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REVIEW 6 major objections 6 minor 69 references

Self-organized fractal architectures driven by motility-dependent chemotactic feedback

T0 review · 6 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A minimal two-rule model of self-chemotaxis produces fractal-like networks and then re-enters a uniform state at very low chemical decay.

desk verdict The simulation phase diagram is likely the contribution; the continuum theory does not independently confirm it because the key threshold is fit to the same simulations. read the letter →

arxiv 2504.16539 v1 pith:Z4B5Y5DA submitted 2025-04-23 physics.bio-ph cond-mat.softcond-mat.stat-mech

Subhashree Subhrasmita Khuntia , Debasish Chaudhuri , Abhishek Chaudhuri This is my paper · ORCID
classification physics.bio-phcond-mat.softcond-mat.stat-mech
keywords self-organizationchemotaxisfractalnetworksagent-basedmodelre-entrantphasetransitionmotility-dependentdepositionlinearstabilityanalysisvasculogenesis
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 argues that two local rules—agents deposit a chemical only while moving, and their motion is biased up the chemical gradient with a sensitivity that saturates at high concentration—are enough to generate the branching, fractal-like networks seen in early blood-vessel formation and in dispersing epithelial cells. As the chemical decay rate is lowered, the model produces a re-entrant sequence: uniform, sparse network, dense fractal network, compact cluster, and then uniform again, because at extremely low decay the chemical field becomes so strong that the agents' response saturates and they stop following it. The authors back this phase diagram with a continuum model whose linear stability analysis gives a finite window of deposition-to-decay ratio for pattern formation, and they show that the cluster and network phases grow by different mechanisms. If correct, the paper supplies a physically grounded mechanism that could be tested in cell cultures and implemented in synthetic swarms.

What carries the argument

The load-bearing object is the feedback loop itself, written in continuum form as coupled equations for particle density $\rho$ and chemical concentration $c$: $\dot{\rho}=-\nabla\cdot[\chi\rho f'(c)\nabla c-D\nabla\rho]$ and $\dot{c}=\alpha\rho(\rho_c-\rho)-\beta c$, with $f(c)=c/(1+c)$. The deposition term $\alpha\rho(\rho_c-\rho)$ encodes the microscopic rule that only moving agents deposit: the source is quadratic in density, vanishes at density $\rho_c$, and therefore peaks at intermediate density, so the interior of a cluster stops producing chemical while its edges continue. Linearizing around the homogeneous state gives the instability condition $C_-<c_0<C_+$ with $c_0=\rho_0(\rho_c-\rho_0)\alpha/\beta$, which the paper uses to locate the low-decay re-entrant boundary. The same equations, with the chemical slaved to the density, also explain the two quench routes: a compact front ejects particles most strongly along the diagonal where diffusive flux is $\sqrt{2}$ times larger, forming fingers, while at high deposition the chemical peak disappears and compact clusters grow by nucleation.

What would settle it

Run the agent-based model at fixed $\beta$ while scanning $\alpha$ over at least two decades and locate the homogeneous-to-network and network-to-homogeneous boundaries from the cluster-size distribution; Eq. (3) says those boundaries shift with $\alpha$, whereas the paper reports them as independent of $\alpha$, so a boundary that moves with $\alpha$ would falsify the stated linear-stability confirmation.

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Extended reading notes

Core claim

The paper's central claim is that motility-dependent chemical deposition together with saturating chemotactic sensitivity produces self-organized, system-spanning fractal-like networks without external gradients or central control. In the agent-based model, particles deposit chemical only when a move is accepted, so particles blocked inside clusters deposit nothing, and they direct their motion by a weighted average of local chemical gradients with a response probability $c/(1+c)$ that saturates at large $c$. The reported phase diagram in deposition rate $\alpha$ and decay rate $\beta$ shows a re-entrant transition: high $\beta$ gives a homogeneous phase, intermediate $\beta$ gives sparse and then dense fractal networks, lower $\beta$ gives compact clusters, and the lowest $\beta$ returns to a homogeneous phase because the chemical field saturates the response. The paper claims a continuum description—coupled equations for density and chemical with source term $\alpha\rho(\rho_c-\rho)$—and its linear stability analysis confirm these transitions and identify the instability window, while quench simulations show nucleation-and-growth into the cluster phase and finger growth into the network phase.

Load-bearing premise

The load-bearing premise is that the continuum deposition rule $\alpha\rho(\rho_c-\rho)$ faithfully captures the microscopic rule that only moving agents deposit, with $\rho_c$ fitted from the same simulations; the paper itself notes that this rule makes the predicted boundary depend on $\alpha$ while the simulated boundary does not, so if the coarse-graining is invalid the theoretical confirmation collapses.

