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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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Gradient sensitivity and the feedback transfer function F(a). (A) By measuring exponential ramp responses in the manner of Figure 2A–H over a range of ramp rates r, we constructed a gradient-sensitivity curve, relating the kinase-activity a, to the steepness of the temporal gradient experienced by cells. The results for two FRET strains considered wild type for chemotaxis (VS104, an RP437 derivative, cyan circles; TSS178, an AW405 derivative, dark blue squares) were essentially identical, and collapsed on to a sigmoidal curve with a steep region near r=0 (slope of fitted line, Δa/Δr≈−30 s). The steady-state activity in the absence of stimuli (i.e. at r=0) was found to be a0≈1/3. The inset in (A) is an expanded view about the point (r=0, a=a0), showing the absence of thresholds, at least down to r=±0.001 s−1. (B) Using our model, the data of (A) can be used to map the feedback transfer function F(a). The steady-state relation r=αF(ac) implies that we can rescale the r axis by the constant factor α, obtained from our calibration of the receptor-module transfer function G, and invert the axes about (r=0, a=a0) to obtain F(a). The shallow slope near this origin, F ′(a0)≈−0.01, implies weak negative feedback. The blue curve is a fit of a Michaelis–Menten reaction scheme ; see text for interpretation of parameters. Source data is available for this figure at www.nature.com/msb.
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f3: Gradient sensitivity and the feedback transfer function F(a). (A) By measuring exponential ramp responses in the manner of Figure 2A–H over a range of ramp rates r, we constructed a gradient-sensitivity curve, relating the kinase-activity a, to the steepness of the temporal gradient experienced by cells. The results for two FRET strains considered wild type for chemotaxis (VS104, an RP437 derivative, cyan circles; TSS178, an AW405 derivative, dark blue squares) were essentially identical, and collapsed on to a sigmoidal curve with a steep region near r=0 (slope of fitted line, Δa/Δr≈−30 s). The steady-state activity in the absence of stimuli (i.e. at r=0) was found to be a0≈1/3. The inset in (A) is an expanded view about the point (r=0, a=a0), showing the absence of thresholds, at least down to r=±0.001 s−1. (B) Using our model, the data of (A) can be used to map the feedback transfer function F(a). The steady-state relation r=αF(ac) implies that we can rescale the r axis by the constant factor α, obtained from our calibration of the receptor-module transfer function G, and invert the axes about (r=0, a=a0) to obtain F(a). The shallow slope near this origin, F ′(a0)≈−0.01, implies weak negative feedback. The blue curve is a fit of a Michaelis–Menten reaction scheme ; see text for interpretation of parameters. Source data is available for this figure at www.nature.com/msb.

Mentions: The constant response in kinase-activity ac that is reached during exponential ramps (Figure 2A–H) can be viewed as the output of time-derivative computations by the chemotaxis network. As the receptor module responds to the logarithmic change of the input signal (Tu et al, 2008; Kalinin et al, 2009), the relevant time derivative is that of the logarithm of input, that is dln[L]/dt, which corresponds in these experiments to the exponential ramp rate r. We therefore conducted exponential ramp-response measurements of the type depicted in Figure 2A and B over a range of ramp rates r. The asymptotic kinase response, ac, obtained through such measurements, is plotted in Figure 3A as a function of r. The steady-state activity in the absence of stimuli (i.e. at r=0) was found to be a0≈1/3. This plot reveals the sensitivity of E. coli to temporal gradients of MeAsp, and the overall shape is sigmoidal, with a steep slope (Δac/Δr≈−30 s) near r=0. This implies that the system is tuned to respond sensitively to very shallow gradients, but it has a relatively narrow dynamic range: at greater absolute ramp rates, it becomes largely insensitive to changes in the gradient. If we define the slope Δac/Δr as the gradient sensitivity, its value is large and nearly constant in the small interval near r=0, but decays rapidly outside of it. Importantly, we observed no response thresholds at small ramp rates (Figure 3A, inset), in contrast to Block et al (1983), in which it was found that the ramp-response magnitude reached zero at low ramp rates (r≈0.005 for up ramps, r≈0.01 for down ramps).


