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A bilayer cellular Potts model predicts epithelial edge matching peaks when both monolayers are fluid-like and coupling balances in-plane and out-of-plane energies.

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2026-07-02 02:23 UTC pith:KGNNJAO5

load-bearing objection The paper adds a single-parameter out-of-plane edge coupling to the cellular Potts model and reports that bilayer edge matching peaks when both layers are fluid-like and coupling is intermediate. the 2 major comments →

arxiv 2607.00400 v1 pith:KGNNJAO5 submitted 2026-07-01 physics.bio-ph cond-mat.soft

A bilayer cellular Potts model of epithelial docking

Troy Singletary , Andrea James , Tyler A. Engstrom This is my paper
classification physics.bio-ph cond-mat.soft
keywords bilayer cellular Potts modelepithelial dockingedge matchingT1 transitionsdomain wallscell shape indexmorphogenesiscell sheet fusion
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper develops a cellular Potts model that couples two standard 2D epithelial sheets through short-range out-of-plane interactions at cell edges. This coupling uses one parameter to represent the net effect of protrusions and adhesions, allowing the model to simulate the docking stage of bilayer fusion. Simulations show that edge matching across the bilayer reaches its highest levels when both layers sit in their fluid-like regime with average shape index above 4.6 and when the coupling strength sits at an intermediate value that balances the two energy scales. Stronger coupling traps the system in metastable configurations with poorer alignment. Coordinated T1 transitions drive the matching process, while long-lived domain walls emerge that separate regions of near-complete matching.

Core claim

The bilayer cellular Potts model demonstrates that edge matching between the two monolayers is maximized when the monolayers operate in their fluid-like regimes, defined by average cell shape index greater than 4.6, and when the strength of the out-of-plane coupling strikes a balance between in-plane and out-of-plane energy scales. At higher coupling values the system becomes trapped in metastable states with suboptimal matching. Pairs and quadruplets of coordinated T1 transitions contribute substantially to the matching process. The model also produces emergent domain walls, which are branching or unbranching curves that cross no matched edges yet separate regions of nearly complete matchin

What carries the argument

The short-range out-of-plane coupling term between cell edges in the bilayer cellular Potts model, implemented with a single adjustable parameter that represents the combined effects of cytoskeletal protrusions, cadherins, and other edge-associated adhesions.

Load-bearing premise

The combined effects of dynamic cytoskeletal protrusions, cadherins, and other adhesion molecules on edge alignment can be captured by a single adjustable parameter.

What would settle it

Direct measurement of edge-matching fraction in cultured epithelial bilayers as cortical tension is increased to push shape index below 4.6 or as adhesion strength is increased to mimic stronger coupling, checking whether matching fraction drops as predicted.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Bilayer edge matching reaches its maximum when both monolayers have average cell shape index greater than 4.6.
  • Optimal matching occurs at intermediate coupling strengths that balance in-plane and out-of-plane energy scales.
  • Stronger coupling causes the system to become trapped in metastable states with reduced edge matching.
  • Coordinated pairs and quadruplets of T1 transitions play a central role in achieving edge matching.
  • Domain walls arise as long-lived separators between regions of high and low matching and can span the entire system.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The requirement for fluid-like behavior suggests that epithelial fusion events in development may be facilitated by lowering cortical tension or increasing cell motility.
  • Domain walls could appear as observable boundaries in live imaging of docking tissues and might influence the final fusion outcome.
  • The speed distributions obtained with bending included could be compared directly to experimental measurements of docking fronts in curved geometries such as neural tube closure.
  • The single-parameter coupling could be refined by adding separate terms for protrusion dynamics versus cadherin binding to test which component most controls the balance point.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a bilayer cellular Potts model that couples two standard 2D area- and perimeter-constrained monolayers via a single-parameter short-range out-of-plane edge interaction. The central claim is that edge matching across the bilayer is maximized when both monolayers are fluid-like (average cell shape index >4.6) and the coupling strength balances in-plane and out-of-plane energy scales; the work further examines the role of coordinated T1 transitions, the emergence of long-lived domain walls, and docking-front statistics under an added bending term.