Editorial extensions

If this is right

  • If the model is right, vascular-like fractal networks can form from purely local rules: moving cells lay trails, and saturating sensing prevents collapse, so no external morphogen source is required.
  • The re-entrant behaviour means that very slow chemical decay suppresses patterning rather than strengthening it; experiments that tune chemoattractant degradation should see patterns form, then disappear again as degradation is blocked.
  • The linear stability window predicts that pattern formation is controlled by the ratio of deposition to decay, giving a concrete control parameter for designing synthetic swarms.
  • At high deposition, effective diffusivity falls and then rises as decay slows, offering a measurable single-particle signature of the re-entrant transition.
  • Quenches into the cluster phase grow as $\langle\bar{n}\rangle\sim t^{1/3}$, while quenches into the network phase amplify small perturbations, giving an experimental signature that distinguishes the two absorbing structures.

Reading between the lines

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

  • Beyond the paper's claims, the $\alpha$-independence of the simulated boundary hints that the fitted threshold $\rho_c$ may itself depend on $\alpha$; checking that dependence would clarify whether the continuum confirmation is genuine or an artifact of the fit.
  • This picture also suggests a direct experimental knob: changing chemical decay (for example by adding degrading enzymes) should reproduce the same phase sequence without touching deposition.
  • A quantitative prediction to test in imaging experiments is that the dense-network fractal dimension $d_f\approx 1.4$ should rise back toward 2 when chemical decay is blocked, signalling the re-entrant homogeneous phase.
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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

6 major / 6 minor

Summary. The paper studies a minimal agent-based model of self-organized pattern formation in which motile agents deposit a chemical only while moving and bias their motion along local chemical gradients with a saturating response. The authors map out a phase diagram in the deposition-decay parameter space (alpha, beta), identifying homogeneous (HP), sparse network (SN), dense network (DN), system-spanning cluster (SC), and a re-entrant homogeneous phase (RHP) at very low decay rates. A continuum model for the density and chemical fields is introduced, with a motility-dependent deposition term alpha*rho*(rho_c - rho), and a linear stability analysis yields an instability window in alpha/beta (Eq. 3). The paper further reports quench dynamics, fractal dimension measurements, cluster-size distributions, mean-squared displacement, and a perturbation study to support the phase classification. The biological discussion relates the networks to vasculogenesis and epithelial dispersal.

Significance. If the theoretical confirmation held up, this would be a valuable contribution: the model is simple, the phase diagram is rich, and the re-entrant homogeneous phase caused by sensitivity saturation is a genuinely interesting prediction that could be tested in artificial active-matter or cell-culture systems. The simulation evidence for the phase diagram, including fractal dimension, system-spanning statistics, and the separate quench and perturbation studies, is substantial and mostly self-consistent. The main weakness is that the continuum linear stability analysis, which is advertised as confirming the transitions, depends on a parameter rho_c fitted to the same simulation data and also fails to reproduce the alpha-independence of the simulated phase boundaries. The central theoretical claim is therefore not independently established in the current version.

