New Perspectives in Active Systems

O2 regulated microphase separation of living cells Self-organization occurs in a variety of biological systems and the concept of active and condensed matter have proven very useful in explaining some of the mechanisms. Microphase separation is a classic example of self-organization, long studied in polymeric material and inert system [1], more recently in biomolecular condensates, which are micron-scale compartment in eukaryotic cells [2]. To the best of our knowledge such microphase separation have never been reported in assemblies of living cells. Under a millimetric nutritive culture medium film, cells of the social amoeba Dictyostelium Discoideum (Dicty), grow until some critical density. Then they stop to grow and assemble in compact domain with a characteristic size of typically 100µm surrounded by a dense cellular gas phase. These domains stay mobile and stable in size during several days. Moreover, if one changes the O2 atmospheric level or the height of the medium, aggregate will quickly equilibrate with a new characteristic size and spacing. These observations as well as our previous experience about aerotatic behaviours of Dicty single cells [3] show that this cellular microphase separation of Dicty cells is oxygen regulated. It results from a balance between competing interaction; a long-range repulsion, trough self-generated O2 gradients due to O2 consumption, and a short-range attraction due to cell-cell adhesion. A simple analytical model and lattice-based Monte Carlo simulations support this simple mechanism which highlights the importance of oxygen regulation and self-generated gradients as an emergent organizing principle for biological matter. This result was recently published in Nature Communication [4]. [1] G.H. Fredickson, The equilibrium theory of inhomogenous polymers, Oxford University Press, 2006 [2] S.F. Banani et al, Biomolecular condensates: Organizers of cellular biochemistry, Nat Rev Mol Cell Bio, 2017 May; 18(5) 285 [3] O. Cochet-Escartin et al, Hypoxia triggers collective aerotactic migration in Dictyostelium Discoideum, elife 2021 10:e6473 [4] Carrère, A., d’Alessandro, J., Cochet-Escartin, O. et al. Microphase separation of living cells. Nat Commun 14, 796 (2023). https://doi.org/10.1038/s41467-023-36395-2

Synthetic active particles (APs) have received considerable interest for biomedical applications and as model systems for non-equilibrium dynamics. However, because an AP's motion strongly depends on the properties of the surrounding liquid, it can additionally serve as a microrheological probe for the properties of the surrounding medium [1,2]. APs in Newtonian media have been studied in great detail, but much less is known when these particles move in complex fluids. Such a fluid's nonlinear rheological properties can lead to a drastically enhanced rotational diffusion (ERD) coefficient [1-3]. In this presentation, we study the motion of an AP in a polydisperse quasi-2D suspension of colloidal rods. Compared to previous studies [1,2], wherein we embedded APs in a spherical colloid suspension, the use of rods allows us to unlock a new mode of fast, local structural dynamics. This dynamics enabled a comprehensive understanding of the mechanism underlying ERD. Combining simulations and experiment, we conclude that minute microstructural fluctuations of rods in near contact with the AP, together with the probe's active motion, generate a fluctuating torque on the AP eventually leading to ERD. These fluctuations can be connected to a local stress relaxation, which may be used in the continuum formalism that was proposed [1,3,4] to capture ERD. Our work thus unifies the previously disjoint continuum and particle-based descriptions for this phenomenon. Beyond the rheological characterization abilities of APs, our findings are important to understand the dynamics of microorganisms in their natural (typically viscoelastic) habitat. [1] C. Lozano, et al., Nat. Mater. 18, 1118 (2019). [2] C. Abaurrea-Velasco, et al., Phys. Rev. Lett. 125, 258002 (2020). [3] J.R. Gomez-Solano et al., Phys. Rev. Lett. 116, 138301 (2016). [4] N. Narinder et al., Phys. Rev. Lett. 121, 078003 (2018).

The interplay between cellular growth and cell-cell signaling is essential for the aggregation and proliferation of bacterial colonies, as well as for the self-organization of cell tissues. To investigate this interplay, we focus here on the collective properties of dividing chemotactic cell assemblies by studying their long-time and large-scale dynamics through a renormalization group approach. Our analysis reveals that a novel effective chemotactic interaction -- corresponding to a polarity-induced mechanism -- is generated by fluctuations at macroscopic scales. This term, usually overlooked in phenomenological approaches, emerges from the interplay of the well-known Keller-Segel chemotactic nonlinearity and cell birth and death processes. Its consequences on the critical dynamics will be discussed.

