Stochastic Delay Accelerates Signaling in Gene Networks

Abstract

The creation of protein from DNA is a dynamic process consisting of numerous reactions, such as transcription, translation and protein folding. Each of these reactions is further comprised of hundreds or thousands of sub-steps that must be completed before a protein is fully mature. Consequently, the time it takes to create a single protein depends on the number of steps in the reaction chain and the nature of each step. One way to account for these reactions in models of gene regulatory networks is to incorporate dynamical delay. However, the stochastic nature of the reactions necessary to produce protein leads to a waiting time that is randomly distributed. Here, we use queueing theory to examine the effects of such distributed delay on the propagation of information through transcriptionally regulated genetic networks. In an analytically tractable model we find that increasing the randomness in protein production delay can increase signaling speed in transcriptional networks. The effect is confirmed in stochastic simulations, and we demonstrate its impact in several common transcriptional motifs. In particular, we show that in feedforward loops signaling time and magnitude are significantly affected by distributed delay. In addition, delay has previously been shown to cause stable oscillations in circuits with negative feedback. We show that the period and the amplitude of the oscillations monotonically decrease as the variability of the delay time increases.

A queueing approach to multi-site enzyme kinetics

“…operations research, suggests that some biologically motivated questions tied to queueing may already have been answered in a different context. Pursuit of the queueing approach to biological problems has indeed been fruitful thus far, leading to progress in gene networks [15][16][17][18][19], metabolic networks [20,21], degradation pathways [22], signalling [23,24] and translational cross talk [25].…”

Stability of Systems with Stochastic Delays and Applications to Genetic Regulatory Networks

“…In this paper, we target the problem of stability analysis of systems with stochastically changing delays. Stochastic delays arise in networked control systems [5], connected vehicles [43], and gene regulatory networks [15, 21]. …”

“…Such studies have been extended to gene networks modeled with delays [48]. However, the biochemical processes that are lumped together by the delay are also stochastic in nature, which results in stochastic delay variations [15, 21]. We analyze corresponding effects and produce stability charts for equilibria on the plane of gain parameters for different distributions of the stochastic delay.…”

The Effects of Time-Varying Temperature on Delays in Genetic Networks

“…The incorporation of delay greatly simplifies models of genetic oscillators while simultaneously maintaining qualitative similarities to experimental data [8, 21, 40, 41]. Delay-based models play a central role in understanding the origin of oscillations in genetic networks [30, 31] and other nonlinear systems [18, 22]. For constant temperatures, the delay time or distribution can be scaled with the Arrhenius equation, just as the reaction rates.…”