Precision and Kinetics of Adaptation in Bacterial Chemotaxis

Biophysical Journal, 2007

An allosteric model is developed to study the cooperative kinase response of wild-type (wt) Escherichia coli cells to the chemoattractant MeAsp in different ambient MeAsp concentrations. The model, together with wt dose response data, reveals the underlying mechanism for E. coli 's ability to maintain high sensitivity over a wide range of backgrounds. We find: 1), Adaptation tunes the system to the steepest part of the dose response curve, where the sensitivity to a given type of stimulus is amplified by the number of corresponding receptors in the (mixed) functional receptor complex. A lower bound on the number of Tar receptor dimers (N a ) in the complex N a *6 is obtained from the measured sensitivity. 2), Accurate adaptation synchronizes the kinase activities from different (uncoupled) receptor complexes in a single cell and is crucial in maintaining the high Hill coefficient in the (population averaged) kinase response curve. 3), The wide dynamic range of the high sensitivity can be explained in our model by either having a very small ratio between ligand dissociation constants of the inactive and the active receptors C ¼ 0.006, N a ¼ 6, and a (methylation level independent) dissociation constant for the inactive Tar receptor K ¼ 18.2 mM or by having K and/or N a increase with receptor methylation level together with a larger value of C . 0.01. Specific experiments are suggested to distinguish these two scenarios. 4), The receptor occupancy in a wt cell should also adapt and exhibit a slow (approximately logarithmic) dependence on the ligand concentration in the adapted state; this general prediction can be tested experimentally to verify/falsify our model.

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.”

Biophysical Journal, 2004

Signaling in bacterial chemotaxis is mediated by several types of transmembrane chemoreceptors. The chemoreceptors form tight polar clusters whose functions are of great biological interest. Here, we study the general properties of a chemotaxis model that includes interaction between neighboring chemoreceptors within a receptor cluster and the appropriate receptor methylation and demethylation dynamics to maintain (near) perfect adaptation. We find that, depending on the receptor coupling strength, there are two steady-state phases in the model: a stationary phase and an oscillatory phase. The mechanism for the existence of the two phases is understood analytically. Two important phenomena in transient response, the overshoot in response to a pulse stimulus and the high gain in response to sustained changes in external ligand concentrations, can be explained in our model, and the mechanisms for these two seemingly different phenomena are found to be closely related. The model also naturally accounts for several key in vitro response experiments and the recent in vivo fluorescence resonance energy transfer experiments for various mutant strains. Quantitatively, our study reveals possible choices of parameters for fitting the existing experiments and suggests future experiments to test the model predictions.

Proceedings of the National Academy of Sciences, 2003

We propose a general theoretical framework for modeling receptor sensitivity in bacterial chemotaxis, taking into account receptor interactions, including those among different receptor species. We show that our model can quantitatively explain the recent in vivo measurements of receptor sensitivity at different ligand concentrations for both mutant and wild-type strains. For mutant strains, our model can fit the experimental data exactly. For the wild-type cell, our model is capable of achieving high gain while having modest values of Hill coefficient for the response curves. Furthermore, the high sensitivity of the wild-type cell in our model is maintained for a wide range of ambient ligand concentrations, facilitated by near-perfect adaptation and dependence of ligand binding on receptor activity. Our study reveals the importance of coupling among different chemoreceptor species, in particular strong interactions between the aspartate (Tar) and serine (Tsr) receptors, which is crucial in explaining both the mutant and wild-type data. Predictions for the sensitivity of other mutant strains and possible improvements of our model for the wild-type cell are also discussed.

Proceedings of the National Academy of Sciences, 2006

The chemotaxis network in Escherichia coli is remarkable for its sensitivity to small relative changes in the concentrations of multiple chemical signals. We present a model for signal integration by mixed clusters of interacting two-state chemoreceptors. Our model results compare favorably to the results obtained by Sourjik and Berg with in vivo fluorescence resonance energy transfer. Importantly, we identify two distinct regimes of behavior, depending on the relative energies of the two states of the receptors. In regime I, coupling of receptors leads to high sensitivity, while in regime II, coupling of receptors leads to high cooperativity, i.e., high Hill coefficient. For homogeneous receptors, we predict an observable transition between regime I and regime II with increasing receptor methylation or amidation. chemotaxis ͉ Monod, Wyman, and Changeux model ͉ receptor clustering Conflict of interest statement: No conflicts declared.

