Thermodynamic Free Energy Methods to Investigate Shape Transitions In Bilayer Membranes

TL;DR

This paper reviews four free energy computational methods applied to bilayer membrane shape transitions, demonstrating their effectiveness in studying membrane protein behavior and membrane tether formation with results aligning well with experiments.

Contribution

It introduces and compares four free energy methods for analyzing membrane shape transitions, including a new approach to address endpoint catastrophe issues.

Findings

Widom insertion effectively measures chemical potential for curvature sensing proteins.

Thermodynamic integration and Bennett acceptance accurately compute free energy differences.

WHAM and thermodynamic integration successfully model tether formation, matching experimental data.

Abstract

The conformational free energy landscape of a system is a fundamental thermodynamic quantity of importance particularly in the study of soft matter and biological systems, in which the entropic contributions play a dominant role. While computational methods to delineate the free energy landscape are routinely used to analyze the relative stability of conformational states, to determine phase boundaries, and to compute ligand-receptor binding energies its use in problems involving the cell membrane is limited. Here, we present an overview of four different free energy methods to study morphological transitions in bilayer membranes, induced either by the action of curvature remodeling proteins or due to the application of external forces. Using a triangulated surface as a model for the cell membrane and using the framework of dynamical triangulation Monte Carlo, we have focused on the methods of Widom insertion, thermodynamic integration, Bennett acceptance scheme, and umbrella sampling and weighted histogram analysis. We have demonstrated how these methods can be employed in a variety of problems involving the cell membrane. Specifically, we have shown that the chemical potential, computed using Widom insertion, and the relative free energies, computed using thermodynamic integration and Bennett acceptance method, are excellent measures to study the transition from curvature sensing to curvature inducing behavior of membrane associated proteins. The umbrella sampling and WHAM analysis has been used to study the thermodynamics of tether formation in cell membranes and the quantitative predictions of the computational model are in excellent agreement with experimental measurements. Furthermore, we also present a method based on WHAM and thermodynamic integration to handle problems related to end-point-catastrophe that are common in most free energy methods