Calculating Transition Energy Barriers and Characterizing Activation States for Steps of Fusion

Abstract

We use continuum mechanics to calculate an entire least energy pathway of membrane fusion, from stalk formation, to pore creation, and through fusion pore enlargement. The model assumes that each structure in the pathway is axially symmetric. The static continuum stalk structure agrees quantitatively with experimental stalk architecture. Calculations show that in a stalk, the distal monolayer is stretched and the stored stretching energy is significantly less than the tilt energy of an unstretched distal monolayer. The string method is used to determine the energy of the transition barriers that separate intermediate states and the dynamics of two bilayers as they pass through them. Hemifusion requires a small amount of energy independently of lipid composition, while direct transition from a stalk to a fusion pore without a hemifusion intermediate is highly improbable. Hemifusion diaphragm expansion is spontaneous for distal monolayers containing at least two lipid components, given sufficiently negative diaphragm spontaneous curvature. Conversely, diaphragms formed from single-component distal monolayers do not expand without the continual injection of energy. We identify a diaphragm radius, below which central pore expansion is spontaneous. For larger diaphragms, prior studies have shown that pore expansion is not axisymmetric, and here our calculations supply an upper bound for the energy of the barrier against pore formation. The major energy-requiring deformations in the steps of fusion are: widening of a hydrophobic fissure in bilayers for stalk formation, splay within the expanding hemifusion diaphragm, and fissure widening initiating pore formation in a hemifusion diaphragm.

Low energy cost for optimal speed and control of membrane fusion

“…Because most published models of the fusion process have focused on these proposed individual energy barriers, our results now make it possible to objectively evaluate the plausibility of these models. For both DOPC and POPC, we measured E a close to 30 k B T. Such a low value for the overall fusion process was never predicted but remains consistent with recently published coarse-grained simulations (14,16) in which there is no prior hypothesis concerning the fusion pathway, thereby allowing the predicted transition structures and activation energies to emerge directly. Our measured global E a is indeed larger than or close to these.…”

“…Our measured global E a is indeed larger than or close to these. According to Smirnova et al (14), 20 k B T are required for stalk formation whereas Ryham et al (16) evaluated activation energies of 31 k B T (stalk) and 35 k B T (fusion pore). Thus, these predictions are compatible with our experimental measurements and may closely reproduce the reality of the fusion process at a molecular scale.…”

Hypothesis – buttressed rings assemble, clamp, and release SNAREpins for synaptic transmission

“…Yet, they show that a simple pressure model provides an explanation at the level of soft matter physics for sub‐millisecond SNARE‐induced fusion following release of the clamp. Note that unlike more granular models of fusion 98, 99, 100 that concern themselves with particular alternative arrangements of lipids in the transition state, the pressure model takes a system‐level approach that avoids these complexities while remaining consistent with the various detailed molecular proposals.Additional notes: The pressure/energy view is valid only when a sufficient number of SNAREpins are involved and delimit a clear area over which the pulling force is applied. When a small number of SNAREpins (1, 2, and maybe 3) are triggering the fusion process, the concept of pressure cannot be used because it becomes difficult to define an area, and alternate views are more appropriate.…”

“…Yet, they show that a simple pressure model provides an explanation at the level of soft matter physics for sub‐millisecond SNARE‐induced fusion following release of the clamp. Note that unlike more granular models of fusion 98, 99, 100 that concern themselves with particular alternative arrangements of lipids in the transition state, the pressure model takes a system‐level approach that avoids these complexities while remaining consistent with the various detailed molecular proposals.…”

Revisit the Correlation between the Elastic Mechanics and Fusion of Lipid Membranes

“…Another possibility is that the variation in K cp is only a consequence of changing the LUV composition and does not directly affects fusion; it is another effect arising from the composition change that is responsible for the differential fusion capabilities. One such candidate is the variation in the tilt modulus, which is associated with the CH chain stretching and tilting when the chains are arranged to form stalk and HD 33,34 . Indeed, raising the chain unsaturation increases the tilt modulus 35,36 and may thus aggravate the related energetic penalties of maintaining stalk and HD 34 .…”