On the Equivalence of Schemes for Simulating Bilayers at Constant Surface Tension

Abstract

Lipid bilayers are simulated using flexible simulation cells in order to allow for relaxations in area per lipid as bilayer content and temperature are varied. We develop a suite of Monte Carlo (MC) moves designed to generate constant surface tension γ and constant pressure P and find that the NPT partition function proposed by Attard [J. Chem. Phys. 1995, 103, 9884−9885] leads to an NPγT partition function with a form invariant to choice of independent shape variables. We then compare this suite of MC moves to NPγT MC moves previously employed in our group as well as a pair of MC moves designed to replicate the NP ∥ P ⊥ T "ensemble" often used in molecular dynamics simulations to yield zero surface tension and constant pressure. A detailed analysis of shape fluctuations in a small bilayer system reveals that the two latter MC move sets are different from one another as well as from our new suite of MC moves, as justified by careful analysis of the partition functions. However, the study of a larger bilayer system reveals that, for practical purposes for this system, all six MC move sets are comparable to one another.

Bending Lipid Bilayers: A Closed-Form Collective Variable for Effective Free-Energy Landscapes in Quantitative Biology

“…Long-range electrostatic interactions were computed with the fourth-order particle-mesh-Ewald method (PME) . This simulation scheme lets the membrane reach a tensionless equilibrium state after a reasonably long period of equilibration …”

“…52 This simulation scheme lets the membrane reach a tensionless equilibrium state after a reasonably long period of equilibration. 53 Free Energy Calculations. The potential of mean force (PMF) for membrane bending was computed by umbrella sampling 54,55 using a set of 31 windows to span the reaction coordinate Ψ in the interval [−0.3,0] for the DPPC bilayer and 51 windows for spanning Ψ in the interval [−0.5,0] for the DPPC−DOPC−CHOL bilayer.…”

Understanding the Phase Behavior of Coarse-Grained Model Lipid Bilayers through Computational Calorimetry

“…Application of the barostat is decoupled in the lateral and normal directions, in order to simulate at zero surface tension. Such barostating is often employed to simulate a tensionless system, and its general applicability is further explored elsewhere . The simulation parameters were kept at default using the example DPPC bilayer from the MARTINI Web site, although we reduced the time step from 40 to 30 fs and increased the pairlist cutoff radius to 1.4 nm, as suggested in recent evaluations of the model. , The electrostatics and vdW forces were treated by shifted Coulomb and Lennard-Jones potentials, respectively.…”

On the algorithm to perform Monte Carlo simulations in cells with constant volume and variable shape

“…The integration is carried out over volume 𝑉 with the set parameter 𝜏. The full partition function then should be constructed as a weighted sum (or integral) over all possible realizations of the additional degree of freedom [12]. In the most general case, one finds:…”