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The phage $\lambda$ infection of an \textit{E. coli} cell has become a paradigm for understanding the molecular processes involved in gene expression and cell signaling. This system provides an example of a genetic switch, as cells with…
We study a stochastic model proposed recently in the genetic literature to explain the heterogeneity of cell populations or of gene products. Cells are located in two colonies, whose sizes fluctuate as birth and migration processes in…
Multipotent stem or progenitor cells undergo a sequential series of binary fate decisions, which ultimately generate the diversity of differentiated cells. Efforts to understand cell fate control have focused on simple gene regulatory…
Morphogenesis of complex body shapes is reproducible despite the noise inherent in the underlying morphogenetic processes. However, how these morphogenetic processes work together to achieve this reproducibility remains unclear. Here, we…
We study the asymptotic behaviors of stochastic cell fate decision between proliferation and differentiation. We propose a model of a self-replicating Langevin system, where cells choose their fate (i.e. proliferation or differentiation)…
Heterogeneity is ubiquitous in stem cells (SC), cancer cells (CS), and cancer stem cells (CSC). SC and CSC heterogeneity is manifested as diverse sub-populations with self-renewing and unique regeneration capacity. Moreover, the CSC progeny…
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…
The process of programmed cell death, namely apoptosis, is a natural mechanism that regulates healthy tissue, multicellular structures, and homeostasis. An improved understanding of apoptosis can significantly enhance our knowledge of…
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…
The observation that phenotypic variability is ubiquitous in isogenic populations has led to a multitude of experimental and theoretical studies seeking to probe the causes and consequences of this variability. Whether it be in the context…
Cycling tissues such as the intestinal epithelium, germ line, and hair follicles, require a constant flux of differentiated cells. These tissues are maintained by a population of stem cells, which generate differentiated progenies and…
During development, spatio-temporal patterns ranging from checkerboard to engulfing occur with precise proportions of the respective cell fates. Key developmental regulators are intracellular transcriptional interactions and intercellular…
Stem cells can precisely and robustly undergo cellular differentiation and lineage commitment, referred to as stemness. However, how the gene network underlying stemness regulation reliably specifies cell fates is not well understood. To…
The deluge of single-cell data obtained by sequencing, imaging and epigenetic markers has led to an increasingly detailed description of cell state. However, it remains challenging to identify how cells transition between different states,…
Due to inherent noise in intracellular networks cellular decisions can be random, so genetically identical cells can display different phenotypic behavior even in identical environments. Most previous work in understanding the…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
Epigenetic modifications of histones crucially affect the eukaryotic gene activity, while the epigenetic histone state is largely determined by the binding of specific factors such as the transcription factors (TFs) to DNA. Here, the way…
Dynamics maintaining diversity of cell types in a multi-cellular system are studied in relationship with the plasticity of cellular states. By adopting a simple theoretical framework for intra-cellular chemical reaction dynamics with…
The dynamics of gene regulatory networks are often modeled with the assumption of cellular homogeneity. However, this assumption contradicts the plethora of experimental results in a variety of systems, which designates that cell…
Accumulating evidence suggests that many tumors have a hierarchical organization, with the bulk of the tumor composed of relatively differentiated short-lived progenitor cells that are maintained by a small population of undifferentiated…