Position-Dependent Diffusion Tensors in Anisotropic Media from Simulation: Oxygen Transport in and through Membranes

Abstract

A Bayesian-based methodology is developed to estimate diffusion tensors from molecular dynamics simulations of permeants in anisotropic media, and is applied to oxygen in lipid bilayers. By a separation of variables in the Smoluchowski diffusion equation, the multidimensional diffusion is reduced to coupled one-dimensional diffusion problems that are treated by discretization. The resulting diffusivity profiles characterize the membrane transport dynamics as a function of the position across the membrane, discriminating between diffusion normal and parallel to the membrane. The methodology is first validated with neat water, neat hexadecane, and a hexadecane slab surrounded by water, the latter being a simple model for a lipid membrane. Next, a bilayer consisting of pure 1-palmitoyl 2-oleoylphosphatidylcholine (POPC), and a bilayer mimicking the lipid composition of the inner mitochondrial membrane, including cardiolipin, are investigated. We analyze the detailed time evolution of oxygen molecules, in terms of both normal diffusion through and radial diffusion inside the membrane. Diffusion is fast in the more loosely packed interleaflet region, and anisotropic, with oxygen spreading more rapidly in the membrane plane than normal to it. Visualization of the propagator shows that oxygen enters the membrane rapidly, reaching its thermodynamically favored center in about 1 ns, despite the free energy barrier at the headgroup region. Oxygen transport is quantified by computing the oxygen permeability of the membranes and the average radial diffusivity, which confirm the anisotropy of the diffusion. The position-dependent diffusion constants and free energies are used to construct compartmental models and test assumptions used in estimating permeability, including Overton's rule. In particular, a hexadecane slab surrounded by water is found to be a poor model of oxygen transport in membranes because the relevant energy barriers differ substantially.

Oxygen Transport to Tissue XL

“…3 presents D⊥(z) and D//(z). Overall, the same trends are found for the new profiles as for the previously investigated POPC/310 and MITO/310 membranes [9]. Each system has a free energy dip at the tail region and at the center of the membrane (Fig.…”

“…The MD simulation consists of two parts: the equilibration (NPT simulation) and the data collection (NVT simulation). Four uncorrelated snapshots of the NPT simulation were selected as the starting point for an NVT simulation of 50 ns [9].…”

“…The protocol to create the profiles is based on BA of the trajectories, assuming that the Smoluchowski equation describes the oxygen diffusion in the inhomogeneous and anisotropic membrane [9,13]. In the analysis, the coordinate of each O2 at time t is compared to its coordinate at time t + τ, while keeping track of its location in the membrane to account for inhomogeneity.…”

“…The diffusion profiles depend on the studied lag time τ. The diffusion profiles with lag times 20, 30, 40 and 50 ps are fitted in order to omit the short time behavior and reach the long time scale diffusive behavior [9]. The POPC/310 system has been reported in [9], which compared them to O2 diffusion in the inner mitochondrial membrane at 310 K. The MITO/310 system in [9] contained 10 oxygens, 72 phospholipids of various types, 2980 waters, and some ions.…”

“…This methodology was previously developed and tested on a model mitochondrial membrane at 310 K [9]. The BA yields the free energy F(z), the diffusion D⊥(z) normal to the membrane, and the diffusion D//(z) parallel to the membrane, which are shown in the Results section.…”