Transition Path from Two Apposed Membranes to a Stalk Obtained by a Combination of Particle Simulations and String Method

Abstract

The formation of an hourglass-shaped passage (stalk) connecting two apposed membranes is an essential initial step in membrane fusion. The most probable transition path from two separate membranes to a stalk, i.e., the minimum free-energy path (MFEP), is constructed using a combination of particle simulations and string method. For the reversible transition path in the coarse-grained membrane model, a collective order parameter, m, can be identified as the local difference of hydrophilic and hydrophobic densities. In particle simulations, the free energy F[m] as a functional of m is not readily available. This difficulty is overcome by an equation-free approach, where the morphology and the excess free energy along the MFEP are obtained by an on-the-fly string method. The transition state is confirmed by diagonalization of order-parameter fluctuations and by the probability of reaching either stalk or bilayer morphology from different positions along the MFEP.

Molecular pathways for defect annihilation in directed self-assembly

“…Importantly, the model has been shown to provide a representation of copolymer thin films that is in good agreement with available experimental data (19,20). We rely on the string method to identify the MFEP between two metastable states on a free energy landscape (21)(22)(23)(24)(25)(26)(27)). An initial string is constructed by linear interpolation between the two end states.…”

Mechanics of membrane fusion/pore formation

“…In practical calculations, however, the single-lipid distribution function contains too much information and, in previous applications (Cheng et al, 2010;Ting et al, 2011;Müller et al, 2012), a simple scalar collective variable field, m(r), that quantifies the local density difference between hydrophilic and hydrophobic interaction centers has been employed to approximately characterize the structure. This collective variable can be computed from the microscopic coordinates of all lipids according tô…”

“…In addition, we used available data from MC simulations based on a polymer-like lipid model (Katsov et al, 2004;Müller et al, 2012) as comparison.…”

Enhanced Sampling in Molecular Dynamics Using Metadynamics, Replica-Exchange, and Temperature-Acceleration

“…This idea has been put to use recently in the "indirect umbrella sampling" method of Patel et al [179] for computing free energies of solvation, and string method (Section 4.2.1.) calculations of lipid bilayer fusion [180]. In a similar vein, there have been recent attempts at variables designed to count the recurrency of groups of atoms positioned according to given templates, such as α-helices paired β-strands in proteins [181].…”