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A modular gradient-sensing network for chemotaxis in Escherichia coli revealed by responses to time-varying stimuli.

Shimizu TS, Tu Y, Berg HC - Mol. Syst. Biol. (2010)

Bottom Line: Feedback near steady state was found to be weak, consistent with strong fluctuations and slow recovery from small perturbations.We found that time derivatives can be computed by the chemotaxis system for input frequencies below 0.006 Hz at 22 degrees C and below 0.018 Hz at 32 degrees C.Our results show how dynamic input-output measurements, time honored in physiology, can serve as powerful tools in deciphering cell-signaling mechanisms.

View Article: PubMed Central - PubMed

Affiliation: Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA 02138, USA.

ABSTRACT
The Escherichia coli chemotaxis-signaling pathway computes time derivatives of chemoeffector concentrations. This network features modules for signal reception/amplification and robust adaptation, with sensing of chemoeffector gradients determined by the way in which these modules are coupled in vivo. We characterized these modules and their coupling by using fluorescence resonance energy transfer to measure intracellular responses to time-varying stimuli. Receptor sensitivity was characterized by step stimuli, the gradient sensitivity by exponential ramp stimuli, and the frequency response by exponential sine-wave stimuli. Analysis of these data revealed the structure of the feedback transfer function linking the amplification and adaptation modules. Feedback near steady state was found to be weak, consistent with strong fluctuations and slow recovery from small perturbations. Gradient sensitivity and frequency response both depended strongly on temperature. We found that time derivatives can be computed by the chemotaxis system for input frequencies below 0.006 Hz at 22 degrees C and below 0.018 Hz at 32 degrees C. Our results show how dynamic input-output measurements, time honored in physiology, can serve as powerful tools in deciphering cell-signaling mechanisms.

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Effects of temperature on sensitivity to gradients and frequency response. (A) Sensitivity to gradients was markedly decreased at 32°C (red triangles; strain TSS178), in which the steady-state activity a0≈1/2. For comparison, the data at 22°C (same as Figure 3A) also are plotted (cyan circles; strains VS104 and TSS178). The slope of the linear fit to the 32°C points near a0 (red curve) was Δa/Δr≈−11 s. (B) The map of F(a) obtained by conversion of the data in (A) has a similar shape as that at 22°C, but the slope at the zero crossing, F ′(a0)≈−0.03, is approximately threefold steeper, implying stronger negative feedback. The red curve is a fit to the same Michaelis–Menten model as in Figure 3B (see text for parameter values and interpretation). (C) The frequency response is also shifted at 32°C (red triangles). The characteristic cutoff frequency νm≈0.018, obtained from the model fit (black curve), is approximately threefold higher than that at 22°C. For comparison, the 22°C data and the corresponding model prediction from Figure 4A also are reproduced here (cyan circles and blue curve). Source data is available for this figure at www.nature.com/msb.
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f5: Effects of temperature on sensitivity to gradients and frequency response. (A) Sensitivity to gradients was markedly decreased at 32°C (red triangles; strain TSS178), in which the steady-state activity a0≈1/2. For comparison, the data at 22°C (same as Figure 3A) also are plotted (cyan circles; strains VS104 and TSS178). The slope of the linear fit to the 32°C points near a0 (red curve) was Δa/Δr≈−11 s. (B) The map of F(a) obtained by conversion of the data in (A) has a similar shape as that at 22°C, but the slope at the zero crossing, F ′(a0)≈−0.03, is approximately threefold steeper, implying stronger negative feedback. The red curve is a fit to the same Michaelis–Menten model as in Figure 3B (see text for parameter values and interpretation). (C) The frequency response is also shifted at 32°C (red triangles). The characteristic cutoff frequency νm≈0.018, obtained from the model fit (black curve), is approximately threefold higher than that at 22°C. For comparison, the 22°C data and the corresponding model prediction from Figure 4A also are reproduced here (cyan circles and blue curve). Source data is available for this figure at www.nature.com/msb.

Mentions: We first apply exponential ramp stimuli—waveforms in which the logarithm of the stimulus level varies linearly with time, at a fixed rate r. It was shown many years ago that during such a stimulus, the kinase output of the pathway changes to a new constant value, ac that is dependent on the applied ramp rate, r (Block et al, 1983). A plot of ac versus r (Figure 5A) can thus be considered as an output of time-derivative computations by the network, and could also be used to study the ‘gradient sensitivity' of bacteria traveling at constant speeds.


