Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated

Curved Tails in Polymerization-Based Bacterial Motility

The curved actin ``comet-tail'' of the bacterium Listeria monocytogenes is a visually striking signature of actin polymerization-based motility. Similar actin tails are associated with Shigella flexneri, spotted-fever Rickettsiae, the Vaccinia virus, and vesicles and microspheres in related in vitro systems. We show that the torque required to produce the curvature in the tail can arise from randomly placed actin filaments pushing the bacterium or particle. We find that the curvature magnitude determines the number of actively pushing filaments, independent of viscosity and of the molecular details of force generation. The variation of the curvature with time can be used to infer the dynamics of actin filaments at the bacterial surface.Comment: 8 pages, 2 figures, Latex2

Identifying the Best Times for Cognitive Functioning Using New Methods: Matching University Times to Undergraduate Chronotypes

University days generally start at fixed times in the morning, often early morning, without regard to optimal functioning times for students with different chronotypes. Research has shown that later starting times are crucial to high school students' sleep, health, and performance. Shifting the focus to university, this study used two new approaches to determine ranges of start times that optimize cognitive functioning for undergraduates. The first is a survey-based, empirical model (SM), and the second a neuroscience-based, theoretical model (NM). The SM focused on students' self-reported chronotype and times they feel at their best. Using this approach, data from 190 mostly first and second year university students were collected and analyzed to determine optimal times when cognitive performance can be expected to be at its peak. The NM synthesized research in sleep, circadian neuroscience, sleep deprivation's impact on cognition, and practical considerations to create a generalized solution to determine the best learning hours. Strikingly the SM and NM results align with each other and confirm other recent research in indicating later start times. They add several important points: (1) They extend our understanding by showing that much later starting times (after 11 a.m. or 12 noon) are optimal; (2) Every single start time disadvantages one or more chronotypes; and (3) The best practical model may involve three alternative starting times with one afternoon shared session. The implications are briefly considered

Quantitative Modeling of Escherichia coli Chemotactic Motion in Environments Varying in Space and Time

Escherichia coli chemotactic motion in spatiotemporally varying environments is studied by using a computational model based on a coarse-grained description of the intracellular signaling pathway dynamics. We find that the cell's chemotaxis drift velocity vd is a constant in an exponential attractant concentration gradient [L]∝exp(Gx). vd depends linearly on the exponential gradient G before it saturates when G is larger than a critical value GC. We find that GC is determined by the intracellular adaptation rate kR with a simple scaling law: . The linear dependence of vd on G = d(ln[L])/dx directly demonstrates E. coli's ability in sensing the derivative of the logarithmic attractant concentration. The existence of the limiting gradient GC and its scaling with kR are explained by the underlying intracellular adaptation dynamics and the flagellar motor response characteristics. For individual cells, we find that the overall average run length in an exponential gradient is longer than that in a homogeneous environment, which is caused by the constant kinase activity shift (decrease). The forward runs (up the gradient) are longer than the backward runs, as expected; and depending on the exact gradient, the (shorter) backward runs can be comparable to runs in a spatially homogeneous environment, consistent with previous experiments. In (spatial) ligand gradients that also vary in time, the chemotaxis motion is damped as the frequency ω of the time-varying spatial gradient becomes faster than a critical value ωc, which is controlled by the cell's chemotaxis adaptation rate kR. Finally, our model, with no adjustable parameters, agrees quantitatively with the classical capillary assay experiments where the attractant concentration changes both in space and time. Our model can thus be used to study E. coli chemotaxis behavior in arbitrary spatiotemporally varying environments. Further experiments are suggested to test some of the model predictions

Voronoi Tessellation Captures Very Early Clustering of Single Primary Cells as Induced by Interactions in Nascent Biofilms

Biofilms dominate microbial life in numerous aquatic ecosystems, and in engineered and medical systems, as well. The formation of biofilms is initiated by single primary cells colonizing surfaces from the bulk liquid. The next steps from primary cells towards the first cell clusters as the initial step of biofilm formation remain relatively poorly studied. Clonal growth and random migration of primary cells are traditionally considered as the dominant processes leading to organized microcolonies in laboratory grown monocultures. Using Voronoi tessellation, we show that the spatial distribution of primary cells colonizing initially sterile surfaces from natural streamwater community deviates from uniform randomness already during the very early colonisation. The deviation from uniform randomness increased with colonisation — despite the absence of cell reproduction — and was even more pronounced when the flow of water above biofilms was multidirectional and shear stress elevated. We propose a simple mechanistic model that captures interactions, such as cell-to-cell signalling or chemical surface conditioning, to simulate the observed distribution patterns. Model predictions match empirical observations reasonably well, highlighting the role of biotic interactions even already during very early biofilm formation despite few and distant cells. The transition from single primary cells to clustering accelerated by biotic interactions rather than by reproduction may be particularly advantageous in harsh environments — the rule rather than the exception outside the laboratory

Cell morphology governs directional control in swimming bacteria

The ability to rapidly detect and track nutrient gradients is key to the ecological success of motile bacteria in aquatic systems. Consequently, bacteria have evolved a number of chemotactic strategies that consist of sequences of straight runs and reorientations. Theoretically, both phases are affected by fluid drag and Brownian motion, which are themselves governed by cell geometry. Here, we experimentally explore the effect of cell length on control of swimming direction. We subjected Escherichia coli to an antibiotic to obtain motile cells of different lengths, and characterized their swimming patterns in a homogeneous medium. As cells elongated, angles between runs became smaller, forcing a change from a run-and-tumble to a run-and-stop/reverse pattern. Our results show that changes in the motility pattern of microorganisms can be induced by simple morphological variation, and raise the possibility that changes in swimming pattern may be triggered by both morphological plasticity and selection on morphology