Spatiotemporal Self-Organization of Fluctuating Bacterial Colonies

Unveiling the Phase Diagram and Reaction Paths of the Active Model B with the Deep Minimum Action Method

Nonequilibrium phase transitions are notably difficult to analyze because their mechanisms depend on the system's dynamics in a complex way due to the lack of time-reversal symmetry. To complicate matters, the system's steady-state distribution is unknown in general. Here, the phase diagram of the active Model B is computed with a deep neural network implementation of the geometric minimum action method (gMAM). This approach unveils the unconventional reaction paths and nucleation mechanism in dimensions 1, 2, and 3, by which the system switches between the homogeneous and inhomogeneous phases in the binodal region. Our main findings are (i) the mean time to escape the phase-separated state is (exponentially) extensive in the system size L, but it increases nonmonotonically with L in dimension 1; (ii) the mean time to escape the homogeneous state is always finite, in line with the recent work of Cates and Nardini [Phys. Rev. Lett. 130, 098203 (2023)PRLTAO0031-900710.1103/PhysRevLett.130.098203]; (iii) at fixed L, the active term increases the stability of the homogeneous phase, eventually destroying the phase separation in the binodal for large but finite systems. Our results are particularly relevant for active matter systems in which the number of constituents hardly goes beyond 10^{7} and where finite-size effects matter.

Socioeconomic agents as active matter in nonequilibrium Sakoda-Schelling models

How robust are socioeconomic agent-based models with respect to the details of the agents' decision rule? We tackle this question by considering an occupation model in the spirit of the Sakoda-Schelling model, historically introduced to shed light on segregation dynamics among human groups. For a large class of utility functions and decision rules, we pinpoint the nonequilibrium nature of the agent dynamics, while recovering an equilibrium-like phase separation phenomenology. Within the mean-field approximation we show how the model can be mapped, to some extent, onto an active matter field description. Finally, we consider nonreciprocal interactions between two populations and show how they can lead to nonsteady macroscopic behavior. We believe our approach provides a unifying framework to further study geography-dependent agent-based models, notably paving the way for joint consideration of population and price dynamics within a field theoretic approach.

Coarsening and wavelength selection far from equilibrium: A unifying framework based on singular perturbation theory

Intracellular protein patterns are described by (nearly) mass-conserving reaction-diffusion systems. While these patterns initially form out of a homogeneous steady state due to the well-understood Turing instability, no general theory exists for the dynamics of fully nonlinear patterns. We develop a unifying theory for nonlinear wavelength-selection dynamics in (nearly) mass-conserving two-component reaction-diffusion systems independent of the specific mathematical model chosen. Previous work has shown that these systems support an extremely broad band of stable wavelengths, but the mechanism by which a specific wavelength is selected has remained unclear. We show that an interrupted coarsening process selects the wavelength at the threshold to stability. Based on the physical intuition that coarsening is driven by competition for mass and interrupted by weak source terms that break strict mass conservation, we develop a singular perturbation theory for the stability of stationary patterns. The resulting closed-form analytical expressions enable us to quantitatively predict the coarsening dynamics and the final pattern wavelength. We find excellent agreement with numerical results throughout the diffusion- and reaction-limited regimes of the dynamics, including the crossover region. Further, we show how, in these limits, the two-component reaction-diffusion systems map to generalized Cahn-Hilliard and conserved Allen-Cahn dynamics, therefore providing a link to these two fundamental scalar field theories. The systematic understanding of the length-scale dynamics of fully nonlinear patterns in two-component systems provided here builds the basis to reveal the mechanisms underlying wavelength selection in multicomponent systems with potentially several conservation laws.

Motility-Induced Phase Separation Mediated by Bacterial Quorum Sensing

We study motility-induced phase separation (MIPS) in living active matter, in which cells interact through chemical signaling, or quorum sensing. In contrast to previous theories of MIPS, our multiscale continuum model accounts explicitly for genetic regulation of signal production and motility. Through analysis and simulations, we derive a new criterion for the onset of MIPS that depends on features of the genetic network. Furthermore, we identify and characterize a new type of oscillatory instability that occurs when gene regulation inside cells promotes motility in higher signal concentrations.

Pattern formation by bacteria-phage interactions

The interactions between bacteria and phages-viruses that infect bacteria-play critical roles in agriculture, ecology, and medicine; however, how these interactions influence the spatial organization of both bacteria and phages remain largely unexplored. Here, we address this gap in knowledge by developing a theoretical model of motile, proliferating bacteria that aggregate via motility-induced phase separation (MIPS) and encounter phage that infect and lyse the cells. We find that the non-reciprocal predator-prey interactions between phage and bacteria strongly alter spatial organization, in some cases giving rise to a rich array of finite-scale stationary and dynamic patterns in which bacteria and phage coexist. We establish principles describing the onset and characteristics of these diverse behaviors, thereby helping to provide a biophysical basis for understanding pattern formation in bacteria-phage systems, as well as in a broader range of active and living systems with similar predator-prey or other non-reciprocal interactions.

