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 that incorporates 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

“…To numerically solve the continuum model described by Eqs. 1-4, we follow the experimentally-validated approach used in our previous work [8,50]. 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 c 0 , and the autoinducer and biofilm concentrations are initially zero, throughout. Furthermore, following previous work [50,[96][97][98][99][100], 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 0.95 cells µm −3 at a location x i , the excess cell concentration is removed from x i and added to the neighboring location, x i + δx, where δx represents the spatial resolution of the simulation, retaining the same ratio of planktonic to biofilm cells in the new location.…”

“…Three key dimensionless quantities, denoted by the tilde ( ˜) notation, emerge from this calculation. The first, β1,0 ≡ γ 1 / (b 1,0 κ 1 /c 0 ), describes the yield of new cells produced as the population consumes nutrientquantified by the rates of cellular proliferation and nutrient consumption, γ 1 and b 1,0 κ 1 /c 0 , respectively [50]. The second, η ≡ αa * /k 1 , describes the competition between S2.…”

“…Specifically, we quantify the dynamics of the leading edge positions of the chemotactic front of planktonic cells and the autoinducer plume, x 1,edge (t) and x a,edge (t), respectively. The front position x 1,edge (t) is known to depend on cellular motility, nutrient diffusion, and nutrient consumption in a non-trivial manner [6,7,41,50], 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 x at which b 1 ≥ 10 −4 b 1,0 . While the plume position x a,edge (t) can also be directly obtained in each simulation, we again develop a more generallyapplicable analytical expression by assuming that the autoinducer continually diffuses from the initial inoculum: x a,edge (t) = x 0 + √ 2D a t. Then, τ c can be directly determined as the time at which x 1,edge (t) begins to exceed x a,edge (t).…”

“…For example, studies of planktonic cells have provided important insights into bacterial motility-which can be either undirected [40][41][42][43] or directed in response to e.g., a chemical gradient via chemotaxis [3][4][5][6][7][8][44][45][46][47][48][49][50]. 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 [3][4][5][6][7][8][40][41][42][43][44][45][46][47][48][49][50]. Thus, the manner in which planktonic bacteria disperse can strongly vary between different species and environmental conditions.…”