Cell-Scale Dynamic Modeling of Membrane Interactions with Arbitrarily Shaped Particles

Didarul Ahasan Redwan; Justin Reicher; Xin Yong

REVIEW 4 major objections 5 minor 25 references

Cell-Scale Dynamic Modeling of Membrane Interactions with Arbitrarily Shaped Particles

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Heavy particles stall membrane wrapping; light ones finish it

desk verdict Solid extension of the authors' spherical wrapping model to arbitrary particle shapes, with a convincing vertex-to-surface benchmark, but the mass-ratio result is confounded with drag and the unit conversion has an error. read the letter →

arxiv 2506.02376 v2 pith:VO4TXRCJ submitted 2025-06-03 cond-mat.soft physics.bio-ph

Didarul Ahasan Redwan , Justin Reicher , Xin Yong This is my paper

classification cond-mat.softphysics.bio-ph

keywords membranewrappingtriangulatedmeshLangevindynamicsrigid-bodyrotationparticleinertiaanisotropicparticlesvesicledeformationMorseadhesion

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 presents a force-based computational framework for simulating how a deformable lipid vesicle membrane wraps around rigid particles of arbitrary shape, which matters for predicting cellular uptake of irregular environmental micro- and nanoplastics and for designing shaped nanocarriers. Its central claim is that a triangulated-mesh representation of both membrane and particle, combined with a vertex-to-surface distance scheme for adhesion, reproduces accurate wrapping energetics and resolves the coupled translation and rotation of the particle. Dynamic simulations show that the particle-to-vesicle mass ratio controls the outcome: lighter particles reorient repeatedly and achieve complete engulfment, while heavier particles keep their initial orientation and settle into partially wrapped states. The same framework reproduces experimentally observed 'surfing' to engulfment sequences for rods and handles cubes, bowls, tetrahedra, and non-spherical vesicles.

What carries the argument

The load-bearing machinery is a pair of triangulated surface meshes: the vesicle is a deformable mesh governed by the Canham-Helfrich bending energy with quadratic area and volume constraints, and the rigid particle is a second mesh whose motion is integrated as a rigid body with quaternion-based rotational updates. Adhesion between the two surfaces is a Morse potential applied per membrane vertex, with the separation computed either by nearest-neighbor vertex bonds (vertex-to-vertex) or by the shortest Euclidean distance to any particle face, edge, or vertex, with the sign of the distance assigned through an angle-weighted pseudonormal (vertex-to-surface). The vertex-to-surface projection is the element that makes the wrapping energetics accurate at high wrapping fractions, and the combination of deterministic Langevin dynamics for membrane vertices with torque-balance rigid-body rotation for the particle is what lets the framework resolve reorientation kinetics.

What would settle it

Run the same cube-on-biconcave-vesicle simulation with random thermal kicks at the kBT level switched on; if heavy particles then still reorient and wrap completely, the predicted inertia-driven arrest is an artifact of the deterministic equations.

Watch

Extended reading notes

Core claim

The central discovery is that wrapping of arbitrarily shaped particles by a vesicle is governed by a three-way interplay of particle orientation, local membrane curvature, and adhesion strength, and that a simulation can capture this interplay if the membrane-particle separation is measured as the true closest-point distance to the particle's triangulated surface. The vertex-to-vertex scheme, which bonds nearest mesh vertices, overestimates bending and total energies once the wrapping fraction exceeds about 0.6 because residual vertex-face distances keep the Morse potential artificially large; the vertex-to-surface scheme eliminates this error and matches the energetics of an ideal parametric sphere. With that scheme, the paper shows that particle inertia acts as a switch: at low particle-to-vesicle mass ratios the particle rotates between corner-attack and face-attack poses and fully wraps, whereas at high mass ratios the heavy particle cannot reorient and remains stuck in a partial wrap. The authors argue that this geometry-agnostic, force-based approach resolves time-resolved entry trajectories, not just equilibrium states, and can be applied to any rigid particle shape represented by a mesh.

