From shallow to full wrapping: geometry and deformability dictate lipid vesicle internalization

Alexander Brown; Halim Kusumaatmaja; Hanumantha Rao Vutukuri; Stijn van der Ham

REVIEW 2 major objections 4 minor 51 references

From shallow to full wrapping: geometry and deformability dictate lipid vesicle internalization

T0 review · 2 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A small vesicle's deformability can suppress its complete engulfment by a larger membrane even when enough membrane area exists, according to experiments and continuum simulations.

desk verdict Careful experiment/simulation study with a credible geometric wrapping transition; the deformability-suppression headline is promising but rests on two points, so treat as conditional. read the letter →

arxiv 2507.17434 v1 pith:WOKUKPVI submitted 2025-07-23 cond-mat.soft physics.bio-ph

Stijn van der Ham , Alexander Brown , Halim Kusumaatmaja , Hanumantha Rao Vutukuri This is my paper · ORCID

classification cond-mat.softphysics.bio-ph

keywords membranewrappinggiantunilamellarvesiclesdepletionadhesionbendo-capillarylengthreducedvolumeHelfrichfreeenergyendocyticengulfmentvesicledeformability

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks what controls whether a small lipid vesicle is swallowed by a larger one, and shows that the answer depends on whether the small vesicle is much larger or about the same size as the bendo-capillary length, the scale at which membrane bending and adhesion energies balance. In the geometry-dominated regime, full engulfment is decided by whether the large vesicle has enough excess membrane area, captured by the effective reduced volume $\nu_\gamma$ from Eq.~7. Near $R_{\rm small}/L \approx 1$, that geometric criterion is no longer enough: a more deformable small vesicle, one with lower reduced volume $\nu_{\rm small}$, needs stronger adhesion or a larger size ratio to become fully wrapped. The support comes from matching three-dimensional confocal reconstructions of real giant unilamellar vesicle pairs to energy-minimized continuum simulations, with the bendo-capillary length calibrated by curvature matching. If the paper is right, the same energy balance explains both endocytic and exocytic uptake and gives a unified framework for soft cargo internalization in synthetic and biological settings.

What carries the argument

The central object is the bendo-capillary length $L = \sqrt{\kappa/w}$, the scale at which membrane bending and adhesion energies balance, together with the reduced volume $\nu_i$ that measures how much excess membrane area a vesicle has and hence how deformable it is. The study organizes the problem around the ratio $R_{\rm small}/L$ and derives an effective reduced volume $\nu_\gamma$ (Eq.~7) for the large vesicle once it has wrapped the small one; the condition $\nu_\gamma \le 1$ is the geometric criterion for full engulfment. Energy-minimized continuum simulations of the Helfrich free energy (Eq.~8), with constant membrane area and volume enforced by Lagrange multipliers, supply the equilibrium morphologies and phase boundaries that the experiments are compared against.

What would settle it

Take a vesicle pair with $\nu_{\rm small} \approx 0.8$ and $R_{\rm small}/L \approx 1$ that lies just below the predicted full-wrapping boundary, slowly raise the adhesion strength until it wraps, then slowly lower it again; if the pair stays fully wrapped below the predicted boundary, or if partial wrapping persists where the boundary predicts full wrapping, the observed states are kinetically trapped rather than equilibrium ones.

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Extended reading notes

Core claim

The paper establishes a two-regime picture of vesicle-vesicle engulfment. When $R_{\rm small}/L \gg 1$, adhesion dominates over bending and the partial-to-full wrapping transition is governed by geometry alone: full engulfment is possible precisely when the effective reduced volume of the large vesicle after wrapping, $\nu_\gamma = (1+\phi)/(\nu_{\rm large}^{-2/3} - \phi^{2/3}\nu_{\rm small}^{-2/3})^{3/2}$, is at most 1. When $R_{\rm small}/L \approx 1$, full engulfment can be suppressed even if $\nu_\gamma < 1$, and the suppression grows as the small vesicle becomes more deformable: the transition curves require increasing adhesion strength, equivalently larger $R_{\rm small}/L$, as $\nu_{\rm small}$ drops from 0.99 to 0.80. Experiments and simulations agree on wrapping fractions and morphologies across volume ratios from 0.001 to 0.8 and size ratios from 1.6 to 19, and the measured bendo-capillary length is $L_{\rm exp} = 0.61 \pm 0.10\,\mu\rm m$. The paper therefore claims that deformability is not a minor correction but a decisive control parameter in the crossover regime, and that the same energetic balance explains both endocytic and exocytic engulfment.