major comments (6)
  1. [Section II D, Eq. 3 vs. Fig. 2(a)] The linear stability condition Eq. 3 is not an independent confirmation of the phase diagram because rho_c is obtained by fitting the steady-state relation c(rho) = a*rho - b*rho^2 to the very same agent-based simulations that Eq. 3 is supposed to explain. The fit is not stable across contexts: SI Fig. S2 reports rho_c = 1.47 for the DN phase at alpha = 5, beta = 0.008 and rho_c = 1.07 for the SC phase at alpha = 100, beta = 0.008, whereas the quench-profile fits in Fig. 3 give rho_c = 1.002 for DN at alpha = 5, beta = 0.008 and rho_c = 2.712 for SC at alpha = 100, beta = 0.008. If rho_c represented a motility or packing threshold of the underlying WCA system, it should be approximately independent of alpha, beta, and of whether one fits a global steady state or a cluster interface. The authors should either derive rho_c from the microscopic deposition rule (e.g., from the probability that a trial move is accepted as a function of local density) or demonstrate that the predicted instability boundary is insensitive to the fitted value over the observed spread; otherwise Eq. 3 should be presented as a consistency check rather than as confirmation.
  2. [Section II D and SI Eq. S1] The paper itself acknowledges that the simulated HP/SN and SC/RHP boundaries are independent of alpha, whereas Eq. 3 depends on alpha/beta through c0. Since Fig. 2(a) draws the solid line from Eq. 3, the figure claims a quantitative match that the text immediately qualifies. This mismatch is load-bearing for the statement that linear stability criteria determine the observed phases. A quantitative comparison is needed: for example, plot the simulated boundaries in the (alpha/beta)-rho0 plane and compare with the theoretical C_- and C_+ contours for fixed rho_c, or show that the alpha-independence emerges in a suitable limit (e.g., when the instability window is wide in alpha/beta). As written, the theoretical boundary does not predict the alpha-dependence of the most prominent transitions.
  3. [Section II E and SI Fig. S1] The continuum model in Eq. 2 is posited rather than derived from the microscopic rules. In particular, the deposition term alpha*rho*(rho_c - rho) is justified only by the steady-state fit in SI Fig. S2, and the effective parameters D, chi, and rho_c are not measured independently from the agent dynamics. The linear stability analysis then becomes a self-consistency argument: the assumed deposition nonlinearity is tuned to reproduce the simulation data, and the instability boundary inherits that tuning. The authors should either (i) coarse-grain the microscopic update rules to derive the deposition term and the effective diffusivity and chemotactic mobility, or (ii) explicitly state that Eq. 2 is a phenomenological model and validate it by testing its predictions (not just its stability boundary) against independent simulation observables, such as front propagation speeds or density profiles.
  4. [Section II D, Eq. 1] The quench-dynamics interpretation in Section II E relies on comparing c(x) = rho(x)[rho_c - rho(x)] with rho_c > 2*rho_i versus rho_c < 2*rho_i to distinguish the SC and DN regimes. However, the rho_c values used for these two cases come from the same fitted functional form, and the figures show only single representative fits (Fig. 3(e) and 3(j)). To support the claim that this criterion predicts whether the network instability is present, the authors should show that the inequality rho_c > 2*rho_i robustly separates the SC and DN regions across a range of alpha and beta, and report the error bars on rho_c in these fits.
  5. [Figure 2(a) caption] Equation (1) introduces the deposition rule through the function h({r, r_dot}), but the connection between this microscopic rule and the continuum closure alpha*rho*(rho_c - rho) is never made explicit. The sentence 'The functional dependence rho(rho - rho_c) captures the decrease in the rate of chemical deposition with reduced motility at high density controlled by rho_c' is not a derivation. Please clarify whether h is meant to be the occupancy-dependent acceptance probability and how the linear-in-density form emerges from it.
  6. The caption of Fig. 2(a) refers to the solid line as 'a linear stability boundary obtained using Eq. 3' but does not list the parameter values (rho_c, chi, D, rho_0) used to generate it. Since those parameters are not all fixed by the simulation protocol, the reader cannot check whether the drawn boundary is representative or tuned. Please provide the parameter values and, ideally, a shaded region showing the full unstable band C_- < c0 < C_+ rather than a single contour.
minor comments (6)
  1. [Abstract and Introduction] The terminology alternates between 'concentration-sensitive feedback', 'saturating sensitivity', and 'concentration-limited responsiveness'; please use one consistent term throughout.
  2. [SI Fig. S2 caption] The caption reports (a,b) and rho_c = a/b, but it does not mention that these values differ substantially from the rho_c values used in the main-text Fig. 3 fits for the same nominal phases and parameters; explicitly flagging this would improve transparency.
  3. [Section II A] The description of the re-entrant phase says particles become 'effectively insensitive to the uniform chemical field'; since the field is uniform in RHP, it would be clearer to state that the gradient is too weak to bias motion even though the concentration is high.
  4. [Methods] The time step is described with r(t+1) but the model is said to be continuous in time; please clarify the discrete-time update and the relation between v0*Delta_t = 1 and the WCA diameter sigma.
  5. [SI Section VI] The growth-law fits (z = 3 for SC and exponential for DN) are presented without confidence intervals or goodness-of-fit measures; adding these would strengthen the claim of two distinct coarsening regimes.
  6. [References] Reference [1] currently appears to have an incomplete author list ('J.-L. Deneubourg, N. R. Franks, J. Sneyd, G. Theraulaz, E. S. C. ... Camazine'); please correct all bibliographic entries for consistency.

Circularity Check

1 steps flagged · score 6.0 of 10

The continuum LSA is not an independent confirmation: its deposition closure is fitted with ρc taken from the same simulations whose boundaries Eq. (3) is said to predict.

  1. fitted input called prediction [Sec. II.D, Eqs. (2)-(3); SI Sec. II, Fig. S2; Fig. 3 caption]
    "˙c = αρ(ρc−ρ)−βc. (2) The functional dependence ρ(ρ− ρc) captures the decrease in the rate of chemical deposition with reduced motility at high density controlled by ρc (see SI; Fig.S1 and S2). ... In Fig. S2, we show the simulation data for chemical concentration versus particle density at steady state ... the corresponding fit to a functional dependence of the chemical concentration of the form c = aρ−bρ^2 shows a good agreement. ... Thus ρc = a/b is 1.47 in (a) and 1.07 in (b)."

