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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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Effect of Adaptation Time on Chemotactic EfficiencyChemotaxis was simulated by assuming that the signaling pathway was approximated by the system of Figure 2B.(A) Different choices of k, and hence different adaptation times, result in varying chemotaxis efficiency. For example, cells with cutoff frequencies of k = 0.04 rad/s and k = 14 rad/s moved approximately 90 μm and 70 μm along the chemoattractant gradient. In contrast, a cell with a cutoff frequency of 3.4 rad/s moved approximately 250 μm along the gradient.(B) These simulations were repeated for a large range of cutoff frequencies. The resulting frequency-dependent chemotactic performance was fitted with a Rayleigh function to estimate the optimal cutoff frequency for chemotaxis (red dashed line). Chemotactic performance was based on the final position along the gradient after 80 s. Each point represents the average of 500 simulation runs, and vertical bars indicate mean plus or minus standard error of the mean. Rotational and translational diffusion coefficients of 0.16 rad2/s and 2.2 × 10−1 μm2/s, respectively, were used. Nominal parameters used: u = 20 μm/s, RT = 2.5 μM, Kd = k−/k+ = 100 μM, L0 = 0.01 μM, and g = 0.2 μM/ μm.
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pcbi-0020154-g003: Effect of Adaptation Time on Chemotactic EfficiencyChemotaxis was simulated by assuming that the signaling pathway was approximated by the system of Figure 2B.(A) Different choices of k, and hence different adaptation times, result in varying chemotaxis efficiency. For example, cells with cutoff frequencies of k = 0.04 rad/s and k = 14 rad/s moved approximately 90 μm and 70 μm along the chemoattractant gradient. In contrast, a cell with a cutoff frequency of 3.4 rad/s moved approximately 250 μm along the gradient.(B) These simulations were repeated for a large range of cutoff frequencies. The resulting frequency-dependent chemotactic performance was fitted with a Rayleigh function to estimate the optimal cutoff frequency for chemotaxis (red dashed line). Chemotactic performance was based on the final position along the gradient after 80 s. Each point represents the average of 500 simulation runs, and vertical bars indicate mean plus or minus standard error of the mean. Rotational and translational diffusion coefficients of 0.16 rad2/s and 2.2 × 10−1 μm2/s, respectively, were used. Nominal parameters used: u = 20 μm/s, RT = 2.5 μM, Kd = k−/k+ = 100 μM, L0 = 0.01 μM, and g = 0.2 μM/ μm.

Mentions: Our simulations indicate a biphasic response: cells with a particular filter-cutoff frequency move farther up the chemoattractant gradient than cells with either higher or lower frequency cutoffs (Figure 3A). Moreover, the range of frequencies for which optimal chemotaxis efficiency is observed was narrow (Figure 3B). For example, an approximately 2-fold increase in cutoff frequency from the optimal (from 3.4 to 7.0 rad/s) significantly decreased the distance traveled (249 ± 13 versus 169 ± 10 μm, SEM, p < 10−5 using Student's t-test). Similarly, a 4-fold decrease in the cutoff frequency (from 3.4 to 0.8 rad/s) also reduced the distance traveled, though less significantly (213 ± 15 μm, SEM, p < 0.04). These trends are also observed in signaling models that included higher order rolloff (Figure S1). These data illustrate that to achieve optimal chemotaxis, it is necessary to have optimal or near-optimal noise-filtering capabilities.


Optimal noise filtering in the chemotactic response of Escherichia coli.

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

Effect of Adaptation Time on Chemotactic EfficiencyChemotaxis was simulated by assuming that the signaling pathway was approximated by the system of Figure 2B.(A) Different choices of k, and hence different adaptation times, result in varying chemotaxis efficiency. For example, cells with cutoff frequencies of k = 0.04 rad/s and k = 14 rad/s moved approximately 90 μm and 70 μm along the chemoattractant gradient. In contrast, a cell with a cutoff frequency of 3.4 rad/s moved approximately 250 μm along the gradient.(B) These simulations were repeated for a large range of cutoff frequencies. The resulting frequency-dependent chemotactic performance was fitted with a Rayleigh function to estimate the optimal cutoff frequency for chemotaxis (red dashed line). Chemotactic performance was based on the final position along the gradient after 80 s. Each point represents the average of 500 simulation runs, and vertical bars indicate mean plus or minus standard error of the mean. Rotational and translational diffusion coefficients of 0.16 rad2/s and 2.2 × 10−1 μm2/s, respectively, were used. Nominal parameters used: u = 20 μm/s, RT = 2.5 μM, Kd = k−/k+ = 100 μM, L0 = 0.01 μM, and g = 0.2 μM/ μm.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-0020154-g003: Effect of Adaptation Time on Chemotactic EfficiencyChemotaxis was simulated by assuming that the signaling pathway was approximated by the system of Figure 2B.(A) Different choices of k, and hence different adaptation times, result in varying chemotaxis efficiency. For example, cells with cutoff frequencies of k = 0.04 rad/s and k = 14 rad/s moved approximately 90 μm and 70 μm along the chemoattractant gradient. In contrast, a cell with a cutoff frequency of 3.4 rad/s moved approximately 250 μm along the gradient.(B) These simulations were repeated for a large range of cutoff frequencies. The resulting frequency-dependent chemotactic performance was fitted with a Rayleigh function to estimate the optimal cutoff frequency for chemotaxis (red dashed line). Chemotactic performance was based on the final position along the gradient after 80 s. Each point represents the average of 500 simulation runs, and vertical bars indicate mean plus or minus standard error of the mean. Rotational and translational diffusion coefficients of 0.16 rad2/s and 2.2 × 10−1 μm2/s, respectively, were used. Nominal parameters used: u = 20 μm/s, RT = 2.5 μM, Kd = k−/k+ = 100 μM, L0 = 0.01 μM, and g = 0.2 μM/ μm.
Mentions: Our simulations indicate a biphasic response: cells with a particular filter-cutoff frequency move farther up the chemoattractant gradient than cells with either higher or lower frequency cutoffs (Figure 3A). Moreover, the range of frequencies for which optimal chemotaxis efficiency is observed was narrow (Figure 3B). For example, an approximately 2-fold increase in cutoff frequency from the optimal (from 3.4 to 7.0 rad/s) significantly decreased the distance traveled (249 ± 13 versus 169 ± 10 μm, SEM, p < 10−5 using Student's t-test). Similarly, a 4-fold decrease in the cutoff frequency (from 3.4 to 0.8 rad/s) also reduced the distance traveled, though less significantly (213 ± 15 μm, SEM, p < 0.04). These trends are also observed in signaling models that included higher order rolloff (Figure S1). These data illustrate that to achieve optimal chemotaxis, it is necessary to have optimal or near-optimal noise-filtering capabilities.

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