Load-bearing premise

The comparison rests on the assumption that each measured vesicle pair has relaxed to the global minimum of the Helfrich free energy at fixed volume and area, so the computed equilibrium phase boundaries describe the experimental morphologies; the paper does not demonstrate that wrapping is reversible or that the states are not kinetically trapped by the narrow neck that forms near full wrapping.

Editorial extensions

If this is right

In the geometry-dominated regime, the outcome of engulfment can be predicted from three measured quantities, the volume ratio and the two reduced volumes, without needing a precise value of the adhesion strength or bending rigidity.
Near $R_{\rm small}/L \approx 1$, modest changes in the deformability of the cargo vesicle shift the adhesion strength required for full uptake, so softness is a practical control parameter for engulfment.
Increasing the excess membrane area of the large vesicle, for example by light-triggered area expansion, drives a pair from shallow to deep to full wrapping and offers an external switch for the process.
Because the same energy balance reproduces both endocytic and exocytic morphologies, the framework should transfer to uptake of soft carriers in synthetic-cell and drug-delivery contexts.
The cargo vesicle changes from oblate to prolate as wrapping deepens, so wrapping fraction and cargo shape co-evolve instead of the cargo staying rigid.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

An untested consequence of the equilibrium picture is reversibility: if adhesion is slowly removed, a fully wrapped vesicle should unwrap along the same path. The paper only shows progressive wrapping, so a direct unwrapping experiment would show whether the phase boundaries are thermodynamic or partly kinetic.
The single outlier near the geometric boundary suggests that bending energy can inhibit full engulfment even when Eq.~7 says it is possible; mapping the transition systematically at intermediate $R_{\rm small}/L$, roughly 2 to 10, would quantify how sharp the crossover really is.
The geometric criterion $\nu_\gamma \le 1$ treats the small vesicle through its volume and area only, so extending the framework to non-spherical or multi-domain cargo would require an effective shape parameter beyond the reduced volume.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a good paper, worth engaging. The experiments are careful, and the combination of 3D confocal reconstruction, Surface Evolver energy minimization, and a simple geometric transition condition (Eq. 7) gives a coherent picture of when GUVs fully engulf smaller GUVs under depletion adhesion. The curvature-matching calibration of L_exp from peak mean curvature is a genuinely useful idea, and the resulting L_exp = 0.61 ± 0.10 µm is credible. The state diagrams in Figs. 4-6 organize the data well.

What's new: the experimental demonstration that for R_small/L >> 1 the full-wrapping transition is set by the effective reduced volume νγ (Eq. 7), and that the data collapse onto that boundary despite a wide range of R_small/L from ~1.9 to 19. The azo-PC area-expansion control experiments are a nice touch, even if the estimated 3% area change is rough. The exocytic vs endocytic comparison is also valuable.

Soft spots: the central claim about deformability suppressing full engulfment near R_small/L ~ 1 rests on exactly two experimental points, both at νγ = 0.93, one fully wrapped at R/L = 7.1 and one partially wrapped at R/L = 2.9. That's a thin basis for the headline, and the text frankly says the outlier is 'close to the boundary' of the geometric regime. The stress-test worry that the partially wrapped state could be kinetically trapped is real but not fatal in my reading: the time series in Fig. 4B shows the system progressing to full wrapping, and the simulations reproduce the shape sequence, so the equilibrium assumption isn't obviously violated. Still, the authors don't test reversibility, and one pair is not enough to pin the deformability effect. I'd ask for more data points, error bars on the wrapping fractions, and a stability check (e.g., starting simulation from the fully wrapped state and seeing if it unwraps) before I'd take the suppression claim as established.

The calibration of L_exp by matching peak curvature to the same model used to predict the phase boundaries is a potential circularity, but it's really just parameter fitting; the wrapping fractions and state diagrams are independent outputs, so I don't see it as a flaw. The gravity explanation for large-vesicle shape mismatches is plausible but not tested directly.

