Navigation of micro-swimmers in steady flow: the importance of symmetries

Abstract

Marine micro-organisms must cope with complex flow patterns and even turbulence as they navigate the ocean. To survive they must avoid predation and find efficient energy sources. A major difficulty in analysing possible survival strategies is that the time series of environmental cues in nonlinear flow is complex and that it depends on the decisions taken by the organism. One way of determining and evaluating optimal strategies is reinforcement learning. In a proof-of-principle study, Colabrese et al. (Phys. Rev. Lett., vol. 118, 2017, 158004) used this method to find out how a micro-swimmer in a vortex flow can navigate towards the surface as quickly as possible, given a fixed swimming speed. The swimmer measured its instantaneous swimming direction and the local flow vorticity in the laboratory frame, and reacted to these cues by swimming either left, right, up or down. However, usually a motile micro-organism measures the local flow rather than global information, and it can only react in relation to the local flow because, in general, it cannot access global information (such as up or down in the laboratory frame). Here we analyse optimal strategies with local signals and actions that do not refer to the laboratory frame. We demonstrate that symmetry breaking is required to find such strategies. Using reinforcement learning, we analyse the emerging strategies for different sets of environmental cues that micro-organisms are known to measure.

Active gyrotactic stability of microswimmers using hydromechanical signals

“…We use reinforcement learning to find candidate strategies. We find that the best strategies found are similar to those found in the two-dimensional frozen flow [25], but it turns out that the slip velocity is the dominant signal, in contrast to the strain rate for the frozen two-dimensional flows. The main result is a simple yet powerful strategy for vertical migration based on a single component of the slip velocity, summarized in Fig.…”

“…We use a model similar to that in Ref. [25], but here we consider a three-dimensional flow. We model the swimmer as a point particle with the shape of an elongated spheroid with aspect ratio λ = a /a ⊥ , where a is the axis length along the symmetry direction and a ⊥ is the transversal radius.…”

“…We model the swimmer as a point particle with the shape of an elongated spheroid with aspect ratio λ = a /a ⊥ , where a is the axis length along the symmetry direction and a ⊥ is the transversal radius. For typical microswimmers in the ocean, inertia of both the swimmer and the fluid can be neglected [25], leading to the following dynamics for the position x, the symmetry direction n, the transversal direction of the antennae p, and the direction q perpendicular to the n-p plane…”

“…bottom-heaviness of the swimmer aligns it against gravity and give efficient upward vertical migration in this limit. But in the presence of turbulent velocity gradients, the model predicts that the upward vertical-migration velocity of copepods with parameters approximated from nature is only a fraction of the swimming speed, and upward migration may even fail due to gravitational settling [23][24][25]. In addition, the model does not explain how some organisms swim downwards [2,26].…”

“…For example, it was shown in Ref. [25] that the symmetry breaking set by gravity allows the swimmer to infer its vertical orientation by sensing only local hydromechanical signals. Using reinforcement learning, efficient steering protocols for upward navigation, based primarily on the local strain rate, were found in frozen (time-independent) two-dimensional flows.…”