Estimating permeabilities from biased molecular dynamics with a Green–Kubo formalism for transport across the blood-brain barrier

In this work, we explore the uses of biased sampling simulations including constant-velocity SMD (cv-SMD) and umbrella sampling to study molecular permeation of three highly distinct solutes spanning over 3 orders of magnitude in the permeability space, across a model of the blood-brain barrier (BBB). These molecules range from among the slowest permeants known (temozolomide; Papp ∼ 10–6 cm s–1) to among the fastest compound known (ethanol; Papp ∼ 10–3 cm s–1). We arrive at the transmembrane solute permeability, Psim, by the Inhomogeneous Solubility-Diffusion equation combined with an unbiasing procedure involving the Green–Kubo relations, to find a ∼1 order of magnitude agreement with experiments. We find that the converged thermodynamics of crossing span distinct topologies for each of the compounds considered, while noting that there is an apparent relationship between the thermodynamic barrier height (ΔG‡) and experimental permeability, Papp for these molecules.