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The development of new techniques to quantitatively measure gene expression in cells has shed light on a number of systems that display oscillations in protein concentration. Here we review the different mechanisms which can produce…
Cells and tissues exhibit oscillatory deformations during remodelling, migration or embryogenesis. Although it has been shown that these oscillations correlate with cell biochemical signalling, it is yet unclear the role of these…
Cell signaling, gene expression, and metabolism are affected by cell-cell heterogeneity and random changes in the environment. The effects of such fluctuations on cell signaling and gene expression have recently been studied intensively…
A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…
Chemical reactions in cell are subject to intense stochastic fluctuations. An important question is how the fundamental physiological behavior of cell is kept stable against those noisy perturbations. In this paper a stochastic model of…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
We explore the joint effect of the intrinsic noise and time delay on the spatial pattern formation within a multi-scale mobile lattice model of the epithelium. The protein fluctuations are driven by transcription/translation processes in…
In this paper we use a continuous model to describe the development of a single cell lineage following the committal of stem cells. Three separate controls are implemented in the model, namely the proliferative control of stem cells, 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…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of…
Existence of a new type of oscillating synchronization that oscillates between three different types of synchronizations (anticipatory, complete and lag synchronizations) is identified in unidirectionally coupled nonlinear time-delay…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
We consider a self-oscillator whose excitation parameter is varied. Frequency of the variation is much smaller then the natural frequency of the oscillator so that oscillations in the system are periodically excited and decay. Also a time…
Inspired by the observation of a distributed time delay in the nonlinear response of an optical resonator, we investigate the effects of a similar delay on a noise-driven mechanical oscillator. For a delay time that is commensurate with the…
Limit cycle oscillations are phenomena arising in nonlinear dynamical systems and characterized by periodic, locally-stable, and self-sustained state trajectories. Systems controlled in a closed loop along a periodic trajectory can also be…
Based on previously published experimental observations and mathematical models for Hes1, p53 and NF-kB gene expression, we improve these models through a distributed delay formulation of the time lag between transcription factor binding…
Delay is an inherent feature of genetic regulatory networks. It represents the time required for the assembly of functional regulator proteins. The protein production process is complex, as it includes transcription, translocation,…
Anaerobic glycolysis in yeast perturbed by the reduction of xenobiotic ketones is studied numerically in two models which possess the same topology but different levels of complexity. By comparing both models' predictions for concentrations…