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REVIEW 4 major objections 5 minor 38 references

A non-reciprocal model for morphogenesis in symbiosis

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read A fluid vesicle and hard-sphere symbionts with unequal two-way interaction strengths generate protrusions, invaginations, budding, cyclic blebs, and a ballistically moving polar vesicle.

desk verdict New non-reciprocal membrane-remodeling mechanism with solid simulations, but the abstract's uniqueness claim needs a same-model reciprocal-active control before publication. read the letter →

arxiv 2506.13299 v2 pith:GWTNE3A6 submitted 2025-06-16 cond-mat.soft physics.bio-phphysics.comp-ph

Maitane Muñoz-Basagoiti , Michael Wassermair , Miguel Amaral , Buzz Baum , An{j̣ela Šarić This is my paper · ORCID
classification cond-mat.softphysics.bio-phphysics.comp-ph
keywords non-reciprocalinteractionsmembraneremodelingsymbiosisactivemattercoarse-grainedsimulationfluidvesiclesmorphogenesissymbioticforce
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 tries to establish that the shapes of cells can be changed by the mere asymmetry of their interactions with symbiotic partners, with no internal motors or self-propulsion required. The authors simulate a fluid vesicle (the host) interacting with hard-sphere symbionts through pairwise forces whose strength depends on direction: $\varepsilon_{sh}$ for symbiont-on-host and $\varepsilon_{hs}$ for host-on-symbiont. When these strengths differ, parameterized by $\Delta\varepsilon=\varepsilon_{sh}-\varepsilon_{hs}$, an unbalanced symbiotic force arises on the contact cluster, pointing toward the symbiont for $\Delta\varepsilon>0$ and toward the membrane for $\Delta\varepsilon<0$. Because the magnitude of this force changes as the membrane wraps, buds, or protrudes, the system feeds its own deformation back into the driving force. The paper reports that this feedback generates branched protrusions, invaginations, budding, cyclic blebs, and a ballistically moving polar vesicle, morphologies it argues are not produced by reciprocal systems with constant activity.

What carries the argument

The central object is the symbiotic force $\vec f_S$, defined as the net force on the cluster of membrane beads and symbiont particles within interaction range. In the reciprocal limit $\Delta\varepsilon=0$, this force cancels by action-reaction; when $\Delta\varepsilon\neq 0$, it is nonzero, grows with $|\Delta\varepsilon|$ and with cluster size, and carries a direction set by the sign of $\Delta\varepsilon$. Its dependence on the wrapping geometry closes the feedback loop: as the membrane deforms, the cluster changes and $\vec f_S$ changes with it. The machinery is implemented as a dynamically triangulated membrane with constrained area and volume, Monte Carlo bond swaps that make the membrane fluid, and a Langevin thermostat that absorbs the unbalanced momentum.

What would settle it

Re-run the triangulated-membrane simulations with $\Delta\varepsilon=0$ and apply to the symbiont an external constant traction equal to the steady-state symbiotic force measured at finite $\Delta\varepsilon$; if the same morphology diagram (protrusions, cyclic blebs, ballistic polar vesicle) still appears, the claim that shape-dependent non-reciprocal feedback drives these morphologies is falsified.

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Extended reading notes

Core claim

The central claim is that the non-reciprocal pairwise force law $\vec F_{k,i\to l,j}=-\phi\varepsilon_{ij}/r^\gamma\,\hat r_{kl}$ for $r<r_c$, with $\varepsilon_{sh}\neq\varepsilon_{hs}$, turns passive contact into an active shape generator for fluid membranes. For $\Delta\varepsilon>0$ the net force on the host-symbiont cluster points toward the symbiont and, once $\Delta\varepsilon/k_BT\gtrsim 5$, extrudes dynamic protrusions; for $\Delta\varepsilon<0$ the force instead pushes symbionts into wrapped, invaginated, or budded states, and with several symbionts produces cyclic blebs and a polar vesicle that moves ballistically. The key point is that the symbiotic force $\vec f_S$ is not fixed: it depends on the geometry of the cluster, so the local membrane deformation alters the very force that drives it. The paper presents this shape-force feedback as the mechanism behind morphologies that are not accessible to reciprocal membranes or to membranes deformed by self-propelled particles.