We investigate the persistence probability p(t) of the position of a Brownian particle with shape asymmetry in two dimensions. The persistence probability is defined as the probability that a stochastic variable has not changed its sign in the given time interval. We explicitly consider two cases—diffusion of a free particle and that of a harmonically trapped particle. The latter is particularly relevant in experiments that use trapping and tracking techniques to measure the displacements. We provide analytical expressions of p(t) for both the scenarios and show that in the absence of the shape asymmetry, the results reduce to the case of an isotropic particle. The analytical expressions of p(t) are further validated against numerical simulation of the underlying overdamped dynamics. We also illustrate that p(t) can be a measure to determine the shape asymmetry of a colloid and the translational and rotational diffusivities can be estimated from the measured persistence probability. The advantage of this method is that it does not require the tracking of the orientation of the particle.

Assembly of the mitotic spindle during cell division is of paramount importance as it segregates the chromosomes into the daughter cells. During prometaphase, microtubules and associated crosslinkers dynamically self-organize and consequently appear to form stable bundles prior to metaphase. Experimental study of the cross-section at the mid zone of vertically oriented spindles shows that a homogeneous array-like distribution of cross-linking proteins forms droplet-like structures as time progresses in prometaphase and the crosslinkers are co-localized with microtubules. Also, it is experimentally found that the kinetochores are the major driver for microtubule bundle formation. In our theoretical work, we develop a mean field theory in which we describe microtubules and crosslinkers by density fields. To describe interactions in the system, we incorporate an attraction between microtubules mediated by crosslinkers, repulsion between individual microtubules and entropic interaction among crosslinkers in the Landau-Ginzberg free energy. In the mean field theory, the kinetochores are represented by attractive Dirac-delta functions placed periodically to form lattice-like structures. We solve the conserved dynamical equation, which is nonlinear in nature, resulting from the free energy and obtain the steady state density profiles of the microtubules. The microtubules are found to form bundles around the kinetochores, and the bundle thickness increases when the crosslinker density is increased. Also, larger bundles are formed as the interkinetochore separation is enhanced. Both, the results agree qualitatively with experimental observations. Moreover, our theory, in the linear regime, shows a possibility of a transition from a homogeneous density state to a state with multiple clusters of microtubules and crosslinking proteins [1]. Reference [1] Kinetochore- and chromosome-driven transition of microtubules into bundles promotes spindle assembly: Nature Communications 13:7307 (2022)

Crowd studies have revealed that large groups of people can display complex collective behaviors. However, the study of high-density crowds has been challenging due to experimental difficulties and a lack of data. In this study, we present an analysis of safe high-density crowds using video footage, which demonstrates the emergence of a collective natural oscillation frequency.

We conducted collective behavior experiments with a human crowd of 30 members moving within the area of a basketball court. This collective motion was recorded using a dron. To generate a possible emergent phenomenon, simple rules were given to the crowd, namely, 1) To move within the basketball court, and 2) To try to stay together at all times, and the crowd was disturbed by a simulated attack. The emergent collective behavior was characterized by extracting individual paths and velocity vectors, and by introducing global and local order parameters. With the latter order parameters we identify that dynamic emergence –defined as an entanglement of rotational (levo and dextro), translational phases in time– is present in our experiment. A numerical model is also proposed, and several interaction rules are tested to see which is the most efficient at mimicking the human collective behavior.

The amoeboid motility mode is a fundamental way in which cells move, classically in cancer and immune cells. Experiments from our collaborators show that amoeboid cells migrate via this mode up a friction gradient, even when stiffness is uniform. We term this friction sensing as ‘frictiotaxis’. We present a simple active gel model of the cell cortex and suggest a possible mechanism for frictiotaxis. The corresponding numerical simulations are still in development, and we show that deterministic simulations with stochastic initial conditions alone does not lead to frictiotaxis. Therefore, we conclude that the model requires stochasticity explicitly in the equations of motion. Overall, this work will demonstrate that an active gel model of the cell cortex can explain directed migration based on friction.

Recently, it has been experimentally discovered, and theoretically proved, that the stationary velocity distribution function of a non-interactive active stochastic system is bimodal. In this work, we theoretically reveal the condition under which a bimodal distribution will arise, and the condition under which this bimodal distribution will become Gaussian. This condition depends on two important time scales in the problem, namely, reorientation and inertial time scales. Briefly, when the inertial time is larger than the orientation time, the active Fokker-Planck stationary solution admits a bimodal structure. The inverse condition is seen to admit a Gaussian structure. *M.S. and P. H. thanks Consejo Nacional de Ciencia y Tecnologia (CONACyT) for support.

