Optimal Noise Filtering in the Chemotactic Response of Escherichia coli

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.

Relationship between cellular response and behavioral variability in bacterial chemotaxis

“…Methylation and demethylation are complex biochemical processes that involve the enhanced recruitment of CheR and CheB to the receptors by a tethering site that is distinct from methylation sites (14,15). As in previous models of chemotaxis (7,(16)(17)(18)(19)(20)(21)(22)(23), we coarse-grain the underlying biochemical details to capture the behavior of the full chemotaxis system obtained from experiments on living cells. In particular, we assume that receptor-kinase complexes can be either active or inactive (23), and we use the Barkai and Leibler activity-dependent feedback in the receptor modification system that yields robust exact adaptation (7,8) (Fig.…”

“…We use Michaelis-Menten kinetics for the methylation-demethylation steps of the complexes. Here, CheR (CheB-P) binds the methylation sites only of inactive (active) receptors (16)(17)(18)(19)(20)(21)(22)(23). But in Sect.…”

“…The value of the low cutoff frequency a Ϫ1 predicted by our model for wild-type level of [CheR] is in agreement with measurements from tethered cells (25). A recent analysis of the noise-filtering properties of the chemotaxis system suggested that a lower cutoff frequency a Ϫ1 corresponds to longer time integration of the input signal and therefore better removal of high-frequency fluctuations (21). However, that study did not take into account the slow fluctuations in kinase activity due to stochastic fluctuations in the methylation-demethylation process.…”

Predicting biomass and grain protein content using Bayesian methods

“…For a given dynamical system describing the evolution of the states and parameters that we wish to estimate, the estimation problem can be viewed as an optimal filtering problem [30], in which the posterior distribution, p(z k |y 0:k ), is recursively updated. Here, the dynamical system is characterized by a Markov…”

Molecular circuits for dynamic noise filtering

“…In quantitative biology, optimal filtering and related concepts have been used in the literature, either to reconstruct biochemical processes from experimental data in silico (16) or to analyze whether existing biochemical networks can act as optimal filters that process intracellular and extracellular signals (17)(18)(19)(20). Along those lines, it has been shown theoretically that the suppression of noise is fundamentally bounded by the precision at which the noise can be estimated from the past (21).…”