Bottom line: the geometric transition (Eq. 7) is solid and likely to be cited; the deformability suppression is promising but under-supported. This deserves peer review and will probably survive with revisions. I'd bring it to our group meeting and cite it.

Referee Report

2 major / 4 minor

Summary. This manuscript combines confocal fluorescence imaging of GUV–GUV engulfment with Surface Evolver continuum simulations to map wrapping morphologies as functions of volume ratio, reduced volumes, and the ratio of small-vesicle size to the bendo-capillary length. The authors derive an analytic geometric condition for full engulfment in the R_small/L >> 1 regime (Eq. 7), calibrate L_exp by matching peak mean curvature, and construct state diagrams for endocytic and exocytic geometries. They report a geometry-dominated regime and a deformability-dominated regime near R_small/L ~ 1, where lower small-vesicle reduced volume suppresses complete wrapping despite sufficient excess area.

Significance. If the central claim holds, this is a valuable direct experimental test of long-standing theoretical predictions that soft-object deformability inhibits full engulfment, with implications for endocytosis, viral entry, and drug delivery. The paper's strengths include quantitative 3D morphometry, the clean analytic formula in Eq. 7, treatment of both endo- and exocytic geometries, and a photo-switchable area-expansion control. The main evidential weakness is that the headline deformability-suppression result rests on two experimental points and an untested equilibrium assumption, so the definitive status of that claim depends on additional experiments and analysis.

major comments (2)

[Modelling the vesicle-vesicle engulfment; Fig. 4B; Fig. 6] The central claim that deformability suppresses full wrapping when R_small/L ≈ 1 assumes each observed pair is at the global minimum of the Helfrich free energy in Eq. 8. Surface Evolver is a local gradient-descent minimizer from an initial guess, and the time series in Fig. 4B only shows progressive wrapping; no spontaneous unwrapping or repeated cycling is reported. A partially wrapped pair at R/L = 2.9 could be kinetically trapped behind the catenoidal-neck barrier rather than representing the equilibrium phase boundary in Fig. 6. Please test reversibility directly, for example by lowering the polymer concentration or switching azo-PC back from cis to trans and showing that partially and fully wrapped states interconvert, and/or by computing and reporting energy barriers from near-full initial configurations. Without such a test, the geometry-dominated result (Eq. 7, Fig. 5) remains secure, but the deformability-suppression claim is not fully supported.
[Fig. 6 and the 'nearly identical parameters' comparison after Fig. 5] The experimental evidence for Fig. 6 consists of two data points at νγ = 0.93 with R/L = 7.1 (fully wrapped) and R/L = 2.9 (partially wrapped). This single comparison carries the headline claim, but the manuscript does not tabulate all four dimensionless parameters for these two pairs, does not provide replicate counts or experimental uncertainties, and does not propagate the ±0.10 µm uncertainty in L_exp to R/L. If the two pairs differ appreciably in φ, ν_small, or ν_large, or if the R/L = 2.9 point has an uncertainty reaching the phase boundary, the attribution to R/L and deformability is confounded. Please provide a table with exact values and errors for all parameters of these pairs, and ideally add more data points in the R/L ≈ 1–5 range at fixed ν_small, with error bars on wrapping fractions as well.

minor comments (4)

[Fig. 3C] The wrapping fractions in Fig. 3C are shown without error bars or replicate counts; please state the number of independent vesicle pairs per condition and the measurement uncertainty, or acknowledge the absence of replicates in the figure caption.
[Eq. 2] As rendered in the arXiv text, Eq. 2 appears to define ν_i as the cube root of (4πV_i/A_i^{3/2}), which is not the standard reduced volume and would be inconsistent with Eq. 7. If the intended expression is ν_i = 3√(4π) V_i / A_i^{3/2}, please typeset it unambiguously.
[Data and materials availability] The availability statement says only that data are present in the paper and/or Supporting Information; please state whether Surface Evolver input files and analysis scripts are available, as this would strengthen reproducibility.
[Azo-PC area expansion] The estimated ~3% membrane area increase is inferred rather than measured directly; please clarify whether this is an upper bound and how the uncertainty affects the inferred ν_large values in Fig. 5B.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the bendo-capillary length is calibrated on curvature, while the central phase-boundary and wrapping-fraction comparisons are independent outputs of energy minimization and geometric bookkeeping.

