A minimal one-dimensional model of pattern formation in bacterial community phototaxis

Synechocystis sp. PCC6803 is a phototactic cyanobacterium that moves directionally in response to a light source. During phototaxis, these bacterial communities show emergent spatial organisation, resulting in the formation of finger-like projections at the propagating front. We propose a one-dimensional analytical model to predict the critical value of the phototactic bias force for instabilities to manifest as finger-like projections. We also predict the wavelengths of the fastest growing mode and the critical mode (above which the instabilities disappear). In addition, our model predicts the observed loss of instabilities in taxD1 mutants, which lack an important photoreceptor. We compare predictions from this minimal, analytically solvable one-dimensional model to results from a 2-dimensional computational model in terms of how the growth rate and the wavelength of the fastest growing mode vary as a function of phototactic bias, the secretion rate of mobility-enhancing slime by bacteria, and the initial bacterial concentration. We also validate our predictions using experimental data obtained from phototaxis assays of Synechocystis communities