Significance. The construction supplies a minimal, single-parameter effective model for a biologically relevant but under-modeled process (bilayer docking). If the reported simulation trends prove robust, the identification of fluid-regime and balanced-coupling optima, together with the mechanistic role of T1 quadruplets and the domain-wall phenomenology, would constitute a useful set of falsifiable predictions for experimental tests of epithelial fusion.

major comments (2)
  1. [Abstract and results sections] Abstract and results sections: the claims of maximized edge matching at shape index >4.6 and intermediate coupling rest entirely on simulation outcomes, yet no quantitative definition of the matching metric, no error bars, no convergence tests with system size or Monte-Carlo steps, and no sensitivity analysis to the single free parameter are supplied; without these the reported maxima cannot be assessed for statistical significance or robustness.
  2. [Model section] Model section: the out-of-plane coupling is introduced as a minimal effective term whose single parameter absorbs multiple biological mechanisms; the manuscript does not demonstrate that the location of the matching maximum is independent of the precise functional form chosen for this term, which is load-bearing for the generality of the fluid-regime prediction.
minor comments (2)
  1. The precise numerical threshold 4.6 for the fluid-like regime should be tied explicitly to the implementation (e.g., the value of the target perimeter or the temperature parameter) rather than left as an implementation-specific number.
  2. Figure captions and methods should state the lattice size, number of independent runs, and burn-in protocol used to generate the reported domain-wall and T1 statistics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract and results sections] Abstract and results sections: the claims of maximized edge matching at shape index >4.6 and intermediate coupling rest entirely on simulation outcomes, yet no quantitative definition of the matching metric, no error bars, no convergence tests with system size or Monte-Carlo steps, and no sensitivity analysis to the single free parameter are supplied; without these the reported maxima cannot be assessed for statistical significance or robustness.

    Authors: We agree that an explicit quantitative definition of the edge-matching metric must be provided, along with statistical measures of robustness. In the revised manuscript we will (i) state the precise definition of the matching metric in the abstract and results, (ii) report error bars obtained from ensemble averages over independent Monte-Carlo realizations, (iii) include convergence tests with respect to system size and number of Monte-Carlo steps, and (iv) add a sensitivity analysis of the reported maxima with respect to the coupling parameter. revision: yes

  2. Referee: [Model section] Model section: the out-of-plane coupling is introduced as a minimal effective term whose single parameter absorbs multiple biological mechanisms; the manuscript does not demonstrate that the location of the matching maximum is independent of the precise functional form chosen for this term, which is load-bearing for the generality of the fluid-regime prediction.

    Authors: The coupling is formulated as a minimal effective interaction. While we expect the fluid-regime optimum to be robust for short-range edge interactions, we acknowledge that explicit tests with an alternative functional form are needed to support generality. In revision we will add simulations employing a modified short-range coupling (e.g., a linear rather than quadratic distance penalty) and verify that the location of the matching maximum remains at shape index >4.6 and intermediate coupling strength. revision: yes

Circularity Check

0 steps flagged

No significant circularity; predictions are simulation outputs

full rationale

The paper defines a standard 2D cellular Potts model for each monolayer, augmented by one explicit out-of-plane coupling term with a single free parameter, then reports numerical outcomes (edge-matching maxima at shape index >4.6 and intermediate coupling). These outcomes are generated by evolving the constructed Hamiltonian; they do not reduce to the inputs by algebraic identity, fitted-parameter renaming, or self-citation chains. The 4.6 threshold is stated as implementation-specific and aligns with known CPM fluid-transition values without circular re-derivation. No load-bearing uniqueness theorems or ansatzes imported from the authors' prior work appear in the abstract or described claims.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Ledger based solely on abstract; full text would allow more complete enumeration of assumptions.

free parameters (1)
  • bilayer coupling strength
    Single adjustable parameter controlling out-of-plane edge interactions; value not specified in abstract.
axioms (2)
  • domain assumption Cells have a tendency to remodel so as to co-localize their bilateral junctions across the bilayer
    Observation motivating the model; stated in abstract as motivation.
  • standard math Standard 2D area- and perimeter-elasticity models apply independently to each monolayer
    Explicitly invoked as the base for the bilayer extension.

pith-pipeline@v0.9.1-grok · 5852 in / 1315 out tokens · 32220 ms · 2026-07-02T02:23:00.776739+00:00 · methodology

