations

We present a simple approach to calculate the kinetic properties of lipid membrane crossing processes from biased molecular dynamics simulations. We demonstrate that by using biased simulations, one can obtain highly accurate kinetic information with significantly reduced computational time with respect to unbiased simulations. We describe how to conveniently calculate the transition rates to enter, cross, and exit the membrane in terms of the mean first passage times. To obtain free energy barriers and relaxation times from biased simulations only, we constructed Markov models using the dynamic histogram analysis method (DHAM). The permeability coefficients that are calculated from the relaxation times are found to correlate highly with experimentally evaluated values. We show that more generally, certain calculated kinetic properties linked to the crossing of the membrane layer (e.g., barrier height and barrier crossing rates) are good indicators of ordering drugs by permeability. Extending the analysis to a 2D Markov model provides a physical description of the membrane crossing mechanism.