jp6b02814_si_001.pdf (1.93 MB)
Two Relations to Estimate Membrane Permeability Using Milestoning
journal contribution
posted on 2016-05-06, 00:00 authored by Lane W. Votapka, Christopher T. Lee, Rommie E. AmaroPrediction
of passive permeation rates of solutes across lipid
bilayers is important to drug design, toxicology, and other biological
processes such as signaling. The inhomogeneous solubility-diffusion
(ISD) equation is traditionally used to relate the position-dependent
potential of mean force and diffusivity to the permeability coefficient.
The ISD equation is derived via the Smoluchowski equation and assumes
overdamped system dynamics. It has been suggested that the complex
membrane environment may exhibit more complicated damping conditions.
Here we derive a variant of the inhomogeneous solubility diffusion
equation as a function of the mean first passage time (MFPT) and show
how milestoning, a method that can estimate kinetic quantities of
interest, can be used to estimate the MFPT of membrane crossing and,
by extension, the permeability coefficient. We further describe a
second scheme, agnostic to the damping condition, to estimate the
permeability coefficient from milestoning results or other methods
that compute a probability of membrane crossing. The derived relationships
are tested using a one-dimensional Langevin dynamics toy system confirming
that the presented theoretical methods can be used to estimate permeabilities
given simulation and milestoning results.