full rationale

The paper's only fitted quantity is L_exp, obtained by matching the peak mean curvature of five experimental vesicle pairs to Surface Evolver simulations with varying L_sim (Eq. 5). This is a standard one-parameter calibration: the observable used in the fit is M*, a local curvature feature, not the wrapping fraction f, the partial/full wrapping state, or the location of the phase boundaries. The central claims are then tested against these independent observables. Eq. 7 is a geometric volume/area-accounting condition for whether full engulfment is geometrically possible; it is derived from the definitions of phi, nu_large and nu_small and does not contain L, so it cannot be forced by the calibration. The Fig. 6 transition curves are computed from total-energy curves as a function of wrapping fraction at fixed input parameters (nu_large = 0.75, three nu_small values), and the two experimental points at nu_gamma = 0.93 are placed on the resulting diagram after the fact; they are not used to construct the curves. No load-bearing uniqueness theorem or ansatz is imported solely from the authors' prior work; the cited prior theoretical studies are corroborative, not the derivation. The remaining reader concerns, such as the untested equilibrium assumption for the R/L = 2.9 partially wrapped pair and the sparse two-point experimental support for the deformability-suppression claim, are correctness or robustness risks rather than circularity: they do not show that any prediction reduces by construction to its fitted input. Accordingly, the derivation chain is self-contained apart from normal parameter calibration, and no circular step is identified.

Assumptions & free parameters 1 free parameters · 7 assumptions · 0 invented entities

The central claim depends on standard Helfrich mechanics, constant volume and area constraints, equal bending rigidities, a single effective adhesion strength, and the equilibrium assumption. The only fitted parameter is L_exp. The model excludes gravity, which is acknowledged to affect large vesicles. No invented entities are introduced.

free parameters (1)

bendo-capillary length L_exp (effective adhesion strength w) = 0.61 +/- 0.10 um
Calibrated by matching peak mean curvature M* between experimental and simulated vesicle shapes for five vesicle pairs. The theoretical estimate from kappa=25 kBT and AO adhesion strength gives 0.37 um; the difference is attributed to unmodeled effects such as polymer flexibility, polydispersity, and membrane fluctuations.

assumptions (7)

domain assumption Zero spontaneous curvature for both vesicle membranes.
Stated in the free energy (Eq. 8) and Methods: 'We assume zero spontaneous curvature.' DOPC membranes can have small spontaneous curvature, which would shift the phase boundaries.
domain assumption Equal bending rigidity for large and small vesicle, kappa_small = kappa_large = kappa.
Stated in Methods: 'We assume both vesicles have equal membrane bending constants.' Both are DOPC, but the small vesicle's curvature stress is not measured.
standard math Constant vesicle volume and membrane area enforced by Lagrange multipliers.
Stated in Modeling section: osmotic constraints and high area compressibility justify fixed V and A; this is standard in vesicle shape analysis.
domain assumption Adhesion energy is proportional to contact area with a single effective adhesion strength w.
Used in Eq. 8 and in the text E_ad = w A_c based on Asakura-Oosawa theory; ignores local curvature dependence, polymer flexibility, and membrane undulations, which the paper acknowledges can lower w.
domain assumption Observed experimental morphologies correspond to global energy minima of the Helfrich-type functional.
The model uses energy minimization and the paper describes 'equilibrium conformations'; no reversibility or hysteresis tests are reported, so metastable states are not ruled out.
domain assumption The catenoidal neck in fully wrapped states has zero bending energy and can be omitted.
Stated in Methods: the neck has zero bending energy, so full wrapping is modeled as two separate bodies; the justification is deferred to Supporting Fig. S6, not shown in the preprint text.
domain assumption Gravitational effects are negligible for most simulated shapes and are not included in the model.
The paper estimates gravity parameter g >= 16 for R_large >= 8.6 um and attributes shape discrepancies to gravity, but simulations do not include gravity.

