Intracellular delay limits cyclic changes in gene expression

Abstract

Based on previously published experimental observations and mathematical models for Hes1, p53 and NF-κB gene expression, we improve these models through a distributed delay formulation of the time lag between transcription factor binding and mRNA production. This description of natural variability for delays introduces a transition from a stable steady state to limit cycle oscillations and then a second transition back to a stable steady state which has not been observed in previously published models. On the basis of our results and following recent discussions about the role of delay-induced oscillations in gene transcription we establish the hypothesis that the period of the delay-induced cyclic changes should be characterized by an upper bound so that it cannot be greater then the period of fundamental biological cycles. We demonstrate our approach for two models. The first model describes Hes1 autorepression with equations for Hes1 mRNA production and Hes1 protein translation. The second model describes Hes1 repression by the protein complex Gro/TLE1/Hes1, where Gro/TLE1 is activated by Hes1 phosphorylation.

Oscillations and bistability in the stochastic model of p53 regulation

“…Undamped oscillations are the manifestation of autonomous limit cycle, a recurrent solution of constant amplitude and period. Such solution may appear when negative feedback is combined with time delay, and/or concurrent positive feedback loop (Tyson, 2006;Rateitschak and Wolkenhauer, 2007).…”

Modelling and Analysis of miRNA Regulation

“…Some of the parameter values used in the numerical analysis were selected according to [4,20,24,29,33] in the form…”

“…Rateitschak and Wolkenhauer in [24] describe a time delay for gene transcription between 10 and 40 min. Finally in [29] a time delay around 7 min is defined and estimated for nucleocytoplasmic shuttling.…”

Stability and Bifurcation Analysis of Cyclic Genetic Regulatory Networks with Mixed Time Delays

“…In this model, variables represent the concentrations of mRNAs and proteins [18]. The dynamic relationships between different nodes with mixed time delays are formulated as follows [8,22]:…”

“…Take all φ i (t) as the form of Gamma distribution delay kernel [22,25] (2.2) φ (t) = β q+1 t q e −βt q! , t ∈ (0, +∞) , q = 0, 1, .…”