Load-bearing premise

The equations of motion assume the membrane and particle move through a uniform, quiet fluid with no random thermal kicks, no position-dependent drag, and no active cellular machinery, so if those effects matter at the nanoscale, the predicted reorientation sequence and the stability of partially wrapped states could change.

Editorial extensions

If this is right

The vertex-to-surface adhesion scheme is the one to use for membrane-wrapping simulations; vertex-to-vertex bonding overestimates energies above a wrapping fraction of about 0.6 and can misstate the engulfment barrier.
Particle inertia is a control parameter for uptake: low particle-to-vesicle mass ratios allow multiple reorientations and complete wrapping, while high ratios stabilize partial wrapping, consistent with slower uptake of heavier nanoparticles observed in macrophages.
The adhesion strength needed for full engulfment depends on shape and initial pose: side-wise rods wrap at lower adhesion than tip-wise rods, and cubical particles at a cigar vesicle's saddle-shaped waist wrap at lower adhesion than at the convex pole.
Complex shapes such as bowls and tetrahedra find wrapping pathways by reorienting to match local membrane curvature; when curvature is complementary full engulfment occurs, otherwise wrapping arrests at the rim or edge.
The framework reproduces the experimentally observed sequence for rod-shaped particles, from initial 'surfing' along the vesicle to reorientation and full engulfment.

Reading between the lines

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

If thermal noise and hydrodynamic interactions were added at the nanoscale, the sharp mass-ratio boundary between full and partial wrapping could soften, because kBT fluctuations can drive barrier crossing that the deterministic equations forbid; the paper explicitly acknowledges this limitation.
The mass-ratio result suggests a testable design rule for drug delivery: for a fixed shape and surface chemistry, hollow or low-density particles should be internalized faster and more completely than dense ones, assuming the same adhesion.
Because the framework treats any closed mesh as a rigid particle, it could be extended to active uptake by adding forces from actin polymerization or curved membrane proteins, with the present passive results serving as the baseline.
The reported dependence of wrapping kinetics on mesh resolution implies that quantitative rates should be interpreted with care, while the qualitative pathways and final states are robust.

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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

Redwan et al. extend their earlier force-based vesicle model from spheres to arbitrarily shaped triangulated particles, adding rigid-body rotation and comparing two adhesion schemes. The strongest part is the benchmark: vertex-to-vertex bonds overestimate energies at high wrapping, while vertex-to-surface reproduces the parametric-sphere results. That is a clean, useful methodological result. The demonstrations with cubes, rods, bowls, and tetrahedra against spherical, cigar, and biconcave vesicles show the tool's versatility, and the rod case compares favorably with van der Ham's experiments.

The soft spots are real but not fatal. The mass-ratio study in Sec. 3.2 varies m_p and gamma_p together (m_p/gamma_p fixed at 1), so the scan changes both inertia and translational drag. The text attributes the reorientation suppression to inertia, but the heavier particle also has lower mobility. The rotational damping torque scales with I, so the angular acceleration from adhesion torques is tau/I, which does decrease with mass; that part is inertial. But the translational response is also slower because gamma_p scales with m_p, so the distinction between inertia and drag is blurred. I'd like to see a control simulation with m_p varied while gamma_p is held constant (or vice versa) before trusting the inertia narrative.

Table 1 also has a unit-conversion inconsistency: with l0 = 10 um and tau = 0.05 s, the listed particle mass (2e-14 kg) and drag (4.1e-6 nN*s/um) give m/gamma approximately 5e-6 s, not 0.05 s. So the advertised m = gamma = 1 intermediate-damping regime does not translate to physical units. The sign convention for adhesion energy in Eqs. 5-6 is ambiguous: V(d) is negative at contact, but Eq. 5 adds a minus sign, giving positive adhesion energy; that seems backwards and needs clarification. The deterministic dynamics is a stated simplification, though it limits quantitative nanoscale claims.

No code or data is released, which is a genuine reproducibility gap for a methods paper. The mesh-convergence checks help, but the framework would be much stronger with open code.

Overall, this is a useful contribution for the membrane-particle simulation community, and the vertex-to-surface scheme is a genuine improvement. It deserves a serious referee. I would recommend major revision: fix the unit conversion, clarify the sign convention, and either re-run the mass-ratio study (or at least re-frame the discussion) to separate inertia from drag. I would not cite the mass-ratio result as established until that is resolved. The paper is aimed at computational soft matter and biophysics researchers modeling particle uptake.

