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Intermittent attractive interactions lead to microphase separation in nonmotile active matter

Henry Alston, Andrew O. Parry, Raphaël Voituriez, and Thibault Bertrand
Phys. Rev. E 106, 034603 – Published 6 September 2022
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  • INTRODUCTION
  • MICROSCOPIC MODEL
  • COARSE-GRAINING PROCEDURE
  • AGENT DENSITY AND ACTIVE MODEL B+
  • MICROPHASE SEPARATION AND ACTIVE MODEL B…
  • DISCUSSION
    • Supplemental Material
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    Abstract

    Nonmotile active matter exhibits a wide range of nonequilibrium collective phenomena yet examples are crucially lacking in the literature. We present a microscopic model inspired by the bacteria Neisseria meningitidis in which diffusive agents feel intermittent attractive forces. Through a formal coarse-graining procedure, we show that this truly scalar model of active matter exhibits the time-reversal-symmetry breaking terms defining the Active Model B+ class. In particular, we confirm the presence of microphase separation by solving the kinetic equations numerically. We show that the switching rate controlling the interactions provides a regulation mechanism tuning the typical cluster size, e.g., in populations of bacteria interacting via type IV pili.

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    • Received 11 January 2022
    • Accepted 26 July 2022

    DOI:https://doi.org/10.1103/PhysRevE.106.034603

    ©2022 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    ClusteringMicrophase separation
    1. Physical Systems
    BacteriaLiving matter & active matter
    1. Techniques
    Theories of collective dynamics & active matter
    Polymers & Soft MatterPhysics of Living SystemsStatistical Physics & Thermodynamics

    Authors & Affiliations

    Henry Alston1, Andrew O. Parry1, Raphaël Voituriez2,3, and Thibault Bertrand1,*

    • 1Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2BZ, United Kingdom
    • 2Laboratoire de Physique Théorique de la Matière Condensée, UMR 7600 CNRS/UPMC, 4 Place Jussieu, 75255 Paris Cedex, France
    • 3Laboratoire Jean Perrin, UMR 8237 CNRS/UPMC, 4 Place Jussieu, 75255 Paris Cedex, France

    • *t.bertrand@imperial.ac.uk

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    Issue

    Vol. 106, Iss. 3 — September 2022

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    • Figure 1
      Figure 1

      Schematic of microscopic interactions. (a) The state of particle i is set by its internal variable, ɛi, which switches between 0 and 1 with fixed rates, kon and koff. The pair potential for neighboring particles depends on the product ɛiɛj. (b) Pair potentials used in the simulations for ɛiɛj=0 (red) and ɛiɛj=1 (green). A WCA potential sets the particle size σ* and the attraction range is set to σc=2σ* [56].

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    • Figure 2
      Figure 2

      Emergent structures in active switching system. (a) Radius of gyration Rgyr, (b) demixing index Idemix, and (c) maximal cluster size smax for switching rates κ∈[10−2,102] and ε≫kBT. Representative configurations obtained in simulations at steady state for (d) κ=0, (e) κ=10−2, (f) κ=10, and (g) κ=100.

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    • Figure 3
      Figure 3

      Measuring Sκ(ρ) numerically. Shape function Sκ(ρ) measured from simulations of the microscopic model with nondimensional switching rates κ∈[10−2,102] and total volume fraction of agents ϕ¯=0.3 as the fraction of on agents in circular regions of radius σc with number of agents per unit area ρ.

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    • Figure 4
      Figure 4

      Numerical analysis of kinetic equations. Numerical solutions of Eqs. (11) for ρ¯=0.16 with ε≫kBT [56]. Steady-state solutions show microphase separation (MPS) for (a) κ=0.01 and (b) κ=1 but full phase separation (FPS) for (c) κ=100. (d) Mean droplet radius 〈rc〉 is nonmonotonic in the switching rate κ across the (i) microphase separated and (ii) full phase separated regimes, in agreement with Fig. 2.

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