    The continuum 'confirmation' is not derived from the microscopic rule 'deposit only while moving': the deposition term in Eq. (2) is imposed by fitting steady-state c(ρ) data from the very same particle simulations whose phase boundaries Eq. (3) is then said to align with. ρc enters χ′=(ρc−2ρ0)χ/[(ρc−ρ0)D] and therefore the C± bounds, so the predicted instability window inherits the fitted parameter; the agreement is partly by construction. The fit is also not a robust microscopic constant: SI Fig. S2 gives ρc=1.47 (DN) and 1.07 (SC), while Fig. 3's quench-profile fits give ρc=2.712 (SC) and 1.002 (DN), and the paper concedes 'the transition boundary in our simulations is independent of α', unlike Eq. (3).

full rationale

The paper's main empirical content—the phase diagram, cluster-size distributions, fractal dimensions, and MSD data—comes directly from the agent-based simulations and is not derived from the continuum model, so that part is self-contained and not circular. The circular burden is concentrated in Sec. II.D, where the continuum equations are presented as 'starting from the microscopic dynamics' but actually replace motility-dependent deposition with the closure αρ(ρc−ρ), with ρc obtained by fitting the same simulations' steady-state density–chemical relation (SI Fig. S2). Because ρc enters the linear stability condition Eq. (3), the statement that Eq. (3) 'aligns with the observed pattern formation' is partly a consistency check of the fitted closure rather than an independent prediction. The fitted nature is underscored by the inconsistent values of ρc between SI Fig. S2 and Fig. 3, and by the authors' own admission that the simulated transition boundary is independent of α, unlike Eq. (3). This is a partial but real circularity: the theoretical confirmation reduces, in part, to a parameter fit to the data it is used to explain. There are no load-bearing self-citations; the few self-citations appear as ordinary background references and do not carry the derivation. The central agent-based phenomenology is genuine and externally reproducible in principle, so this is not a case where the whole derivation is equivalent to its input; rather, the continuum-level 'confirmation' is partly built from the simulation output.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a continuum model whose coefficients (rho_c, chi, D) are either fitted to the same simulation data or chosen without a microscopic derivation. No new physical entities are introduced; the chemical field is a standard diffusive chemoattractant. The fractal dimension claim relies on an unverified scaling-range assumption.

free parameters (3)
  • rho_c (density threshold for deposition suppression) = 1.47 (DN phase), 1.07 (SC phase) from c = a*rho - b*rho^2 fits
    Controls the density dependence of chemical deposition in the continuum model and enters the linear stability condition Eq. 3; fitted to steady-state simulation data in SI Fig. S2.
  • chi (chemotactic sensitivity in continuum model) = not specified; set to 1.0 in SI numerical integrations
    The chemotactic drift term chi*rho*f'(c) is not coarse-grained from the agent-based rules; its value is chosen for the analysis and affects the stability window through chi'.
  • D (collective diffusivity) = not specified; D = 0.01 in SI integrations
    The effective diffusivity D = D_T + 2*lambda is introduced ad hoc; its value influences the stability boundary but is not derived from microscopic parameters.
assumptions (4)
  • domain assumption The continuum density equation (Eq. 2) is a valid mean-field description of the agent-based model.
    No coarse-graining derivation is provided; the drift-diffusion form is assumed in Sec. II D.
  • ad hoc to paper Chemical deposition decays linearly with density as alpha*rho*(rho_c - rho).
    Introduced in Sec. II D/Eq. 2 to mimic reduced motility in dense regions; the linear form is motivated but not derived, and rho_c is fit from data.
  • standard math The homogeneous state (rho0, c0) is a valid base state for linear stability analysis.
    Linearization around a uniform state is standard when such a state exists; the analysis assumes the homogeneous solution c0 = rho0(rho_c - rho0)*alpha/beta is physically relevant in the parameter regimes considered.
  • domain assumption The correlation dimension estimates a true fractal scaling range.
    The fractal dimension df is computed via the Grassberger-Procaccia method, assuming a power-law C(r) ~ r^df; the scaling range is not verified in the SI, so the 'fractal' label may be a finite-size artifact.

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Cite this review

Pith. "Pith review of Self-organized fractal architectures driven by motility-dependent chemotactic feedback." pith.science (2026). https://pith.science/paper/Z4B5Y5DA

@misc{pith2026250416539,
  author       = {Pith},
  title        = {Pith review of: Self-organized fractal architectures driven by motility-dependent chemotactic feedback},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Z4B5Y5DA}},
  note         = {Machine review of arXiv:2504.16539}
}
read the original abstract

Complex spatial patterns in biological systems often arise through self-organization without a central coordination, guided by local interactions and chemical signaling. In this study, we explore how motility-dependent chemical deposition and concentration-sensitive feedback can give rise to fractal-like networks, using a minimal agent-based model. Agents deposit chemicals only while moving, and their future motion is biased by local chemical gradients. This interaction generates a rich variety of self-organized structures resembling those seen in processes like early vasculogenesis and epithelial cell dispersal. We identify a diverse phase diagram governed by the rates of chemical deposition and decay, revealing transitions from uniform distributions to sparse and dense networks, and ultimately to full phase separation. At low chemical decay rates, agents form stable, system-spanning networks; further reduction leads to re-entry into a uniform state. A continuum model capturing the co-evolution of agent density and chemical fields confirms these transitions and reveals how linear stability criteria determine the observed phases. At low chemical concentrations, diffusion dominates and promotes fractal growth, while higher concentrations favor nucleation and compact clustering. These findings unify a range of biological phenomena - such as chemotaxis, tissue remodeling, and self-generated gradient navigation - within a simple, physically grounded framework. Our results also offer insights into designing artificial systems with emergent collective behavior, including robotic swarms or synthetic active matter.