Referee Report

4 major / 5 minor

Summary. The manuscript presents a force-based triangulated-mesh simulation framework for studying dynamic interactions between deformable lipid vesicles and rigid particles of arbitrary shape. Both the vesicle and the particle are represented by triangulated surfaces, and Langevin dynamics is used to evolve membrane vertices and rigid-body particle translation/rotation. Two adhesion schemes are compared: a vertex-to-vertex nearest-neighbor bond model and a vertex-to-surface closest-point projection. The vertex-to-surface scheme is benchmarked against a parametric-sphere model and shown to reproduce wrapping energetics accurately. The paper then applies the framework to cubical, rod-like, bowl-shaped, and tetrahedral particles interacting with spherical, cigar-shaped, and biconcave vesicles. The central dynamic claim is that lower particle-to-vesicle mass ratios promote reorientation and complete wrapping, while higher mass ratios stabilize partial wrapping.

Significance. The vertex-to-surface adhesion scheme and its validation against a parametric sphere are a useful methodological contribution, and the demonstration of wrapping dynamics for geometrically complex particles (bowls, tetrahedra, non-spherical vesicles) shows real versatility. The authors are transparent about the deterministic, noiseless, constant-drag approximation and its limitations, which is a strength. However, the load-bearing dynamic conclusion about particle inertia is confounded with damping in the current implementation, and there are sign and unit-conversion inconsistencies that need to be resolved before the central narrative can be accepted. For a methods-focused paper the framework is promising, but the mass-ratio result requires either reanalysis or substantially softened claims.

major comments (4)

[Sec. 2.3, Eqs. (8)-(10); Sec. 3.2] The mass-ratio study does not isolate particle inertia. The text states 'We fix m_p/γ_p = 1' (Sec. 2.3, Eq. (8)), and the rotational drag torque in Eq. (10) is proportional to the principal moments of inertia. Consequently, when m_p/m_v is increased from 0.0001 to 0.001, the translational drag γ_p scales with m_p and the rotational damping torque also scales with I. The inertia-to-drag ratio is therefore constant, so the observed suppression of reorientation for the heaviest particle could be caused by increased dissipation rather than by inertia. Please either perform control simulations with γ_p and γ̃_rot held fixed while varying m_p, or revise the interpretation to describe a combined inertia-damping effect.
[Sec. 2.3, Eqs. (5)-(6)] There is a sign inconsistency in the adhesion energy. Eq. (5) defines E_adh = -Σ V(d_i) A_i, while the Morse potential in Eq. (6) is negative for all finite d_i and equals -U at d_i = 0. With the minus sign, E_adh is positive for adhered contact, so the adhesion contribution raises the total energy, contradicting the statement that adhesion lowers the free energy. The definition of the wrapping fraction χ = E_adh/(U A_p) is also affected, since a negative V would give a negative χ unless an additional sign is intended. Please correct the sign convention or define E_adh explicitly as the negative of the integrated potential; this is needed to make Fig. 4 and χ unambiguous.
[Table 1, Sec. 2.3] The physical unit conversion in Table 1 is not internally consistent. With l0 = 10 μm and τ = 0.05 s, the stated vertex mass 2×10^-14 kg and drag coefficient 4.1×10^-6 nN·s/μm give m/γ ≈ 4.9×10^-6 s, not the 0.05 s implied by setting m = γ = 1 in simulation units. The Morse range ρ = 0.01 is also listed as 100 μm, which is 10^3 times larger than 0.1 μm obtained from ρ·l0. These discrepancies undermine the claim that the simulations operate in an 'intermediate damping regime' and should be corrected or the results explicitly restricted to dimensionless/simulation units.
[Sec. 2.3, Eq. (7); Sec. 3.2] The deterministic Langevin equation omits thermal noise, and the authors correctly acknowledge that this limits quantitative predictive power. However, the central dynamic result — that low mass ratios promote repeated reorientation and complete wrapping while high mass ratios stabilize partial wrapping — is a statement about kinetic pathways, which can be sensitive to noise and to the constant-drag approximation. I ask the authors to at least briefly assess the robustness of the mass-ratio trend to stochastic forces (e.g., by adding a Langevin noise term for one or two cases) or to soften the abstract and conclusion claims accordingly.

