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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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Calibration of the receptor-module transfer function, G([L],m). (A) FRET responses in kinase activity (points) to step stimuli of the attractant MeAsp were measured in a series of mutants in which the modification state of Tar receptors were fixed by deletions of the cheR and cheB genes. To reveal the response of the Tar receptor, these measurements were conducted in a genetic background in which Tsr and Tap receptors are not expressed. Fits to the allosteric MWC model (equations (6), (7) and (8)), with parameters N=6, KI/KA=0.0062 are shown as solid lines. The gray level of the points and solid curves indicate the modification state of the mutant strain, and is tabulated in the legend (lighter shades of gray for higher modification levels). The blue points and curve, denoted wt in this figure, is the strain VS178, which has the same receptor complement as the other mutants (Tsr−Tap−), but retains the wild-type genes for CheR and CheB. Kinase activity is shown normalized to the pre-stimulus value for the strain VS104. (B) Values of fm, obtained for each modification state represented in (A), plotted against the number of modified sites. The data for modification states containing only glutamate (E) and glutamine (Q) residues (black points) fell on a straight line (dotted) when plotted as a function of the number of E → Q transitions (nE → Q; black points). The data for modification states containing only Q's and methylated glutamates (Em) fell on a different straight line (dashed), when plotted as a function of the number of Q → Em transitions (nQ → Em; magenta points). The values for the two extreme methylation levels, EEEE (corresponding to m=0) and EmEmEmEm (corresponding to m=4), were obtained by extrapolation of the two straight lines, as they could not be obtained directly from fits to the FRET data (cells with the Tar population fixed in this state did not respond to any concentration of MeAsp, as is seen in (A)). The solid line connecting these two extreme states reveals the dependence of fm on the E → Em transitions (nE → Em; gray points), and the CheR+CheB+ strain VS178 (blue point, denoted wt) falls on this line, as expected. When fitted by equation (9), this line yields the parameters m0≈0.5 and α≈2 kT used throughout this study. Source data is available for this figure at www.nature.com/msb.
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f7: Calibration of the receptor-module transfer function, G([L],m). (A) FRET responses in kinase activity (points) to step stimuli of the attractant MeAsp were measured in a series of mutants in which the modification state of Tar receptors were fixed by deletions of the cheR and cheB genes. To reveal the response of the Tar receptor, these measurements were conducted in a genetic background in which Tsr and Tap receptors are not expressed. Fits to the allosteric MWC model (equations (6), (7) and (8)), with parameters N=6, KI/KA=0.0062 are shown as solid lines. The gray level of the points and solid curves indicate the modification state of the mutant strain, and is tabulated in the legend (lighter shades of gray for higher modification levels). The blue points and curve, denoted wt in this figure, is the strain VS178, which has the same receptor complement as the other mutants (Tsr−Tap−), but retains the wild-type genes for CheR and CheB. Kinase activity is shown normalized to the pre-stimulus value for the strain VS104. (B) Values of fm, obtained for each modification state represented in (A), plotted against the number of modified sites. The data for modification states containing only glutamate (E) and glutamine (Q) residues (black points) fell on a straight line (dotted) when plotted as a function of the number of E → Q transitions (nE → Q; black points). The data for modification states containing only Q's and methylated glutamates (Em) fell on a different straight line (dashed), when plotted as a function of the number of Q → Em transitions (nQ → Em; magenta points). The values for the two extreme methylation levels, EEEE (corresponding to m=0) and EmEmEmEm (corresponding to m=4), were obtained by extrapolation of the two straight lines, as they could not be obtained directly from fits to the FRET data (cells with the Tar population fixed in this state did not respond to any concentration of MeAsp, as is seen in (A)). The solid line connecting these two extreme states reveals the dependence of fm on the E → Em transitions (nE → Em; gray points), and the CheR+CheB+ strain VS178 (blue point, denoted wt) falls on this line, as expected. When fitted by equation (9), this line yields the parameters m0≈0.5 and α≈2 kT used throughout this study. Source data is available for this figure at www.nature.com/msb.

Mentions: As Δf (ac) is independent of the degree of receptor cooperativity, N, we can use equation (3) to extract from our experimental data an estimate for the parameter N. Although it recently has been reported (Endres et al, 2008) that the degree of receptor cooperativity seems, under certain conditions, to depend on the modification level of receptors (i.e. that N could depend on m, which is changing during our ramp measurements), the fact that we observe a constant activity during exponential ramps suggests that such changes in the organization of the receptor complex occur on time scales considerably slower than that of our time-varying stimuli. We, therefore, apply equation (3) to infer a single value of N from the set of t1 values extracted from our ramp-response data. Although accurate determination of t1 is difficult, because its estimation is more sensitive to experimental noise, the approximate linear scaling of the product rt1∼N−1 Δf (ac) follows immediately from equation (3), and is more robust to noise than t1 itself (as the factor r conveniently diminishes the error more strongly in which Δac is small, and errors in estimating t1 tend to be large). In Figure 6B, we plot rt1 against Δf (ac), in which the slope of the fitted line gives an estimate N∼4.9, which is in satisfactory agreement with the more reliable value of N=6, estimated through fits to dose–response curves to step stimuli (Mello and Tu, 2007; see also Materials and methods and Figure 7).