Figures

Figures reproduced from arXiv: 2504.16539 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Schematic of agent-based rules: (a-i) A focal particle (red-shaded circle) senses chemical concentration from [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Phase diagram showing structural transitions with [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Typical configurations during quench from a homogeneous to SC phase at [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a–b) Log-log plots of mean squared displacement for [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

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Works this paper leans on

69 extracted references · 60 canonical work pages

  1. [1]

    Deneubourg, N

    J.-L. Deneubourg, N. R. Franks, J. Sneyd, G. Theraulaz, and E. B. S. Camazine, Self-Organization in Biological Systems (2001)

    work page 2001

  2. [2]

    Bonabeau, G

    E. Bonabeau, G. Theraulaz, J.-L. Deneubourg, S. Aron, and S. Camazine, Self-organization in social insects, Trends in Ecology & Evolution 12, 188 (1997)

    work page 1997

  3. [3]

    A. X. da Silveira dos Santos and P. Liberali, From single cells to tissue self-organization, The FEBS Journal 286, 1495 (2019)

    work page 2019

  4. [4]

    X. Xu, Z. Zhao, R. Li, and H. Zhang, Brain- inspired stigmergy learning, IEEE Access7, 10.1109/AC- CESS.2019.2913182 (2019)

    arXiv 2019

  5. [5]

    Giuggioli, J

    L. Giuggioli, J. R. Potts, D. I. Rubenstein, and S. A. Levin, Stigmergy, collective actions, and animal social spacing, Proceedings of the National Academy of Sci- ences 110, 10.1073/pnas.1307071110 (2013). 8

    work page doi:10.1073/pnas.1307071110 2013

  6. [6]

    J. R. Potts and M. A. Lewis, Spatial memory and taxis- driven pattern formation in model ecosystems, Bulletin of Mathematical Biology 81, 10.1007/s11538-019-00626- 9 (2019)

    work page doi:10.1007/s11538-019-00626- 2019

  7. [7]

    E. S. Gloag, L. Turnbull, and C. B. Whitchurch, Bac- terial stigmergy: An organising principle of multicellu- lar collective behaviours of bacteria, Scientifica 2015, 10.1155/2015/387342 (2015)

    work page doi:10.1155/2015/387342 2015

  8. [8]

    A. G. Checa, F. Linares, C. Grenier, E. Griesshaber, A. B. Rodr´ ıguez-Navarro, and W. W. Schmahl, The arg- onaut constructs its shell via physical self-organization and coordinated cell sensorial activity, iScience 24, 103288 (2021)

    work page 2021

Show all 69 references
  1. [9]

    Boettiger, B

    A. Boettiger, B. Ermentrout, and G. Oster, The neural origins of shell structure and pattern in aquatic mollusks, Proceedings of the National Academy of Sciences 106, 6837 (2009)

    2009

  2. [10]

    P. C. Antonello, T. F. Varley, J. Beggs, M. Porcionatto, O. Sporns, and J. Faber, Self-organization of in vitro neuronal assemblies drives to complex network topology, eLife 11, 10.7554/eLife.74921 (2022)

    2022 doi

  3. [11]

    Chaudhuri, P

    D. Chaudhuri, P. Borowski, and M. Zapotocky, Model of fasciculation and sorting in mixed populations of ax- ons, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 84, 10.1103/PhysRevE.84.021908 (2011)

    2011 doi

  4. [12]

    Feinerman and A

    O. Feinerman and A. Korman, Individual versus collec- tive cognition in social insects, Journal of Experimental Biology 220, 10.1242/jeb.143891 (2017)

    2017 doi

  5. [13]

    Y. Yang, L. Liu, J. Huo, H. Liu, and L. Li, Self-organized motion coordination based on ant-like agent, in 2006 Semantics, Knowledge and Grid, Second International Conference on (IEEE, 2006)

    2006

  6. [14]

    S. T. Rutherford and B. L. Bassler, Bacterial quorum sensing: Its role in virulence and possibilities for its con- trol, Cold Spring Harbor Perspectives in Medicine 2, a012427 (2012)

    2012

  7. [15]

    Mukherjee and B

    S. Mukherjee and B. L. Bassler, Bacterial quorum sens- ing in complex and dynamically changing environments, Nature Reviews Microbiology 17, 371 (2019)

    2019

  8. [16]

    H. Chen, L. Wang, J. Di, and S. Ping, Bacterial forag- ing optimization based on self-adaptive chemotaxis strat- egy, Computational Intelligence and Neuroscience 2020, 10.1155/2020/2630104 (2020)

    2020 doi

  9. [17]

    Agudo-Canalejo and R

    J. Agudo-Canalejo and R. Golestanian, Active phase sep- aration in mixtures of chemically interacting particles, Physical Review Letters 123, 018101 (2019)

    2019

  10. [18]

    M´ ehes and T

    E. M´ ehes and T. Vicsek, Collective motion of cells: from experiments to models, Integr. Biol. 6, 831 (2014)

    2014

  11. [19]

    Liebchen and H

    B. Liebchen and H. L¨ owen, Synthetic chemotaxis and col- lective behavior in active matter, Accounts of Chemical Research 51, 10.1021/acs.accounts.8b00215 (2018)

    2018 doi

  12. [20]

    Laganenka, R

    L. Laganenka, R. Colin, and V. Sourjik, Chemo- taxis towards autoinducer 2 mediates autoaggrega- tion in escherichia coli, Nature Communications 7, 10.1038/ncomms12984 (2016)

    2016 doi

  13. [21]

    A. H. Robles and L. Giuggioli, Phase transitions in stigmergic territorial systems, Physical Review E 98, 10.1103/PhysRevE.98.042115 (2018)

    2018 doi

  14. [22]

    Khuong, J

    A. Khuong, J. Gautrais, A. Perna, C. Sba¨ ı, M. Combe, P. Kuntz, C. Jost, and G. Theraulaz, Stigmergic con- struction and topochemical information shape ant nest architecture, Proceedings of the National Academy of Sciences 113, 10.1073/pnas.1509829113 (2016)

    2016 doi

  15. [23]

    Dussutour, V

    A. Dussutour, V. Fourcassi´ e, D. Helbing, and J. Deneubourg, Optimal traffic organization in ants under crowded conditions, Nature 428, 70 (2004)

    2004

  16. [24]

    M. A. Breau and A. Trembleau, Chemical and mechanical control of axon fasciculation and defasciculation, Semi- nars in Cell & Developmental Biology Special issue: Driv- ing forces behind the wiring of neuronal circuits, 140, 72–81 (2023)

    2023

  17. [25]

    Chaudhuri, P

    D. Chaudhuri, P. Borowski, and M. Zapotocky, Model of fasciculation and sorting in mixed populations of axons, Physical Review E 84, 021908 (2011)

    2011

  18. [26]

    Helbing, J

    D. Helbing, J. Keltsch, and P. Moln´ ar, Modelling the evo- lution of human trail systems, Nature 388, 47–50 (1997)

    1997

  19. [27]

    C. H. Stuelten, C. A. Parent, and D. J. Montell, Cell motility in cancer invasion and metastasis: insights from simple model organisms, Nature Reviews Cancer 18, 296 (2018)

    2018

  20. [28]

    Insall, The interaction between pseudopods and ex- tracellular signalling during chemotaxis and directed mi- gration, Current opinion in cell biology 25, 526 (2013)

    R. Insall, The interaction between pseudopods and ex- tracellular signalling during chemotaxis and directed mi- gration, Current opinion in cell biology 25, 526 (2013)

    2013

  21. [29]

    R. H. Insall, P. Paschke, and L. Tweedy, Steering yourself by the bootstraps: how cells create their own gradients for chemotaxis, Trends in Cell Biology 32, 585 (2022)

    2022

  22. [30]

    Don` a, J

    E. Don` a, J. D. Barry, G. Valentin, C. Quirin, A. Khmelin- skii, A. Kunze, S. Durdu, L. R. Newton, A. Fernandez- Minan, W. Huber, et al. , Directional tissue migration through a self-generated chemokine gradient, Nature 503, 285 (2013)

    2013

  23. [31]

    Tweedy, P

    L. Tweedy, P. A. Thomason, P. I. Paschke, K. Martin, L. M. Machesky, M. Zagnoni, and R. H. Insall, Seeing around corners: Cells solve mazes and respond at a dis- tance using attractant breakdown, Science369, eaay9792 (2020)

    2020

  24. [32]

    Tweedy, D

    L. Tweedy, D. A. Knecht, G. M. Mackay, and R. H. Insall, Self-generated chemoattractant gradients: attractant de- pletion extends the range and robustness of chemotaxis, PLoS biology 14, e1002404 (2016)

    2016

  25. [33]

    Alert, A

    R. Alert, A. Mart´ ınez-Calvo, and S. S. Datta, Cellular sensing governs the stability of chemotactic fronts, Phys- ical Review Letters 128, 148101 (2022)

