Solid-Liquid Transition of Deformable and Overlapping Active Particles

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Solid-Liquid Transition of Deformable and Overlapping Active Particles

Benjamin Loewe, Michael Chiang, Davide Marenduzzo, and M. Cristina Marchetti

Phys. Rev. Lett. 125, 038003 – Published 15 July 2020

Abstract

Experiments and theory have shown that cell monolayers and epithelial tissues exhibit solid-liquid and glass-liquid transitions. These transitions are biologically relevant to our understanding of embryonic development, wound healing, and cancer. Current models of confluent epithelia have focused on the role of cell shape, with less attention paid to cell extrusion, which is key for maintaining homeostasis in biological tissue. Here, we use a multiphase field model to study the solid-liquid transition in a confluent monolayer of deformable cells. Cell overlap is allowed and provides a way for modeling the precursor for extrusion. When cells overlap rather than deform, we find that the melting transition changes from continuous to first order like, and that there is an intermittent regime close to the transition, where solid and liquid states alternate over time. By studying the dynamics of five- and sevenfold disclinations in the hexagonal lattice formed by the cell centers, we observe that these correlate with spatial fluctuations in the cellular overlap, and that cell extrusion tends to initiate near fivefold disclinations.

Received 27 December 2019
Revised 24 April 2020
Accepted 16 June 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.038003

Physics Subject Headings (PhySH)

Collective behavior Liquid-solid phase transition Topological defects

Cells Epithelial cells Living matter & active matter

Phase-field modeling

Physics of Living SystemsPolymers & Soft Matter

Authors & Affiliations

Benjamin Loewe ^1,*, Michael Chiang², Davide Marenduzzo², and M. Cristina Marchetti¹

¹Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
²SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom

^*Corresponding author. baloewe@uc.cl

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Issue

Vol. 125, Iss. 3 — 17 July 2020

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Images

Figure 1
Simulation snapshots of the stationary state for different deformability (quantified by $d$ ) and motility (quantified by Pe). The contours of the cells correspond to the level ${ϕ_{i} = 1}_{i = 1}^{N}$ , while the coloring corresponds to the cell index at $t = 0$ (for visualizing cell rearrangements). (a), (b) The initial condition of the monolayer at (a) $d = 0.1$ and (b) $d = 2.0$ . Note that cells overlap at low $d$ , whereas at high $d$ cells deform rather than overlap. (c)–(f) Snapshots of the system at $D_{r} t = 250$ . The system remains in a crystal-like state at low motility [(c), (d)]. At sufficiently high motility, the system melts and cells exchange neighbors [(e), (f)]. See also Supplemental Movies 1–4 [49].
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Figure 2
Phase diagram of melting in our confluent system. The transition lines separating the solid, intermittent (labeled as SL), and liquid phases are interpolation of the boundaries identified based on the system’s diffusivity ${\bar{D}}_{eff}$ , its global bond-orientational order $| Ψ_{6} |$ , and the fraction of structural defects $⟨ | Δ N_{nn} | ⟩$ in the system.
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Figure 3
Intermittence at low deformability. (a)–(c) Intermittent behavior at $(d, Pe) = (0.1, 2.4)$ . (a) Time series of $| Ψ_{6} |$ . (b) Time series of the fraction of defects $⟨ | Δ N_{nn} | ⟩$ . (c) Voronoi tessellation of the system depicting instantaneous configurations in the solid and liquid states, and highlighting the presence of topological defects in the latter. The color scheme denotes the topological charge—i.e., the deviation from a coordination number of six. (d) PDFs of $| Ψ_{6} |$ at $d = 0.1$ with increasing motility. As the system goes through the intermittent regime, the PDF goes from unimodal (solid), to bimodal (intermittent), and back to unimodal (liquid).
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Figure 4
Correlation between local overlap and defects at $(d, Pe) = (0.1, 2.4)$ . (a) Simulation snapshot. Color denotes the degree of local overlap–i.e., the fraction of a cell’s area overlapped by other cells, which is given by $χ_{i} = A_{i}^{- 1} \int_{Ω_{i}} d^{2} r χ_{i} (r)$ , where $Ω_{i}$ is the region where $ϕ_{i} > 1$ and $A_{i}$ is its area. (b) Voronoi tessellation of (a), colored by the topological charge of each cell [see Fig. 3]. Black arrows point to the same two cells with defects in (a) and (b) to highlight that cells with fivefold disclinations have higher local overlap than those with sevenfold disclinations. (c) PDFs of the local overlap for different defect types. (d) PDFs of the mean separation $d_{nn}$ of a cell from its nearest neighbors for different defect types.
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