A modular gradient-sensing network for chemotaxis in Escherichia coli revealed by responses to time-varying stimuli.

Shimizu TS, Tu Y, Berg HC - Mol. Syst. Biol. (2010)

Effects of temperature on sensitivity to gradients and frequency response. (A) Sensitivity to gradients was markedly decreased at 32°C (red triangles; strain TSS178), in which the steady-state activity a0≈1/2. For comparison, the data at 22°C (same as Figure 3A) also are plotted (cyan circles; strains VS104 and TSS178). The slope of the linear fit to the 32°C points near a0 (red curve) was Δa/Δr≈−11 s. (B) The map of F(a) obtained by conversion of the data in (A) has a similar shape as that at 22°C, but the slope at the zero crossing, F ′(a0)≈−0.03, is approximately threefold steeper, implying stronger negative feedback. The red curve is a fit to the same Michaelis–Menten model as in Figure 3B (see text for parameter values and interpretation). (C) The frequency response is also shifted at 32°C (red triangles). The characteristic cutoff frequency νm≈0.018, obtained from the model fit (black curve), is approximately threefold higher than that at 22°C. For comparison, the 22°C data and the corresponding model prediction from Figure 4A also are reproduced here (cyan circles and blue curve). Source data is available for this figure at www.nature.com/msb.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2913400&req=5

f5: Effects of temperature on sensitivity to gradients and frequency response. (A) Sensitivity to gradients was markedly decreased at 32°C (red triangles; strain TSS178), in which the steady-state activity a0≈1/2. For comparison, the data at 22°C (same as Figure 3A) also are plotted (cyan circles; strains VS104 and TSS178). The slope of the linear fit to the 32°C points near a0 (red curve) was Δa/Δr≈−11 s. (B) The map of F(a) obtained by conversion of the data in (A) has a similar shape as that at 22°C, but the slope at the zero crossing, F ′(a0)≈−0.03, is approximately threefold steeper, implying stronger negative feedback. The red curve is a fit to the same Michaelis–Menten model as in Figure 3B (see text for parameter values and interpretation). (C) The frequency response is also shifted at 32°C (red triangles). The characteristic cutoff frequency νm≈0.018, obtained from the model fit (black curve), is approximately threefold higher than that at 22°C. For comparison, the 22°C data and the corresponding model prediction from Figure 4A also are reproduced here (cyan circles and blue curve). Source data is available for this figure at www.nature.com/msb.
Mentions: We first apply exponential ramp stimuli—waveforms in which the logarithm of the stimulus level varies linearly with time, at a fixed rate r. It was shown many years ago that during such a stimulus, the kinase output of the pathway changes to a new constant value, ac that is dependent on the applied ramp rate, r (Block et al, 1983). A plot of ac versus r (Figure 5A) can thus be considered as an output of time-derivative computations by the network, and could also be used to study the ‘gradient sensitivity' of bacteria traveling at constant speeds.

Bottom Line: Feedback near steady state was found to be weak, consistent with strong fluctuations and slow recovery from small perturbations.We found that time derivatives can be computed by the chemotaxis system for input frequencies below 0.006 Hz at 22 degrees C and below 0.018 Hz at 32 degrees C.Our results show how dynamic input-output measurements, time honored in physiology, can serve as powerful tools in deciphering cell-signaling mechanisms.

View Article: PubMed Central - PubMed

Affiliation: Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA 02138, USA.

ABSTRACT
The Escherichia coli chemotaxis-signaling pathway computes time derivatives of chemoeffector concentrations. This network features modules for signal reception/amplification and robust adaptation, with sensing of chemoeffector gradients determined by the way in which these modules are coupled in vivo. We characterized these modules and their coupling by using fluorescence resonance energy transfer to measure intracellular responses to time-varying stimuli. Receptor sensitivity was characterized by step stimuli, the gradient sensitivity by exponential ramp stimuli, and the frequency response by exponential sine-wave stimuli. Analysis of these data revealed the structure of the feedback transfer function linking the amplification and adaptation modules. Feedback near steady state was found to be weak, consistent with strong fluctuations and slow recovery from small perturbations. Gradient sensitivity and frequency response both depended strongly on temperature. We found that time derivatives can be computed by the chemotaxis system for input frequencies below 0.006 Hz at 22 degrees C and below 0.018 Hz at 32 degrees C. Our results show how dynamic input-output measurements, time honored in physiology, can serve as powerful tools in deciphering cell-signaling mechanisms.

Show MeSH
Related in: MedlinePlus