    2022

  26. [34]

    A. J. Muinonen-Martin, O. Susanto, Q. Zhang, E. Smethurst, W. J. Faller, D. M. Veltman, G. Kalna, C. Lindsay, D. C. Bennett, O. J. Sansom, et al. , Melanoma cells break down lpa to establish local gradi- ents that drive chemotactic dispersal, PLoS biology 12, e1001966 (2014)

    2014

  27. [35]

    Sucgang, C

    R. Sucgang, C. J. Weijer, F. Siegert, J. Franke, and R. H. Kessin, Null mutations of thedictyosteliumcyclic nucleotide phosphodiesterase gene block chemotactic cell movement in developing aggregates, Developmental biol- ogy 192, 181 (1997)

    1997

  28. [36]

    S. E. Leggett, Z. J. Neronha, D. Bhaskar, J. Y. Sim, T. M. Perdikari, and I. Y. Wong, Motility-limited aggregation of mammary epithelial cells into fractal-like clusters, Pro- ceedings of the National Academy of Sciences 116, 17298 (2019)

    2019

  29. [37]

    Risau and I

    W. Risau and I. Flamme, Vasculogenesis, Annual review of cell and developmental biology 11, 73 (1995)

    1995

  30. [38]

    Szabo, E

    A. Szabo, E. Mehes, E. Kosa, and A. Czirok, Multi- cellular sprouting in vitro, Biophysical journal 95, 2702 (2008)

    2008

  31. [39]

    Gamba, D

    A. Gamba, D. Ambrosi, A. Coniglio, A. de Candia, S. Di Talia, E. Giraudo, G. Serini, . f. L. Preziosi, and F. Bussolino, Percolation, morphogenesis, and burgers 9 dynamics in blood vessels formation, Physical review let- ters 90, 118101 (2003)

    2003

  32. [40]

    R. M. Merks, S. V. Brodsky, M. S. Goligorksy, S. A. New- man, and J. A. Glazier, Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent re- modeling, Developmental biology 289, 44 (2006)

    2006

  33. [41]

    R. M. Merks, E. D. Perryn, A. Shirinifard, and J. A. Glazier, Contact-inhibited chemotaxis in de novo and sprouting blood-vessel growth, PLoS computational bi- ology 4, e1000163 (2008)

    2008

  34. [42]

    Kleinmeier, G

    B. Kleinmeier, G. K¨ oster, and J. Drury, Agent-based simulation of collective cooperation: from experiment to model, Journal of The Royal Society Interface 17, 10.1098/rsif.2020.0396 (2020)

    2020

  35. [43]

    Valckenaers, M

    Hadeli, P. Valckenaers, M. Kollingbaum, and H. V. Brussel, Multi-agent coordination and control using stigmergy, Computers in Industry 53, 10.1016/S0166- 3615(03)00123-4 (2004)

    2004 doi

  36. [44]

    Meyer, L

    M. Meyer, L. Schimansky-Geier, and P. Romanczuk, Active brownian agents with concentration-dependent chemotactic sensitivity, Physical Review E 89, 022711 (2014)

    2014

  37. [45]

    T. J. Czaczkes, C. Gr¨ uter, and F. L. W. Ratnieks, Neg- ative feedback in ants: crowding results in less trail pheromone deposition, Journal of The Royal Society In- terface 10, 20121009 (2013)

    2013

  38. [46]

    E. G. Rens, M. T. Zeegers, I. Rabbers, A. Szab´ o, and R. M. H. Merks, Autocrine inhibition of cell motility can drive epithelial branching morphogenesis in the absence of growth, Philosophical Transactions of the Royal Soci- ety B: Biological Sciences 375, 20190386 (2020)

    2020

  39. [47]

    Grassberger and I

    P. Grassberger and I. Procaccia, Measuring the strangeness of strange attractors, Physica D: Nonlinear Phenomena 9, 189 (1983)

    1983

  40. [48]

    S. H. Strogatz, Nonlinear dynamics and chaos: With ap- plications to physics, biology, chemistry, and engineering (CRC Press, 2018) Chap. 11, pp. 418–423

    2018

  41. [49]

    S. N. Majumdar, S. Krishnamurthy, and M. Barma, Nonequilibrium phase transitions in models of aggrega- tion, adsorption, and dissociation, Physical Review Let- ters 81, 3691 (1998)

    1998

  42. [50]

    Peruani and M

    F. Peruani and M. B¨ ar, A kinetic model and scaling prop- erties of non-equilibrium clustering of self-propelled par- ticles, New Journal of Physics 15, 065009 (2013)

    2013

  43. [51]

    J. D. Weeks, D. Chandler, and H. C. Andersen, Role of repulsive forces in determining the equilibrium structure of simple liquids, J. Chem. Phys. 54, 5237 (1971)

