Regulatory dynamics of standard two-component systems in bacteria

A widespread mechanism of bacterial signaling occurs through two-component systems, comprised of a sensor histidine kinase (SHK) and a transcriptional response regulator (RR). The SHK activates RR by phosphorylation. The most common two-component system structure involves expression from a single operon, the transcription of which is activated by its own phosphorylated RR. The role of this feedback is poorly understood, but it has been associated with an overshooting kinetic response and with fast recovery of previous interrupted signaling events in different systems. Mathematical models show that overshoot is only attainable with negative feedback that also improves response time. Our models also predict that fast recovery of previous interrupted signaling depends on high accumulation of SHK and RR, which is more likely in a positive feedback regime. We use Monte Carlo sampling of the parameter space to explore the range of attainable model behaviors. The model predicts that the effective feedback sign can change from negative to positive depending on the signal level. Variations in two-component system architectures and parameters may therefore have evolved to optimize responses in different bacterial lifestyles. We propose a conceptual model where low signal conditions result in a responsive system with effectively negative feedback while high signal conditions with positive feedback favor persistence of system output.

The machinery for transduction of chemotactic stimuli in the bacterium E. coli is one of the most completely characterized signal transduction systems, and because of its relative simplicity, quantitative analysis of this system is possible. Here we discuss models which reproduce many of the important behaviors of the system. The important characteristics of the signal transduction system are excitation and adaptation, and the latter implies that the transduction system can function as a "derivative sensor" with respect to the ligand concentration in that the DC component of a signal is ultimately ignored if it is not too large. This temporal sensing mechanism provides the bacterium with a memory of its passage through spatially-or temporally-varying signal fields, and adaptation is essential for successful chemotaxis. We also discuss some of the spatial patterns observed in populations and indicate how cell-level behavior can be embedded in population-level descriptions.

Journal of The Royal Society Interface, 2012

Population-level measurements of phenotypic behaviour in biological systems may not necessarily reflect individual cell behaviour. To assess qualitative changes in the behaviour of a single cell, when alone and when part of a community, we developed an agent-based model describing the metabolic states of a population of quorum-coupled cells. The modelling is motivated by published experimental work of a synthetic genetic regulatory network (GRN) used in Escherichia coli cells that exhibit oscillatory behaviour across the population. To decipher the mechanisms underlying oscillations in the system, we investigate the behaviour of the model via numerical simulation and bifurcation analysis. In particular, we study the effect of an increase in population size as well as the spatio-temporal behaviour of the model. Our results demonstrate that oscillations are possible only in the presence of a high concentration of the coupling chemical and are due to a time scale separation in key regulatory components of the system. The model suggests that the population establishes oscillatory behaviour as the system's preferred stable state. This is achieved via an effective increase in coupling across the population. We conclude that population effects in GRN design need to be taken into consideration and be part of the design process. This is important in planning intervention strategies or designing specific cell behaviours.

Nature, 2010

The chemotaxis signalling network in Escherichia coli that controls the locomotion of bacteria is a classic model system for signal transduction. This pathway modulates the behaviour of flagellar motors to propel bacteria towards sources of chemical attractants. Although this system relaxes to a steady state in response to environmental changes, the signalling events within the chemotaxis network are noisy and cause large temporal variations of the motor behaviour even in the absence of stimulus. That the same signalling network governs both behavioural variability and cellular response raises the question of whether these two traits are independent. Here, we experimentally establish a fluctuation-response relationship in the chemotaxis system of living bacteria. Using this relationship, we demonstrate the possibility of inferring the cellular response from the behavioural variability measured before stimulus. In monitoring the pre- and post-stimulus switching behaviour of individual bacterial motors, we found that variability scales linearly with the response time for different functioning states of the cell. This study highlights that the fundamental relationship between fluctuation and response is not constrained to physical systems at thermodynamic equilibrium but is extensible to living cells. Such a relationship not only implies that behavioural variability and cellular response can be coupled traits, but it also provides a general framework within which we can examine how the selection of a network design shapes this interdependence.

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.”

