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. 2017 Mar 27;6:e22964. doi: 10.7554/eLife.22964

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© 2017, Wu et al

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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Figure 7. — The mathematical model describes a mechanism of pore expansion in which SNARE-crowding generates entropic expansion forces. (a) Open-pore free-energy landscape $U (r_{p o})$ for different SNARE copy numbers. Increasing SNARE copy numbers in NLP discs softens the energy barrier against pore expansion. For vNLP30 discs, the profile starts rising above $r_{p o} \approx 7$ nm (expected maximum size $r_{p o, m a x}^{N L P} \approx 7 - 8$ nm). If a vesicle were fusing instead of a NLP, dilation would presumably relax pore curvature and lower the energy (dashed curve marked ‘vesicle’). vMSP data were obtained in earlier work (Wu et al., 2016) using smaller, ~16 nm diameter nanodiscs stabilized by the membrane scaffold protein (MSP), with 7–9 v-SNARE copies. The maximum allowable pore size is limited to slightly above the 2 nm radius of MSP discs. The same energy minimum around $r_{p o} \approx 0.5$ nm is found regardless of copy numbers or the size of disc used, suggesting that this minimum represents an inherent property of fusing bilayers. (b) Corresponding free-energy profiles predicted by a mathematical model of the fusion pore with SNAREs (Materials and methods, Figure 7—figure supplement 1, and Table 1). Each curve shows the copy number and the net inward force (averaged over all pore sizes $r_{p o} > 1.5 nm$ ) tending to close down the pore to the minimum energy value. Membrane bending and tension resist pore expansion with a total force ~22 pN (SNARE-free pore, blue). In the presence of SNAREs, crowding effects produce an expansive entropic force that reduces the net inward force. The net force is progressively lowered with increasing numbers of SNAREs, reaching ~5 pN with 15 SNAREs. (c) Schematic illustrating a proposed SNARE-mediated pore expansion mechanism. Left: a few SNAREs can nucleate a pore, but dilation beyond a few nm is unlikely. Right: with many SNAREs, crowding generates expansion forces that are sufficient to offset the intrinsic bilayer resistance and to expand the pore. $h, δ, D$ and $ϕ$ are the height of the pore, the thickness of the membrane, the mean diameter of the vNLP discs, and the angle of twisting of the ApoE proteins, respectively. For definitions of other model parameters, see Materials and methods.

DOI: http://dx.doi.org/10.7554/eLife.22964.020

Figure 7—figure supplement 1. — The mathematical model describes a mechanism of pore expansion in which SNARE-crowding generates entropic expansion forces. (a) Open-pore free-energy landscape $U (r_{p o})$ for different SNARE copy numbers. Increasing SNARE copy numbers in NLP discs softens the energy barrier against pore expansion. For vNLP30 discs, the profile starts rising above $r_{p o} \approx 7$ nm (expected maximum size $r_{p o, m a x}^{N L P} \approx 7 - 8$ nm). If a vesicle were fusing instead of a NLP, dilation would presumably relax pore curvature and lower the energy (dashed curve marked ‘vesicle’). vMSP data were obtained in earlier work (Wu et al., 2016) using smaller, ~16 nm diameter nanodiscs stabilized by the membrane scaffold protein (MSP), with 7–9 v-SNARE copies. The maximum allowable pore size is limited to slightly above the 2 nm radius of MSP discs. The same energy minimum around $r_{p o} \approx 0.5$ nm is found regardless of copy numbers or the size of disc used, suggesting that this minimum represents an inherent property of fusing bilayers. (b) Corresponding free-energy profiles predicted by a mathematical model of the fusion pore with SNAREs (Materials and methods, Figure 7—figure supplement 1, and Table 1). Each curve shows the copy number and the net inward force (averaged over all pore sizes $r_{p o} > 1.5 nm$ ) tending to close down the pore to the minimum energy value. Membrane bending and tension resist pore expansion with a total force ~22 pN (SNARE-free pore, blue). In the presence of SNAREs, crowding effects produce an expansive entropic force that reduces the net inward force. The net force is progressively lowered with increasing numbers of SNAREs, reaching ~5 pN with 15 SNAREs. (c) Schematic illustrating a proposed SNARE-mediated pore expansion mechanism. Left: a few SNAREs can nucleate a pore, but dilation beyond a few nm is unlikely. Right: with many SNAREs, crowding generates expansion forces that are sufficient to offset the intrinsic bilayer resistance and to expand the pore. $h, δ, D$ and $ϕ$ are the height of the pore, the thickness of the membrane, the mean diameter of the vNLP discs, and the angle of twisting of the ApoE proteins, respectively. For definitions of other model parameters, see Materials and methods.

DOI: http://dx.doi.org/10.7554/eLife.22964.020