Related papers: Oscillation patterns in negative feedback loops
Genetically encoded regulatory circuits control biological function. A major focus of systems biology is to understand these circuits by establishing the relationship between specific structures and functions. Of special interest are…
According to the chemical reaction network theory, the topology of a certain class of chemical reaction networks, regardless of the kinetic details, sets a limit on the dynamical properties that a particular network can potentially admit;…
We analyze a class of network motifs in which a short, two-node positive feed- back motif is inserted in a three-node negative feedback loop. We demonstrate that such networks can undergo a bifurcation to a state where a stable fixed point…
Mounting evidence shows that oscillatory activity is widespread in cell signaling. Here we review some of this recent evidence, focusing on both the molecular mechanisms that potentially underlie such dynamical behavior, and the potential…
The transient response to a stimulus and subsequent recovery to a steady state are the fundamental characteristics of a living organism. Here we study the relaxation kinetics of autoregulatory gene networks based on the chemical master…
The dynamic behaviors of microRNA and mRNA under external stress are studied with biological experiments and mathematics models. In this study, we developed a mathematic model to describe the biological phenomenon and for the first time…
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…
Engineering genetic networks to be both predictable and robust is a key challenge in synthetic biology. Synthetic circuits must reliably function in dynamic, stochastic and heterogeneous environments, and simple circuits can be studied to…
Collective oscillation of cells in a population has been reported under diverse biological contexts and with vastly different molecular constructs. Could there be common principles similar to those that govern spontaneous oscillation in…
We study the problem of controlling oscillations in closed loop by combining positive and negative feedback in a mixed configuration. We develop a complete design procedure to set the relative strength of the two feedback loops to achieve…
We study the noise characteristics of stochastic oscillations in protein number dynamics of simple genetic oscillatory systems. Using the three-component negative feedback transcription regulatory system called the repressilator as a…
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…
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…
We study a system of dynamical units, each of which shows excitable or oscillatory behavior, depending on the choice of parameters. When we couple these units with repressive bonds, we can control the duration of collective oscillations for…
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…
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…
Auto-regulatory feedback loops are one of the most common network motifs. A wide variety of stochastic models have been constructed to understand how the fluctuations in protein numbers in these loops are influenced by the kinetic…
Biological oscillators are very diverse but can be classified based on dynamical motifs such as the types of feedback loops present. The S. Elongatus circadian clock is a remarkable phosphorylation-based oscillator that can be reconstituted…
We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables…