On the effect of applied lateral tension on the deformation energetics of biological membranes and the lipid dynamics within

Yein Christina Park; Giacomo Fiorin; José D. Faraldo‐Gómez

doi:10.1016/j.bpj.2026.09.038

Biophysical JournalSep 1, 2026BiophysicsPeer-reviewed journal article

On the effect of applied lateral tension on the deformation energetics of biological membranes and the lipid dynamics within

Yein Christina Park iD, Giacomo Fiorin iD, José D. Faraldo‐Gómez iD

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Abstract

A broad range of cellular functions involve transient or persistent changes in the morphology of lipid membranes, from the organellar to the molecular scale. By and large, the thermodynamics of protein-mediated remodeling, which often distort the membrane beyond its thermally accessible undulations, remain to be understood. Molecular Dynamics simulations enhanced by advanced sampling methods are uniquely suited to examine and quantitate these phenomena. Here, we leverage the Multi-Map simulation method to directly quantify how applied lateral tension impacts the energetics of both global and localized membrane perturbations induced extrinsically. We obtain free-energy profiles of curvature and thickness deformations with and without tension, which allow us to test the quadratic approximations of Helfrich-based continuum theories. We find that these continuum models are applicable up to ~ 20 kBT, beyond which they under-estimate the free-energy cost of bending. However, we find that the effect of tension on these deformations is primarily driven by changes in the projected area of the membrane, and therefore consistent with continuum theory, even beyond 30 kBT. These changes outpace the effects of tension on lipid packing and diffusion, and importantly we find that tension levels preceding rupture ([≤] 10 mN/m) do not impede complete lipid mixing. Finally, we investigate the free-energy landscapes of membrane thickness and lipid enrichment with a heterogeneous lipid composition and show that strong enrichment can be sustained even under steady exchange of the constituent lipid molecules.

In-depth summary

Claude Opus 5.5 · xhigh effort · 8 Nov 2026 · from the full text of version 2 (31 Aug 2026) · CC0 1.0

MARTINI 2.2 simulations show lateral tension changes the free energies of membrane bending and thickness deformations through a projected-area term (γΔΔA), while leaving lipid mixing, residence and exchange essentially unchanged.

Mechanosensitive channels respond to membrane stretch, but whether tension acts through lipid residence near proteins ('pulling' or delipidation models) or through the energetic cost of membrane deformations has been unclear. Continuum models (Helfrich and extensions) had not been tested on large, thermally inaccessible curvature and thickness deformations under tension; Multi-Map enhanced-sampling simulations here compute those free energies from molecular forces alone.

Key results

ShownApplied tension does not push lipids outward. A randomly chosen half of the POPC lipids was biased into or out of a central cylinder, and the free energy, entry rates and dwell times were the same with or without 10 mN/m stretch.
At 0 and 10 mN/m, PMFs for POPCspecial occupancy of a 10-Å-radius cylinder (~8 lipids per leaflet, 800 POPC) both follow the entropic prediction (Eq. 10), with minima at 50% occupancy. Virtually all lipids entered within 5 µs, and dwell-time distributions (tens of ns to µs) were unchanged. Lipid mixing was nearly complete by 2 µs whatever the tension or thickness defect. · Does applied lateral stretch influence the…; Effect of applied lateral stretch on localized…; Figure legends
ShownUnder 10 mN/m, the extra cost of sinusoidally bending a 155-Å POPC bilayer equals the tension times the loss of projected area (γΔΔA). This holds even where the PMF is no longer quadratic in curvature and the Helfrich prediction fails.
A Helfrich-based prediction using kc and kt from resting runs matches the tensionless PMF up to ~20 kBT, then deviates. Adding γΔΔA (Eq. 8) to the tensionless PMF gives a curve nearly identical to the PMF computed directly at 10 mN/m. Sampling used 41 umbrella windows of 1 µs; PMF errors range from 0.002 to 0.19 kBT. · Effect of applied lateral stretch on global…; Umbrella-sampling simulations using Multi-Map…; Figure legends
ShownTension shifts the free-energy profile of a localized thickness defect toward thinner states, again explained by γΔΔA (which penalizes thickening and favors thinning). Aligned at their minima, the stretched and unstretched profiles have a similar shape for changes under 5 Å.
10 mN/m thins the bulk bilayer (tb) by ~0.7 Å. The tensionless PMF plus γΔΔA (Eq. 9, σ = 8 Å) closely matches the PMF computed at 10 mN/m over 6 Å thinning to 6 Å thickening. The continuum model fits reasonably well, and better at large deformations with a Poisson ratio of 0.425 than with 0.5. · Effect of applied lateral stretch on localized…; Comparison of free-energy profiles to…; Figure legends
ShownIn bilayers at rest, tension up to 10 mN/m changes structure linearly but leaves the bending and tilt moduli unchanged. Its main effect is to damp long-wavelength undulations; it barely affects the <100 Å scale relevant to proteins.
Area per lipid rises 0.31% (200 lipids) and 0.34% (5,000 lipids) per mN/m, giving KA of 322 ± 38 and 294 ± 11 mN/m; diffusivity rises ~0.6% per mN/m. kc = 16.3 ± 0.7 kcal/mol and kt = 0.15 ± 0.02 kcal/mol/Å^2 fit every tension. 10 mN/m suppresses 400, 100 and 50 Å modes by 76%, 13% and 2% (1.43, 0.14 and 0.02 kBT). · Effect of applied lateral stretch on membranes…; Figure legends
ShownIn a 1:1 POPC:DLPC bilayer, the thickness-defect PMF shifts toward thinner states more than it does under tension, following the thinner bulk. DLPC spontaneously gathers in thinned defects and leaves thickened ones, without slowing lipid exchange.
Mixed bulk thickness is ~2.3 Å below pure POPC (tb 28.2 Å), against ~0.07 Å per mN/m from tension. Aligned PMFs differ only by slight softening beyond ~5 Å thinning or ~3 Å thickening. DLPC departs from 1:1 by up to 80% in the thinned defect; de-mixing entropy is ~2-2.5 kBT at the extremes. All lipids visited the defect within 4 µs, with near-identical dwell times. · Localized thinning and thickening defects in a…; Figure legends