Frontiers in Cellular and Infection Microbiology, 2014

The choice that bacteria make between sporulation and competence when subjected to stress provides a prototypical example of collective cell fate determination that is stochastic on the individual cell level, yet predictable (deterministic) on the population level. This collective decision is performed by an elaborated gene network. Considerable effort has been devoted to simplify its complexity by taking physics approaches to untangle the basic functional modules that are integrated to form the complete network: (1) A stochastic switch whose transition probability is controlled by two order parameters-population density and internal/external stress. (2) An adaptable timer whose clock rate is normalized by the same two previous order parameters. (3) Sensing units which measure population density and external stress. (4) A communication module that exchanges information about the cells' internal stress levels. (5) An oscillating gate of the stochastic switch which is regulated by the timer. The unique circuit architecture of the gate allows special dynamics and noise management features. The gate opens a window of opportunity in time for competence transitions, during which the circuit generates oscillations that are translated into a chain of short intervals with high transition probability. In addition, the unique architecture of the gate allows filtering of external noise and robustness against variations in circuit parameters and internal noise. We illustrate that a physics approach can be very valuable in investigating the decision process and in identifying its general principles. We also show that both cell-cell variability and noise have important functional roles in the collectively controlled individual decisions.

Frontiers in Bioengineering and Biotechnology, 2022

In free-living bacteria, the ability to regulate gene expression is at the core of adapting and interacting with the environment. For these systems to have a logic, a signal must trigger a genetic change that helps the cell to deal with what implies its presence in the environment; briefly, the response is expected to include a feedback to the signal. Thus, it makes sense to think of genetic sensory mechanisms of gene regulation. Escherichia coli K-12 is the bacterium model for which the largest number of regulatory systems and its sensing capabilities have been studied in detail at the molecular level. In this special issue focused on biomolecular sensing systems, we offer an overview of the transcriptional regulatory corpus of knowledge for E. coli that has been gathered in our database, RegulonDB, from the perspective of sensing regulatory systems. Thus, we start with the beginning of the information flux, which is the signal’s chemical or physical elements detected by the cell a...

Biophysical Journal, 2004

Evolution has provided many organisms with sophisticated sensory systems that enable them to respond to signals in their environment. The response frequently involves alteration in the pattern of movement, either by directed movement, a process called taxis, or by altering the speed or frequency of turning, which is called kinesis. Chemokinesis has been most thoroughly studied in the peritrichous bacterium Escherichia coli, which has four helical flagella distributed over the cell surface, and swims by rotating them. When rotated counterclockwise the flagella coalesce into a propulsive bundle, producing a relatively straight ''run,'' and when rotated clockwise they fly apart, resulting in a ''tumble'' which reorients the cell with little translocation. A stochastic process generates the runs and tumbles, and in a chemoeffector gradient, runs that carry the cell in a favorable direction are extended. The cell senses spatial gradients as temporal changes in receptor occupancy and changes the probability of counterclockwise rotation (the bias) on a fast timescale, but adaptation returns the bias to baseline on a slow timescale, enabling the cell to detect and respond to further concentration changes. The overall structure of the signal transduction pathways is well characterized in E. coli, but important details are still not understood. Only recently has a source of gain in the signal transduction network been identified experimentally, and here we present a mathematical model based on dynamic assembly of receptor teams that can explain this observation.

Molecular Microbiology, 2008

Bacterial two-component systems (TCS) are key signal transduction networks regulating global responses to environmental change. Environmental signals may modulate the phosphorylation state of sensor kinases (SK). The phosphorylated SK transfers the phosphate to its cognate response regulator (RR), which causes physiological response to the signal. Frequently, the SK is bifunctional and, when unphosphorylated, it is also capable of dephosphorylating the RR. The phosphatase activity may also be modulated by environmental signals. Using the EnvZ/OmpR system as an example, we constructed mathematical models to examine the steady-state and kinetic properties of the network. Mathematical modelling reveals that the TCS can show bistable behaviour for a given range of parameter values if unphosphorylated SK and RR form a dead-end complex that prevents SK autophosphorylation. Additionally, for bistability to exist the major dephosphorylation flux of the RR must not depend on the unphosphorylated SK. Structural modelling and published affinity studies suggest that the unphosphorylated SK EnvZ and the RR OmpR form a dead-end complex. However, bistability is not possible because the dephosphorylation of OmpR∼P is mainly done by unphosphorylated EnvZ. The implications of this potential bistability in the design of the EnvZ/OmpR network and other TCS are discussed.

Cell, 2003