Proceedings of the National Academy of Sciences of the United States of America, 2011

Sensory systems rescale their response sensitivity upon adaptation according to simple strategies that recur in processes as diverse as single-cell signaling, neural network responses, and whole-organism perception. Here, we study response rescaling in Escherichia coli chemotaxis, where adaptation dynamically tunes the cells' motile response during searches for nutrients. Using in vivo fluorescence resonance energy transfer (FRET) measurements on immobilized cells, we demonstrate that the design of this prokaryotic signaling network follows the fold-change detection (FCD) strategy, responding faithfully to the shape of the input profile irrespective of its absolute intensity. Using a microfluidics-based assay for free swimming cells, we confirm intensity-independent gradient responses at the behavioral level. By theoretical analysis, we identify a set of sufficient conditions for FCD in E. coli chemotaxis, which leads to the prediction that the adaptation timescale is invariant ...

Proceedings of the National Academy of Sciences, 2012

Escherichia coli chemotaxis serves as a paradigm for the way living cells respond and adapt to changes in their environment. The chemotactic response has been characterized at the level of individual flagellar motors and in populations of swimming cells. However, it has not been previously possible to quantify accurately the adaptive response of a single, multiflagellated cell. Here, we use our recently developed optical trapping technique to characterize the swimming behavior of individual bacteria as they respond to sudden changes in the chemical environment. We follow the adaptation kinetics of E. coli to varying magnitudes of step-up and stepdown changes in concentration of chemoattractant. We quantify two features of adaptation and how they vary with stimulus strength: abruptness (the degree to which return to prestimulus behavior occurs within a small number of run/tumble events) and overshoot (the degree of excessive response before the return to prestimulus behavior). We also characterize the asymmetry between step-up and step-down responses, observed at the singlecell level. Our findings provide clues to an improved understanding of chemotactic adaptation.

Nature Communications

Many regulatory and signaling proteins have multiple modification sites. In bacterial chemotaxis, each chemoreceptor has multiple methylation sites that are responsible for adaptation. However, whether the ordering of the multisite methylation process affects adaptation remains unclear. Furthermore, the benefit of having multiple modification sites is also unclear. Here, we show that sequentially ordered methylation/demethylation is critical for perfect adaptation; adaptation accuracy decreases as randomness in the multisite methylation process increases. A tradeoff between adaptation accuracy and response gain is discovered. We find that this accuracy-gain tradeoff is lifted significantly by having more methylation sites, but only when the multisite modification process is sequential. Our study suggests that having multiple modification sites and a sequential modification process constitute a general strategy to achieve both accurate adaptation and high response gain simultaneously...

2017

A stochastic version of the Barkai-Leibler model of chemotaxis receptors in Escherichia coli is studied here with the goal of elucidating the effects of intrinsic network noise in their conformational dynamics. The model was originally proposed to explain the robust and near-perfect adaptation of E. coli observed across a wide range of spatially uniform attractant/repellent (ligand) concentrations. In the model, a receptor is either active or inactive and can stochastically switch between the two states. The enzyme CheR methylates inactive receptors while CheB demethylates active receptors and the probability for a receptor to be active depends on its level of methylation and ligand occupation. In a simple version of the model with two methylation sites per receptor (M = 2), we show rigorously, under a quasi-steady state approximation, that the mean active fraction of receptors is an ultrasensitive function of [CheR]/[CheB] in the limit of saturating receptor concentration. Hence th...

Protein Science, 2009

Sensory adaptation in bacterial chemotaxis is mediated by methylation and demethylation of specific glutamyl residues in the cytoplasmic domain of chemoreceptors. Methylation is catalyzed by methyltransferase CheR. In E. coli and related organisms, methylation sufficiently rapid to be physiologically effective requires a carboxyl terminal pentapeptide sequence on the receptor being modified or, via adaptational assistance, on a neighboring homodimer in a receptor cluster. Pentapeptide-enhanced methylation is thought to be mediated by a~30 residue, potentially disordered sequence that serves as a flexible arm connecting the receptor body and pentapeptide-bound methyltransferase, thus allowing diffusionally restricted enzyme to reach methyl-accepting sites. However, it was not known how many or which sites on the same or neighboring receptors were accessible to the tethered enzyme. We investigated using molecular modeling and found that, in a hexagonal array of trimers of receptor dimers, CheR tethered to a dimer of chemoreceptor Tar by its native 30-residue flexible-arm sequence could reach all methyl-accepting sites on the dimer to which it was tethered plus 48 methyl-accepting sites distributed among nine neighboring dimers, equivalent to the total sites carried by six receptors. This modeling-determined methylation neighborhood of one enzyme-binding dimer and six neighbors corresponds precisely with the experimentally identified neighborhood of seven. Thus, the experimentally observed adaptational assistance can occur by docking of pentapeptidebound, diffusionally restricted enzyme to methyl-accepting sites on neighboring receptors. Our analysis introduces the notion that physiologically relevant adaptational assistance could occur even if only a subset of sites on a particular receptor are within reach.