A hemifused complex is the hub in a network of pathways to membrane fusion.

Membrane fusion is a critical step for many essential processes, from neurotransmission to fertilization. For over 40 years, protein-free fusion driven by calcium or other cationic species has provided a simplified model of biological fusion, but the mechanisms remain poorly understood. Cation-mediated membrane fusion and permeation are essential in their own right to drug delivery strategies based on cell-penetrating peptides or cation-bearing lipid nanoparticles. Experimental studies suggest calcium drives anionic membranes to a hemifused intermediate that constitutes a hub in a network of pathways, but the pathway selection mechanism is unknown. Here we develop a mathematical model that identifies the network hub as a highly dynamic hemifusion complex. Multivalent cations drive expansion of this high-tension hemifusion interface between interacting vesicles during a brief transient. The fate of this interface determines the outcome, either fusion, dead-end hemifusion, or vesicle lysis. The model reproduces the unexplained finding that calcium-driven fusion of vesicles with planar membranes typically stalls at hemifusion, and we show the equilibrated hemifused state is a novel lens-shaped complex. Thus, membrane fusion kinetics follow a stochastic trajectory within a network of pathways, with outcome weightings set by a hemifused complex intermediate.

Model of influenza virus acidification.

Internal acidification of the influenza virus, mediated by the M2 proton channel, is a key step in its life cycle. The interior M1 protein shell dissolves at pH~5.5 to 6.0, allowing the release of vRNA to the cytoplasm upon fusion of the viral envelope with the endosomal membrane. Previous models have described the mechanisms and rate constants of M2-mediated transport but did not describe the kinetics of pH changes inside the virus or consider exterior pH changes due to endosome maturation. Therefore, we developed a mathematical model of M2-mediated virion acidification. We find that ~32,000 protons are required to acidify a typically-sized virion. Predicted acidification kinetics were consistent with published in vitro experiments following internal acidification. Finally, we applied the model to the in vivo situation. For all rates of endosomal maturation considered, internal acidification lagged ~1 min behind endosomal acidification to pH 6. For slow endosomal maturation requiring several minutes or more, internal and endosomal pH decay together in pseudo-equilibrium to the late endosomal pH~5.0. For fast endosomal maturation (≲2 min), a lag of tens of seconds continued toward the late endosomal pH. Recent experiments suggest in vivo maturation is in this "fast" regime where lag is considerable. We predict that internal pH reaches the threshold for M1 shell solvation just before the external pH triggers membrane fusion mediated by the influenza protein hemagglutinin, critical because outward proton diffusion through a single small fusion pore is faster than the collective M2-mediated transport inward.

Entropic forces drive self-organization and membrane fusion by SNARE proteins.

SNARE proteins are the core of the cell's fusion machinery and mediate virtually all known intracellular membrane fusion reactions on which exocytosis and trafficking depend. Fusion is catalyzed when vesicle-associated v-SNAREs form trans-SNARE complexes ("SNAREpins") with target membrane-associated t-SNAREs, a zippering-like process releasing ∼65 kT per SNAREpin. Fusion requires several SNAREpins, but how they cooperate is unknown and reports of the number required vary widely. To capture the collective behavior on the long timescales of fusion, we developed a highly coarse-grained model that retains key biophysical SNARE properties such as the zippering energy landscape and the surface charge distribution. In simulations the ∼65-kT zippering energy was almost entirely dissipated, with fully assembled SNARE motifs but uncomplexed linker domains. The SNAREpins self-organized into a circular cluster at the fusion site, driven by entropic forces that originate in steric-electrostatic interactions among SNAREpins and membranes. Cooperative entropic forces expanded the cluster and pulled the membranes together at the center point with high force. We find that there is no critical number of SNAREs required for fusion, but instead the fusion rate increases rapidly with the number of SNAREpins due to increasing entropic forces. We hypothesize that this principle finds physiological use to boost fusion rates to meet the demanding timescales of neurotransmission, exploiting the large number of v-SNAREs available in synaptic vesicles. Once in an unfettered cluster, we estimate ≥15 SNAREpins are required for fusion within the ∼1-ms timescale of neurotransmitter release.

Cholesterol Increases the Openness of SNARE-Mediated Flickering Fusion Pores.