We implement an evolutionary algorithm on a system of elastically coupled active agents to study the emergence of structures in a minimal model of biological complexity. In this mechanical model, active agents are connected by springs, so the resulting dynamics depend on factors such as the damping coefficients, self-propulsion speeds, spring constants, and relative agent positions. We evolve these systems by mutating their shape and selecting those that exhibit certain movement preferences, to then examine the resulting structures. We find that alternating fitness requests, such as switching between maximizing horizontal and vertical motion, tend to produce complex structures that can evolve from one task to the other in just a few generations and are often modular. These findings shed light on the origins of modularity in living systems, providing insights into how such systems can evolve higher and higher levels of complexity over time.

Classic computational models of collective motion suggest that simple local averaging rules can promote many observed group-level patterns. Recent studies, however, suggest that rules simpler than local averaging may be at play in real organisms; for example, fish stochastically align towards only one randomly chosen neighbour and yet the schools are highly polarized. Here, we ask—how do organisms maintain group cohesion? Using a spatially explicit model, inspired from empirical investigations, we show that group cohesion can be achieved in finite groups even when organisms randomly choose only one neighbour to interact with. Cohesion is maintained even in the absence of local averaging that requires interactions with many neighbours. Furthermore, we show that choosing a neighbour randomly is a better way to achieve cohesion than interacting with just its closest neighbour. To understand how cohesion emerges from these random pairwise interactions, we turn to a graph-theoretic analysis of the underlying dynamic interaction networks. We find that randomness in choosing a neighbour gives rise to well-connected networks that essentially cause the groups to stay cohesive. We compare our findings with the canonical averaging models (analogous to the Vicsek model). In summary, we argue that randomness in the choice of interacting neighbours plays a crucial role in achieving cohesion.

Non-reciprocal interactions manifest their drastic impact on the collective dynamics of active matter systems by changing, for example, the general type of observed instabilities [1] and leading to time-dependent states [2,3]. In particular, the combination of non-reciprocity and chirality in terms of intrinsically rotating chiral active particles ("circle swimmers") reveals intriguing non-trivial time-dependent collective dynamics [1]. After having developed an understanding of the collective dynamics on the continuum level in previous work [1], we here present first results of particle-based simulations of chiral active particle systems with non-reciprocal alignment couplings. Indeed, quantitative predictions from continuum approaches are somewhat limited by the approximations made during the coarse-graining process. Thus, the first goal of our particle-based simulations is to explore the validity of the previously obtained continuum results regarding the overall state diagram. Second, we aim at investigating microscopic aspects of the various time-dependent states. Finally, we discuss possibilities to characterize the thermodynamic behavior of the non-reciprocal chiral system based on the stochastic trajectories obtained in particle-resolved simulations. [1] K. L. Kreienkamp and S. H. L. Klapp, New J. Phys. (2022). [2] M. Fruchart et al., Nature 592, 363 (2021). [3] Z. You et al., PNAS 117, 19767 (2020).

Authors: Andrea Lama (andrea.lama-ssm@unina.it), Mario di Bernardo (mdiberna@unina.it) Scuola Superiore Meridionale and University of Naples Federico II The emergence of coordinated action between groups of interacting agents is a common feature of multi-agent systems in Nature and Technology. In some situations it can be advantageous for a group of agents to tame the collective behaviour of another group of agents, e.g. dogs shepherding flocks of sheep, drones performing search-and-rescue operations of animals in dangerous situations etc. We formalize this scenario as the {\em herding control problem}, which has been studied in the literature generally relying on assumptions such as that the targets are cohesive due to their interactions, or that each herder knows at all times the positions of all the other agents. Instead, relaxing these assumptions, we discuss the problem of steering a group of non-interacting self-propelled stochastic targets in a desired region of the plane, and we devise, also inspired by how humans play virtual herding games, simple yet effective feedback strategies for a group of autonomous artificial herders with limited sensing capabilities. We then investigate general conditions for which a group of targets is herdable, and we use both numerical experiments and theoretical derivations to show that the limited sensing of the herders induces surprisingly that a minimum density for the targets' is required for the herding to be successful. Given that the considered targets' dynamics lacks any kind of structure that the herders could rely on, we argue that the condition on the targets' density may be a general condition for a group of targets to be herdable. This could mean that, under some circumstances, adopting a dispersive rather than a cohesive behaviour may indeed enhance the survival chances of the targets.

