Modeling bacterial chemotaxis inside a cell

2021

This thesis describes the development of an agent-based simulation of E. coli chemotaxis in C# and the Unity game engine. The agents use a mathematical model of the chemical pathway underlying chemotaxis to produce either forward-motion (running) or rotation (tumbling), in response to the concentration of ligand in their immediate environment. This model consists of a system of ODEs from Edgington and Tindall [1] and elements of survival analysis. A tool for analysing data from these simulations was also developed, and used to make quantitative comparisons between simulations. This is used to compare our model to a simplified model of chemotaxis, designed to always display chemotactic behaviour. It is concluded that both models display chemotactic movement, with the simplified model being more effective at finding the ligand source, but the ODE-based model being more adaptive

PloS one, 2013

Using a minimal model of metabolism, we examine the limitations of behavior that is (a) solely in response to environmental phenomena or (b) solely in response to metabolic dynamics, showing that basic forms of each of these kinds of behavior are incapable of driving survival-prolonging behavior in certain situations. Inspired by experimental evidence of concurrent metabolism-based and metabolism-independent chemotactic mechanisms in Escherichia coli and Rhodobacter sphaeroides, we then investigate how metabolism-independent and metabolism-based sensitivities can be integrated into a single behavioral response, demonstrating that a simple switching mechanism can be sufficient to effectively integrate metabolism-based and metabolism-independent behaviors. Finally, we use a spatial simulation of bacteria to show that the investigated forms of behavior produce different spatio-temporal patterns that are influenced by the metabolic-history of the bacteria. We suggest that these patterns...

Siam Journal on Applied Mathematics, 2004

Bacterial chemotaxis is widely studied from both the microscopic (cell) and macroscopic (population) points of view, and here we connect these different levels of description by deriving the classical macroscopic description for chemotaxis from a microscopic model of the behavior of individual cells. The analysis is based on the velocity jump process for describing the motion of individuals such as

Journal of Mathematical Analysis and Applications, 1999

WIREs Systems Biology and Medicine, 2012

Research into understanding bacterial chemotactic systems has become a paradigm for Systems Biology. Experimental and theoretical researchers have worked handin-hand for over 40 years to understand the intricate behavior driving bacterial species, in particular how such small creatures, usually not more than 5 μm in length, detect and respond to small changes in their extracellular environment. In this review we highlight the importance that theoretical modeling has played in providing new insight and understanding into bacterial chemotaxis. We begin with an overview of the bacterial chemotaxis sensory response, before reviewing the role of theoretical modeling in understanding elements of the system on the single cell scale and features underpinning multiscale extensions to population models.

PLoS Computational Biology, 2008

The chemotaxis system in the bacterium Escherichia coli is remarkably sensitive to small relative changes in the concentrations of multiple chemical signals over a broad range of ambient concentrations. Interactions among receptors are crucial to this sensitivity as is precise adaptation, the return of chemoreceptor activity to prestimulus levels in a constant chemoeffector environment. Precise adaptation relies on methylation and demethylation of chemoreceptors by the enzymes CheR and CheB, respectively. Experiments indicate that when transiently bound to one receptor, these enzymes act on small assistance neighborhoods (AN) of five to seven receptor homodimers. In this paper, we model a strongly coupled complex of receptors including dynamic CheR and CheB acting on ANs. The model yields sensitive response and precise adaptation over several orders of magnitude of attractant concentrations and accounts for different responses to aspartate and serine. Within the model, we explore how the precision of adaptation is limited by small AN size as well as by CheR and CheB kinetics (including dwell times, saturation, and kinetic differences among modification sites) and how these kinetics contribute to noise in complex activity. The robustness of our dynamic model for precise adaptation is demonstrated by randomly varying biochemical parameters.

Proceedings of The National Academy of Sciences, 2008

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 sine-wave 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.”

Biochemical Society Transactions, 2010

Bacteria are capable of sensing and responding to changes in their environment. One of the ways they do this is via chemotaxis, regulating swimming behaviour. The chemotaxis pathway senses chemoattractant gradients and uses a feedback loop to change the bacterial swimming pattern; this feedback loop differs in detail between species. In the present article, we summarize the current understanding of the regulatory mechanisms in three species and how these pathways can be viewed and analysed through the ideas of feedback control systems engineering.

Journal of Mathematical Biology, 2001

The diffusion gradient chamber (DGC) is a novel device developed to study the response of chemotactic bacteria to combinations of nutrients and attractants [7]. Its purpose is to characterize genetic variants that occur in many biological experiments. In this paper, a mathematical model which describes the spatial distribution of a bacterial population within the DGC is developed. Mathematical analysis of the model concerning positivity and boundedness of the solutions are given. An ADI (Alternating Direction Implicit) method is constructed for finding numerical solutions of the model and carrying out computer simulations. The numerical results of the model successfully reproduced the patterns that were observed in the experiments using the DGC.

Biophysical Journal, 2010

The chemotaxis network of the bacterium Escherichia coli is perhaps the most studied model for adaptation of a signaling system to persistent stimuli. Although adaptation in this system is generally considered to be precise, there has been little effort to quantify this precision, or to understand how and when precision fails. Using a Fö rster resonance energy transfer-based reporter of signaling activity, we undertook a systematic study of adaptation kinetics and precision in E. coli cells expressing a single type of chemoreceptor (Tar). Quantifiable loss of precision of adaptation was observed at levels of the attractant MeAsp as low 10 mM, with pronounced differences in both kinetics and precision of adaptation between addition and removal of attractant. Quantitative modeling of the kinetic data suggests that loss of precise adaptation is due to a slowing of receptor methylation as available modification sites become scarce. Moreover, the observed kinetics of adaptation imply large cell-to-cell variation in adaptation rates-potentially providing genetically identical cells with the ability to ''hedge their bets'' by pursuing distinct chemotactic strategies.