Related papers: Bifurcation in cell cycle dynamics regulated by p5…
Ordinary differential equations (ODEs) can model the transition of cell states over time. Bifurcation theory is a branch of dynamical systems which studies changes in the behavior of an ODE system while one or more parameters are varied. We…
The oscillatory dynamics of natural and man-made systems can be disrupted by their time-varying interactions, leading to oscillation quenching phenomena in which the oscillations are suppressed. We introduce a framework for analyzing,…
The present work continues studies of the mathematical model of a metabolic process of the Krebs cycle. We study the dependence of its cyclicity on the cell respiration intensity determined by the formation level of carbon dioxide. We…
This paper investigates the different behaviors of the process equation and parameters of their occurrences. The process equation is a multistable one dimensional map with nonlinear feedback and can show various behaviors such as period…
Ordered distributive double phosphorylation is a recurrent motif in intracellular signaling and control. It is either sequential (where the site phosphorylated last is dephosphorylated first) or cyclic (where the site phosphorylated first…
Irradiation of cell monolayers by monoenergetic ions has made it possible to establish survival curves at individual values of linear energy transfer. The two-step model of radiobiological mechanism proposed recently by Judas and Lokajicek…
Systemic properties of living cells are the result of molecular dynamics governed by so-called genetic regulatory networks (GRN). These networks capture all possible features of cells and are responsible for the immense levels of adaptation…
Periodic forcing of nonlinear oscillators leads to a large number of dynamic behaviors. The coupling of the cell-cycle to the circadian clock provides a biological realization of such forcing. Using high throughput single-cell microscopy,…
Hematopoiesis is a complex biological process that leads to the production and regulation of blood cells. It is based upon differentiation of stem cells under the action of growth factors. A mathematical approach of this process is proposed…
In eukaryotic cells, motor proteins (MP) bind to cytoskeletal filaments and move along them in a directed manner generating active stresses. During cell division a spindle structure of overlapping antiparallel microtubules (MT) form whose…
All stem cell fate transitions, including the metabolic reprogramming of stem cells and the somatic reprogramming of fibroblasts into pluripotent stem cells, can be understood from a unified theoretical model of cell fates. Each cell fate…
Induced effects by direct exposure to ionizing radiation (IR) are a central issue in many fields like radiation protection, clinic diagnosis and oncological therapies. Direct irradiation at certain doses induce cell death, but similar…
During cell division paired (sister) chromosomes are observed to perform approximate saw-tooth oscillations across the cell mid-plane. Experimental data suggests that these oscillations are regulated through intersister tension. We propose…
Understanding cell fate selection remains a central challenge in developmental biology. We present a class of simple yet biologically-motivated mathematical models for cell differentiation that generically generate oscillations and hence…
Cells often exhibit different and stable phenotypes from the same DNA sequence. Robustness and plasticity of such cellular states are controlled by diverse transcriptional and epigenetic mechanisms, among them the modification of…
We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips,…
This study investigates the linear stability of phototactic bioconvection in a rotating porous medium under collimated light, incorporating the effects of critical intensity, Darcy number, and Taylor number. Using a mathematical model and…
In this work we prove occurrence of a super-critical Hopf bifurcation in a model of white blood cell formation structured by three maturation stages. We provide an explicit analytical expression for the bifurcation point depending on model…
Many cell types exhibit oscillatory activity, such as repetitive action potential firing due to the Hodgkin-Huxley dynamics of ion channels in the cell membrane or reveal intracellular inositol triphosphate (IP$_3$) mediated calcium…
We analyze the asymptotic stability of a nonlinear system of two differential equations with delay describing the dynamics of blood cell production. This process takes place in the bone marrow where stem cells differentiate throughout…