minor comments (5)

[Section numbering] There are two subsections numbered 2.3; the second, 'Time integration scheme', should be renumbered as 2.4.
[Sec. 2.3] The word 'pseudomonal' should be 'pseudonormal' in the description of the angle-weighted pseudonormal.
[Appendix] In the vertex-to-vertex algorithm, 'Computer the shortest distance' should be 'Compute the shortest distance'.
[Sec. 2.3] The numerical cutoff r_c for the Morse potential is described only as 'on the order of potential range'; please give the actual value used.
[Sec. 3.3 and Supplementary Figures] The reference to 'Figure S3a, b' for rod reorientation appears to point to the mesh-density figure; the rod snapshots are in Figure S4. Please check the cross-references.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: predictions are emergent simulation outputs, not fitted inputs, and the self-cited benchmark is supplemented by independent comparisons.

full rationale

The derivation chain is not circular. The vertex-to-surface adhesion scheme is benchmarked against the authors' prior parametric-sphere model (Ref. 47), which is a self-citation, but this is not the sole support: the paper also compares against the independent simulation data of Yu et al. for cube wrapping (Figure S1) and against experimental observations of rod engulfment by van der Ham et al. (Figure S4). The mass-ratio study in Section 3.2 is an emergent simulation result, not a fitted reproduction of a target: adhesion strength, range, and mass ratio are control parameters, and no parameter is adjusted to force the observed reorientation or wrapping-fraction trends. The reader-flagged concerns that fixing m_p/γ_p=1 makes the mass-ratio scan co-vary translational and rotational drag, and that the physical unit conversion in Table 1 appears internally inconsistent (m/γ from the listed values is ~5e-6 s rather than the stated 0.05 s time unit), are quantitative correctness risks that affect the interpretation of the inertial mechanism, but they are not reductions of a prediction to its own input by construction. No equation in the paper defines an output in terms of the quantity it claims to predict, and no fitted parameter is renamed as a prediction. The self-citation to Ref. 47 for mesh generation and the parametric-sphere energy curves is ordinary prior-work grounding; because those curves are not generated from the present paper's fitted values and independent benchmarks are included, the self-citation is not load-bearing. Accordingly, the circularity score is 1, reflecting the minor self-citation without treating it as a circular derivation.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central results rest on hand-set simulation parameters (adhesion strength, range, moduli, mass ratios) and on modeling assumptions such as deterministic dynamics without thermal noise. No new physical entities are introduced.

free parameters (7)

Morse adhesion strength U (or reduced u_mod) = u_mod from 2.0 to 10.0
Chosen by hand to explore wrapping transitions; not fitted to data.
Morse potential range rho = 0.01 (simulation units, 100 nm physical)
Set to a fixed value; wrapping energetics depend on it.
Area expansion modulus kappa_a = 1.0 (simulation units)
Chosen to maintain vesicle area; value is a modeling choice.
Volume constraint modulus kappa_v = 2.0 (or 0.0 for uncontrolled)
Chosen to control vesicle volume; different values for different simulations.
Particle-to-vesicle mass ratio m_p/m_v = 0.0001, 0.0005, 0.001
Control variable for inertia study; chosen to show effect.
Rotational damping coefficient gamma_tilde_rot = 1.0
Set equal to translational damping; no physical calibration.
Vesicle target reduced volume = 0.65, 0.7
Chosen to create biconcave and cigar shapes.

assumptions (5)

standard math Canham-Helfrich bending energy with Gaussian curvature neglected via Gauss-Bonnet theorem.
Equation (1); valid when vesicle topology does not change.
domain assumption Membrane represented by a triangulated mesh with discrete differential geometry.
From Section 2.1 and Ref. 47; the discrete energies approximate the continuum Helfrich model.
domain assumption Adhesion between membrane and particle follows a Morse potential integrated over the membrane surface.
Equations (4)-(6); an idealization of receptor-ligand or van der Waals adhesion.
ad hoc to paper Dynamics governed by deterministic Langevin equation with zero thermal noise and constant drag coefficient.
Equation (7) and Section 2.3; the authors acknowledge this limits quantitative predictive power at the nanoscale.
domain assumption The rigid particle does not deform and its motion follows Newton-Euler rigid-body dynamics with quaternion kinematics.
Section 2.3; appropriate for stiff particles, but excludes deformable colloids.