Load-bearing premise

The model stands on the assumption that a symbiont can push on a host more strongly than the host pushes back, as an instantaneous pairwise force with the surrounding fluid absorbing the missing momentum; if real host-symbiont coupling is mechanically reciprocal or mediated mainly by chemical fields, the predicted shapes would not arise.

Editorial extensions

If this is right

  • A single symbiont with $\Delta\varepsilon/k_BT\gtrsim 5$ extrudes a persistent membrane protrusion even though no agent explicitly pulls the membrane.
  • For $\Delta\varepsilon<0$, symbionts become wrapped, invaginated, or budded by the host, and at intermediate symbiont numbers the membrane produces blebs in a cyclic sequence.
  • The number of symbionts controls the mode: independent protrusions at low coverage, cooperative branched protrusions at intermediate coverage, and suppression by membrane tension at high coverage.
  • Asymmetric symbiont distributions can create a polar vesicle that moves ballistically.
  • These regimes are not found in reciprocal systems with constant intrinsic activity, so their observation would indicate a genuinely interaction-derived driving force.

Reading between the lines

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

  • Because $\gamma=2$ maps the same force law onto phoretic interactions between catalytically coated colloids, the model suggests a direct experimental test: two colloid species with independently tunable surface chemistry paired with a giant vesicle should show protrusion for one sign of $\Delta\varepsilon$ and invagination or blebbing for the other; this goes beyond the paper, which does not propo
  • The shape-dependent $\vec f_S$ could be coarse-grained into a local active tension or curvature-dependent force in a continuum membrane theory, letting future work predict phase boundaries for cyclic blebbing or polar motion without resolving every particle; the authors do not make this connection.
  • If the interaction strengths track metabolic exchange rates, the results imply that a biological cell could switch between protrusive, invaginated, and blebbing morphologies purely by tuning what it gives to and receives from a partner, without invoking cytoskeletal machinery; this is an inference from the authors' discussion, not a claim they test.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. Muñoz-Basagoiti et al. introduce a coarse-grained model in which a host vesicle (dynamically triangulated membrane) and symbiont particles interact via pairwise forces that violate action–reaction symmetry. The force on a particle of species j from species i is given by Eq. (1), with strength ε_ij; the asymmetry is parameterized by Δε = ε_sh − ε_hs. The authors show by molecular dynamics/HMC simulations that a single symbiont produces stable protrusions for Δε > 0 and invaginations, catenoids, or budding for Δε < 0, and that the net 'symbiotic force' fS on the interacting cluster is proportional to |Δε| and depends on the cluster geometry, establishing a feedback between membrane shape and drive. With multiple symbionts, they report cooperative and suppressed protrusions for Δε > 0, and for Δε < 0 cyclic blebbing, ballistic polar vesicles, and 'inside-out' protrusions. Results are checked with a second membrane model (one-particle-thick) and against an equilibrium wrapping limit (γ=7, φ=6/σ̃, Δε=0) and a tether-pulling control.

Significance. If the results hold, the paper offers a minimal mechanism—non-reciprocal interaction alone—for generating a rich set of membrane morphologies relevant to symbiosis, and may inspire synthetic cell experiments. Strengths: explicit non-reciprocal pair style in LAMMPS; two independent membrane models; multiple replicas for the single-symbiont phase diagram; clear definition of fS and its shape feedback; code availability. The central open issue is the abstract's uniqueness claim relative to reciprocal active systems, which is not tested with a same-model baseline.