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Cite this review

Pith. "Pith review of From shallow to full wrapping: geometry and deformability dictate lipid vesicle internalization." pith.science (2026). https://pith.science/paper/WOKUKPVI

@misc{pith2026250717434,
  author       = {Pith},
  title        = {Pith review of: From shallow to full wrapping: geometry and deformability dictate lipid vesicle internalization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WOKUKPVI}},
  note         = {Machine review of arXiv:2507.17434}
}

read the original abstract

The deformability of vesicles critically influences their engulfment by lipid membranes, a process central to endocytosis, viral entry, drug delivery, and intercellular transport. While theoretical models have long predicted this influence, direct experimental validation has remained elusive. Here, we combine experiments with continuum simulations to quantify how vesicle deformability affects the engulfment of small giant unilamellar vesicles (GUVs) by larger GUVs under depletion-induced adhesion. Using 3D confocal reconstructions, we extract vesicle shape, curvature, wrapping fraction, and the bendo-capillary length, a characteristic length scale that balances membrane bending and adhesion forces. We find that when vesicle size exceeds this length scale, engulfment is primarily governed by geometry. In contrast, when vesicle size is comparable to this scale, deformability strongly affects the transition between shallow, deep, and fully wrapped states, leading to suppression of full engulfment of vesicles. These findings connect theoretical predictions with direct measurements and offer a unified framework for understanding vesicle-mediated uptake across both synthetic and biological systems, including viral entry, synthetic cell design, drug delivery, and nanoparticle internalization.

Figures

Figures reproduced from arXiv: 2507.17434 by the authors.

**Figure 2.** FIG. 2. Calibration of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. Endo- (A) and exocytic (B) vesicle engulfment as a function of volume ratio [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4. State diagram of endocytic vesicle engulfment as a function of [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: FIG. 5. A) State diagram of the partially and fully wrapped state as a function of [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: FIG. 6. The partial to full wrapping transition as a function [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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Reference graph

Works this paper leans on

51 extracted references · 50 canonical work pages

[1]

Gy¨ orgy, T

B. Gy¨ orgy, T. G. Szab´ o, M. P´ aszt´ oi, Z. P´ al, P. Misj´ ak, B. Aradi, V. L´ aszl´ o, E. P´ allinger, E. Pap, A. Kittel,et al., Membrane vesicles, current state-of-the-art: emerging role of extracellular vesicles, Cellular and Molecular Life Sciences68, 2667 (2011)

work page 2011
[2]

Arandjelovic and K

S. Arandjelovic and K. S. Ravichandran, Phagocytosis of apoptotic cells in homeostasis, Nature Immunology16, 907 (2015)

work page 2015
[3]

F. S. Cohen, How viruses invade cells, Biophysical Jour- nal110, 1028 (2016)

work page 2016
[4]

Marsh and A

M. Marsh and A. Helenius, Virus entry: open sesame, Cell124, 729 (2006)

work page 2006
[5]

Klein, M

S. Klein, M. Cortese, S. L. Winter, M. Wachsmuth-Melm, C. J. Neufeldt, B. Cerikan, M. L. Stanifer, S. Boulant, R. Bartenschlager, and P. Chlanda, Sars-cov-2 structure and replication characterized by in situ cryo-electron to- mography, Nature Communications11, 5885 (2020)

work page 2020
[6]

Bayati, R

A. Bayati, R. Kumar, V. Francis, and P. S. McPher- son, Sars-cov-2 infects cells after viral entry via clathrin- mediated endocytosis, Journal of Biological Chemistry 296(2021)

work page 2021
[7]

T. M. Allen and P. R. Cullis, Liposomal drug delivery systems: from concept to clinical applications, Advanced Drug Delivery Reviews65, 36 (2013)

work page 2013
[8]

Guimar˜ aes, A

D. Guimar˜ aes, A. Cavaco-Paulo, and E. Nogueira, Design of liposomes as drug delivery system for therapeutic ap- plications, International Journal of Pharmaceutics601, 120571 (2021)

work page 2021

Show all 51 references

[9]

L. M. Bareford and P. W. Swaan, Endocytic mechanisms for targeted drug delivery, Advanced Drug Delivery Re- views59, 748 (2007)