0 comments
read the original abstract

Fusion of two epithelial cell sheets brought together in a bilayer configuration is a common step in animal morphogenesis, yet, in contrast to other epithelial fusion processes such as wound healing in a monolayer of cells, it has not been a strong focus of modeling efforts. Here we consider a preliminary stage of bilayer fusion, recently termed "docking." In multiple instances of docking that span apical and basal varieties, cells appear to have a tendency to remodel so as to co-localize their bilateral junctions (match their edges) across the bilayer. Motivated by this observation, we introduce a bilayer cellular Potts model that couples two standard 2D area- and perimeter-elasticity models via short-range, out-of-plane interactions between cell edges. The new coupling involves a single adjustable parameter that minimally models the combined effect of dynamic cytoskeletal protrusions, cadherins, and other potential edge-associated adhesion molecules. Our model predicts that bilayer edge matching is maximized when the two monolayers are in their fluid-like regimes (average cell shape index greater than 4.6 in our implementation), and when the bilayer coupling strength strikes a balance between in-plane and out-of-plane energy scales. At higher coupling strengths, the system tends to get stuck in metastable states with sub-optimal edge matching. Exploration of the mechanisms of edge matching reveals that pairs and quadruplets of coordinated T1 transitions play a particularly important role. We also find numerous examples of emergent features we term "domain walls" - branching or unbranching curves that cross no matched edges, but that separate regions of nearly complete matching. These domain walls can be both system spanning and long lived. Finally, we extend our model to crudely account for bending of the two sheets, and study the distributions of docking front speeds that result.

Figures

Figures reproduced from arXiv: 2607.00400 by Andrea James, Troy Singletary, Tyler A. Engstrom.

Figure 1
Figure 1. Figure 1: FIG. 1. Multiple forms of epithelial docking may be amenable [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. An example of cell edge matching in the BCPM, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Initial cell positions are generated by pseudo [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Spatiotemporally coordinated T1 transitions are a [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Edge match ratio [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. BCPM regime maps parameterized by [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: It’s noteworthy that this edge rotation mecha [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a) Approximation of bending as kinks in two oth [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Distributions of speeds [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Cell center MSD vs time curves for various [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. (a) A regime map of scaling exponent [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. An example of an event with two neighbor changes, [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

56 extracted references · 56 canonical work pages

  1. [1]

    due to fewer time intervals included in the averag- ing at higher ∆tand correlations in particle positions between times in a computational simulation. With pe- riodic boundary conditions used in our simulations the position over time data⃗ r(t) of some of the cells spikes when those cells cross a periodic boundary, introducing another source of error. Th...

    work page 2000

  2. [2]

    L. E. Cote and J. L. Feldman, Won’t you be my neighbor: How epithelial cells connect together to build global tis- sue polarity, Frontiers in Cell and Developmental Biology 10, 1 (2022)

    work page 2022

  3. [3]

    D. J. Andrew and A. J. Ewald, Morphogenesis of epithe- lial tubes: Insights into tube formation, elongation and elaboration, Developmental Biology341, 34 (2010)

    work page 2010

  4. [4]

    H. J. Ray and L. Niswander, Mechanisms of tissue fusion during development, Development139, 1701 (2012)

    work page 2012

  5. [5]

    Ishihara, A

    K. Ishihara, A. Mukherjee, E. Gromberg, J. Brugu´ es, E. M. Tanaka, and F. J¨ ulicher, Topological morphogene- sis of neuroepithelial organoids, Nature Physics19, 177 (2023)

    work page 2023

  6. [6]

    Nikolopoulou, G

    E. Nikolopoulou, G. L. Galea, A. Rolo, N. D. E. Greene, and A. J. Copp, Neural tube closure: cellular, molecular and biomechanical mechanisms, Development144, 552 (2017)

    work page 2017

  7. [7]

    M. A. Mol` e, G. L. Galea, A. Rolo, A. Weberling, O. Ny- chyk, S. C. De Castro, D. Savery, R. F¨ assler, P. Ybot- 12 Gonz´ alez, N. D. E. Greene, and A. J. Copp, Integrin- mediated focal anchorage drives epithelial zippering dur- ing mouse neural tube closure, Developmental Cell52, 321 (2020)

    work page 2020

  8. [8]