Methods, data and reproducibility

MARTINI 2.2 molecular dynamics of POPC and 1:1 POPC:DLPC bilayers at 0 to 10 mN/m tension: ~100 µs conventional runs gave structure and bending/tilt moduli from fluctuation spectra. Multi-Map umbrella sampling gave PMFs for sinusoidal bending and a Gaussian thickness defect, compared with continuum predictions, and for biased lipid occupancy of a cylinder, compared with a purely entropic prediction.

POPC bilayer, 78 × 78 Å^2, conventional MD at several tensions from 0 to 10 mN/m (~100 µs per tension) · n = 200 lipids
POPC bilayer, 390 × 390 Å^2, conventional MD at several tensions from 0 to 10 mN/m; used for fluctuation spectra and diffusivity · n = 5,000 lipids
POPC bilayer, 155 × 155 Å^2, built with insane; Multi-Map umbrella sampling of bending, thickness defect and lipid occupancy at 0 and 10 mN/m · n = 800 lipids; 22,944 water particles
1:1 POPC:DLPC bilayer, 155 × 155 Å^2, symmetric leaflets; thickness-defect umbrella sampling without tension · n = 800 lipids; 23,753 water particles

Methods & tools: GROMACS 2018.8, NAMD 2.14, MARTINI 2.2 force field, insane, Multi-Map, Colvars, umbrella sampling, WHAM, MOSAICS, MDAnalysis, martini2_in_namd
Code: https://github.com/1004parky/martini2_in_namd https://colvars.github.io/https://www.ks.uiuc.edu/Research/namd/
Software & environment: GROMACS 2018.8 and NAMD 2.14 with the MARTINI 2.2 force field; representative GROMACS .mdp and NAMD .in parameter files deposited on Zenodo.
Reproducibility gaps: Zenodo deposit (initial/final snapshots, parameter files) is mentioned without a link or DOI; full trajectories (1.5 TB) only on request from the authors; the study-specific Python code is said to be on GitHub, but the only repository link given is the MARTINI-to-NAMD converter.

Limitations (5)

All bilayers are protein-free. The authors state they saw the same behaviour in systems with embedded proteins, but that evidence is not presented here. · noted in this summary
The conclusion that lipid de-mixing leaves elastic properties unchanged is qualified as holding for MARTINI 2.2 lipids, and the slight PMF softening beyond 5 Å lies within the estimated error of the moduli. · stated by the authors
Helfrich-based bending predictions diverge from the simulated PMF above ~20 kBT, possibly because these models are quadratic approximations. Volume incompressibility (Poisson ratio 0.5) did not hold, so 0.425 was estimated from the simulations. · stated by the authors
Only one lipid mixture was studied. The authors call for other mixtures, and for atomistic, asymmetric or non-planar bilayers, in future work. · stated by the authors
Induced deformations were tested at a single nonzero tension (10 mN/m), and the mixed POPC:DLPC thickness PMF is reported only without tension, so the effect of tension in heterogeneous membranes is not directly tested. · noted in this summary

Read this if you study mechanosensitive channels or membrane-protein energetics and want simulation evidence that tension acts through deformation cost (γΔΔA) rather than lipid residence, or a Multi-Map protocol for membrane free energies.