Optimal noise filtering in the chemotactic response of Escherichia coli.
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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.
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Affiliation: Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, Maryland, United States of America.
ABSTRACT
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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. Related in: MedlinePlus |
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Mentions: The optimal cutoff frequency for chemoattractant estimation represents the averaging time that best compromises the tradeoff between noise attenuation and signal amplification. This is illustrated in Figure 7A, which highlights the contributions of the noise and signal power spectral densities (PSDs) to this tradeoff. As binding noise increases, the noise PSD shifts upward, and the optimal cutoff frequency (ωcf) decreases, thus yielding a longer time over which to average ligand measurements so that the additional noise may be attenuated. This trend was seen in the chemotaxis simulations (Figure 4D). As fluctuations of the signal increase (e.g., by increasing the effect of rotational diffusion), the signal PSD shifts upward, and ωcf increases to yield shorter averaging times that are necessary for observing the more rapidly changing signal; see Figure 4E. |
View Article: PubMed Central - PubMed
Affiliation: Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, Maryland, United States of America.