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)

Gradient sensitivity and the feedback transfer function F(a). (A) By measuring exponential ramp responses in the manner of Figure 2A–H over a range of ramp rates r, we constructed a gradient-sensitivity curve, relating the kinase-activity a, to the steepness of the temporal gradient experienced by cells. The results for two FRET strains considered wild type for chemotaxis (VS104, an RP437 derivative, cyan circles; TSS178, an AW405 derivative, dark blue squares) were essentially identical, and collapsed on to a sigmoidal curve with a steep region near r=0 (slope of fitted line, Δa/Δr≈−30 s). The steady-state activity in the absence of stimuli (i.e. at r=0) was found to be a0≈1/3. The inset in (A) is an expanded view about the point (r=0, a=a0), showing the absence of thresholds, at least down to r=±0.001 s−1. (B) Using our model, the data of (A) can be used to map the feedback transfer function F(a). The steady-state relation r=αF(ac) implies that we can rescale the r axis by the constant factor α, obtained from our calibration of the receptor-module transfer function G, and invert the axes about (r=0, a=a0) to obtain F(a). The shallow slope near this origin, F ′(a0)≈−0.01, implies weak negative feedback. The blue curve is a fit of a Michaelis–Menten reaction scheme ; see text for interpretation of parameters. Source data is available for this figure at www.nature.com/msb.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Gradient sensitivity and the feedback transfer function F(a). (A) By measuring exponential ramp responses in the manner of Figure 2A–H over a range of ramp rates r, we constructed a gradient-sensitivity curve, relating the kinase-activity a, to the steepness of the temporal gradient experienced by cells. The results for two FRET strains considered wild type for chemotaxis (VS104, an RP437 derivative, cyan circles; TSS178, an AW405 derivative, dark blue squares) were essentially identical, and collapsed on to a sigmoidal curve with a steep region near r=0 (slope of fitted line, Δa/Δr≈−30 s). The steady-state activity in the absence of stimuli (i.e. at r=0) was found to be a0≈1/3. The inset in (A) is an expanded view about the point (r=0, a=a0), showing the absence of thresholds, at least down to r=±0.001 s−1. (B) Using our model, the data of (A) can be used to map the feedback transfer function F(a). The steady-state relation r=αF(ac) implies that we can rescale the r axis by the constant factor α, obtained from our calibration of the receptor-module transfer function G, and invert the axes about (r=0, a=a0) to obtain F(a). The shallow slope near this origin, F ′(a0)≈−0.01, implies weak negative feedback. The blue curve is a fit of a Michaelis–Menten reaction scheme ; see text for interpretation of parameters. Source data is available for this figure at www.nature.com/msb.
Mentions: The constant response in kinase-activity ac that is reached during exponential ramps (Figure 2A–H) can be viewed as the output of time-derivative computations by the chemotaxis network. As the receptor module responds to the logarithmic change of the input signal (Tu et al, 2008; Kalinin et al, 2009), the relevant time derivative is that of the logarithm of input, that is dln[L]/dt, which corresponds in these experiments to the exponential ramp rate r. We therefore conducted exponential ramp-response measurements of the type depicted in Figure 2A and B over a range of ramp rates r. The asymptotic kinase response, ac, obtained through such measurements, is plotted in Figure 3A as a function of r. The steady-state activity in the absence of stimuli (i.e. at r=0) was found to be a0≈1/3. This plot reveals the sensitivity of E. coli to temporal gradients of MeAsp, and the overall shape is sigmoidal, with a steep slope (Δac/Δr≈−30 s) near r=0. This implies that the system is tuned to respond sensitively to very shallow gradients, but it has a relatively narrow dynamic range: at greater absolute ramp rates, it becomes largely insensitive to changes in the gradient. If we define the slope Δac/Δr as the gradient sensitivity, its value is large and nearly constant in the small interval near r=0, but decays rapidly outside of it. Importantly, we observed no response thresholds at small ramp rates (Figure 3A, inset), in contrast to Block et al (1983), in which it was found that the ramp-response magnitude reached zero at low ramp rates (r≈0.005 for up ramps, r≈0.01 for down ramps).

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