Over the past 20 years, it has been widely accepted that membrane fusion proceeds via a hemifusion step before opening of the productive fusion pore. An initial hourglass-shaped lipid structure, the fusion stalk, is formed between the adjacent membrane leaflets (cis leaflets). It remains controversial if and how fusion proteins drive the subsequent transition (expansion) of the stalk into a fusion pore. Here, we propose a comprehensive and consistent thermodynamic understanding in terms of the underlying free-energy landscape of stalk expansion. We illustrate how the underlying free energy landscape of stalk expansion and the concomitant pathway is altered by subtle differences in membrane environment, such as leaflet composition, asymmetry, and flexibility. Nonleaky stalk expansion (stalk widening) requires the formation of a critical trans-leaflet contact. The fusion machinery can mechanically enforce trans-leaflet contact formation either by directly enforcing the trans-leaflets in close proximity, or by (electrostatically) condensing the area of the cis leaflets. The rate of these fast fusion reactions may not be primarily limited by the energetics but by the forces that the fusion proteins are able to exert.embrane fusion is a fundamental process in cell biophysics, being involved in viral infection, endo-and exocytosis, and fertilization. The textbook example of membrane fusion comprises three experimentally observed metastable lipidic structures-namely, the rhombohedral stalk (1, 2), the hemifusion diaphragm (HD) (3-5), and the toroidal fusion pore (6). These structures represent (local) free energy minima that are connected via transient states (free energy barriers) within the fusion pathway. How the stalk transitions (expands) into the fusion pore remains controversial (7-9). Different pathways have been proposed based on experimental observations (3, 5, 10-13), molecular simulations (8,9,(14)(15)(16)(17)(18)(19)(20), continuum elastic models (15,21,22), and self-consistent field theory (23,24).Arguably, the best-studied fusion reactions are the ones mediated by influenza hemagglutinin and soluble N-ethylmaleimidesensitive-factor attachment receptor (SNARE) molecules. Hemagglutinin-mediated fusion displays an unusual sensitivity toward point mutations in its amphiphilic fusion peptide. Here, even single point mutations can selectively trap the fusion reaction in a hemifused state (25). Hemagglutinin therefore very likely plays an active, essential role in the subsequent evolution of hemifusion intermediates (20). In contrast, it remains unclear if SNARE molecules play a role therein. SNARE molecules subject force on the membrane via the ends of the transmembrane domains (TMDs) (26). The X-ray-resolved structure of the postfusion neuronal SNARE complex suggests that TMDs come together during the fusion reaction, and may actively drive fusion up to the expansion of the fusion pore (27). However, in vitro and in vivo experiments, where the TMD was either replaced by a lipid anchor or partly truncated, pro...

A complete physical description of membrane remodeling processes, such as fusion or fission, requires knowledge of the underlying free energy landscapes, particularly in barrier regions involving collective shape changes, topological transitions, and high curvature, where Canham-Helfrich (CH) continuum descriptions may fail. To calculate these free energies using atomistic simulations, one must address not only the sampling problem due to high free energy barriers, but also an orthogonal sampling problem of combinatorial complexity stemming from the permutation symmetry of identical lipids. Here, we solve the combinatorial problem with a permutation reduction scheme to map a structural ensemble into a compact, nondegenerate subregion of configuration space, thereby permitting straightforward free energy calculations via umbrella sampling. We applied this approach, using a coarse-grained lipid model, to test the CH description of bending and found sharp increases in the bending modulus for curvature radii below 10 nm. These deviations suggest that an anharmonic bending term may be required for CH models to give quantitative energetics of highly curved states. DOI: 10.1103/PhysRevLett.117.188102 Membrane remodeling is essential for many cellular transport functions, notably fusion [1] and fission [2]. However, despite continued interest, the underlying lipidic mechanisms and energetics are not fully understood. Atomistic and near-atomistic molecular dynamics (MD) simulations provide sufficient temporal and spatial resolution to probe lipidic mechanisms. However, standard MD fails to reach the high energy barriers (≫k B T) which often dictate mechanisms and kinetics. Biasing methods are thus required to address the sampling problem for high energy barriers.An additional and ubiquitous obstacle, in both describing and biasing lipidic transitions, is the N! degeneracy of lipid configuration space arising from the permutation symmetry of N identical lipids. The same combinatorial symmetry lies at the heart of the Gibbs paradox [3][4][5], which is resolved by a 1=N! scaling of the partition function, to account for physically indistinguishable (degenerate) states.In contrast to this straightforward analytical correction, this permutation symmetry poses a severe challenge to atomistic simulations and free energy calculations involving lipids: sampling the space of degenerate states (via self-diffusion) shrouds the collective structural changes of interest and precludes the use of lipidic collective coordinate biasing schemes. Accordingly, special purpose methods (that circumvent this hindrance) have been developed to direct lipidic transitions using boundary conditions [6,7], external guiding potentials [8,9], probe particles [10], density biasing [11,12], and single-lipid restraints [13,14].Here, we describe and apply a rigorous method to directly address this N! degeneracy, using permutation reduction (PR) [15,16]. The method exploits permutation symmetry by remapping structures from the full N! degenerate configur...