    1971

  44. [52]

    Chandler, J

    D. Chandler, J. D. Weeks, and H. C. Andersen, Hy- drophobic hydration: Theory and experiment, Science 220, 787 (1983)

    1983

  45. [53]

    Carmeliet and R

    P. Carmeliet and R. K. Jain, Angiogenesis in cancer and other diseases, nature 407, 249 (2000)

    2000

  46. [54]

    Helmlinger, M

    G. Helmlinger, M. Endo, N. Ferrara, L. Hlatky, and R. K. Jain, Formation of endothelial cell networks, Nature405, 139 (2000)

    2000

  47. [55]

    Coultas, K

    L. Coultas, K. Chawengsaksophak, and J. Rossant, En- dothelial cells and vegf in vascular development, Nature 438, 937 (2005)

    2005

  48. [56]

    Gory-Faur´ e, M.-H

    S. Gory-Faur´ e, M.-H. Prandini, H. Pointu, V. Roullot, I. Pignot-Paintrand, M. Vernet, and P. Huber, Role of vascular endothelial-cadherin in vascular morphogenesis, Development 126, 2093 (1999)

    1999

  49. [57]

    E. D. Perryn, A. Czir´ ok, and C. D. Little, Vascular sprout formation entails tissue deformations and ve-cadherin- dependent cell-autonomous motility, Developmental bi- ology 313, 545 (2008)

    2008

  50. [58]

    M´ ehes and T

    E. M´ ehes and T. Vicsek, Collective motion of cells: from experiments to models, Integrative biology 6, 831 (2014)

    2014

  51. [59]

    I. Y. Wong, S. Javaid, E. A. Wong, S. Perk, D. A. Haber, M. Toner, and D. Irimia, Collective and individual mi- gration following the epithelial–mesenchymal transition, Nature materials 13, 1063 (2014)

    2014

  52. [60]

    M. D. Pope, N. A. Graham, B. K. Huang, and A. R. Asthagiri, Automated quantitative analysis of epithelial cell scatter, Cell adhesion & migration 2, 110 (2008)

    2008

  53. [61]

    Omelchenko, J

    T. Omelchenko, J. M. Vasiliev, I. Gelfand, H. Feder, and E. Bonder, Rho-dependent formation of epithelial “leader” cells during wound healing, Proceedings of the National Academy of Sciences 100, 10788 (2003)

    2003

  54. [62]

    Scherber, A

    C. Scherber, A. J. Aranyosi, B. Kulemann, S. P. Thayer, M. Toner, O. Iliopoulos, and D. Irimia, Epithelial cell guidance by self-generated egf gradients, Integrative Bi- ology 4, 259 (2012)

    2012

  55. [63]

    C. Jin, C. Kr¨ uger, and C. C. Maass, Chemotaxis and au- tochemotaxis of self-propelling droplet swimmers, Pro- ceedings of the National Academy of Sciences 114, 5089 (2017)

    2017

  56. [64]

    D. Ralt, M. Manor, A. Cohen-Dayag, I. Tur-Kaspa, I. Ben-Shlomo, A. Makler, I. Yuli, J. Dor, S. Blumberg, S. Mashiach, et al. , Chemotaxis and chemokinesis of hu- man spermatozoa to follicular factors, Biology of repro- duction 50, 774 (1994)

    1994

  57. [65]

    K. Son, F. Menolascina, and R. Stocker, Speed- dependent chemotactic precision in marine bacteria, Pro- ceedings of the National Academy of Sciences 113, 8624 (2016)

    2016

  58. [66]

    J. L. Moran, P. M. Wheat, N. A. Marine, and J. D. Pos- ner, Chemokinesis-driven accumulation of active colloids in low-mobility regions of fuel gradients, Scientific Re- ports 11, 4785 (2021)

    2021

  59. [67]

    Garnier, J

    S. Garnier, J. Gautrais, and G. Theraulaz, The biological principles of swarm intelligence, Swarm intelligence 1, 3 (2007)

    2007

  60. [68]

    Gompper, R

    G. Gompper, R. G. Winkler, T. Speck, A. Solon, C. Nar- dini, F. Peruani, H. L¨ owen, R. Golestanian, U. B. Kaupp, L. Alvarez, T. Kiorboe, E. Lauga, W. C. Poon, A. Desi- mone, S. Muinos-Landin, A. Fischer, N. A. S¨ oker, F. Ci- chos, R. Kapral, P. Gaspard, M. Ripoll, F. Sagues,...

    2020

  61. [69]

    T. M. Inc., MATLAB version: 9.13.0 (R2022b) (The MathWorks Inc., Natick, Massachusetts, United States, 2022). 1 Supplemental Materials: Self-organized fractal architectures driven by motility-dependent chemotactic feedback I. LINEAR ST ABILITY ANAL YSIS In this section, we per...

    2022

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