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Optimal noise filtering in the chemotactic response of Escherichia coli.

Andrews BW, Yi TM, Iglesias PA - PLoS Comput. Biol. (2006)

Bottom Line: Through simulation, we first show that the cutoff frequency has a dramatic effect on the chemotactic efficiency of the cell.There was good agreement between the theory, simulations, and published experimental data.This paper furnishes a simple quantitative framework for interpreting many of the key notions about bacterial chemotaxis, and, more generally, it highlights the constraints on biological systems imposed by noise.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, Maryland, United States of America.

ABSTRACT
Information-carrying signals in the real world are often obscured by noise. A challenge for any system is to filter the signal from the corrupting noise. This task is particularly acute for the signal transduction network that mediates bacterial chemotaxis, because the signals are subtle, the noise arising from stochastic fluctuations is substantial, and the system is effectively acting as a differentiator which amplifies noise. Here, we investigated the filtering properties of this biological system. Through simulation, we first show that the cutoff frequency has a dramatic effect on the chemotactic efficiency of the cell. Then, using a mathematical model to describe the signal, noise, and system, we formulated and solved an optimal filtering problem to determine the cutoff frequency that bests separates the low-frequency signal from the high-frequency noise. There was good agreement between the theory, simulations, and published experimental data. Finally, we propose that an elegant implementation of the optimal filter in combination with a differentiator can be achieved via an integral control system. This paper furnishes a simple quantitative framework for interpreting many of the key notions about bacterial chemotaxis, and, more generally, it highlights the constraints on biological systems imposed by noise.

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Frequency Dependence of the Signaling Response(A) The frequency-dependent filtering responses for the optimal filter (red solid line) and experimental data (green dashed line; [20]). The experimental data, obtained as the Fourier transform of the response of cells to an impulse of chemoattractant [20] and adjusted to remove the differentiator and downstream phosphorylation cascade (Materials and Methods), also exhibits the characteristics of a low-pass filter. Parameters used for the theoretical filter shown here are L0 = 1 μM, g = 1.5 μM/μm, and u = 20 μm/s. Also included is the frequency response of the model (blue dashed line) linearized about a ligand input of L0 = 1 μM. The dotted black line shows a dependency of (frequency)−1.(B) The predicted optimal cutoff frequency is compared with that of the filter for a range of chemoattractant gradients and mean concentrations. The line through which both surfaces intersect represents the chemoattractant profiles for which E. coli filters out disturbances optimally with respect to the parameters used for the model.(C) Plot of the concentration gradient against mean concentration for the points where the surfaces in (B) intersect. The linear dependence suggests that E. coli is conditioned for optimal filtering in chemoattractant concentration profiles of constant relative gradient.
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pcbi-0020154-g006: Frequency Dependence of the Signaling Response(A) The frequency-dependent filtering responses for the optimal filter (red solid line) and experimental data (green dashed line; [20]). The experimental data, obtained as the Fourier transform of the response of cells to an impulse of chemoattractant [20] and adjusted to remove the differentiator and downstream phosphorylation cascade (Materials and Methods), also exhibits the characteristics of a low-pass filter. Parameters used for the theoretical filter shown here are L0 = 1 μM, g = 1.5 μM/μm, and u = 20 μm/s. Also included is the frequency response of the model (blue dashed line) linearized about a ligand input of L0 = 1 μM. The dotted black line shows a dependency of (frequency)−1.(B) The predicted optimal cutoff frequency is compared with that of the filter for a range of chemoattractant gradients and mean concentrations. The line through which both surfaces intersect represents the chemoattractant profiles for which E. coli filters out disturbances optimally with respect to the parameters used for the model.(C) Plot of the concentration gradient against mean concentration for the points where the surfaces in (B) intersect. The linear dependence suggests that E. coli is conditioned for optimal filtering in chemoattractant concentration profiles of constant relative gradient.

Mentions: We next determined the degree to which the cutoff frequencies of the optimal filter for chemoattractant estimation matched the frequency-dependent behavior observed experimentally. To this end we used published data describing the behavior of the E. coli chemotactic system [20,27], adjusted to comprise only the primary filtering component by removing the differentiator and the phosphorylation cascade modeled in [28] (Materials and Methods). Additionally, we used our full model of the E. coli signaling pathway as a proxy for the wild-type E. coli chemotaxis behavior. We linearized the model (valid for moderately large step changes in ligand, Materials and Methods) and computed the corresponding low-pass filter component to compare with our theoretical results. Linearizations of other models [17] also revealed similar low-pass filtering characteristics (Materials and Methods). Interestingly, the cutoff frequencies observed from the experimental data and calculated from the model matched reasonably well the theoretical optimal value for a particular gradient and ligand concentration (Figure 6A). This agreement suggests that the chemotaxis signal transduction pathway in E. coli is acting as an optimal filter. It should also be noted that other experimental evidence suggests lower cutoff frequencies (adaptation times on the order of several minutes) [13]. This may be due to strain differences or saturation of the methylation machinery from large ligand stimulants.


