Membrane permeability of small molecules from unbiased molecular dynamics simulations

Abstract

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 maximumlikelihood 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 Nose-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.

O2 permeability of lipid bilayers is low, but increases with membrane cholesterol

“…As discussed in detail below, the present results are greatly at variance with P O2 values of lipid bilayers reported from several ESR measurements [ 11 ] and MD simulations [ 12 , 13 , 18 – 20 ] by one to four orders of magnitude. In addition, we find that membrane cholesterol increases P O2 , whereas with ESR [ 11 ] and MD simulations [ 20 , 21 ], a moderate decrease in P O2 is observed.…”

“…However, it has been shown in much detail, e.g. by molecular dynamics simulations, that the lipid bilayer is highly inhomogeneous with respect to free energy, O 2 solubility and diffusivity [ 12 , 13 , 18 , 19 ]. Our data shed no light on these intra-membrane properties.…”

“…In recent years, however, this assumption has been rebutted by several studies, at least for carbon dioxide, for which it has been shown that membranes can present a significant diffusion resistance that drastically rises with higher cholesterol levels in the membrane [1][2][3][4][5][6], and on the other hand, can be greatly alleviated by the incorporation of protein gas channels such as aquaporin-1 or Rhesus-associated glycoprotein [2,[7][8][9][10]. In the case of the permeation of oxygen across membranes, current data mainly obtained from ESR spin label studies [11], or other indirect biophysical techniques such as fluorescence quenching and molecular dynamics (MD) simulations [12][13][14] have reported for liposomes extremely high permeabilities of 20-125 cm/s that would physiologically amount to zero resistance in the case of a cell membrane. O 2 permeabilities between 10 and 100 cm/s are shown at the end of this paper to exert no detectable influence on the deoxygenation kinetics of red cells.…”

Membrane thickness, lipid phase and sterol type are determining factors in the permeability of membranes to small solutes

“…The permeation dynamics is assumed to be diffusive in the ISD model. Deviations from such an assumption may lead to inaccurate estimates of the permeability coefficients for permeants that interact strongly with one another or with the membrane 67,68 . Also, for higher concentrations, the ISD model does not capture the collective behavior of the permeating solute and its effects on the membrane.…”

“…However, for compounds at low concentrations the estimates of the permeability coefficients from the ISD model are comparable to the unbiased estimates from transition-based counting 68 . Further studies on the permeability of small solutes through lipid membranes and the ISD in various scenarios are provided in the references 16,[67][68][69][70] .…”