Drift velocity of bacterial chemotaxis in dynamic chemical environments

Chemotaxis allows swimming bacteria to navigate through chemical landscapes. To date, continuum models of chemotactic populations (e.g. Patlak-Keller-Segel models) have considered bacteria responding only to spatial chemical gradients. In these models, chemotactic advection is modelled through a drift velocity proportional to the spatial chemical gradient. In nature and industry, however, bacterial populations experience dynamic, spatio-temporally varying chemical environments, such as the neighbourhood of lysing phytoplankton cells. Recent analyses have shown how temporal gradients can 'confuse' individual bacteria, impacting the precision of their gradient estimation. However, very few studies have considered how temporal gradients influence the chemotactic drift velocity of whole populations. Here, we use Monte Carlo simulations to infer the drift velocity of a population when both spatial and temporal gradients are present. We propose an ansatz for the drift velocity, which fits the simulations well. This ansatz allows us to account for how temporal gradients can significantly impact chemotaxis of bacterial populations up a spatial gradient. We explore the consequences of this new effect through a Patlak-Keller-Segel type model applied to single decaying and oscillating pulses of chemoattractant. Finally, we discuss possible biological consequences of our results and extensions of our modelling framework.This article is part of the theme issue 'Biological fluid dynamics: emerging directions'.