Finite-Size-Corrected Rotational Diffusion Coefficients of Membrane Proteins and Carbon Nanotubes from Molecular Dynamics Simulations.

Martin Vögele,Gerhard Hummer,Jürgen Köfinger

doi:10.1021/acs.jpcb.9b01656

Abstract

We investigate system-size effects on the rotational diffusion of membrane proteins and other membrane-embedded molecules in molecular dynamics simulations. We find that the rotational diffusion coefficient slows down relative to the infinite-system value by a factor of one minus the ratio of protein and box areas. This correction factor follows from the hydrodynamics of rotational flows under periodic boundary conditions and is rationalized in terms of Taylor–Couette flow. For membrane proteins like transporters, channels, or receptors in typical simulation setups, the protein-covered area tends to be relatively large, requiring a significant finite-size correction. Molecular dynamics simulations of the protein adenine nucleotide translocase (ANT1) and of a carbon nanotube porin in lipid membranes show that the hydrodynamic finite-size correction for rotational diffusion is accurate in standard-use cases. The dependence of the rotational diffusion on box size can be used to determine the membrane viscosity.

Highlights

Diffusion in molecular dynamics (MD) simulations under periodic boundary conditions (PBC) depends on the size and shape of the simulation box due to hydrodynamic selfinteractions with the periodic images.[1−3] In cubic boxes of increasing size, both the translational[3] and the rotational diffusion coefficients[4,5] converge with increasing box volume as predicted by hydrodynamic theory
We investigate system-size effects on the rotational diffusion of membrane proteins and other membrane-embedded molecules in molecular dynamics simulations
By performing MD simulations of the protein adenine nucleotide translocase (ANT1) and by reanalyzing earlier simulations of ANT112 and carbon nanotube porins,[16] we show that the hydrodynamic description quantitatively captures the finite-size effects

Summary

Introduction

Diffusion in molecular dynamics (MD) simulations under periodic boundary conditions (PBC) depends on the size and shape of the simulation box due to hydrodynamic selfinteractions with the periodic images.[1−3] In cubic boxes of increasing size, both the translational[3] and the rotational diffusion coefficients[4,5] converge with increasing box volume as predicted by hydrodynamic theory. For asymmetrically increased box volumes, translational diffusion becomes anisotropic and either does not converge or converges to values different from the correct infinite-system limit.[6−10] This problem especially affects membrane simulations for which practicable corrections have been provided.[9,11,12] In contrast to translational diffusion, the finite-size behavior of rotational diffusion in the membrane has remained largely unstudied, even though corrections may be required for meaningful comparisons to experiment.[13,14]. We investigate the influence of the simulation box width on the rotational diffusion coefficient of membrane proteins and other membrane-embedded macromolecules. In the Theory section, we present three different hydrodynamic models that give consistent expressions for the finite-size correction of the rotational diffusion coefficient. The first model extends the original derivation of Saffman and Delbrück[15] to two-dimensional (2D) rotational flow under

Methods

Results

Conclusion