Abstract
Cellular signaling involves the transmission of environmental information through cascades of stochastic biochemical reactions, inevitably introducing noise that compromises signal fidelity. Each stage of the cascade often takes the form of a kinase-phosphatase push-pull network, a basic unit of signaling pathways whose malfunction is linked with a host of cancers. We show this ubiquitous enzymatic network motif effectively behaves as a Wiener-Kolmogorov (WK) optimal noise filter. Using concepts from umbral calculus, we generalize the linear WK theory, originally introduced in the context of communication and control engineering, to take nonlinear signal transduction and discrete molecule populations into account. This allows us to derive rigorous constraints for efficient noise reduction in this biochemical system. Our mathematical formalism yields bounds on filter performance in cases important to cellular function---like ultrasensitive response to stimuli. We highlight features of the system relevant for optimizing filter efficiency, encoded in a single, measurable, dimensionless parameter. Our theory, which describes noise control in a large class of signal transduction networks, is also useful both for the design of synthetic biochemical signaling pathways, and the manipulation of pathways through experimental probes like oscillatory input.
Highlights
Extracting signals from time series corrupted by noise is a challenge in a number of seemingly unrelated areas
For constructing synthetic signaling networks, we would like to make the most efficient communication pathway with a limited set of resources. To answer these questions, using the enzymatic pushpull loop as an example, we introduce a new mathematical framework, inspired by the Wiener-Kolmogorov (WK) theory for optimal noise filtration
Exploiting the power of exact analytical techniques based on umbral calculus [20], we overcome these limitations, generalizing the WK approach
Summary
Extracting signals from time series corrupted by noise is a challenge in a number of seemingly unrelated areas. For constructing synthetic signaling networks, we would like to make the most efficient communication pathway with a limited set of resources (free-energy costs). To answer these questions, using the enzymatic pushpull loop as an example, we introduce a new mathematical framework, inspired by the Wiener-Kolmogorov (WK) theory for optimal noise filtration. Exploiting the power of exact analytical techniques based on umbral calculus [20], we overcome these limitations, generalizing the WK approach This crucial theoretical development enables us to provide a rigorous solution to the filter optimization problem, taking into account discrete populations and nonlinearity. Illustrated using a push-pull loop, the theory is applicable to a large class of signaling networks, including more complex features such as negative feedback or multisite phosphorylation of substrates
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