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Several experimental groups have recently reported self-assembly of fullerene derivatives on metal substrates. These studies have shown that both the size of the substituent moiety and the presence of hydrogen-bonding functional groups affect the observed adlayer symmetries. However, little theoretical work has been carried out to explain these results. Accordingly, we have carried out classical rigid body Monte Carlo simulations of a variety of fullerene derivatives on a rigid Au(111) surface. We consider several fullerene derivatives functionalized with carboxylic acid groups attached to the fullerene using "arms" of phenyl rings of variable length. A pairwise-additive united-atom potential energy function was constructed using data from a variety of sources. The potential reproduces many of the details observed in experimental studies of C 60 on Au(111). For fullerenes containing two hydrogen-bonding groups, ordered rows of molecules can self-assemble if the fullerenes are able to form a close-packed layer. Steric effects may inhibit close-packing of the fullerenes, resulting in "glassy" adlayers. In addition, the rotational barriers must be sufficiently low that they allow orientational ordering of the molecular adlayer. We have identified two distinct adlayer geometries which can be formed from extended one-dimensional hydrogen-bonding rows. When the barriers to rotation are too high, as is the case when the molecules become sterically hindered, orientational ordering is not possible. Simulations with molecules bearing a single carboxylic acid functionality lead to close-packing and hydrogenbonded orientational dimers. However, the dimers do not self-assemble into a globally ordered adlayer (with the parametrization used here). In addition, we show that molecules without hydrogen-bonding functional groups can self-assemble into herringbone patterns, provided the conditions for close-packing and orientational ordering have been met. Our findings rationalize several of the experimental results in the literature.

Membrane topology changes such as poration, stalk formation, and hemi-fusion rupture are essential to cellular function, but their molecular details, energetics, and kinetics are still not fully understood. Here we present a unified energetic and mechanistic picture of metastable pore defects in tensionless lipid membranes. We used an exhaustive committor analysis to test and select optimal reaction coordinates and also to determine the nucleation mechanism. These reaction coordinates were used to calculate free energy landscapes that capture the full process and end states. The identified barriers agree with the committor analysis. To enable sufficient sampling of the complete transition path for our atomistic simulations, we developed a novel "gizmo" potential biasing scheme. The simulations suggest that the essential step in the nucleation is the initial merger of lipid headgroups at the nascent pore center. To facilitate this event, an indentation pathway is energetically preferred to a hydrophobic defect. Continuous water columns that span the indentation were determined to be on-path transients that precede the nucleation barrier. This study gives a quantitative description of the nucleation mechanism and energetics of small metastable pores and illustrates a systematic approach to uncover the mechanisms of diverse cellular membrane remodeling processes. STATEMENT OF SIGNIFICANCEThe primary steps and nucleation of lipid membrane pore formation are key to membrane fusion, viral infection, and vesicular cellular transport. Despite decades experimental and theoretical studies, the underlying mechanisms are still not fully understood at the atomic level. Using a committor-based reaction coordinate and atomistic simulations, we report new structural and energetics insight into the full poration process. We find that the pore nucleates via an elastic indentation rather than by forming a hydrophobic defect. Subsequently, water pierces the thinned slab as a prerequisite for the following axial merger of the first lipid headgroups from opposite monolayers, which precedes and best characterizes the transition state. We also identify a metastable prepore basin, thereby explaining previous indirect experimental evidence.