Nonequilibrium currents in stochastic field theories: A geometric insight

We introduce a formalism to study nonequilibrium steady-state probability currents in stochastic field theories. We show that generalizing the exterior derivative to functional spaces allows identification of the subspaces in which the system undergoes local rotations. In turn, this allows prediction of the counterparts in the real, physical space of these abstract probability currents. The results are presented for the case of the Active Model B undergoing motility-induced phase separation, which is known to be out of equilibrium but whose steady-state currents have not yet been observed, as well as for the Kardar-Parisi-Zhang equation. We locate and measure these currents and show that they manifest in real space as propagating modes localized in regions with nonvanishing gradients of the fields.

Biophysical aspects underlying the swarm to biofilm transition

Bacteria organize in a variety of collective states, from swarming-rapid surface exploration, to biofilms-highly dense immobile communities attributed to stress resistance. It has been suggested that biofilm and swarming are oppositely controlled, making this transition particularly interesting for understanding the ability of bacterial colonies to adapt to challenging environments. Here, the swarm to biofilm transition is studied in Bacillus subtilis by analyzing the bacterial dynamics both on the individual and collective scales. We show that both biological and physical processes facilitate the transition. A few individual cells that initiate the biofilm program cause nucleation of large, approximately scale-free, stationary aggregates of trapped swarm cells. Around aggregates, cells continue swarming almost unobstructed, while inside, trapped cells are added to the biofilm. While our experimental findings rule out previously suggested purely physical effects as a trigger for biofilm formation, they show how physical processes, such as clustering and jamming, accelerate biofilm formation.

Heterogeneous bacterial swarms with mixed lengths

Heterogeneous systems of active matter exhibit a range of complex emergent dynamical patterns. In particular, it is difficult to predict the properties of the mixed system based on its constituents. These considerations are particularly significant for understanding realistic bacterial swarms, which typically develop heterogeneities even when grown from a single cell. Here, mixed swarms of cells with different aspect ratios are studied both experimentally and in simulations. In contrast with previous theory, there is no macroscopic phase segregation. However, locally, long cells act as nucleation cites, around which aggregates of short, rapidly moving cells can form, resulting in enhanced swarming speeds. On the other hand, high fractions of long cells form a bottleneck for efficient swarming. Our results suggest a physical advantage for the spontaneous heterogeneity of bacterial swarm populations.

Role of Friction in Multidefect Ordering

We use continuum simulations to study the impact of friction on the ordering of defects in an active nematic. Even in a frictionless system, +1/2 defects tend to align side by side and orient antiparallel reflecting their propensity to form, and circulate with, flow vortices. Increasing friction enhances the effectiveness of the defect-defect interactions, and defects form dynamically evolving, large-scale, positionally, and orientationally ordered structures, which can be explained as a competition between hexagonal packing, preferred by the -1/2 defects, and rectangular packing, preferred by the +1/2 defects.

Lamellar to Micellar Phases and Beyond: When Tactic Active Systems Admit Free Energy Functionals

We consider microscopic models of active particles whose velocities, rotational diffusivities, and tumbling rates depend on the gradient of a local field that is either externally imposed or depends on all particle positions. Despite the fundamental differences between active and passive dynamics at the microscopic scale, we show that a large class of such tactic active systems admit fluctuating hydrodynamics equivalent to those of interacting Brownian colloids in equilibrium. We exploit this mapping to show how taxis may lead to the lamellar and micellar phases observed for soft repulsive colloids. In the context of chemotaxis, we show how the competition between chemoattractant and chemorepellent may lead to a bona fide equilibrium liquid-gas phase separation in which a loss of thermodynamic stability of the fluid signals the onset of a chemotactic collapse.

Stealth Entropy Production in Active Field Theories near Ising Critical Points

We address the steady-state entropy production rate (EPR) of active scalar ϕ^{4} theories, which lack time-reversal symmetry, close to a phase-separation critical point. We consider both nonconserved (model A) and conserved (model B) dynamics at Gaussian level, and also address the former at leading order in ε=4-d. In each case, activity is irrelevant in the RG sense: the active model lies in the same (dynamic Ising) universality class as its time-reversible counterpart. Hence one might expect that activity brings no new critical behavior. Here we show instead that, on approach to criticality in these models, the singular part of the EPR per (diverging) spacetime correlation volume either remains finite or itself diverges. A nontrivial critical scaling for entropy production thus ranks among universal dynamic Ising-class properties.

Spatial propagation of electrical signals in circular biofilms: A combined experimental and agent-based fire-diffuse-fire study

Bacterial biofilms are a risk to human health, playing critical roles in persistent infections. Recent studies have observed electrical signaling in biofilms and thus biofilms represent a new class of active excitable matter in which cell division is the active process and the spiking of the individual bacterial cells is the excitable process. Electrophysiological models have predominantly been developed to describe eukaryotic systems, but we demonstrate their use in understanding bacterial biofilms. Our agent-based fire-diffuse-fire (ABFDF) model successfully simulates the propagation of both centrifugal (away from the center) and centripetal (toward the center) electrical signals through biofilms of Bacillus subtilis. Furthermore, the ABFDF model allows realistic spatial positioning of the bacteria in two dimensions to be included in the fire-diffuse-fire model and this is the crucial factor that improves agreement with experiments. The speed of propagation is not constant and depends on the radius of the propagating electrical wave front. Centripetal waves are observed to move faster than centrifugal waves, which is a curvature driven effect and is correctly captured by our simulations.