Emergent pattern formation in active matter is a ubiquitous phenomenon observed in a plethora of natural systems. The spatial properties of congregations such as mills and clusters have been studied extensively in the extant literature, however, there is scarce literature on the temporal characteristics of such aggregations. The current talk proposes using chaos analysis and synchronisation theory as techniques to understand the underlying temporal and phase characteristics of the novel patterns observed in different active systems. In systems where active particles are subjected to competing drives of alignment and repulsion, the aforementioned techniques lead to the detection of a frequency-locked chaotic state in the seemingly periodic mills with clusters phase. Symmetry-breaking phenomena such as weak chimera are also detected in certain milling formations. In systems with dissimilar active groups, the motility-induced segregation of the active species is found to occur concurrently with the detection of the weak chimera signature in one of the species.

Self-propelled active systems, modeling phenomena commonly found in nature, often exhibit complex collective dynamics, i.e, collective motion. These systems are frequently described using agent-based modeling. The set of interactions governing these systems can be categorized into three categories: alignment-based interactions (based on the exchange of orientation information), position-and-alignment-based interactions (based on the exchange of orientation and position information), and position-based interactions (based on the exchange of position information only). When position information is required, it is the relative position of the neighbors that, in polar coordinates, can be decomposed in the exchange of relative range and bearing. In this work, we introduce a new perspective by considering the design of active systems that rely solely on the exchange of range information with no bearing exchange. However, eliminating bearing information from the system presents a significant challenge, as it is difficult to define rules that will achieve effective coordination and control of collective dynamics. To overcome this challenge, we explore the utility of learning methods for designing a system with interactions based solely on local range information. The example presented utilizes deep reinforcement learning to train particles to avoid collisions with their neighbors while moving through a shared space. We discuss the advantages of the learning approach, including scalability and adaptability, and highlight the potential of learning methods for a wide range of applications. Furthermore, this work proposes the future possibility of applying it to gain deeper insights into the underlying principles governing the interactions among particles in different systems and open the discussion to the role of constrained sensing and interactions to enable access to different system designs

From flocking of birds, school of fish to biofilm formation in motile bacteria, collective pattern formation is ubiquitous in many living active matter. Interestingly, this phenomenon is likewise generic for many synthetic settings which are far from equilibrium. In biological active systems, such global ordering behavior might be cognitive and has been shown theoretically to result from local interactions among individuals. Clearly, the nature of such inter-individual interactions must be fundamental in comprehending the coordination at the group scale, not only for living but also for synthetic active matter, for instance: autonomously propelled active colloids which continuously convert energy from their environment into mechanical work. While in the past few years, for the artificial systems, pair or two-body interactions have been researched quite extensively from a theoretical point of view,[1,2] it has very rarely been observed in detail in experimental systems. In laboratory settings studying such pairwise interactions is not straightforward because of the interfering many-body interactions limiting experimental research. Therefore, in this work we engineer special microgrooves to confine two catalytically active Janus spheres to make cleaner pairwise observations. Most importantly we compare pair interaction between two contrasting types of Janus colloids: the standard Pt@SiO2 colloids[3] which move inert-forward and the newly introduced Cu@SiO2 colloids which move cap-forward.[4] We find interesting differences in their pairwise interactions.[5] Finally, using these one dimensional experiments we extract relevant parameters which we then use to reproduce experiments in two dimensions using a theoretical model. These results can lay the foundation for future work on understanding colloidal interactions at the group scale. References: [1] Pairing, waltzing and scattering of chemotactic active colloids, S Saha, S Ramaswamy, R Golestanian, New Journal of Physics, 21(6), 063006, 2019. [2] Exact phoretic interaction of two chemically active particles, B Nasouri, R Golestanian, Physical review letters, 124(16), 168003, 2020. [3] Study of active Janus particles in the presence of an engineered oil–water interface, P Sharan, W Postek, T Gemming, P Garstecki, J Simmchen, Langmuir 37(1), 204-210, 2020. [4] Upstream rheotaxis of catalytic Janus spheres, P Sharan, Z Xiao, V Mancuso, WE Uspal, J Simmchen, ACS nano 16(3), 4599-4608, 2022. [5] Pair interaction between catalytically active colloids, P Sharan, A Daddi-Moussa-Ider, J Agudo-Canalejo, R Golestanian, J Simmchen, https://assets.researchsquare.com/files/rs-1976290/v1_covered.pdf?c=1661887475, 2022.

