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Pattern Formation in Catalytic Colloidal Microswimmers

Periodic Reporting for period 1 - PFCCMS (Pattern Formation in Catalytic Colloidal Microswimmers)

Reporting period: 2015-04-01 to 2017-03-31

"Chemical signalling among cells is responsible for many of the fascinating self-organization processes observed in the biological world. Some Dictyostelium cells for example, can excrete certain chemicals which other Dictyostelium cells can ""smell"". These other Dictyostelium cells feel attracted by the smell of the chemicals and move towards the former ones, leading to aggregation or clustering.

Very recently, it has become possible to design micrometer small synthetic particles which are able to ""swim"" through a fluid due to chemical reactions taking place predominantly on half of their surface. These reactions lead to an accumulation of certain molecules on the reactive side of the particle and ultimately lead to its motion through a fluid. Similar to Dictyostelium cells, these synthetic swimmers can effectively smell the chemicals produced by other swimmers and sometimes move towards them, which can lead to their aggregation and the formation of clusters. (The 'smelling' occurs because the synthetic particles do not only swim due to the reactions on their own surfaces, but also due to reactions produced by other ones)

The aim of the present project was to develop a new description for such signalling particles (both biological and synthetic ones) to uncover novel routes to aggregation and pattern formation in microswimmers with chemical interactions. In the framework of the present action, we have successfully developed a description for signalling microswimmers. Conversely to previous studies which have suggested pattern formation scenarios in cases where microswimmers attract each other, we have uncovered a novel route to pattern formation applying to microswimmers migrating away from each other. Our route might be relevant for the self-assembly of active material or may shed new light on the collective behaviour of biological microorganisms."
"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.
Our work on chemically signalling microswimmers has uncovered novel instability mechanisms for particles with repulsive chemical interactions, which has led to an unexpected and generic route to pattern formation in active matter. One limitation in the research fields understanding on chemical (or more generally 'phoretic') interactions among synthetic colloids was lack of knowledge of the coefficient determining the strength and relevance of these interactions. We have also developed a theory relating this coupling coefficient to well-known parameters leading to a massive collapse of parameter space for autophoretic Janus colloids. This collapse leads to a phase diagram showing that chemical cross-interactions among colloids completely change the phase diagram and generically lead to structure formation, even at very low densities.

Besides its relevance to understand the collective behaviour of Janus colloids, our route to pattern formation might also be of interdisciplinary relevance, for example for active self-assembly of microstructures or to predict/understand the collective behaviour of microorganisms with repulsive signalling