Curvature as a Collective Coordinate in Enhanced Sampling Membrane Simulations

Abstract

The plasticity of membranes plays an important functional role in cells, cell components and micelles, where bending, budding and remodeling implement numerous recognition and communication processes. Comparatively, molecular simulation methods to induce, control and quantitatively characterize such deformations remain scarce. This work defines a novel collective coordinate associated with membrane bending, which strives to combine realism (by preserving the notion of local atomic curvatures) and low computational cost (allowing its evaluation at every time step of a molecular dynamics simulation). Enhanced sampling simulations along this conformational coordinate provide convenient access to the underlying bending free energy landscape. To showcase its potential, the method is applied to three state-of-the-art problems: the determination of the bending free energy landscape of a POPE bilayer, the formation of a POPE liposome, and the study of the influence of the Pseudomonas quinolone signal on the budding of Gram-negative bacterial outer membranes.

Density Field Thermodynamic Integration (DFTI): A “Soft” Approach to Calculate the Free Energy of Surfactant Self-Assemblies

“…This method is highly effective when structural changes are characterized by a dominant collective mode such as, for example, the bending of a membrane sheet . Large collective modes can be alternatively modeled by explicitly using membrane curvature as a collective reaction coordinate . However, smoothly enforcing the structure through a transition state of single molecular nature (our two example systems) is difficult to achieve by coupling only to a single or even a few collective modes.…”

“…17 Large collective modes can be alternatively modeled by explicitly using membrane curvature as a collective reaction coordinate. 41 However, smoothly enforcing the structure through a transition state of single molecular nature (our two example systems) is difficult to achieve by coupling only to a single or even a few collective modes. Consequently, ensuring thermodynamic reversibility may thus be rather challenging.…”

Molecular Dynamics Simulations of Curved Lipid Membranes

“…A more controlled way to induce and sustain curvature by virtual forces, is to impose a specific radius by a collective variable. A couple of such curvature-controlling collective variables have been derived in recent years [ 63 , 64 , 65 ]. An elegant implementation, EnCurv, exploits PLUMED [ 66 , 67 ] to implement a collective variable that can enforce a specific curvature to a bicelle or a patch of a periodic membrane [ 48 ] ( Figure 4 D).…”

How proteins open fusion pores: insights from molecular simulations

“…This method is highly effective when structural changes are characterized by a dominant collective mode such as, for example, bending of a membrane sheet (Bubnis and Risselada 2016). Large collective modes can be alternatively modeled by explicitly using membrane curvature as a collective reaction coordinate (Bouvier 2019). However, smoothly enforcing the structure through a transition state of single molecular nature-such as the formation of a stalk -is hard to achieve by coupling to only a single or even a few collective modes.…”