major comments (4)
  1. [Abstract and Sec. III.C] The claim that the observed morphologies are 'not reported in reciprocal systems with constant activity' and 'not accessible to systems which rely on intrinsic force production via motile filaments or other self-propelled agents' is not supported by a same-model control. The only quantitative control (SI Fig. S5) uses a reciprocal interaction plus an external constant pulling force on a tethered symbiont; this is not equivalent to a self-propelled (active Brownian) particle. No simulation with ε_hs = ε_sh and a constant self-propulsion force on the symbionts is reported. Please add such simulations (e.g., active Langevin dynamics of symbionts with reciprocal membrane interactions) at overlapping parameters, or soften the claims to 'not observed in our reciprocal control' and 'differ from previously reported active-membrane studies.' Without this, the abstract's novelty statement is not verifiable from the presented data.
  2. [Sec. III.A and Fig. 2A] The protrusion region is defined by heuristic thresholds (p ≥ 30% protrusion probability, acylindricity a ≤ 1, cutoff d = 5σ) and the phase boundaries are only guides for the eye. The sensitivity of the phase diagram to these thresholds is not characterized. Since the existence of a distinct protrusion regime is a central result, please report the underlying probability distributions or a threshold-sensitivity analysis so the reader can judge whether the boundaries correspond to sharp or gradual crossovers.
  3. [Sec. III.C, Figs. 4B and 5] The multi-symbiont phase diagrams are based on only three replicas per parameter set, yet they identify several dynamical phases (cyclic blebbing, polar vesicle, inside-out protrusions). For stochastic classification of transient morphologies, three replicas is low, especially for distinguishing cyclic blebbing from stochastic membrane fluctuations. Please provide additional replicas for the dynamic phases or give quantitative order parameters with error bars, and state explicitly how 'cyclic' blebbing is defined and measured.
  4. [Sec. II.C and Sec. III.B] The model relies on the Langevin thermostat to absorb the momentum imbalance produced by the non-reciprocal forces. The sensitivity of the results to the thermostat damping coefficient and to simulation box size is not reported, and these choices could affect the persistence or magnitude of the symbiotic force fS. Please add a short parameter check (e.g., two damping values and two box sizes) to show that the morphologies and the fS scaling in Fig. 3B are robust to the thermostatting protocol.
minor comments (5)
  1. [Sec. III.C and Fig. 5 caption] The caption of Fig. 5 states ε_sh/kBT = 2 while Sec. III.C states ε_hs/kBT = 2; please clarify which interaction strength is held fixed in the Δε < 0 multi-symbiont simulations, since the wrapping state and hence the available symbiotic force depend on it.
  2. [Fig. 2A caption and Sec. III.A] The caption refers to 'white data points' while the text later refers to 'white diamond symbols' for the same region; please make the symbol terminology consistent.
  3. [SI Fig. S5 caption] The caption calls the control 'reciprocal and non-reciprocal pulling'; the control is actually a reciprocal interaction plus an external force, which is a different driving protocol. Please rephrase to avoid implying that it is an active self-propulsion baseline.
  4. [Abstract and Introduction] The sentence 'The shape of a cell influences, and it is influenced by its interactions with its neighbours' is grammatically awkward; consider rephrasing for clarity.
  5. [Sec. II and SI Sec. I] The initial placement of symbionts (distance from the vesicle, equilibration protocol) is not fully specified; please add the exact initialization details used for the single- and multi-symbiont simulations.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the model's morphologies are simulation outputs of the stated non-reciprocal interaction, and the one definitional relation (fS proportional to |Δε|) is explicitly acknowledged by the authors.

full rationale

The paper's derivation chain is a simulation study: Eq. (1) defines a non-reciprocal pairwise force, and the 'symbiotic force' fS is then defined as the net force on the host-symbiont cluster. The authors explicitly state that the proportionality of fS to |Δε| follows by definition and that the shape-force coupling is 'by design' (Section IV, Discussion). These are model characterizations, not fitted predictions or disguised inputs; the morphology diagrams in Figs. 2, 4, and 5 are simulation outputs rather than fits to target data. The reciprocal-equilibrium comparison and the one-particle-thick membrane cross-check in the SI provide independent controls. The only caveat is the abstract's uniqueness claim that the morphologies are 'not reported in reciprocal systems with constant activity': this rests on a literature comparison and on SI Fig. S5, which uses an external tether pull rather than a reciprocal-interaction-plus-constant-activity baseline. That is an evidentiary/completeness gap in the comparative claim, but it is not a circular reduction, because the central non-reciprocal phenomenology is not obtained by fitting or by defining the output into the input. Self-citations concerning the simulation method and equilibrium adhesion benchmarks are not load-bearing for the non-reciprocal results.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The model introduces no new physical entities. The 'symbiotic force' fS is a derived observable (net force on the interacting cluster), and the non-reciprocal pairwise interaction is a coarse-grained effective force law, not a new mediator. The list of free parameters includes all interaction and constraint strengths the central morphology diagram depends on.