2007
[10]

B. S. Joshi, M. A. de Beer, B. N. Giepmans, and I. S. Zuhorn, Endocytosis of extracellular vesicles and release of their cargo from endosomes, ACS Nano14, 4444 (2020)

2020
[11]

S. D. Conner and S. L. Schmid, Regulated portals of entry into the cell, Nature422, 37 (2003)

2003
[12]

Lipowsky and H.-G

R. Lipowsky and H.-G. D¨ obereiner, Vesicles in contact with nanoparticles and colloids, Europhysics Letters43, 219 (1998)

1998
[13]

Dasgupta, T

S. Dasgupta, T. Auth, and G. Gompper, Shape and ori- entation matter for the cellular uptake of nonspherical particles, Nano Letters14, 687 (2014)

2014
[14]

van der Ham, J

S. van der Ham, J. Agudo-Canalejo, and H. R. Vutukuri, Role of shape in particle-lipid membrane interactions: from surfing to full engulfment, ACS Nano18, 10407 (2024)

2024
[15]

A. H. Bahrami, Orientational changes and impaired in- ternalization of ellipsoidal nanoparticles by vesicle mem- branes, Soft Matter9, 8642 (2013)

2013
[16]

Agudo-Canalejo and R

J. Agudo-Canalejo and R. Lipowsky, Critical particle sizes for the engulfment of nanoparticles by membranes and vesicles with bilayer asymmetry, ACS Nano9, 3704 (2015)

2015
[17]

Agudo-Canalejo, Particle engulfment by strongly asymmetric membranes with area reservoirs, Soft Mat- ter17, 298 (2021)

J. Agudo-Canalejo, Particle engulfment by strongly asymmetric membranes with area reservoirs, Soft Mat- ter17, 298 (2021)

2021
[18]

H. T. Spanke, R. W. Style, C. Fran¸ cois-Martin, M. Fe- ofilova, M. Eisentraut, H. Kress, J. Agudo-Canalejo, and E. R. Dufresne, Wrapping of microparticles by floppy lipid vesicles, Physical Review Letters125, 198102 (2020)

2020
[19]

A. H. Bahrami, M. Raatz, J. Agudo-Canalejo, R. Michel, E. M. Curtis, C. K. Hall, M. Gradzielski, R. Lipowsky, and T. R. Weikl, Wrapping of nanoparticles by mem- branes, Advances in Colloid and Interface Science208, 214 (2014)

2014
[20]

X. Yi, X. Shi, and H. Gao, Cellular uptake of elas- tic nanoparticles, Physical Review Letters107, 098101 (2011)

2011
[21]

Yi and H

X. Yi and H. Gao, Incorporation of soft particles into lipid vesicles: Effects of particle size and elasticity, Lang- muir32, 13252 (2016)

2016
[22]

Imoto, S

Y. Imoto, S. Raychaudhuri, Y. Ma, P. Fenske, E. San- doval, K. Itoh, E.-M. Blumrich, H. T. Matsubayashi, L. Mamer, F. Zarebidaki,et al., Dynamin is primed at en- docytic sites for ultrafast endocytosis, Neuron110, 2815 (2022)

2022
[23]

H. Tang, H. Zhang, H. Ye, and Y. Zheng, Wrapping of a deformable nanoparticle by the cell membrane: insights into the flexibility-regulated nanoparticle-membrane in- teraction, Journal of Applied Physics120(2016)

2016
[24]

Midya, T

J. Midya, T. Auth, and G. Gompper, Membrane- mediated interactions between nonspherical elastic par- ticles, ACS Nano17, 1935 (2023)

2023
[25]

Satarifard and R

V. Satarifard and R. Lipowsky, Mutual remodeling of interacting nanodroplets and vesicles, Communications Physics6, 6 (2023)

2023
[26]

Kusumaatmaja and R

H. Kusumaatmaja and R. Lipowsky, Droplet-induced budding transitions of membranes, Soft Matter7, 6914 (2011)

2011
[27]

