Collective dynamics of soft active particles

Inertia changes evolution of motility-induced phase separation in active matter across particle activity

The effects of inertia in active matter and motility-induced phase separation (MIPS) have attracted growing interest but still remain poorly studied. We studied MIPS behavior in the Langevin dynamics across a broad range of particle activity and damping rate values with molecular dynamic simulations. Here we show that the MIPS stability region across particle activity values consists of several domains separated by discontinuous or sharp changes in susceptibility of mean kinetic energy. These domain boundaries have fingerprints in the system's kinetic energy fluctuations and characteristics of gas, liquid, and solid subphases, such as the number of particles, densities, or the power of energy release due to activity. The observed domain cascade is most stable at intermediate damping rates but loses its distinctness in the Brownian limit or vanishes along with phase separation at lower damping values.

Group formation and collective motion of colloidal rods with an activity triggered by visual perception

We investigate the formation of cohesive groups and the collective diffusion of colloidal spherocylinders with a motility driven by a simple visual perception model. For this, we perform Brownian dynamics simulations without hydrodynamic interactions. The visual perception is based on sight cones attached to the spherocylinders and perception functions quantifying the visual stimuli. If the perception function of a particle reaches a predefined threshold, an active component is added to its motion. We find that, in addition to the opening angle of the cone of sight, the aspect ratio of the particles plays an important role for the formation of cohesive groups. If the elongation of the particles is increased, the maximum angle for which the rods organize themselves into such groups decreases distinctly. After a system forms a cohesive group, it performs a diffusive motion, which can be quantified by an effective diffusion coefficient. For increasing aspect ratios, the spatial expansion of the cohesive groups and the effective diffusion coefficient of the collective motion increase, while the number of active group members decreases. We also find that a larger particle number, a smaller propulsion velocity of the group members, and a smaller threshold for the visual stimulus increase the maximum opening angle for which cohesive groups form. Based on our results, we expect anisotropic particles to be of great relevance for the adjustability of visual perception-dependent motility.

Collective excitations in active fluids: Microflows and breakdown in spectral equipartition of kinetic energy

The effect of particle activity on collective excitations in active fluids of microflyers is studied. With an in silico study, we observed an oscillating breakdown of equipartition (uniform spectral distribution) of kinetic energy in reciprocal space. The phenomenon is related to short-range velocity-velocity correlations that were realized without forming of long-lived mesoscale vortices in the system. This stands in contrast to well-known mesoscale turbulence operating in active nematic systems (bacterial or artificial) and reveals the features of collective dynamics in active fluids, which should be important for structural transitions and glassy dynamics in active matter.

Topological data analysis of collective and individual epithelial cells using persistent homology of loops

Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase transitions have been described based on local ordering, which may not capture structural features at larger length scales. Instead, topological data analysis (TDA) determines the stability of spatial connectivity at varying length scales (i.e. persistent homology), and can compare different particle configurations based on the "cost" of reorganizing one configuration into another. Here, we demonstrate a topology-based machine learning approach for unsupervised profiling of individual and collective phases based on large-scale loops. We show that these topological loops (i.e. dimension 1 homology) are robust to variations in particle number and density, particularly in comparison to connected components (i.e. dimension 0 homology). We use TDA to map out phase diagrams for simulated particles with varying adhesion and propulsion, at constant population size as well as when proliferation is permitted. Next, we use this approach to profile our recent experiments on the clustering of epithelial cells in varying growth factor conditions, which are compared to our simulations. Finally, we characterize the robustness of this approach at varying length scales, with sparse sampling, and over time. Overall, we envision TDA will be broadly applicable as a model-agnostic approach to analyze active systems with varying population size, from cytoskeletal motors to motile cells to flocking or swarming animals.

