Hybrid Modeling of Noise Reduction by a Negatively Autoregulated System

Abstract

We analyze the reduction of intrinsic noise caused by transition of a promoter between its active and inactive state in a negatively regulated genetic network, i.e., transcription of the gene is inhibited by its own gene product. To measure the noise attenuation, we compare its behavior to an inducible gene for which activation and deactivation of the gene take place at constant rates. As a model, we choose a hybrid approach in which some of the reaction channels are modeled as discrete events, and other reactions are modeled as continuous processes. Such a model is appropriate for investigations of noise caused by low reactant numbers. By focusing on intrinsic noise originating from the switching behavior of the regulatory system of a particular gene, we model only the transition between two different promoter states as a discrete event. We show that the stationary distributions of the unregulated and the autoregulated system are given as a solution of two coupled ordinary differential equations. Also, beside the distribution densities, the first two central moments are derived in closed analytical forms. We give conditions on the parameters when one or the other system shows lower fluctuations.

Stochastic hybrid systems for studying biochemical processes

“…We illustrate this with the simplest possible network: an autoregulatory gene network where a protein inhibits or activates its own gene expression (figure 4a). Zeiser et al (2009) models autoregulatory gene networks as an SHS with two discrete states, which represent a gene in an 'ON' or 'OFF' state (figure 4b). The protein count represents the continuous state of the SHS and evolves according to a linear differential equation with production and degradation in the 'ON' state, and only degradation in the 'OFF' state.…”

“…A negative feedback can be easily implemented in the above SHS model by assuming that the promoter is more likely to transition to the OFF state if the protein count increases within the cell. Analysis of these models not only predicts conditions under which feedback will provide the best suppression of gene expression noise but also determines the (Zeiser et al 2009). fundamental limits of noise suppression possible through negative autoregulation (Singh & Hespanha 2009a,b). Counterintuitively, these models also show that, in some cases, introducing a negative feedback may actually increase gene expression noise rather than decreasing it (Stekel & Jenkins 2008;Zeiser et al 2009).…”

Piecewise-Deterministic Markov Processes as Limits of Markov Jump Processes

“…An alternative approach to describe systems possessing species appearing in high and low numbers is to use a class of piecewise-deterministic Markov processes (PDMPs) [5]. In several recently published works gene regulatory networks were modelled by such a class of stochastic processes; see [15], [16], and [17].…”

Piecewise-Deterministic Markov Processes as Limits of Markov Jump Processes

“…An alternative approach to describe systems possessing species appearing in high and low numbers is to use a class of piecewise-deterministic Markov processes (PDMPs) [5]. In several recently published works gene regulatory networks were modelled by such a class of stochastic processes; see [15], [16], and [17].…”