A. C. Anselmo, M. Zhang, S. Kumar, D. R. Vogus, S. Menegatti, M. E. Helgeson, and S. Mitragotri, Elas- ticity of nanoparticles influences their blood circulation, phagocytosis, endocytosis, and targeting, ACS Nano9, 3169 (2015)

2015
[28]

J. Sun, L. Zhang, J. Wang, Q. Feng, D. Liu, Q. Yin, D. Xu, Y. Wei, B. Ding, X. Shi,et al., Tunable rigidity of (polymeric core)-(lipid shell) nanoparticles for regulated cellular uptake., Advanced Materials27, 1402 (2014)

2014
[29]

Dimova and C

R. Dimova and C. Marques,The giant vesicle book(CRC Press, 2019)

2019
[30]

Dinsmore, D

A. Dinsmore, D. Wong, P. Nelson, and A. Yodh, Hard spheres in vesicles: curvature-induced forces and particle- induced curvature, Physical Review Letters80, 409 (1998)

1998
[31]

Asakura and F

S. Asakura and F. Oosawa, On interaction between two bodies immersed in a solution of macromolecules, The Journal of Chemical Physics22, 1255 (1954)

1954
[32]

Machado, V

S. Machado, V. Mercier, and N. Chiaruttini, Limeseg: a coarse-grained lipid membrane simulation for 3d image segmentation, BMC Bioinformatics20, 1 (2019)

2019
[33]

Schindelin, I

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid,et al., Fiji: an open-source plat- form for biological-image analysis, Nature Methods9, 676 (2012)

2012
[34]

Seifert, K

U. Seifert, K. Berndl, and R. Lipowsky, Shape trans- formations of vesicles: Phase diagram for spontaneous- curvature and bilayer-coupling models, Physical Review A44, 1182 (1991). 14

1991
[35]

H. A. Faizi, C. J. Reeves, V. N. Georgiev, P. M. Vla- hovska, and R. Dimova, Fluctuation spectroscopy of gi- ant unilamellar vesicles using confocal and phase contrast microscopy, Soft Matter16, 8996 (2020)

2020
[36]

Francois, D

J. Francois, D. Sarazin, T. Schwartz, and G. Weill, Poly- acrylamide in water: molecular weight dependence of <R2>and [η] and the problem of the excluded vol- ume exponent, Polymer20, 969 (1979)

1979
[37]

Tuinier and H

R. Tuinier and H. Lekkerkerker, Excluded-volume polymer-induced depletion interaction between parallel flat plates, The European Physical Journal E6, 129 (2001)

2001
[38]

Helfrich and R

W. Helfrich and R. M. Servuss, Undulations, steric in- teraction and cohesion of fluid membranes, Il Nuovo Ci- mento D3, 137 (1984)

1984
[39]

Lipowsky and E

R. Lipowsky and E. Sackmann,Structure and dynamics of membranes: I. from cells to vesicles/II. generic and specific interactions(Elsevier, 1995)

1995
[40]

N.-N. Deng, M. Yelleswarapu, L. Zheng, and W. T. Huck, Microfluidic assembly of monodisperse vesosomes as ar- tificial cell models, Journal of the American Chemical Society139, 587 (2017)

2017
[41]

Kraus, U

M. Kraus, U. Seifert, and R. Lipowsky, Gravity-induced shape transformations of vesicles, Europhysics Letters 32, 431 (1995)

1995
[42]

Pernpeintner, J

C. Pernpeintner, J. A. Frank, P. Urban, C. R. Roeske, S. D. Pritzl, D. Trauner, and T. Lohmu¨ uller, Light- controlled membrane mechanics and shape transitions of photoswitchable lipid vesicles, Langmuir33, 4083 (2017)

2017
[43]

Aleksanyan, A

M. Aleksanyan, A. Grafm¨ uller, F. Crea, V. N. Georgiev, N. Yandrapalli, S. Block, J. Heberle, and R. Dimova, Photomanipulation of minimal synthetic cells: Area in- crease, softening, and interleaflet coupling of membrane models doped with azobenzene-lipid photoswitches, Ad- v...

