Spontaneous Curvature and Differential Leaflet Tension Are Additive Drives for Outward Membrane Budding
- 1Slovakia
Abstract
Two recent models derive outward plasma-membrane budding from different starting points. Mahapatra, Malingen and Rangamani treat a microparticle as a Helfrich membrane in which phosphatidylserine exposed on the outer leaflet imposes a local spontaneous curvature over a prescribed domain, coupled to cortex linkers modelled as springs. Our own treatment derives an energetic threshold from the differential tension between leaflets generated by a net transbilayer lipid flux, with vesicle size as an output rather than an input. Here we show that the two are not alternatives: they are the two linear terms of one energy functional. Writing the bud energy with both a spontaneous curvature c0 and a differential leaflet tension ∆τ , the expression collapses—once the energy the flat reference state already carries at the same spontaneous curvature is subtracted—to the canonical form ∆E(r) = 8πκ − 4πFr + 4πΣr2, with an additive drive F = 2κc0 + h ∆τ and a resistance Σ = σ + w + KAh2/R2 containing neither drive. Budding requires F 2 > 8κΣ; the bud radius is r∗ = F/2Σ, equal to √ 2κ/Σ on the threshold locus. The additivity is exact. It is the single effective combination already known from area-difference elasticity [5, 7], written here as a force and thereby made comparable between the two treatments. A dimensionless ratio Ξ = 2κc0/(h∆τ) orders the contributions, and we exhibit a case in which each drive alone leaves the membrane below threshold, at 0.25 and 0.49 of it, while together they carry it across at 1.44 and bud at 91 nm. Evaluated with the bending moduli and boundary tensions of the curvature model, r∗ spans 41–414 nm and brackets the 45–63 nm domain sizes that model takes as input, which is a consistency check rather than a discriminating test. Retaining the KAh2/R2 term repairs the tension-free limit: the threshold does not vanish but tends to ∆ac → √ 2κ/KA/h, recovering the O(1) areadifference criterion as a derived result. We then argue that the two drives are not simultaneous—one scramblase generates differential leaflet tension transiently and spontaneous curvature persistently, so Ξ sweeps across a single calcium response, and the departing bud exports the phosphatidylserine that drove it—which makes the discriminating experiment a time course rather than a titration.
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BibTeX
@misc{mikulas2026spontaneous,
title = {{Spontaneous Curvature and Differential Leaflet Tension Are Additive Drives for Outward Membrane Budding}},
author = {Peter Mikuláš},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15010825/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010825/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Spontaneous Curvature and Differential Leaflet Tension Are Additive Drives for Outward Membrane Budding
AU - Peter Mikuláš
PY - 2026
DA - 2026/10/22
PB - ChemRxiv
DO - 10.26434/chemrxiv.15010825/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010825/v1
AB - Two recent models derive outward plasma-membrane budding from different starting points. Mahapatra, Malingen and Rangamani treat a microparticle as a Helfrich membrane in which phosphatidylserine exposed on the outer leaflet imposes a local spontaneous curvature over a prescribed domain, coupled to cortex linkers modelled as springs. Our own treatment derives an energetic threshold from the differential tension between leaflets generated by a net transbilayer lipid flux, with vesicle size as an output rather than an input. Here we show that the two are not alternatives: they are the two linear terms of one energy functional. Writing the bud energy with both a spontaneous curvature c0 and a differential leaflet tension ∆τ , the expression collapses—once the energy the flat reference state already carries at the same spontaneous curvature is subtracted—to the canonical form ∆E(r) = 8πκ − 4πFr + 4πΣr2, with an additive drive F = 2κc0 + h ∆τ and a resistance Σ = σ + w + KAh2/R2 containing neither drive. Budding requires F 2 > 8κΣ; the bud radius is r∗ = F/2Σ, equal to √ 2κ/Σ on the threshold locus. The additivity is exact. It is the single effective combination already known from area-difference elasticity [5, 7], written here as a force and thereby made comparable between the two treatments. A dimensionless ratio Ξ = 2κc0/(h∆τ) orders the contributions, and we exhibit a case in which each drive alone leaves the membrane below threshold, at 0.25 and 0.49 of it, while together they carry it across at 1.44 and bud at 91 nm. Evaluated with the bending moduli and boundary tensions of the curvature model, r∗ spans 41–414 nm and brackets the 45–63 nm domain sizes that model takes as input, which is a consistency check rather than a discriminating test. Retaining the KAh2/R2 term repairs the tension-free limit: the threshold does not vanish but tends to ∆ac → √ 2κ/KA/h, recovering the O(1) areadifference criterion as a derived result. We then argue that the two drives are not simultaneous—one scramblase generates differential leaflet tension transiently and spontaneous curvature persistently, so Ξ sweeps across a single calcium response, and the departing bud exports the phosphatidylserine that drove it—which makes the discriminating experiment a time course rather than a titration.
ER -