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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 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."

SUBMITTER: Tu Y

PROVIDER: S-EPMC2551628 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description: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 v(d) is a constant in an exponential attractant concentration gradient [L] proportional, variantexp(Gx). v(d) depends linearly on the exponential gradient G before it saturates when G is larger than a critical value G(C). We find that G(C) is determined by the intracellular adaptation rate k(R) with a simple scaling law: G(C) infinity k(1/2)(R). The linear dependence of v(d) 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 G(C) and its scaling with k(R) 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 omega of the time-varying spatial gradient becomes faster than a critical value omega(c), which is controlled by the cell's chemotaxis adaptation rate k(R). 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.

Project description:The alternative sigma factor RpoS is a central regulator of many stress responses in Escherichia coli The level of functional RpoS differs depending on the stress. The effect of these differing concentrations of RpoS on global transcriptional responses remains unclear. We investigated the effect of RpoS concentration on the transcriptome during stationary phase in rich media. We found that 23% of genes in the E. coli genome are regulated by RpoS, and we identified many RpoS-transcribed genes and promoters. We observed three distinct classes of response to RpoS by genes in the regulon: genes whose expression changes linearly with increasing RpoS level, genes whose expression changes dramatically with the production of only a little RpoS ("sensitive" genes), and genes whose expression changes very little with the production of a little RpoS ("insensitive"). We show that sequences outside the core promoter region determine whether an RpoS-regulated gene is sensitive or insensitive. Moreover, we show that sensitive and insensitive genes are enriched for specific functional classes and that the sensitivity of a gene to RpoS corresponds to the timing of induction as cells enter stationary phase. Thus, promoter sensitivity to RpoS is a mechanism to coordinate specific cellular processes with growth phase and may also contribute to the diversity of stress responses directed by RpoS.IMPORTANCE The sigma factor RpoS is a global regulator that controls the response to many stresses in Escherichia coli Different stresses result in different levels of RpoS production, but the consequences of this variation are unknown. We describe how changing the level of RpoS does not influence all RpoS-regulated genes equally. The cause of this variation is likely the action of transcription factors that bind the promoters of the genes. We show that the sensitivity of a gene to RpoS levels explains the timing of expression as cells enter stationary phase and that genes with different RpoS sensitivities are enriched for specific functional groups. Thus, promoter sensitivity to RpoS is a mechanism that coordinates specific cellular processes in response to stresses.

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

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