    Hashimoto, F

    H. Hashimoto, F. B. Robin, K. M. Sherrard, and E. M. Munro, Sequential contraction and exchange of apical junctions drives zippering and neural tube closure in a simple chordate, Developmental Cell32, 241 (2015)

    work page 2015

  9. [9]

    Hashimoto and E

    H. Hashimoto and E. Munro, Differential expression of a classic cadherin directs tissue-level contractile asymme- try during neural tube closure, Developmental Cell51, 158 (2019)

    work page 2019

  10. [10]

    MacGowan, M

    J. MacGowan, M. Cardenas, and M. K. Williams, Fold- and-fuse neurulation in zebrafish requires vangl2, Devel- opmental Biology524, 55 (2025)

    work page 2025

  11. [11]

    K. K. Billmyre, M. Hutson, and J. Klingensmith, One shall become two: separation of the esophagus and tra- chea from the common foregut tube, Developmental Dy- namics244, 277 (2015)

    work page 2015

  12. [12]

    N. A. Edwards, S. A. Rankin, A. Kashyap, A. Warren, Z. N. Agricola, A. P. Kenny, M. Kofron, Y. Shen, W. K. Chung, and A. M. Zorn, Disrupted endosomal trafficking of the vangl-celsr polarity complex underlies congenital anomalies inXenopustrachea-esophageal morphogene- sis, Developmental Cell60, 2487 (2025)

    work page 2025

  13. [13]

    C. S. Teng, S. W. Curtis, G. C. Brewer, E. J. Leslie- Clarkson, and J. O. Bush, Actomyosin contractility and a threshold of cadherin cell adhesion are required during tissue fusion, Journal of Cell Biology225, 1 (2026)

    work page 2026

  14. [14]

    M. A. Palmer and C. M. Nelson, Fusion of airways during avian lung development constitutes a novel mechanism for the formation of continuous lumena in multicellular epithelia, Developmental Dynamics249, 1318 (2020)

    work page 2020

  15. [15]

    R. M. Kao, A. Vasilyev, A. Miyawaki, I. A. Drummond, and A. P. McMahon, Invasion of distal nephron pre- cursors associates with tubular interconnection during nephrogenesis, J. Am. Soc. Nephrol.23, 1682 (2012)

    work page 2012

  16. [16]

    James, C

    A. James, C. Lee, A. M. Williams, K. Angileri, K. L. Lathrop, and J. M. Gross, The hyaloid vasculature fa- cilitates basement membrane breakdown during choroid fissure closure in the zebrafish eye, Developmental Biol- ogy419, 262 (2016)

    work page 2016

  17. [17]

    Gestri, N

    G. Gestri, N. Bazin-Lopez, C. Scholes, and S. W. Wilson, Cell behaviors during closure of the choroid fissure in the developing eye, Frontiers in Cellular Neuroscience12, 1 (2018)

    work page 2018

  18. [18]

    C. S. Bernstein, M. T. Anderson, C. Gohel, K. Slater, J. M. Gross, and S. Agarwala, The cellular bases of choroid fissure formation and closure, Developmental Bi- ology440, 137 (2018)

    work page 2018

  19. [19]

    Eckert, M

    P. Eckert, M. D. Knickmeyer, and S. Heermann, In vivo analysis of optic fissure fusion in zebrafish: Pioneer cells, basal lamina, hyaloid vessels, and how fissure fusion is affected by BMP, International Journal of Molecular Sci- ences21, 1 (2020)

    work page 2020

  20. [20]

    B. H. C. Chan, M. Moosajee, and J. Rainger, Closing the gap: Mechanisms of epithelial fusion during optic fissure closure, Frontiers in Cell and Developmental Biology8, 1 (2021)

    work page 2021

  21. [21]

    M. F. Portereiko and S. E. Mango, Early morphogenesis of theCaenorhabditis eleganspharynx, Developmental Biology233, 482 (2001)

    work page 2001

  22. [22]

    L. E. Cote, M. D. Sallee, R. K. Ng, M. A. Pickett, J. Magescas, and J. L. Feldman, Re- ciprocal e-cadherin signaling aligns apical surfaces between neighboring epithelial tissues to complete theC. elegansdigestive tract, bioRxiv preprint https://doi.org/10.1101/2025.10.06.680605 (2025)

    work page doi:10.1101/2025.10.06.680605 2025

  23. [23]

