{"id":"b41328e8-6065-4126-b029-7fa9d8d304ee","arxiv_id":"2506.02376","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A force-based simulation framework with triangulated meshes and rigid-body dynamics models wrapping of arbitrarily shaped particles by vesicles, finding that low particle-to-vesicle mass ratios enable reorientation and complete engulfment.","lead":"This paper presents a computational method for simulating how deformable lipid membrane vesicles wrap around rigid particles of arbitrary shape, such as microplastics. The method captures particle rotation and translation during wrapping, and shows that lighter particles reorient more easily and get fully wrapped while heavier ones stay partially wrapped.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Mass-ratio simulations co-vary particle mass and drag (m_p/γ_p fixed), so the reported inertia-driven reorientation effect may be a damping artifact.","rationale":"The reader's weakest assumption was the omission of thermal noise and hydrodynamics, which the authors themselves acknowledge and which mainly limits quantitative nanoscale predictions. My stress-test focuses on a more direct and correctable issue: the design of the mass-ratio study in Sec. 3.2 does not isolate inertia from drag. Because the particle's translational drag is fixed to equal its mass (m_p/γ_p = 1), increasing the mass ratio by a factor of 10 also increases the drag coefficient by a factor of 10. In the deterministic Langevin equation (Eq. 8), the acceleration is F/m_p while the damping force is γ_p v; with m_p and γ_p scaled together, both inertial resistance and dissipative resistance grow. The rotational drag torque in Eq. 10 scales with the moment of inertia, so heavier particles additionally receive stronger rotational damping for a given angular velocity. Hence the observed 'inertia' effect is confounded with a drag effect. This is not merely a semantic issue: the central dynamic conclusion advertised in the abstract depends on identifying the cause of arrested reorientation. If the effect survives only because drag was increased, then the physical interpretation changes from 'inertia prevents reorientation' to 'higher damping slows reorientation,' which has different implications for uptake kinetics. The Table 1 inconsistency strengthens this concern by showing that the claimed m = γ = 1 regime does not match the physical conversion; the actual vertex relaxation time is about 10^4 times smaller than the characteristic time τ, so the system is strongly overdamped rather than intermediate. This does not necessarily overturn the qualitative wrapping phase behavior or the benchmark comparisons, so the appropriate verdict remains conditional pending the controlled drag-isolation test. I disagree with the reader's choice of weakest assumption because the co-variation of mass and drag is a more pointed, directly testable threat to the paper's headline dynamic claim.","tokens_in":20234,"tokens_out":6791,"duration_ms":65372,"concrete_test":"Re-run the Sec. 3.2 biconcave-vesicle/cube simulations at m_p/m_v = 0.0005 and 0.001 with m_p increased but γ_p held fixed at the value used for m_p/m_v = 0.0001 (and similarly for the rotational damping coefficient). If wrapping fractions and reorientation histories are unchanged from the light-particle case, the reported inertia effect is actually a drag effect. As a second check, recompute the physical values in Table 1 from the stated mapping (l0 = 10 μm, τ = 0.05 s, κ_b = 20 k_BT at 0.01): the vertex relaxation time m/γ should equal 0.05 s if m = γ = 1; if it does not, the unit conversion is internally inconsistent.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The load-bearing dynamic result is the claim (abstract, Sec. 3.2) that lower particle-to-vesicle mass ratios facilitate reorientation and complete wrapping, while higher ratios stabilize partial wrapping. In Sec. 2.3 the authors state 'We fix m_p/γ_p = 1' for the particle (Eq. 8), so changing the mass ratio m_p/m_v also changes γ_p in the same proportion. The variable scanned in Sec. 3.2 is therefore not particle inertia alone: a heavier particle also experiences a proportionally larger translational drag, and through Eq. 10 (τ_d^b ∝ I) a larger rotational damping torque. The observed suppression of reorientation for m_p/m_v = 0.001 could be produced by increased dissipation rather than by inertia. The text motivates the mass ratio via 'force–torque coupling' and 'inertia' (Sec. 3.2), but the fix m_p/γ_p = 1 means the inertia-to-drag ratio is held constant. A second, supporting inconsistency appears in Table 1: using l0 = 10 μm and τ = 0.05 s, the stated vertex mass 2×10^-14 kg and drag 4.1×10^-6 nN·s/μm give m/γ ≈ 5×10^-6 s, not 0.05 s; hence the 'intermediate damping regime' (m = γ = 1) claimed in Sec. 2.3 is not reproduced by the physical conversion. This does not invalidate the vertex-to-surface benchmark or shape-versatility demonstrations, but it does undermine the central inertial-wrapping narrative.