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Permeability is a key property in various fields such as membrane technology for chemical separation and transport of substances through cell membranes. At the molecular scale, the counting method uses the number of membrane crossings in a conventional unbiased molecular dynamics simulation to predict the permeability. This contribution investigates under which conditions the counting method has insufficient statistics. An equation is derived for a compartmental model based on the inhomogeneous solubility–diffusion (Smoluchowski) model, giving insight into how the flux correlates with the solubility of permeants. This equation shows that a membrane crossing is a rare event not only when the membrane forms a large free energy barrier but also when the membrane forms a deep free energy well that traps permeants. Such a permeant trap has a high permeability; yet, the counting method suffers from poor statistics. To illustrate this, coarse-grained MD was run for 16 systems of dipalmitoylphosphatidylcholine bilayer membranes with different permeant types. The composition rule for permeability is shown to also hold for fluxes, and it is highlighted that the considered thickness of the membrane causes uncertainty in the permeability calculation of highly permeable membranes. In conclusion, a high permeability in itself is not an effective indicator of the sampling efficiency of the counting method, and caution should be taken for permeants whose solubility varies greatly over the simulation box. A practical consequence relevant in, e.g., drug design is that a drug with high membrane permeability might get trapped by membranes thus reducing its efficacy. [ABSTRACT FROM AUTHOR]

Permeation of many small molecules through lipid bilayers can be directly observed in molecular dynamics simulations on the nano- and microsecond timescale. While unbiased simulations provide an unobstructed view of the permeation process, their feasibility for computing permeability coefficients depends on various factors that differ for each permeant. The present work studies three small molecules for which unbiased simulations of permeation are feasible within less than a microsecond, one hydrophobic (oxygen), one hydrophilic (water), and one amphiphilic (ethanol). Permeabilities are computed using two approaches: counting methods and a maximum-likelihood estimation for the inhomogeneous solubility diffusion (ISD) model. Counting methods yield nearly model-free estimates of the permeability for all three permeants. While the ISD-based approach is reasonable for oxygen, it lacks precision for water due to insufficient sampling and results in misleading estimates for ethanol due to invalid model assumptions. It is also demonstrated that simulations using a Langevin thermostat with collision frequencies of 1/ps and 5/ps yield oxygen permeabilities and diffusion constants that are lower than those using Nosé–Hoover by statistically significant margins. In contrast, permeabilities from trajectories generated with Nosé–Hoover and the microcanonical ensemble do not show statistically significant differences. As molecular simulations become more affordable and accurate, calculation of permeability for an expanding range of molecules will be feasible using unbiased simulations. The present work summarizes theoretical underpinnings, identifies pitfalls, and develops best practices for such simulations. [ABSTRACT FROM AUTHOR]