Calculating diffusion and permeability coefficients with the oscillating forward-reverse method.

The forward-reverse or FR method is an efficient bidirectional work method for determining the potential of mean force w(z) and also supposedly gives in principle the position-dependent diffusion coefficient D(z). Results from a variation called the OFR (oscillating FR) method suggest inconsistencies in the D(z) values when calculated as prescribed by the FR method. A new steering protocol has thus been developed and applied to the OFR method for the accurate determination of D(z) and also provides greater convergence for w(z) in molecular dynamics simulations. The bulk diffusion coefficient for water was found to be (6.03±0.16)×10(-5) cm2/s at 350 K with system size dependence within the statistical error bars. Using this steering protocol, D(z) and w(z) for water permeating a dipalmitoylphosphatidylcholine (DPPC) bilayer were determined. The potential of mean force is shown to have a barrier of peak height, wmax/(kBT)=8.4, with a width of about 10 Å on either side from the membrane center. The diffusion constant is shown to be highest in the core region of the membrane [peak value ∼(8.0±0.8)×10(-5) cm2/s], lowest in the head-group region [minimum value ∼(2.0±0.3)×10(-5) cm2/s], and to tend toward the bulk value as the water molecule leaves the membrane. The permeability coefficient P for H2O in DPPC was determined using the simulated D(z) and w(z) to give values of (0.129±0.075) cm/s at 323 K and (0.141±0.043) cm/s at 350 K. The results show more spatial detail than results presented in previous work while reducing the computational and user effort.