    M. A. Palmer and C. M. Nelson, Epithelial tube fusion as a mechanism for the development of complex lumen- containing organs, Trends in Developmental Biology10, 57 (2018)

    work page 2018

  24. [24]

    Jacinto, W

    A. Jacinto, W. Wood, T. Balayo, M. Turmaine, A. Martinez-Arias, and P. Martin, Dynamic actin-based epithelial adhesion and cell matching duringDrosophila dorsal closure, Current Biology10, 1420 (2000)

    work page 2000

  25. [25]

    Jacinto, A

    A. Jacinto, A. Martinez-Arias, and P. Martin, Mecha- nisms of epithelial fusion and repair, Nature Cell Biology 3, E117 (2001)

    work page 2001

  26. [26]

    Popkova, U

    A. Popkova, U. Andrenˇ sek, S. Pagnotta, P. Ziherl, M. Krajnc, and M. Rauzi, A mechanical wave travels along a genetic guide to drive the formation of an epithe- lial furrow duringDrosophilagastrulation, Developmen- tal Cell59, 400 (2024)

    work page 2024

  27. [27]

    C. Y. Gregory-Evans, M. J. Williams, and K. Gregory- Evans, Ocular coloboma: a reassessment in the age of molecular neuroscience, J. Med. Genet.41, 881 (2004)

    work page 2004

  28. [28]

    Kondo, O

    A. Kondo, O. Kamihira, and H. Ozawa, Neural tube de- fects: Prevalence, etiology, and prevention, International Journal of Urology16, 49 (2009)

    work page 2009

  29. [29]

    M. J. Dixon, M. L. Marazita, T. H. Beaty, and J. C. Murray, Cleft lip and palate: understanding genetic and environmental influences, Nature Reviews Genetics12, 167 (2011)

    work page 2011

  30. [30]

    Okuda, Y

    S. Okuda, Y. Inoue, and T. Adachi, Three-dimensional vertex model for simulating multicellular morphogenesis, Biophysics and Physicobiology12, 13 (2015)

    work page 2015

  31. [31]

    Zhang and J

    T. Zhang and J. M. Schwarz, Topologically-protected in- terior for three-dimentional confluent cellular collectives, Physical Review Research4, 1 (2022)

    work page 2022

  32. [32]

    Sarkar and M

    T. Sarkar and M. Krajnc, Reentrant rigidity transition in planar epithelia with volume and area elasticity, Physical Review Letters136, 068404 (2026)

    work page 2026

  33. [33]

    Merkel and M

    M. Merkel and M. L. Manning, A geometrically con- trolled rigidity transition in a model for confluent 3d tis- sues, New Journal of Physics20, 1 (2018)

    work page 2018

  34. [34]

    M. H. Swat, G. L. Thomas, J. M. Belmonte, A. Shirini- fard, D. Hmeljak, and J. A. Glazier, Chapter 13 - multi- scale modeling of tissues using compucell3d, inComputa- tional Methods in Cell Biology, Methods in Cell Biology, Vol. 110, edited by A. R. Asthagiri and A. P. Arkin (El- sevier, 2012) pp. 325–366

    work page 2012

  35. [35]

    Runser, R

    S. Runser, R. Vetter, and D. Iber, Simucell3d: three- dimensional simulation of tissue mechanics with cell po- larization, Nature Computatioal Science4, 299 (2024)

    work page 2024

  36. [36]

    Ongenae, H

    S. Ongenae, H. Svitina, T. E. R. Belpaire, J. Vangheel, T. Martens, P. V. Berghe, I. Papantoniou, and B. Smeets, Active foam dynamics of tissue spheroid fusion, Nature Communications16, 10467 (2025)

    work page 2025

  37. [37]

    R. J. Tetley, M. F. Staddon, D. Heller, A. Hoppe, S. Banerjee, and Y. Mao, Tissue fluidity promotes ep- ithelial wound healing, Nature Physics15, 1195 (2019)

    work page 2019

  38. [38]

    A. R. Noppe, A. P. Roberts, A. S. Yap, G. A. Gomez, and Z. Neufeld, Modelling wound closure in an epithelial cell sheet using the cellular Potts model, Integrative Biology 7, 1253 (2015)

    work page 2015

  39. [39]

