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Stem cells are characterized by their ability to self-renew, as well as to differentiate and give rise to new populations of cells. Stem cell divisions are crucial for generative processes that occur during early development, and later in…
The mating pathway in \emph{Saccharomyces cerevisiae} is one of the best understood signal transduction pathways in eukaryotes. It transmits the mating signal from plasma membrane into the nucleus through the G-protein coupled receptor and…
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…
Hybrid modeling provides an effective solution to cope with multiple time scales dynamics in systems biology. Among the applications of this method, one of the most important is the cell cycle regulation. The machinery of the cell cycle,…
Living cells provide a fluctuating, out-of-equilibrium environment in which genes must coordinate cellular function. DNA looping, which is a common means of regulating transcription, is very much a stochastic process; the loops arise from…
In multi-cellular organisms, cells differentiate into multiple types as they divide. States of these cell types, as well as their numbers, are known to be robust to external perturbations; as conceptualized by Waddington's epigenetic…
Reconstructing transcriptional regulatory networks is an important task in functional genomics. Data obtained from experiments that perturb genes by knockouts or RNA interference contain useful information for addressing this reconstruction…
Genetic systems with multiple loci can have complex dynamics. For example, mean fitness need not always increase and stable cycling is possible. Here, we study the dynamics of a genetic system inspired by the molecular biology of…
The inherent stochasticity of cellular processes leads to significant cell-to-cell variation in protein abundance. Although this noise has already been characterized and modeled, its broader implications and significance remain unclear. In…
Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node…
Understanding to what extent stem cell potential is a cell-intrinsic property, or an emergent behavior coming from global tissue dynamics and geometry, is a key outstanding question of systems and stem cell biology. Here, we propose a…
Signal transduction networks can form highly interconnected systems within cells due to network crosstalk, the sharing of input signals between multiple downstream responses. To better understand the evolutionary design principles…
Regulatory networks consist of interacting molecules with a high degree of mutual chemical specificity. How can these molecules evolve when their function depends on maintenance of interactions with cognate partners and simultaneous…
The purpose of this paper is trifold -- to serve as an instructive resource and a reference catalog for biologically plausible modeling with i) conductance-based models, coupled with ii) strength-varying slow synapse models, culminating in…
We consider a heteroclinic network in the framework of winnerless competition of species. It consists of two levels of heteroclinic cycles. On the lower level, the heteroclinic cycle connects three saddles, each representing the survival of…
Genetic sequences are known to possess non-trivial composition together with symmetries in the frequencies of their components. Recently, it has been shown that symmetry and structure are hierarchically intertwined in DNA, suggesting a…
Biological networks have evolved to be highly functional within uncertain environments while remaining extremely adaptable. One of the main contributors to the robustness and evolvability of biological networks is believed to be their…
A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or…
Motility is characteristic of life, but a common basis for movement has remained to be identified. Diverse systems in motion shift between two states depending on interactions that turnover at the rate of an applied cycle of force. Although…
A protocell model consisting of mutually catalyzing molecules is studied in order to investigate how chemical compositions are transferred recursively through cell divisions under replication errors. Depending on the path rate, the numbers…