Research Objective (RO) 1 and associated tasks: The swimming mechanism of artificial microswimmers (Janus colloids) hinges on an asymmetry in the production of chemicals on their surface. The same chemicals which are relevant for swimming lead to cross-interactions among different microswimmers. While previous models had neglected the impact of this asymmetry for the collective behaviour of many microswimmers we were expecting that this asymmetry could create a novel route to pattern formation. We have complemented our corresponding objective to develop a model for signalling microswimmers accounting for an asymmetry in the chemical production. We have also performed computer simulations to understand the dynamics of this model and have numerically calculated a phase diagram, revealing that the asymmetry in the production process does indeed lead to a new route to pattern formation. We have published the corresponding results in the Physical Review Letters, have made them commonly accessible via the arXiv (green open access route) and have reported them at a number of conferences and seminars in the UK, Germany and France.
RO2 and tasks:
Our second goal was to derive a simplified theory of our model to understand the mechanism underlying the instability leading to pattern formation in our model. We have derived a corresponding simplified model which generalizes a classical model in the literature (Keller-Segel model) to account for anisotropic production effects (and for cases where the response of a particle to a chemical gradient is repulsive). Based on this model, we could derive a simple instability criterion and could understand how anisotropic production effects can lead to pattern formation. Strikingly, however, it turned out that our phase diagram shows a second pattern forming regime, which could not be explained by our theory. We have unveiled the existence of a second instability mechanism hinging on a delay in the response of microswimmers to chemicals created by other microswimmers creating a cyclic feedback loop inducing wave patterns. We have published these results along with the above mentioned results in the Physical Review Letters and have presented and discussed on a number of conferences and in seminar talks.
RO3 and tasks:
While our considerations so far have been based on a purely deterministic description, we were interested in the impact of (multiplicative) noise on these patterns. Very recently, we have performed particle based simulations to explore the robustness and response of our patterns on fluctuations. While the instability mechanisms turned out to be robust to fluctuations, noise can enrich the appearance of the emerging patterns in an interesting way. The resulting patterns are more amorphous and seemingly more similar to patterns observed with signalling artificial microswimmers in experiments (dynamic clustering experiments). We have published these results very recently on the arXiv (green open access route) to make them generally available.
RO 4 and tasks:
Our objective was to transfer the experience to develop and analyse advection-reaction-diffusion like models for chemically interacting microswimmers to other problems in the biological world. While, we had speculated in the original proposal to apply our experience to understand gene 'surfing' in expanding populations, the corresponding experience has so far proven particularly useful for a different biophysical problem: the intracellular pattern formation of the actin filaments of the cell skeleton ("actin waves"). Here, we have developed a minimal model relating the emergence of pattern formation in recovering Dictyostelium cells (after destroying the cytoskeleton with latrunculin) with the theory of flocking developed in active matter physics. Our results propose that actin wave formation can occur based on three simple and generic ingredients (i) treadmilling (self-advection of actin fibres) (ii) alignment of fibres (iii) polymerization. Accordingly, and in contrast to previous works, our work suggests the existence of a universal route to actin wave formation not hinging on any nonlinear and system-specific biochemistry. We have published the corresponding results in the Physical Review Letters and disseminated them at conferences in Germany and France and in the framework of seminar talks.