Flickering of fusion pores during exocytotic release of hormones and neurotransmitters is well documented, but without assays that use biochemically defined components and measure single-pore dynamics, the mechanisms remain poorly understood. We used total internal reflection fluorescence microscopy to quantify fusion-pore dynamics in vitro and to separate the roles of soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) proteins and lipid bilayer properties. When small unilamellar vesicles bearing neuronal v-SNAREs fused with planar bilayers reconstituted with cognate t-SNARES, lipid and soluble cargo transfer rates were severely reduced, suggesting that pores flickered. From the lipid release times we computed pore openness, the fraction of time the pore is open, which increased dramatically with cholesterol. For most lipid compositions tested, SNARE-mediated and nonspecifically nucleated pores had similar openness, suggesting that pore flickering was controlled by lipid bilayer properties. However, with physiological cholesterol levels, SNAREs substantially increased the fraction of fully open pores and fusion was so accelerated that there was insufficient time to recruit t-SNAREs to the fusion site, consistent with t-SNAREs being preclustered by cholesterol into functional docking and fusion platforms. Our results suggest that cholesterol opens pores directly by reducing the fusion-pore bending energy, and indirectly by concentrating several SNAREs into individual fusion events.

Evolution of the hemifused intermediate on the pathway to membrane fusion.

The pathway to membrane fusion in synthetic and biological systems is thought to pass through hemifusion, in which the outer leaflets are fused while the inner leaflets engage in a hemifusion diaphragm (HD). Fusion has been proposed to be completed by lysis of the expanded HD that matures from a localized stalklike initial connection. However, the process that establishes the expanded HD is poorly understood. Here we mathematically modeled hemifusion of synthetic vesicles, where hemifusion and fusion are most commonly driven by calcium and membrane tension. The model shows that evolution of the hemifused state is driven by these agents and resisted by interleaflet frictional and tensile stresses. Predicted HD growth rates depend on tension and salt concentration, and agree quantitatively with experimental measurements. For typical conditions, we predict that HDs expand at ~30 µm(2)/s, reaching a final equilibrium area ~7% of the vesicle area. Key model outputs are the evolving HD tension and area during the growth transient, properties that may determine whether HD lysis occurs. Applying the model to numerous published experimental studies that reported fusion, our results are consistent with a final fusion step in which the HD ruptures due to super-lysis HD membrane tensions.

The hemifused state on the pathway to membrane fusion.

Fusion of compartments enclosed by membrane bilayers enables secretion and other vital cellular processes and is widely studied in model synthetic membrane systems. Experiments suggest the fusion pathway passes through a hemifused intermediate where only outer monolayers are fused. Here we show membrane tension and divalent cations drive vesicles to hemifused equilibrium with expanded hemifusion diaphragms (HDs) where inner monolayers engage. Predicted HD sizes agree with recent measurements of Nikolaus et al. [Biophys. J. 98, 1192 (2010).]. The fusion pathway is completed by HD lysis provided HD tension is sufficiently high.

Model of SNARE-mediated membrane adhesion kinetics.

SNARE proteins are conserved components of the core fusion machinery driving diverse membrane adhesion and fusion processes in the cell. In many cases micron-sized membranes adhere over large areas before fusion. Reconstituted in vitro assays have helped isolate SNARE mechanisms in small membrane adhesion-fusion and are emerging as powerful tools to study large membrane systems by use of giant unilamellar vesicles (GUVs). Here we model SNARE-mediated adhesion kinetics in SNARE-reconstituted GUV-GUV or GUV-supported bilayer experiments. Adhesion involves many SNAREs whose complexation pulls apposing membranes into contact. The contact region is a tightly bound rapidly expanding patch whose growth velocity v(patch) increases with SNARE density Gamma(snare). We find three patch expansion regimes: slow, intermediate, fast. Typical experiments belong to the fast regime where v(patch) ~ (Gamma(snare)(2/3) depends on SNARE diffusivities and complexation binding constant. The model predicts growth velocities ~10 - 300 microm/s. The patch may provide a close contact region where SNAREs can trigger fusion. Extending the model to a simple description of fusion, a broad distribution of fusion times is predicted. Increasing SNARE density accelerates fusion by boosting the patch growth velocity, thereby providing more complexes to participate in fusion. This quantifies the notion of SNAREs as dual adhesion-fusion agents.