Collective motion is a ubiquitous phenomenon observed in social organisms ranging from flocks of birds and fish schools to human crowds and cell groups. Swarms of birds and fish are particularly interesting as they do not only exhibit coordinated behavior but also rapid escape maneuvers when attacked by predators. Marginally coordinated critical motion is hypothesized to be an optimal trade-off to deal with conflicting imperatives such as the need to behave cohesively as a unique entity and being highly responsive to information from exceptionally well-informed individuals. However, traditional models of collective motion only show criticality at the phase transition between unordered and ordered motion conforming to the behavior of the majority. In this work, we present an agent-based model extending the Vicsek model by a minority interaction. We propose that an individual in a group essentially follows the trajectory of its neighbors, with the addition of a minority interaction, where an individual moving in the opposite direction of a sufficiently aligned group triggers a cascade of agents following this defector instead of the majority. Our model shows rich behavior such as large-scale fluctuations and a scale-free return time distribution of the order parameter, as well as a scale-free velocity fluctuation distribution, reminiscent of self-organized criticality. Our work highlights the biological relevance of minority interactions in swarming models and poses questions about their role in the emergence of critical behavior.

We study how the structure of the interaction network affects self-organized collective motion in two minimal models of self-propelled agents: the Vicsek model and the Active-Elastic (AE) model. We perform simulations with topologies that interpolate between a nearest-neighbour network and random networks with different degree distributions to analyse the relationship between the interaction topology and the resilience to noise of the ordered state. For the Vicsek case, we find that a higher fraction of random connections with homogeneous or power-law degree distribution increases the critical noise, and thus the resilience to noise, as expected due to small-world effects. Surprisingly, for the AE model, a higher fraction of random links with power-law degree distribution can decrease this resilience, despite most links being long-range. We explain this effect through a simple mechanical analogy, arguing that the larger presence of agents with few connections contributes to localized low-energy modes that are easily excited by noise, thus hindering the collective dynamics. These results demonstrate the strong effects of the interaction topology on self-organization. Our work suggests potential roles of the interaction network structure in biological collective behaviour and could also help improve decentralized swarm robotics control and other distributed consensus systems. Authors: Ali Emre Turgut, İhsan Caner Boz, İlkin Ege Okay, Eliseo Ferrante and Cristián Huepe

Interaction between active materials and the boundaries of geometrical confinement is key to many emergent phenomena in active systems. For living active matter consisting of animal cells or motile bacteria, the confinement boundary is often a deformable interface, and it has been unclear how activity-induced interface dynamics might lead to morphogenesis and pattern formation. Here we studied the evolution of bacterial active matter confined by a deformable boundary. We discovered that an ordered morphological pattern emerged at the interface characterized by periodically-spaced interfacial protrusions; behind the interfacial protrusions, bacterial swimmers self-organized into multicellular clusters displaying +1/2 nematic defects. Subsequently, a hierarchical sequence of transitions from interfacial protrusions to creeping branches allowed the bacterial active drop to rapidly invade surrounding space with a striking self-similar branch pattern. We found that this interface patterning is geometrically controlled by the local curvature of the interface, a phenomenon we denote as collective curvature sensing. Using a continuum active model, we revealed that the collective curvature sensing arises from enhanced active stresses near high-curvature regions, with the active length-scale setting the characteristic distance between the interfacial protrusions. Our findings reveal a protrusion-to-branch transition as a unique mode of active matter invasion and suggest a new strategy to engineer pattern formation of active materials.

Authors: Weizhen Tang, Yating Zheng, Guozheng Lin, Zhangang Han, Amir Shee, Pawel Romanczuk, Cristián Huepe We study a general model of a dense system of active polar disks with repulsive linear interactions, confined by boundaries. Each disk is an active agent that tends to advance at a preferred self-propulsion speed and turns about an axis of rotation that is behind its barycenter. It can thus interact with overlapping neighbors as it moves or rotates through forces and torques. We characterize the phases and collective states in this system, resulting from variations in its density, its heterogeneity, its noise, and the self-propulsion speed and geometry of its agents.For homogeneous cases with identical disks, we find a density-driven transition from a global milling state to localized collective rotational motion, which seems to coincide with the liquid-to-solid transition. For binary mixtures of disks with different speeds or geometrical properties, we find various forms of phase separation and describe their underlying mechanisms and dynamics.This numerical work could inspire real-world experiments with dense systems of natural or artificial active agents in confined spaces, which could range from cells on a substrate to swarming autonomous robots in an arena. Our results demonstrate the type of collective states that can be expected to emerge in such systems.