Universal aspects of collective behavior in chemotactic systems

Nonreciprocal Cahn-Hilliard Model Emerges as a Universal Amplitude Equation

Oscillatory behavior is ubiquitous in out-of-equilibrium systems showing spatiotemporal pattern formation. Starting from a linear large-scale oscillatory instability-a conserved-Hopf instability-that naturally occurs in many active systems with two conservation laws, we derive a corresponding amplitude equation. It belongs to a hierarchy of such universal equations for the eight types of instabilities in homogeneous isotropic systems resulting from the combination of three features: large-scale vs small-scale instability, stationary vs oscillatory instability, and instability without and with conservation law(s). The derived universal equation generalizes a phenomenological model of considerable recent interest, namely, the nonreciprocal Cahn-Hilliard model, and may be of a similar relevance for the classification of pattern forming systems as the complex Ginzburg-Landau equation.

Suppression of coarsening and emergence of oscillatory behavior in a Cahn-Hilliard model with nonvariational coupling

We investigate a generic two-field Cahn-Hilliard model with variational and nonvariational coupling. It describes, for instance, passive and active ternary mixtures, respectively. Already a linear stability analysis of the homogeneous mixed state shows that activity not only allows for the usual large-scale stationary (Cahn-Hilliard) instability of the well-known passive case but also for small-scale stationary (Turing) and large-scale oscillatory (Hopf) instabilities. In consequence of the Turing instability, activity may completely suppress the usual coarsening dynamics. In a fully nonlinear analysis, we first briefly discuss the passive case before focusing on the active case. Bifurcation diagrams and selected direct time simulations are presented that allow us to establish that nonvariational coupling (i) can partially or completely suppress coarsening and (ii) may lead to the emergence of drifting and oscillatory states. Throughout, we emphasize the relevance of conservation laws and related symmetries for the encountered intricate bifurcation behavior.

Demixing of two species via reciprocally concentration-dependent diffusivity

We propose a model for demixing of two species by assuming a density-dependent effective diffusion coefficient of the particles. Both sorts of microswimmers diffuse as active overdamped Brownian particles with a noise intensity that is determined by the surrounding density of the respective other species within a sensing radius r_{s}. A higher concentration of the first (second) sort will enlarge the diffusion and, in consequence, the intensity of the noise experienced by the second (first) sort. Numerical and analytical investigations of steady states of the macroscopic equations prove the demixing of particles due to this reciprocally concentration-dependent diffusivity. An ambiguity of the numerical integration scheme for the purely local model (r_{s}→0) is resolved by considering nonvanishing sensing radii in a nonlocal model with r_{s}>0.

A Micro-Optic Stalk (μOS) System to Model the Collective Migration of Retinal Neuroblasts

Contemporary regenerative therapies have introduced stem-like cells to replace damaged neurons in the visual system by recapitulating critical processes of eye development. The collective migration of neural stem cells is fundamental to retinogenesis and has been exceptionally well-studied using the fruit fly model of Drosophila Melanogaster. However, the migratory behavior of its retinal neuroblasts (RNBs) has been surprisingly understudied, despite being critical to retinal development in this invertebrate model. The current project developed a new microfluidic system to examine the collective migration of RNBs extracted from the developing visual system of Drosophila as a model for the collective motile processes of replacement neural stem cells. The system scales with the microstructure of the Drosophila optic stalk, which is a pre-cursor to the optic nerve, to produce signaling fields spatially comparable to in vivo RNB stimuli. Experiments used the micro-optic stalk system, or μOS, to demonstrate the preferred sizing and directional migration of collective, motile RNB groups in response to changes in exogenous concentrations of fibroblast growth factor (FGF), which is a key factor in development. Our data highlight the importance of cell-to-cell contacts in enabling cell cohesion during collective RNB migration and point to the unexplored synergy of invertebrate cell study and microfluidic platforms to advance regenerative strategies.