Enhanced persistence and collective migration in cooperatively aligning cell clusters

Most cells possess the capacity to locomote. Alone or collectively, this allows them to adapt, to rearrange, and to explore their surroundings. The biophysical characterization of such motile processes, in health and in disease, has so far focused mostly on two limiting cases: single-cell motility on the one hand and the dynamics of confluent tissues such as the epithelium on the other. The in-between regime of clusters, composed of relatively few cells moving as a coherent unit, has received less attention. Such small clusters are, however, deeply relevant in development but also in cancer metastasis. In this work, we use cellular Potts models and analytical active matter theory to understand how the motility of small cell clusters changes with N, the number of cells in the cluster. Modeling and theory reveal our two main findings: cluster persistence time increases with N, whereas the intrinsic diffusivity decreases with N. We discuss a number of settings in which the motile properties of more complex clusters can be analytically understood, revealing that the focusing effects of small-scale cooperation and cell-cell alignment can overcome the increased bulkiness and internal disorder of multicellular clusters to enhance overall migrational efficacy. We demonstrate this enhancement for small-cluster collective durotaxis, which is shown to proceed more effectively than for single cells. Our results may provide some novel, to our knowledge, insights into the connection between single-cell and large-scale collective motion and may point the way to the biophysical origins of the enhanced metastatic potential of small tumor cell clusters.

Chimeralike states in a minimal network of active camphor ribbons

A chimeralike state is the spatiotemporal pattern in an ensemble of homogeneous coupled oscillators, described as the emergence of coexisting coherent (synchronized) and incoherent (unsynchronized) groups. We demonstrate the existence of these states in three active camphor ribbons, which are camphor infused rectangular pieces of paper. These pinned ribbons rotate on the surface of the water due to Marangoni effect driven forces generated by the surface tension gradients. The ribbons are coupled via a camphor layer on the surface of the water. In the minimal network of globally coupled camphor ribbons, chimeralike states are characterized by the coexistence of two synchronized and one unsynchronized ribbons. We present a numerical model, simulating the coupling between ribbons as repulsive Yukawa interactions, which was able to reproduce these experimentally observed states.

Rotational synchronization of camphor ribbons in different geometries

We present experiments on multiple pinned self-propelled camphor ribbons, which is a rectangular piece of paper with camphor infused in its matrix. Experiments were performed on three, four, and five ribbons placed in linear and polygonal geometries. The pinned ribbons rotate on the surface of water, due to the surface tension gradient introduced by the camphor layer in the neighborhood of the ribbon. This camphor layer leads to a chemical coupling between the ribbons. In different geometries, the ribbons have been observed to rotationally synchronize in all the possible configurations. A numerical model, emulating the interactions between the ribbons as Yukawa interaction was studied, which was qualitatively able to reproduce the experimental findings.

Group formation and cohesion of active particles with visual perception-dependent motility

Group formation in living systems typically results from a delicate balance of repulsive, aligning, and attractive interactions. We found that a mere motility change of the individuals in response to the visual perception of their peers induces group formation and cohesion. We tested this principle in a real system of active particles whose motilities are controlled by an external feedback loop. For narrow fields of view, individuals gathered into cohesive nonpolarized groups without requiring active reorientations. For wider fields of view, cohesion could be achieved by lowering the response threshold. We expect this motility-induced cohesion mechanism to be relevant not only for the self-organization of living systems, but also for the design of robust and scalable autonomous systems.

Pattern, growth, and aging in aggregation kinetics of a Vicsek-like active matter model

Via molecular dynamics simulations, we study kinetics in a Vicsek-like phase-separating active matter model. Quantitative results, for isotropic bicontinuous pattern, are presented on the structure, growth, and aging. These are obtained via the two-point equal-time density-density correlation function, the average domain length, and the two-time density autocorrelation function. Both the correlation functions exhibit basic scaling properties, implying self-similarity in the pattern dynamics, for which the average domain size exhibits a power-law growth in time. The equal-time correlation has a short distance behavior that provides reasonable agreement between the corresponding structure factor tail and the Porod law. The autocorrelation decay is a power-law in the average domain size. Apart from these basic similarities, the overall quantitative behavior of the above-mentioned observables is found to be vastly different from those of the corresponding passive limit of the model which also undergoes phase separation. The functional forms of these have been quantified. An exceptionally rapid growth in the active system occurs due to fast coherent motion of the particles, mean-squared-displacements of which exhibit multiple scaling regimes, including a long time ballistic one.

