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To explore the coupling between a growing population of microorganisms suchas E. coli and a nonuniform nutrient distribution, we formulate a minimalisticmodel. It consists of active Brownian particles that divide and grow at anutrient-dependent rate following the Monod equation. The nutrientconcentration obeys a diffusion equation with a consumption term and a pointsource. In this setting the heterogeneity in the nutrient distribution can betuned by the diffusion coefficient.  In particle-based simulations, we demonstrate that passive and weakly activeparticles form proliferation-induced clusters when the nutrient is localized,without relying on further mechanisms such as chemotaxis or adhesion. Incontrast, strongly active particles disperse in the whole system during theirlifetime and no clustering is present. The steady population is unaffected byactivity or nonuniform nutrient distribution and only determined by the ratioof nutrient influx and bacterial death. However, the transient dynamicsstrongly depends on the nutrient distribution and activity. Passive particlesin almost uniform nutrient profiles display a strong population overshoot, withclusters forming all over the system. In contrast, when slowly diffusingnutrients remain centred around the source, the bacterial population quicklyapproaches the steady state due to its strong coupling to the nutrient.Conversely, the population overshoot of highly active particles becomesstronger when the nutrient localisation increases. We successfully map thetransient population dynamics onto a uniform model where the effect of thenonuniform nutrient and bacterial distributions are rationalized by twoeffective areas.

Dividing active and passive particles in nonuniform nutrient environments