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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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Model of E. coli Signaling NetworkA model of the bacterial signaling network is shown for a cluster of N receptors with M methylation sites each. The receptor cluster can exist in a ligand bound or unbound form, each with up to a total of NM sites methylated. The methylation (demethylation) rate of a particular state is proportional to the probability of the state being inactive (active).
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pcbi-0020154-g008: Model of E. coli Signaling NetworkA model of the bacterial signaling network is shown for a cluster of N receptors with M methylation sites each. The receptor cluster can exist in a ligand bound or unbound form, each with up to a total of NM sites methylated. The methylation (demethylation) rate of a particular state is proportional to the probability of the state being inactive (active).

Mentions: We developed a model of the E. coli signal transduction network combining the basic receptor-modification model of Barkai and Leibler [17] with more recent models of receptor clustering [19,35]. We assume the cell senses ligand with a cluster of N receptors, each with M methylation sites. In general, each receptor in the complex can exist in either an “on” or “off” state and can be either ligand-bound or ligand-unbound. The probability of a receptor being on depends on the free energy difference between the on and off states of the receptor and on that of neighboring receptors. Here, we assume the entire cluster is either occupied or unoccupied by ligand and that the free energy difference between the on and off states of each receptor in the cluster is dictated by the cluster's occupancy (not the occupancy of the individual receptors). We treat the cluster as one system with 2(NM + 1) states: ligand-unbound with j∈{0,1,2,...,NM} sites methylated (denoted Rj) or ligand-bound with j sites methylated (denoted RLj); see Figure 8.


Optimal noise filtering in the chemotactic response of Escherichia coli.

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

Model of E. coli Signaling NetworkA model of the bacterial signaling network is shown for a cluster of N receptors with M methylation sites each. The receptor cluster can exist in a ligand bound or unbound form, each with up to a total of NM sites methylated. The methylation (demethylation) rate of a particular state is proportional to the probability of the state being inactive (active).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-0020154-g008: Model of E. coli Signaling NetworkA model of the bacterial signaling network is shown for a cluster of N receptors with M methylation sites each. The receptor cluster can exist in a ligand bound or unbound form, each with up to a total of NM sites methylated. The methylation (demethylation) rate of a particular state is proportional to the probability of the state being inactive (active).
Mentions: We developed a model of the E. coli signal transduction network combining the basic receptor-modification model of Barkai and Leibler [17] with more recent models of receptor clustering [19,35]. We assume the cell senses ligand with a cluster of N receptors, each with M methylation sites. In general, each receptor in the complex can exist in either an “on” or “off” state and can be either ligand-bound or ligand-unbound. The probability of a receptor being on depends on the free energy difference between the on and off states of the receptor and on that of neighboring receptors. Here, we assume the entire cluster is either occupied or unoccupied by ligand and that the free energy difference between the on and off states of each receptor in the cluster is dictated by the cluster's occupancy (not the occupancy of the individual receptors). We treat the cluster as one system with 2(NM + 1) states: ligand-unbound with j∈{0,1,2,...,NM} sites methylated (denoted Rj) or ligand-bound with j sites methylated (denoted RLj); see Figure 8.

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