Influence of confinement on the spreading of bacterial populations

Abstract

The spreading of bacterial populations is central to processes in agriculture, the environment, and medicine. However, existing models of spreading typically focus on cells in unconfined settings—despite the fact that many bacteria inhabit complex and crowded environments, such as soils, sediments, and biological tissues/gels, in which solid obstacles confine the cells and thereby strongly regulate population spreading. Here, we develop an extended version of the classic Keller-Segel model of bacterial spreading via motility that also incorporates cellular growth and division, and explicitly considers the influence of confinement in promoting both cell-solid and cell-cell collisions. Numerical simulations of this extended model demonstrate how confinement fundamentally alters the dynamics and morphology of spreading bacterial populations, in good agreement with recent experimental results. In particular, with increasing confinement, we find that cell-cell collisions increasingly hinder the initial formation and the long-time propagation speed of chemotactic pulses. Moreover, also with increasing confinement, we find that cellular growth and division plays an increasingly dominant role in driving population spreading—eventually leading to a transition from chemotactic spreading to growth-driven spreading via a slower, jammed front. This work thus provides a theoretical foundation for further investigations of the influence of confinement on bacterial spreading. More broadly, these results help to provide a framework to predict and control the dynamics of bacterial populations in complex and crowded environments.

A biophysical threshold for biofilm formation

“…Three key dimensionless quantities, denoted by the tilde notation, emerge from this calculation. The first, , describes the yield of new cells produced as the population consumes nutrient—quantified by the rates of cellular proliferation and nutrient consumption, and , respectively ( Amchin et al, 2022 ). The second, , describes the competition between autoinducer loss and production, quantified by their respective rates and , at the single-cell scale.…”

“…Specifically, we quantify the dynamics of the leading edge positions of the chemotactic front of planktonic cells and the autoinducer plume, and , respectively. The front position is known to depend on cellular motility, nutrient diffusion, and nutrient consumption in a non-trivial manner ( Berg, 2004 ; Cremer et al, 2019 ; Fu et al, 2018 ; Amchin et al, 2022 ), and we are not aware of a way to compute this quantity a priori from input parameters; instead, we extract this sole quantity from each simulation by identifying the largest value of at which . While the plume position can also be directly obtained in each simulation, we again develop a more generally applicable analytical expression by assuming that the autoinducer continually diffuses from the initial inoculum: .…”

“…To numerically solve the continuum model described by Equations 1–4 , we follow the experimentally validated approach used in our previous work ( Bhattacharjee et al, 2021 ; Amchin et al, 2022 ). Specifically, we use an Adams-Bashforth-Moulton predictor-corrector method in which the order of the predictor and corrector are 3 and 2, respectively.…”

“…Nutrient is initially uniform at a fixed concentration , and the autoinducer and biofilm concentrations are initially zero, throughout. Furthermore, following previous work ( Amchin et al, 2022 ; Dell’Arciprete et al, 2018 ; Volfson et al, 2008 ; Farrell et al, 2013 ; Klapper and Dockery, 2002 ; Head, 2013 ), we also incorporate jammed growth expansion of the population in which growing cells push outward on their neighbors when the total concentration of bacteria is large enough. In particular, whenever the total concentration of bacteria (planktonic and biofilm) exceeds the jamming limit of at a location , the excess cell concentration is removed from and added to the neighboring location, , where represents the spatial resolution of the simulation, retaining the same ratio of planktonic to biofilm cells in the new location.…”

“…For example, studies of planktonic cells have provided important insights into bacterial motility—which can be either undirected ( Berg, 2018 ; Berg, 2004 ; Bhattacharjee and Datta, 2019a ; Bhattacharjee and Datta, 2019b ) or directed in response to e.g., a chemical gradient via chemotaxis ( Adler, 1966b ; Adler, 1966a ; Saragosti et al, 2011 ; Fu et al, 2018 ; Cremer et al, 2019 ; Bhattacharjee et al, 2021 ; Keller and Segel, 1971 ; Odell and Keller, 1976 ; Keller and Odell, 1975 ; Lauffenburger, 1991 ; Seyrich et al, 2019 ; Croze et al, 2011 ; Amchin et al, 2022 ). These processes are now known to be regulated not just by intrinsic cellular properties, such as swimming kinematics and the amplitude and frequency of cell body reorientations, but also by the properties of their environment, such as cellular concentration, chemical/nutrient conditions, and confinement by surrounding obstacles ( Berg, 2018 ; Berg, 2004 ; Bhattacharjee and Datta, 2019a ; Bhattacharjee and Datta, 2019b ; Adler, 1966b ; Adler, 1966a ; Saragosti et al, 2011 ; Fu et al, 2018 ; Cremer et al, 2019 ; Bhattacharjee et al, 2021 ; Keller and Segel, 1971 ; Odell and Keller, 1976 ; Keller and Odell, 1975 ; Lauffenburger, 1991 ; Seyrich et al, 2019 ; Croze et al, 2011 ; Amchin et al, 2022 ). Thus, the manner in which planktonic bacteria disperse can strongly vary between different species and environmental conditions.…”