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Cell-fate transition can be modeled by ordinary differential equations (ODEs) which describe the behavior of several molecules in interaction, and for which each stable equilibrium corresponds to a possible phenotype (or 'biological…
Ring oscillators are biochemical circuits consisting of a ring of interactions capable of sustained oscillations. The non-linear interactions between genes hinder the analytical insight into their function, usually requiring computational…
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…
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…
This work concerns the question of how two important dynamical properties, oscillations and bistability, emerge in an important biological signaling network. Specifically, we consider a model for dual-site phosphorylation and…
We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE…
The multiple futile cycle is an important building block in networks of chemical reactions arising in molecular biology. A typical process which it describes is the addition of n phosphate groups to a protein. It can be modelled by a system…
In this article, we investigate the problem of exponential stabilization via output feedback for a cascaded system composed of an ordinary differential equation (ODE) and a wave partial differential equation (PDE) under boundary control.…
This paper discusses the stability of an equilibrium point of an ordinary differential equation (ODE) arising from a feed-forward position control for a musculoskeletal system. The studied system has a link, a joint and two muscles with…
An important design principle for biological oscillators divides the oscillators into two classes: fixed frequency, variable amplitude and fixed amplitude, variable frequency. Because of the interplay of nonlinearity and feedback, both…
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.…
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…
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 present a design framework to induce stable oscillations through mixed feedback control. We provide conditions on the feedback gain and on the balance between positive and negative feedback contributions to guarantee robust oscillations.…
We revisit quantum dynamics of the damped and driven nonlinear oscillator. In the classical case this system has two stationary solutions (the limit cycles) in the certain parameter region, which is the origin of the celebrated bistability…
We consider the problem of network stability in finite-buffer systems. We observe that finite buffer may affect stability even in simplest network structure, and we propose an ordinary differential equation (ODE) model to capture the…
In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge represents either down- or up-regulation, and is modeled by…
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…
Mixed positive and negative feedback loops are often found in biological systems which support oscillations. In this work we consider a prototype of such systems, which has been recently found at the core of many genetic circuits showing…
For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that is very different from the predictions of…