Collective motion of cells crawling on a substrate: roles of cell shape and contact inhibition

Contact inhibition plays a crucial role in cell motility, wound healing, and tumour formation. By mimicking the mechanical motion of cells crawling on a substrate, we constructed a minimal model of migrating cells that naturally gives rise to contact inhibition of locomotion (CIL). The model cell consists of two disks, a front disk (a pseudopod) and a back disk (cell body), which are connected by a finite extensible spring. Despite the simplicity of the model, the collective behaviour of the cells is highly non-trivial and depends on both the shape of the cells and whether CIL is enabled. Cells with a small front disk (i.e., a narrow pseudopod) form immobile colonies. In contrast, cells with a large front disk (e.g., a lamellipodium) exhibit coherent migration without any explicit alignment mechanism in the model. This result suggests that crawling cells often exhibit broad fronts because this helps facilitate alignment. After increasing the density, the cells develop density waves that propagate against the direction of cell migration and finally stop at higher densities.

Artificial living crystals in confined environment

Similar to the spontaneous formation of colonies of bacteria, flocks of birds, or schools of fish, "living crystals" can be formed by artificial self-propelled particles such as Janus colloids. Unlike usual solids, these "crystals" are far from thermodynamic equilibrium. They fluctuate in time forming a crystalline structure, breaking apart and re-forming again. We propose a method to stabilize living crystals by applying a weak confinement potential that does not suppress the ability of the particles to perform self-propelled motion, but it stabilizes the structure and shape of the dynamical clusters. This gives rise to such configurations of living crystals as "living shells" formed by Janus colloids. Moreover, the shape of the stable living clusters can be controlled by tuning the potential strength. Our proposal can be verified experimentally with either artificial microswimmers such as Janus colloids, or with living active matter.

Physical models of collective cell motility: from cell to tissue

In this article, we review physics-based models of collective cell motility. We discuss a range of techniques at different scales, ranging from models that represent cells as simple self-propelled particles to phase field models that can represent a cell's shape and dynamics in great detail. We also extensively review the ways in which cells within a tissue choose their direction, the statistics of cell motion, and some simple examples of how cell-cell signaling can interact with collective cell motility. This review also covers in more detail selected recent works on collective cell motion of small numbers of cells on micropatterns, in wound healing, and the chemotaxis of clusters of cells.

Collective Signal Processing in Cluster Chemotaxis: Roles of Adaptation, Amplification, and Co-attraction in Collective Guidance

Single eukaryotic cells commonly sense and follow chemical gradients, performing chemotaxis. Recent experiments and theories, however, show that even when single cells do not chemotax, clusters of cells may, if their interactions are regulated by the chemoattractant. We study this general mechanism of "collective guidance" computationally with models that integrate stochastic dynamics for individual cells with biochemical reactions within the cells, and diffusion of chemical signals between the cells. We show that if clusters of cells use the well-known local excitation, global inhibition (LEGI) mechanism to sense chemoattractant gradients, the speed of the cell cluster becomes non-monotonic in the cluster's size-clusters either larger or smaller than an optimal size will have lower speed. We argue that the cell cluster speed is a crucial readout of how the cluster processes chemotactic signals; both amplification and adaptation will alter the behavior of cluster speed as a function of size. We also show that, contrary to the assumptions of earlier theories, collective guidance does not require persistent cell-cell contacts and strong short range adhesion. If cell-cell adhesion is absent, and the cluster cohesion is instead provided by a co-attraction mechanism, e.g. chemotaxis toward a secreted molecule, collective guidance may still function. However, new behaviors, such as cluster rotation, may also appear in this case. Co-attraction and adaptation allow for collective guidance that is robust to varying chemoattractant concentrations while not requiring strong cell-cell adhesion.

Emergent Collective Chemotaxis without Single-Cell Gradient Sensing

Many eukaryotic cells chemotax, sensing and following chemical gradients. However, experiments show that even under conditions when single cells cannot chemotax, small clusters may still follow a gradient. This behavior is observed in neural crest cells, in lymphocytes, and during border cell migration in Drosophila, but its origin remains puzzling. Here, we propose a new mechanism underlying this "collective guidance," and study a model based on this mechanism both analytically and computationally. Our approach posits that contact inhibition of locomotion, where cells polarize away from cell-cell contact, is regulated by the chemoattractant. Individual cells must measure the mean attractant value, but need not measure its gradient, to give rise to directional motility for a cell cluster. We present analytic formulas for how the cluster velocity and chemotactic index depend on the number and organization of cells in the cluster. The presence of strong orientation effects provides a simple test for our theory of collective guidance.