Modeling the chemotactic response of Escherichia coli to time-varying stimuli

Abstract

In their natural environment, cells need to extract useful information from complex temporal signals that vary over a wide range of intensities and time scales. Here, we study how such signals are processed by Escherichia coli during chemotaxis by developing a general theoretical model based on receptor adaptation and receptor-receptor cooperativity. Measured responses to various monotonic, oscillatory, and impulsive stimuli are all explained consistently by the underlying adaptation kinetics within this model. For exponential ramp signals, an analytical solution is discovered that reveals a remarkable connection between the dependence of kinase activity on the exponential ramp rate and the receptor methylation rate function. For exponentiated sinewave signals, spectral analysis shows that the chemotaxis pathway acts as a lowpass filter for the derivative of the signal with the cutoff frequency determined by an intrinsic adaptation time scale. For large step stimuli, we find that the recovery time is determined by the constant maximum methylation rate, which provides a natural explanation for the observed recovery time additivity. Our model provides a quantitative system-level description of the chemotaxis signaling pathway and can be used to predict E. coli chemotaxis responses to arbitrary temporal signals. This model of the receptor system reveals the molecular origin of Weber's law in bacterial chemotaxis. We further identify additional constraints required to account for the related observation that the output of this pathway is constant under exponential ramp stimuli, a feature that we call ''logarithmic tracking.'' adaptation kinetics ͉ bacterial chemotaxis ͉ signal processing ͉ Monod-Wyman-Changeux model M ost studies of the kinetics of biological signaling pathways are based on measuring responses to simple controllable stimuli, such as a sudden change of ligand concentration. For example, bacterial chemotaxis is studied by subjecting cells to a step-function change in chemo-effector concentration and measuring the fraction of time that the flagellar motor spins counterclockwise (CCW) or clockwise (CW), for tethered cells (1), or more recently, by measuring the activity of the response regulator (CheY-P) by using FRET (2). Measurements of responses to these step-function stimuli over a range of ambient concentrations have been very useful in revealing the underlying signaling pathway for Escherichia coli chemotaxis (see refs. 3-5 for recent reviews). However, such a simple temporal stimulus is unlikely to be the typical signal encountered by E. coli cells in their natural environment, which changes/fluctuates continuously in time. How does an E. coli cell processes complex time-varying signals to obtain useful information? This is the question we try to address in this article by using a modeling approach tested by comparison with relevant existing experiments. A quantitative model based on microscopic pathway kinetics serves as a natural bridge between the experimentally measured responses to simple si...

Microfluidics for bacterial chemotaxis

“…coli's chemotaxis signalling network, as described in the model of Tu et al [33], though different from these transcriptional networks, was found on theoretical grounds to exhibit the FCD property [72]. This was tested experimentally in this study.…”

Propulsion and Chemotaxis in Bacteria‐Driven Microswimmers

“…Chemotaxis Signaling Pathway Model : The chemotaxis signaling pathway of E. coli was modeled with three major components, and their corresponding models were adapted from recent studies 37, 38, 39, 40, 41, 42, 43. The first component, MCP complex, was represented with a Monod–Wyman–Changeux (MWC) model52 to describe the allosteric effects of receptor clusters with identical receptors.…”

“…Thus far, the taxis‐based guiding method constitutes the major way to regulate the otherwise highly stochastic motion of bacteria‐driven microswimmers, which has been studied both in vitro17, 20, 21, 22, 23, 24, 25 and in vivo 14, 16. Chemotaxis, one of the most common taxis behaviors in bacteria, has been well understood36 and its signaling pathway has been mathematically modeled 37, 38, 39, 40, 41, 42, 43. In general, the chemotaxis of free‐swimming bacteria associates with a biased random walk, enabled by preferentially suppressed tumble tendency when the bacteria travel up a chemoattractant gradient; whereas in an uniform medium, the tumble tendency is isotropic over all swimming directions.…”

Fast, high-throughput measurement of collective behaviour in a bacterial population

“…This behaviour is interpreted as a change from a low background concentration response regime, where the bacteria respond to absolute changes in concentration to a high-concentration response regime, where they respond to relative change in concentration ('logarithmic sensing'), as previously observed [26]. Semi-empirical mean-field models have been developed [22,27,37] to explain the large dynamic range of the chemotaxis system. The chemoreceptors cluster in groups of dimers, containing N Tar receptor dimers, which form active or inactive complexes, responding according to an allosteric two-state model to attractant binding [38].…”