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Cite this review

Pith. "Pith review of Cell-Scale Dynamic Modeling of Membrane Interactions with Arbitrarily Shaped Particles." pith.science (2026). https://pith.science/paper/VO4TXRCJ

@misc{pith2026250602376,
  author       = {Pith},
  title        = {Pith review of: Cell-Scale Dynamic Modeling of Membrane Interactions with Arbitrarily Shaped Particles},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VO4TXRCJ}},
  note         = {Machine review of arXiv:2506.02376}
}

read the original abstract

Modeling membrane interactions with arbitrarily shaped colloidal particles, such as environmental micro- and nanoplastics, at the cell scale remains particularly challenging, owing to the complexity of particle geometries and the need to resolve fully coupled translational and rotational dynamics. Here, we present a force-based computational framework capable of capturing dynamic interactions between deformable lipid vesicles and rigid particles of irregular shapes. Both vesicle and particle surfaces are represented using triangulated meshes, and Langevin dynamics resolves membrane deformation alongside rigid-body particle motion. Adhesive interactions between the particle and membrane surfaces are modeled using two numerical schemes: a vertex-to-vertex mapping and a vertex-to-surface projection. The latter yields more accurate wrapping energetics, as demonstrated by benchmark comparisons against ideal spheres. The dynamic simulations reveal that lower particle-to-vesicle mass ratios facilitate frequent particle reorientation and complete membrane wrapping, while higher mass ratios limit orientation changes and stabilize partial wrapping. To illustrate the framework's versatility, we simulate interactions involving cubical, rod-like, bowl-shaped, and tetrahedral particles with spherical, cigar-shaped, or biconcave vesicles. This generalizable modeling approach enables predictive, cell-scale studies of membrane-particle interactions across a wide range of geometries, with applications in environmental biophysics and nanomedicine.

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Reference graph

Works this paper leans on

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

C. Zhu, C. T. Lee and P. Rangamani, Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry, Biophysical Reports, 2022, 2, 100062

work page 2022

[2] [2]

X. Bian, S. Litvinov and P. Koumoutsakos, Bending models of lipid bilayer membranes: Spontaneous curvature and area -difference elasticity, Computer Methods in Applied Mechanics and Engineering, 2020, 359, 112758

work page 2020

[3] [3]

P. Iyer, G. Gompper and D. A. Fedosov, Non- equilibrium shapes and dynamics of active vesicles, Soft Matter, 2022, 18, 6868-6881

work page 2022

[4] [4]

P. Iyer, G. Gompper and D. A. Fedosov, Dynamic shapes of floppy vesicles enclosing active Brownian particles with membrane adhesion, Soft Matter, 2023, 19, 3436-3449

work page 2023

[5] [5]

Ni and G

H. Ni and G. A. Papoian, Membrane -MEDYAN: Simulating Deformable Vesicles Containing Complex Cytoskeletal Networks, The Journal of Physical Chemistry B , 2021, 125, 10710-10719

work page 2021

[6] [6]

D. A. Redwan, K. Du and X. Yong, Probing wrapping dynamics of spherical nanoparticles by 3D vesicles using force-based simulations, Soft Matter, 2024, 20, 4548-4560

work page 2024

[7] [7]

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 membranes, Advances in Colloid and Interface Science, 2014, 208, 214-224

work page 2014

[8] [8]

A. H. Bahrami, R. Lipowsky and T. R. Weikl, Tubulation and Aggregation of Spherical Nanoparticles Adsorbed on Vesicles, Physical Review Letters, 2012, 109, 188102

work page 2012