2023
[44]

Mangiarotti, M

A. Mangiarotti, M. Aleksanyan, M. Siri, T.-W. Sun, R. Lipowsky, and R. Dimova, Photoswitchable endocy- tosis of biomolecular condensates in giant vesicles, Ad- vanced Science11, 2309864 (2024)

2024
[45]

Agudo-Canalejo, Engulfment of ellipsoidal nanopar- ticles by membranes: full description of orientational changes, Journal of Physics: Condensed Matter32, 294001 (2020)

J. Agudo-Canalejo, Engulfment of ellipsoidal nanopar- ticles by membranes: full description of orientational changes, Journal of Physics: Condensed Matter32, 294001 (2020)

2020
[46]

H. R. Vutukuri, M. Hoore, C. Abaurrea-Velasco, L. van Buren, A. Dutto, T. Auth, D. A. Fedosov, G. Gompper, and J. Vermant, Active particles induce large shape de- formations in giant lipid vesicles, Nature586, 52 (2020)

2020
[47]

A. Moga, N. Yandrapalli, R. Dimova, and T. Robinson, Optimization of the inverted emulsion method for high- yield production of biomimetic giant unilamellar vesicles, ChemBioChem20, 2674 (2019)

2019
[48]

J. A. Frank, D. A. Yushchenko, D. J. Hodson, N. Lip- stein, J. Nagpal, G. A. Rutter, J.-S. Rhee, A. Gottschalk, N. Brose, C. Schultz,et al., Photoswitchable diacylglyc- erols enable optical control of protein kinase c, Nature Chemical Biology12, 755 (2016)

2016
[49]

H. M. Weakly, K. J. Wilson, G. J. Goetz, E. L. Pruitt, A. Li, L. Xu, and S. L. Keller, Several common meth- ods of making vesicles (except an emulsion method) cap- ture intended lipid ratios, Biophysical Journal123, 3452 (2024)

2024
[50]

E. E. Diel, J. W. Lichtman, and D. S. Richardson, Tu- torial: avoiding and correcting sample-induced spherical aberration artifacts in 3d fluorescence microscopy, Nature Protocols15, 2773 (2020)

2020
[51]

Jacobson, D

A. Jacobson, D. Panozzo,et al., libigl: A sim- ple C++ geometry processing library (2018), https://libigl.github.io/

2018

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Gy¨ orgy, T

B. Gy¨ orgy, T. G. Szab´ o, M. P´ aszt´ oi, Z. P´ al, P. Misj´ ak, B. Aradi, V. L´ aszl´ o, E. P´ allinger, E. Pap, A. Kittel,et al., Membrane vesicles, current state-of-the-art: emerging role of extracellular vesicles, Cellular and Molecular Life Sciences68, 2667 (2011)

work page 2011

[2] [2]

Arandjelovic and K

S. Arandjelovic and K. S. Ravichandran, Phagocytosis of apoptotic cells in homeostasis, Nature Immunology16, 907 (2015)

work page 2015

[3] [3]

F. S. Cohen, How viruses invade cells, Biophysical Jour- nal110, 1028 (2016)

work page 2016

[4] [4]

Marsh and A

M. Marsh and A. Helenius, Virus entry: open sesame, Cell124, 729 (2006)

work page 2006

[5] [5]

Klein, M

S. Klein, M. Cortese, S. L. Winter, M. Wachsmuth-Melm, C. J. Neufeldt, B. Cerikan, M. L. Stanifer, S. Boulant, R. Bartenschlager, and P. Chlanda, Sars-cov-2 structure and replication characterized by in situ cryo-electron to- mography, Nature Communications11, 5885 (2020)

work page 2020

[6] [6]

Bayati, R

A. Bayati, R. Kumar, V. Francis, and P. S. McPher- son, Sars-cov-2 infects cells after viral entry via clathrin- mediated endocytosis, Journal of Biological Chemistry 296(2021)

work page 2021

[7] [7]

T. M. Allen and P. R. Cullis, Liposomal drug delivery systems: from concept to clinical applications, Advanced Drug Delivery Reviews65, 36 (2013)

work page 2013

[8] [8]

Guimar˜ aes, A

D. Guimar˜ aes, A. Cavaco-Paulo, and E. Nogueira, Design of liposomes as drug delivery system for therapeutic ap- plications, International Journal of Pharmaceutics601, 120571 (2021)

work page 2021