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Organisms are equipped with regulatory systems that display a variety of dynamical behaviours ranging from simple stable steady states, to switching and multistability, to oscillations. Earlier work has shown that oscillations in protein…
Gene Regulatory Networks(GRNs) with feedback are essential components of many cellular processes and may exhibit oscillatory behavior. Analyzing such systems becomes increasingly complex as the number of components increases. Since gene…
A wide range of organisms use circadian clocks to keep internal sense of daily time and regulate their behavior accordingly. Most of these clocks use intracellular genetic networks based on positive and negative regulatory elements. The…
Oscillatory chemical reactions often serve as a timing clock of cellular processes in living cells. The temporal dynamics of protein concentration levels is thus of great interest in biology. Here we propose a theoretical framework to…
We study the oscillatory behaviour of a gene regulatory network with interlinked positive and negative feedback loop. Frequency and amplitude are two important properties of oscillation. Studied network produces two different modes of…
Gene networks exhibiting oscillatory dynamics are widespread in biology. The minimal regulatory designs giving rise to oscillations have been implemented synthetically and studied by mathematical modeling. However, most of the available…
Negative and positive transcriptional feedback loops are present in natural and synthetic genetic oscillators. A single gene with negative transcriptional feedback needs a time delay and sufficiently strong nonlinearity in the transmission…
This paper is concerned with conditions for the existence of oscillations in gene regulatory networks with negative cyclic feedback, where time delays in transcription, translation and translocation process are explicitly considered. The…
Oscillatory gene circuits are ubiquitous to biology and are involved in fundamental processes of cell cycle, circadian rhythms and developmental systems. The synthesis of small, non-natural oscillatory genetic circuits have been…
Feedback delay has been identified as a key ingredient in the quorum sensing synchronization of synthetic gene oscillators. While this influence has been evidenced at the theoretical level in a simplified system of degrade-and-fire…
We revisit the dynamics of a gene repressed by its own protein in the case where the transcription rate does not adapt instantaneously to protein concentration but is a dynamical variable. We derive analytical criteria for the appearance of…
In this paper, we study the stability of an Ordinary Differential Equation (ODE) usually referred to as Cyclic Feedback Loop, which typically models a biological network of molecules where each molecule regulates its successor in a cycle.…
Oscillatory dynamics are common features of complex networks, often playing essential roles in regulating function. Across scales from gene regulatory networks to ecosystems, delayed feedback mechanisms are key drivers of system-scale…
Oscillations lie at the core of many biological processes, from the cell cycle, to circadian oscillations and developmental processes. Time-keeping mechanisms are essential to enable organisms to adapt to varying conditions in environmental…
We show that noise-induced oscillations in a gene circuit model display stochastic coherence, that is, a maximum in the regularity of the oscillations as a function of noise amplitude. The effect is manifest as a system-size effect in a…
Ring topologies of repressing genes have qualitatively different long-term dynamics if the number of genes is odd (they oscillate) or even (they exhibit bistability). However, these attractors may not fully explain the observed behavior in…
Genes are connected in complex networks of interactions where often the product of one gene is a transcription factor that alters the expression of another. Many of these networks are based on a few fundamental motifs leading to switches…
Feedback loops are major components of biochemical systems. Many systems show multiple such (positive or negative) feedback loops. Nevertheless, very few quantitative analyses address the question how such multiple feedback loops evolved.…
In biochemical signaling, information is often encoded in oscillatory signals. However, the advantages of such a coding strategy over an amplitude encoding scheme of constant signals remain unclear. Here we study the dynamics of a simple…
The problem of reliability of the dynamics in biological regulatory networks is studied in the framework of a generalized Boolean network model with continuous timing and noise. Using well-known artificial genetic networks such as the…