Stochasticity and negative feedback lead to pulsed dynamics and distinct gene activity patterns

Abstract

Gene expression is an inherently stochastic process that depends on the structure of the biochemical regulatory network in which the gene is embedded. Here we study the interplay between stochastic gene switching and the widespread negative feedback regulatory loop. Using a simple hybrid model, we find that stochasticity in gene switching by itself can induce pulses in the system. Furthermore, we find that our simple model is able to reproduce both exponential and peaked distributions of gene active and inactive times similar to those that have been observed experimentally. Our hybrid modelling approach also allows us to link these patterns to the dynamics of the system for each gene state.Cells need to provide an adapted response to external stimuli, which requires the production of the adequate proteins following different temporal patterns. This is achieved through biochemical networks in which a stimulus triggers a cascade of reactions that eventually lead to the activation of transcription factors, proteins that activate or repress the expression of specific gene sets. Thus, the temporal regulation of gene activity will be determined by the structure of the network in which the gene is embedded [1]. A common regulatory structure is the negative feedback loop, in which a transcription factor activates the production of a protein that contributes to its own inhibition. This motif regulates the activity of important transcription factors such as NF-κB [2] and p53 [3] and has been shown to give rise to pulses in the concentration of the proteins of the network (see e.g. [4,5]) as predicted by mathematical models [6]. The role of this pulsed dynamics is not fully understood though: theoretical studies suggest that they can give rise to a more reliable protein production [7] while experiments show that oscillatory dynamics can determine the cell fate [8].On the other hand, gene expression is an intrinsically noisy process [9] and models in which the gene state switches randomly between active and inactive states are able to fit well experimental data [10]. By contrast, some genes show peaked distributions of active/inactive times [11][12][13] that deviate from the exponential distributions obtained with simple random models. These distributions can be obtained using multi-step models mirroring the multiple steps of gene activation [14], but they could also arise from the interplay between the stochastic gene activity and the structure of the regulatory network in which the gene is embedded. Some insights about this interplay have been gained by showing the emergence of oscillations when a gene is an autorepressor [15], of noiseenhanced persistence of biochemical species [16] and how stochasticity dephases genetic oscillators [17]. A major obstacle in this context is the difficulty of providing analytical insights on the nonlinear stochastic systems in-volved (often modelling species with very low copy numbers). For this reason, we are far from having a complete picture of the type of regulation that emerges from s...

First responders shape a prompt and sharp NF-κB–mediated transcriptional response to TNF-α

“…For our qualitative exploration of NF-κB mediated transcription we used a simple model of the NF-κB system able to recapitulate the essential features of NF-κB nuclear localization dynamics upon TNF-α [3]. In such model for simplicity it is considered that we can either have free NF-κB (hence nuclear and transcriptionally active) or forming a complex with the inhibitor IκB, NF-κB:IκB (the cytosolic and transcriptionally inactive form).…”

“…The copy numbers of the transcript and the inhibitor protein are written below as IκB RN A and IκB respectively. The deterministic model for this system [3] can be written as:…”

“…To simulate the intrinsic variability of the system, an alternative is to take the biochemical reactions that give rise to the mass action kinetic equations described above (details provided in [3]) and to perform stochastic simulations using e.g. the Gillespie algorithm.…”

“…They are based on those used in our model of the NF-κB system, which were themselves derived from the literature (details in Ref. [3]). Since models i and iii do not contemplate stripping, their effective value of reference inactivation rate (k of f,0 ) is equal to the one of model ii (with stripping) multiplied by the average IκB levels 3 hours post-stimulation.…”