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)

Calibration of the receptor-module transfer function, G([L],m). (A) FRET responses in kinase activity (points) to step stimuli of the attractant MeAsp were measured in a series of mutants in which the modification state of Tar receptors were fixed by deletions of the cheR and cheB genes. To reveal the response of the Tar receptor, these measurements were conducted in a genetic background in which Tsr and Tap receptors are not expressed. Fits to the allosteric MWC model (equations (6), (7) and (8)), with parameters N=6, KI/KA=0.0062 are shown as solid lines. The gray level of the points and solid curves indicate the modification state of the mutant strain, and is tabulated in the legend (lighter shades of gray for higher modification levels). The blue points and curve, denoted wt in this figure, is the strain VS178, which has the same receptor complement as the other mutants (Tsr−Tap−), but retains the wild-type genes for CheR and CheB. Kinase activity is shown normalized to the pre-stimulus value for the strain VS104. (B) Values of fm, obtained for each modification state represented in (A), plotted against the number of modified sites. The data for modification states containing only glutamate (E) and glutamine (Q) residues (black points) fell on a straight line (dotted) when plotted as a function of the number of E → Q transitions (nE → Q; black points). The data for modification states containing only Q's and methylated glutamates (Em) fell on a different straight line (dashed), when plotted as a function of the number of Q → Em transitions (nQ → Em; magenta points). The values for the two extreme methylation levels, EEEE (corresponding to m=0) and EmEmEmEm (corresponding to m=4), were obtained by extrapolation of the two straight lines, as they could not be obtained directly from fits to the FRET data (cells with the Tar population fixed in this state did not respond to any concentration of MeAsp, as is seen in (A)). The solid line connecting these two extreme states reveals the dependence of fm on the E → Em transitions (nE → Em; gray points), and the CheR+CheB+ strain VS178 (blue point, denoted wt) falls on this line, as expected. When fitted by equation (9), this line yields the parameters m0≈0.5 and α≈2 kT used throughout this study. 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

f7: Calibration of the receptor-module transfer function, G([L],m). (A) FRET responses in kinase activity (points) to step stimuli of the attractant MeAsp were measured in a series of mutants in which the modification state of Tar receptors were fixed by deletions of the cheR and cheB genes. To reveal the response of the Tar receptor, these measurements were conducted in a genetic background in which Tsr and Tap receptors are not expressed. Fits to the allosteric MWC model (equations (6), (7) and (8)), with parameters N=6, KI/KA=0.0062 are shown as solid lines. The gray level of the points and solid curves indicate the modification state of the mutant strain, and is tabulated in the legend (lighter shades of gray for higher modification levels). The blue points and curve, denoted wt in this figure, is the strain VS178, which has the same receptor complement as the other mutants (Tsr−Tap−), but retains the wild-type genes for CheR and CheB. Kinase activity is shown normalized to the pre-stimulus value for the strain VS104. (B) Values of fm, obtained for each modification state represented in (A), plotted against the number of modified sites. The data for modification states containing only glutamate (E) and glutamine (Q) residues (black points) fell on a straight line (dotted) when plotted as a function of the number of E → Q transitions (nE → Q; black points). The data for modification states containing only Q's and methylated glutamates (Em) fell on a different straight line (dashed), when plotted as a function of the number of Q → Em transitions (nQ → Em; magenta points). The values for the two extreme methylation levels, EEEE (corresponding to m=0) and EmEmEmEm (corresponding to m=4), were obtained by extrapolation of the two straight lines, as they could not be obtained directly from fits to the FRET data (cells with the Tar population fixed in this state did not respond to any concentration of MeAsp, as is seen in (A)). The solid line connecting these two extreme states reveals the dependence of fm on the E → Em transitions (nE → Em; gray points), and the CheR+CheB+ strain VS178 (blue point, denoted wt) falls on this line, as expected. When fitted by equation (9), this line yields the parameters m0≈0.5 and α≈2 kT used throughout this study. Source data is available for this figure at www.nature.com/msb.
Mentions: As Δf (ac) is independent of the degree of receptor cooperativity, N, we can use equation (3) to extract from our experimental data an estimate for the parameter N. Although it recently has been reported (Endres et al, 2008) that the degree of receptor cooperativity seems, under certain conditions, to depend on the modification level of receptors (i.e. that N could depend on m, which is changing during our ramp measurements), the fact that we observe a constant activity during exponential ramps suggests that such changes in the organization of the receptor complex occur on time scales considerably slower than that of our time-varying stimuli. We, therefore, apply equation (3) to infer a single value of N from the set of t1 values extracted from our ramp-response data. Although accurate determination of t1 is difficult, because its estimation is more sensitive to experimental noise, the approximate linear scaling of the product rt1∼N−1 Δf (ac) follows immediately from equation (3), and is more robust to noise than t1 itself (as the factor r conveniently diminishes the error more strongly in which Δac is small, and errors in estimating t1 tend to be large). In Figure 6B, we plot rt1 against Δf (ac), in which the slope of the fitted line gives an estimate N∼4.9, which is in satisfactory agreement with the more reliable value of N=6, estimated through fits to dose–response curves to step stimuli (Mello and Tu, 2007; see also Materials and methods and Figure 7).

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