Abstract
A main question for the study of collective motion in living organisms is the origin of orientational polar order, i.e., how organisms align and what are the benefits of such collective behaviour. In the case of micro-organisms swimming at a low Reynolds number, steric repulsion and long-range hydrodynamic interactions are not sufficient to explain a homogeneous polar order state in which the direction of motion is aligned. An external symmetry-breaking guiding field such as a mechanism of taxis appears necessary to understand this phonemonon. We have investigated the onset of polar order in the velocity field induced by phototaxis in a suspension of a motile micro-organism, the algae Chlamydomonas reinhardtii, for density values above the limit provided by the hydrodynamic approximation of a force dipole model. We show that polar order originates from a combination of both the external guiding field intensity and the population density. In particular, we show evidence for a linear dependence of a phototactic guiding field on cell density to determine the polar order for dense suspensions and demonstrate the existence of a density threshold for the origin of polar order. This threshold represents the density value below which cells undergoing phototaxis are not able to maintain a homogeneous polar order state and marks the transition to ordered collective motion. Such a transition is driven by a noise dominated phototactic reorientation where the noise is modelled as a normal distribution with a variance that is inversely proportional to the guiding field strength. Finally, we discuss the role of density in dense suspensions of phototactic micro-swimmers.
Highlights
Independent of length scales, collective motion phenomena of many biological systems result in a polar order of the direction of motion in which the velocities of moving entities are directionally aligned
We have demonstrated that the polar order of the velocity field depends linearly on the density
This dependence is due to nearest neighbour interactions that dominate in dense suspensions
Summary
Independent of length scales, collective motion phenomena of many biological systems result in a polar order of the direction of motion in which the velocities of moving entities are directionally aligned. Coherent directional movement of micro-organism blooms attempts to achieve optimal light or nutrient uptake to satisfy the energy needs of the organisms or increase their reproductive success [6] In each of these examples, a coherent direction of motion arises in aggregations and clusters of living species, underlining a strict relationship between population density and the ability of the population to respond coherently at a defined strength of an external stimulus. This suggests that the aggregation of a specific cluster density plays a key role in determining the presence of a polar order response, which may result in an evolutionary advantage [3]
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