Divergent Diffusion Coefficients in Simulations of Fluids and Lipid Membranes

Abstract

We investigate the dependence of single-particle diffusion coefficients on the size and shape of the simulation box in molecular dynamics simulations of fluids and lipid membranes. We find that the diffusion coefficients of lipids and a carbon nanotube embedded in a lipid membrane diverge with the logarithm of the box width. For a neat Lennard-Jones fluid in flat rectangular boxes, diffusion becomes anisotropic, diverging logarithmically in all three directions with increasing box width. In elongated boxes, the diffusion coefficients normal to the long axis diverge linearly with the height-to-width ratio. For both lipid membranes and neat fluids, this behavior is predicted quantitatively by hydrodynamic theory. Mean-square displacements in the neat fluid exhibit intermediate regimes of anomalous diffusion, with t ln t and t(3/2) components in flat and elongated boxes, respectively. For membranes, the large finite-size effects, and the apparent inability to determine a well-defined lipid diffusion coefficient from simulation, rationalize difficulties in comparing simulation results to each other and to those from experiments.

Transient hydrodynamic finite-size effects in simulations under periodic boundary conditions

“…The same scaling was found independently [3] and has been confirmed in molecular dynamics simulations of a number of simple fluids [2], including several water models [4,5], ionic liquids [6] or more complex fluids such as solutions of star polymers [7]. More recently, the extension to anisotropic boxes was also investigated [8,9] and interpreted in terms of the same hydrodynamic arguments [10,11]. The distortion of the flow field due to the finite size of the system (and the associated use of PBC) does not only affect the diffusion coefficient D of particles, but in principle all dynamical properties.…”

“…Following Dünweg and Kremer [1], Yeh and Hummer [2] proposed a complete analysis of the finite size effect on the diffusion coefficient of fluid particles in a cubic box based on the mobility tensor T: . More recently, the extension to anisotropic boxes was also investigated [8,9] and interpreted in terms of the same hydrodynamic arguments [10,11]. The distortion of the flow field due to the finite size of the system (and the associated use of PBC) does not only affect the diffusion coefficient D of particles, but in principle all dynamical properties.…”

Toward Hydrodynamics with Solvent Free Lipid Models: STRD Martini

“…(32) This indicates that the STRD Martini approach accurately models the quasi-two-dimensional hydrodynamics of lipid bilayers. The STRD Martini method should therefore find application for modeling more complex problems, such as lipid and protein diffusion in heterogeneous membranes, in non-freestanding geometries, or in membranes coupled to the cytoskeleton, for which there is no theory.…”

The plasma membrane as a competitive inhibitor and positive allosteric modulator of KRas4B signaling

“…N-terminal residue M1 has a backbone NH 3 prior to evaluating molecular diffusion (73). Diffusion coefficients computed from these simulations are not corrected for finite size effects stemming from hydrodynamic interactions (74)(75)(76)(77). Since all systems have similar dimensions, we compare unmodified diffusion coefficients.…”