    R. F. Almada, N. A. M. Ara´ ujo, and P. Patr´ ıcio, Physical models of embryonic epithelial healing, arXiv preprint 13 https://arxiv.org/abs/2510.13374v2 (2026)

    work page arXiv 2026

  40. [40]

    A. L. Godeau, M. Marin-Riera, E. Trubuil, S. Rogalla, G. Bengoetxea, L. Backov´ a, T. Pujol, J. Colombelli, J. Sharpe, E. Martin-Blanco, and J. Solon, A transient contractile seam promotes epithelial sealing and sequen- tial assembly of body segments, Nature Communications 16, 1 (2025)

    work page 2025

  41. [41]

    Nagai and H

    T. Nagai and H. Honda, A dynamic cell model for the formation of epithelial tissues, Philosophical Magazine B 81, 699 (2001)

    work page 2001

  42. [42]

    A. G. Fletcher, M. Osterfield, R. E. Baker, and S. Y. Shvartsman, Vertex models of epithelial morphogenesis, Biophysical Journal106, 2291 (2014)

    work page 2014

  43. [43]

    D. Bi, J. H. Lopez, J. M. Schwarz, and M. L. Manning, A density-independent rigidity transition in biological tis- sues, Nature Physics11, 1074 (2015)

    work page 2015

  44. [44]

    S. Chen, B. Lewis, A. Moran, and T. Xie, Cadherin- mediated cell adhesion is critical for the closing of the mouse optic fissure, PLOS ONE7, 1 (2012)

    work page 2012

  45. [45]

    Graner and J

    F. Graner and J. A. Glazier, Simulation of biological cell sorting using a two-dimensional extended Potts model, Physical Review Letters69, 2013 (1992)

    work page 2013

  46. [46]

    J. A. Glazier and F. Graner, Simulation of the differ- ential adhesion driven rearrangement of biological cells, Physical Review E47, 2128 (1993)

    work page 1993

  47. [47]

    Hogeweg, Evolving mechanisms of morphogenesis: on the interplay between differential adhesion and cell dif- ferentiation, Journal of Theoretical Biology203, 317 (2000)

    P. Hogeweg, Evolving mechanisms of morphogenesis: on the interplay between differential adhesion and cell dif- ferentiation, Journal of Theoretical Biology203, 317 (2000)

    work page 2000

  48. [48]

    Chiang and D

    M. Chiang and D. Marenduzzo, Glass transitions in the cellular Potts model, Euro Physics Letters116, 28009 (2016)

    work page 2016

  49. [49]

    Sadhukhan and S

    S. Sadhukhan and S. K. Nandi, Theory and simulation for equilibrium glassy dynamics in cellular Potts model of confluent biological tissue, Physical Review E103, 062403 (2021)

    work page 2021

  50. [50]

    A. J. Devanny, D. J. Lee, L. Kampman, and L. J. Kaufman, Signatures of jamming in the cellular Potts model, bioRxiv preprint https://doi.org/10.1101/2023.07.10.548321

    work page doi:10.1101/2023.07.10.548321 2023

  51. [51]

    Nemati and J

    H. Nemati and J. de Graaf, The cellular Potts model on disordered lattices, Soft Matter20, 8337 (2024)

    work page 2024

  52. [52]

    D. Bi, X. Yang, M. C. Marchetti, and M. L. Manning, Motility-driven glass and jamming transitions in biolog- ical tissues, Physical Review X6, 021011 (2016)

    work page 2016

  53. [53]

    [url to be inserted by publisher] (2026)

    work page 2026

  54. [54]

    Michalet, Mean square displacement analysis of single- particle trajectories with localization error: Brownian motion in an isotropic medium, Phys

    X. Michalet, Mean square displacement analysis of single- particle trajectories with localization error: Brownian motion in an isotropic medium, Phys. Rev. E82, 041914 (2010)

    work page 2010

  55. [55]

    P. C. Dal-Castel, G. L. Thomas, G. C. Perrone, and R. M. de Almeida, Compucell3d model of cell migration repro- duces chemotaxis, Physica A: Statistical Mechanics and its Applications666, 130524 (2025)

    work page 2025

  56. [56]

    J. T. Bullerjahn, S. von B¨ ulow, and G. Hummer, Opti- mal estimates of self-diffusion coefficients from molecular dynamics simulations, The Journal of Chemical Physics 153, 024116 (2020)

    work page 2020