free parameters (8)
  • epsilon_hs (host-on-symbiont force strength) = scanned; e.g., 10 kBT in protrusion runs, 2 kBT for Delta-epsilon < 0 diagrams
    Sets the reference reciprocal interaction; phase diagram is mapped over it.
  • Delta-epsilon = epsilon_sh - epsilon_hs = varied from -12 to +12 kBT
    The central control parameter for asymmetry; not fitted to data.
  • gamma (force exponent) = 7 (checked at 2)
    Chosen to match Lennard-Jones; robustness verified for gamma = 2.
  • phi (force scale) = 6 / sigma_tilde
    Chosen to connect Eq. (1) to canonical Lennard-Jones force.
  • r_c (interaction cutoff) = 1.5 sigma_tilde
    Sets interaction range; model parameter.
  • sigma_s (symbiont diameter) = 5 sigma, 10 sigma, 20 sigma
    Controls cluster geometry; varied across figures.
  • kappa_A,V (area/volume constraint stiffness) = 2.5e5 kBT
    Sets membrane tension, which drives the suppression/cooperation regimes at high N_S; chosen simulation parameter.
  • kappa_B (bending rigidity) = 20 kBT
    Standard value for a fluid vesicle; chosen.
assumptions (5)
  • domain assumption Non-reciprocal pairwise forces can drive particle dynamics when the momentum imbalance is absorbed by an implicit solvent (Langevin thermostat).
    Standard in active matter coarse-graining; enables simulation of action-reaction breaking at pair level.
  • domain assumption The host cell can be modeled as a fluid vesicle with fixed topology; topological changes (budding, rupture) are secondary for the reported regimes.
    Acknowledged limitation; SI Sec IV checks with a topology-changing model.
  • domain assumption Symbiont biology is representable by hard spheres with pairwise distance-dependent forces, without chemical fields or internal degrees of freedom.
    Coarse-graining assumption of the model; mapping to phoretic forces (gamma = 2) is only far-field.
  • ad hoc to paper The parameter mapping gamma = 7 and phi = 6/sigma_tilde connects the non-reciprocal force to Lennard-Jones adhesion, so Delta-epsilon = 0 recovers equilibrium wrapping.
    Chosen for comparability with prior equilibrium results, not derived from biology.
  • ad hoc to paper Morphology classification thresholds (30% protrusion probability, d = 5 sigma, acylindricity <= 1, N/Nmax >= 0.9 for budding) correctly separate the reported phases.
    Heuristic geometric cutoffs; boundaries in phase diagrams are guides for the eye.

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Pith. "Pith review of A non-reciprocal model for morphogenesis in symbiosis." pith.science (2026). https://pith.science/paper/GWTNE3A6

@misc{pith2026250613299,
  author       = {Pith},
  title        = {Pith review of: A non-reciprocal model for morphogenesis in symbiosis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GWTNE3A6}},
  note         = {Machine review of arXiv:2506.13299}
}
read the original abstract

The shape of a cell influences, and it is influenced by its interactions with its neighbours. Here, we introduce a coarse-grained computational model of non-reciprocal interactions between single-cell organisms to study emergent morphologies during symbiotic association. We show that the cell membrane can be remodelled into branched protrusions, invaginations, transient blebs and other dynamical morphologies that depend on the number of interacting partners, the asymmetry, and the magnitude of partnership activity. Our model finds a dynamical feedback between the local deformation of the membrane and its driving force, leading to membrane morphologies not reported in reciprocal systems with constant activity.

Figures

Figures reproduced from arXiv: 2506.13299 by the authors.

Figure 1
Figure 1. ). This suggests that our results can account for metabolically-coupled symbiotic partners, i.e., in￾tercellular communication driven by the exchange of chemicals. III. RESULTS The interaction between organisms can be of favor￾able or unfavorable nature. In our model this is de￾termined by the sign of εij , which dictates whether the force between organisms is attractive (εij > 0), repulsive (εij < 0) or whether the… view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

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