Optimal noise filtering in the chemotactic response of Escherichia coli.

Andrews BW, Yi TM, Iglesias PA - PLoS Comput. Biol. (2006)

Frequency Dependence of the Signaling Response(A) The frequency-dependent filtering responses for the optimal filter (red solid line) and experimental data (green dashed line; [20]). The experimental data, obtained as the Fourier transform of the response of cells to an impulse of chemoattractant [20] and adjusted to remove the differentiator and downstream phosphorylation cascade (Materials and Methods), also exhibits the characteristics of a low-pass filter. Parameters used for the theoretical filter shown here are L0 = 1 μM, g = 1.5 μM/μm, and u = 20 μm/s. Also included is the frequency response of the model (blue dashed line) linearized about a ligand input of L0 = 1 μM. The dotted black line shows a dependency of (frequency)−1.(B) The predicted optimal cutoff frequency is compared with that of the filter for a range of chemoattractant gradients and mean concentrations. The line through which both surfaces intersect represents the chemoattractant profiles for which E. coli filters out disturbances optimally with respect to the parameters used for the model.(C) Plot of the concentration gradient against mean concentration for the points where the surfaces in (B) intersect. The linear dependence suggests that E. coli is conditioned for optimal filtering in chemoattractant concentration profiles of constant relative gradient.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC1636674&req=5

pcbi-0020154-g006: Frequency Dependence of the Signaling Response(A) The frequency-dependent filtering responses for the optimal filter (red solid line) and experimental data (green dashed line; [20]). The experimental data, obtained as the Fourier transform of the response of cells to an impulse of chemoattractant [20] and adjusted to remove the differentiator and downstream phosphorylation cascade (Materials and Methods), also exhibits the characteristics of a low-pass filter. Parameters used for the theoretical filter shown here are L0 = 1 μM, g = 1.5 μM/μm, and u = 20 μm/s. Also included is the frequency response of the model (blue dashed line) linearized about a ligand input of L0 = 1 μM. The dotted black line shows a dependency of (frequency)−1.(B) The predicted optimal cutoff frequency is compared with that of the filter for a range of chemoattractant gradients and mean concentrations. The line through which both surfaces intersect represents the chemoattractant profiles for which E. coli filters out disturbances optimally with respect to the parameters used for the model.(C) Plot of the concentration gradient against mean concentration for the points where the surfaces in (B) intersect. The linear dependence suggests that E. coli is conditioned for optimal filtering in chemoattractant concentration profiles of constant relative gradient.
Mentions: We next determined the degree to which the cutoff frequencies of the optimal filter for chemoattractant estimation matched the frequency-dependent behavior observed experimentally. To this end we used published data describing the behavior of the E. coli chemotactic system [20,27], adjusted to comprise only the primary filtering component by removing the differentiator and the phosphorylation cascade modeled in [28] (Materials and Methods). Additionally, we used our full model of the E. coli signaling pathway as a proxy for the wild-type E. coli chemotaxis behavior. We linearized the model (valid for moderately large step changes in ligand, Materials and Methods) and computed the corresponding low-pass filter component to compare with our theoretical results. Linearizations of other models [17] also revealed similar low-pass filtering characteristics (Materials and Methods). Interestingly, the cutoff frequencies observed from the experimental data and calculated from the model matched reasonably well the theoretical optimal value for a particular gradient and ligand concentration (Figure 6A). This agreement suggests that the chemotaxis signal transduction pathway in E. coli is acting as an optimal filter. It should also be noted that other experimental evidence suggests lower cutoff frequencies (adaptation times on the order of several minutes) [13]. This may be due to strain differences or saturation of the methylation machinery from large ligand stimulants.

Bottom Line: Through simulation, we first show that the cutoff frequency has a dramatic effect on the chemotactic efficiency of the cell.There was good agreement between the theory, simulations, and published experimental data.This paper furnishes a simple quantitative framework for interpreting many of the key notions about bacterial chemotaxis, and, more generally, it highlights the constraints on biological systems imposed by noise.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, Maryland, United States of America.

ABSTRACT
Information-carrying signals in the real world are often obscured by noise. A challenge for any system is to filter the signal from the corrupting noise. This task is particularly acute for the signal transduction network that mediates bacterial chemotaxis, because the signals are subtle, the noise arising from stochastic fluctuations is substantial, and the system is effectively acting as a differentiator which amplifies noise. Here, we investigated the filtering properties of this biological system. Through simulation, we first show that the cutoff frequency has a dramatic effect on the chemotactic efficiency of the cell. Then, using a mathematical model to describe the signal, noise, and system, we formulated and solved an optimal filtering problem to determine the cutoff frequency that bests separates the low-frequency signal from the high-frequency noise. There was good agreement between the theory, simulations, and published experimental data. Finally, we propose that an elegant implementation of the optimal filter in combination with a differentiator can be achieved via an integral control system. This paper furnishes a simple quantitative framework for interpreting many of the key notions about bacterial chemotaxis, and, more generally, it highlights the constraints on biological systems imposed by noise.

Show MeSH
Related in: MedlinePlus