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":20579,"tokens_out":12584,"duration_ms":115023,"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":[{"comment":"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.","section":"Sec. 2.3, Eqs. (8)-(10); Sec. 3.2"},{"comment":"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.","section":"Sec. 2.3, Eqs. (5)-(6)"},{"comment":"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.","section":"Table 1, Sec. 2.3"},{"comment":"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.","section":"Sec. 2.3, Eq. (7); Sec. 3.2"}],"minor_comments":[{"comment":"There are two subsections numbered 2.3; the second, 'Time integration scheme', should be renumbered as 2.4.","section":"Section numbering"},{"comment":"The word 'pseudomonal' should be 'pseudonormal' in the description of the angle-weighted pseudonormal.","section":"Sec. 2.3"},{"comment":"In the vertex-to-vertex algorithm, 'Computer the shortest distance' should be 'Compute the shortest distance'.","section":"Appendix"},{"comment":"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.","section":"Sec. 2.3"},{"comment":"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.","section":"Sec. 3.3 and Supplementary Figures"}],"recommendation":"major_revision","confidential_remarks":"The main risk is that the mass-ratio conclusion in Sec. 3.2 is a damping artifact rather than an inertial effect. I would ask the editor to require either disentangling simulations (varying mass at fixed damping) or a reframed conclusion. The sign convention and Table 1 issues are fixable, but they affect core definitions and the physical mapping. The paper is within scope for Soft Matter, and the vertex-to-surface benchmarking is a solid contribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nThe 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.\n\nTable 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.\n\nNo 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.\n\nOverall, 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.","headline":"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.","tokens_in":21091,"tokens_out":7635,"would_cite":true,"duration_ms":70683,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Heavy particles stall membrane wrapping; light ones finish it","keywords":["membrane wrapping","triangulated mesh","Langevin dynamics","rigid-body rotation","particle inertia","anisotropic particles","vesicle deformation","Morse adhesion"],"falsifier":"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.","tokens_in":20008,"feed_emoji":"🧫","tokens_out":6446,"duration_ms":58670,"temperature":0.7,"pith_summary":"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.","feed_headline":"Heavy particles stall membrane wrapping; light ones finish it","feed_subtitle":"Mesh-based simulations of cubes, rods, bowls, and tetrahedra show inertia and local curvature govern whether engulfment completes.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the force-based vesicle model this work extends and the parametric-sphere energetics benchmark.","marker":"[47]"},{"why":"Provides the cube-like particle wrapping benchmark and the superellipsoid shape equations used for mesh generation.","marker":"[23]"},{"why":"Gives the experimental rod-vesicle 'surfing' to engulfment sequence that the dynamic simulations are compared against.","marker":"[25]"},{"why":"Provides the angle-weighted pseudonormal method used to assign the sign of the vertex-to-surface distance.","marker":"[62]"},{"why":"Supplies mesh processing and closest-point distance routines for arbitrarily shaped particle meshes.","marker":"[56]"},{"why":"Offers experimental evidence that heavier nanoparticles are internalized more slowly, supporting the mass-ratio mechanism.","marker":"[77]"}],"fun_headline_variants":["Light particles wrap fully; heavy ones stay half-swallowed","Particle mass determines if membranes finish engulfment","Heavy particles can't reorient, trapping them in partial wraps","For any shape, mass ratio dictates wrap completeness"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Light particles wrap fully; heavy ones stay half-swallowed","Particle mass determines if membranes finish engulfment","Heavy particles can't reorient, trapping them in partial wraps","For any shape, mass ratio dictates wrap completeness"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000655,"raw_usage":{"total_tokens":3022,"prompt_tokens":988,"completion_tokens":2034,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":604,"completion_tokens_details":{"reasoning_tokens":1968}},"tokens_in":604,"tokens_out":2034,"duration_ms":13518,"temperature":1.0,"reasoning_tokens":1968,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:25:19.647367+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Yi and H","cited_arxiv_id":null,"evidence_quote":"Provides the cube-like particle wrapping benchmark and the superellipsoid shape equations used for mesh generation."},{"cited_title":"van der Ham, J","cited_arxiv_id":null,"evidence_quote":"Gives the experimental rod-vesicle 'surfing' to engulfment sequence that the dynamic simulations are compared against."}],"review_version":1}