Minimal model for stem-cell differentiation

Journal of Theoretical Biology, 2008

In multicellular organisms, several cell states coexist. For determining each cell type, cell-cell interactions are often essential, in addition to intracellular gene expression dynamics. Based on dynamical systems theory, we propose a mechanism for cell differentiation with regulation of populations of each cell type by taking simple cell models with gene expression dynamics. By incorporating several interaction kinetics, we found that the cell models with a single intracellular positive-feedback loop exhibit a cell fate switching, with a change in the total number of cells. The number of a given cell type or the population ratio of each cell type is preserved against the change in the total number of cells, depending on the form of cell-cell interaction. The differentiation is a result of bifurcation of cell states via the intercellular interactions, while the population regulation is explained by self-consistent determination of the bifurcation parameter through cell-cell interactions. The relevance of this mechanism to development and differentiation in several multicellular systems is discussed.

Science, 2012

During development, cells undergo a unidirectional course of differentiation that progressively decreases the number of cell types they can potentially become. Stem cells, however, keep their potential to both proliferate and differentiate. A very important issue then is to understand the characteristics that distinguish stem cells from other cell types and allow them to conduct stable proliferation and differentiation. Here, we review relevant dynamical-systems approaches to describe the state transition between stem and differentiated cells, with an emphasis on fluctuating and oscillatory gene expression levels, as these represent the specific properties of stem cells. Relevance between recent experimental results and dynamical-systems descriptions of stem cell differentiation is also discussed.

Nature Precedings, 2010

Cell differentiation is a complex phenomenon whereby a stem cell becomes progressively more specialized and eventually gives rise to a specific cell type. Differentiation can be either stochastic or, when appropriate signals are present, it can be driven to take a specific route. Induced pluripotency has also been recently obtained by overexpressing some genes in a differentiated cell. Here we show that a stochastic dynamical model of genetic networks can satisfactorily describe all these important features of differentiation, and others. The model is based on the emergent properties of generic genetic networks, it does not refer to specific control circuits and it can therefore hold for a wide class of lineages. The model points to a peculiar role of cellular noise in differentiation, which has never been hypothesized so far, and leads to non trivial predictions which could be subject to experimental testing.

Journal of Theoretical Biology, 2001

Based on extensive study of a dynamical systems model of the development of a cell society, a novel theory for stem cell differentiation and its regulation is proposed as the "chaos hypothesis". Two fundamental features of stem cell systems -stochastic differentiation of stem cells and the robustness of a system due to regulation of this differentiation -are found to be general properties of a system of interacting cells exhibiting chaotic intra-cellular reaction dynamics and cell division, whose presence does not depend on the detail of the model. It is found that stem cells differentiate into other cell types stochastically due to a dynamical instability caused by cell-cell interactions, in a manner described by the Isologous Diversification theory. This developmental process is shown to be stable not only with respect to molecular fluctuations but also with respect to removal of cells. With this developmental process, the irreversible loss of multipotency accompanying the change from a stem cell to a differentiated cell is shown to be characterized by a decrease in the chemical diversity in the cell and of the complexity of the cellular dynamics. The relationship between the division speed and this loss of multipotency is also discussed. Using our model, some predictions that can be tested experimentally are made for a stem cell system.

The European Physical Journal Special Topics

Cell development from an undifferentiated stem cell to a differentiated one is essential in forming an organism. In this paper, various bifurcations of a stem cell during this process are studied using a model based on Furusawa and Kaneko's hypothesis. Furusawa and Kaneko's hypothesis tells that the gene expression of stem cells is chaotic. By developing to a differentiated cell, the gene expression in more order, which is the cause of losing pluripotency. In this model, the chaotic dynamics of gene expression in the stem cells become ordered during the developments. Various patterns and bifurcation points can be seen during development. The bifurcation points and their predictions during the process of cell development are studied in this paper. Some well-known critical slowing down indicators are used to show the variations of slowness during the cell's development and predict the bifurcation points. It is vital since the unexpected changes of the state can cause a disaster. All of the indicators have a proper trend by approaching the bifurcation points and faring away.

Physica A: Statistical Mechanics and its Applications, 2000

A dynamical systems scenario for developmental cell biology is proposed, based on numerical studies of a system with interacting units with internal dynamics and reproduction. Diversiÿcation, formation of discrete and recursive types, and rules for di erentiation are found as a natural consequence of such a system. "Stem cells" that either proliferate or di erentiate to di erent types stochastically are found to appear when intra-cellular dynamics are chaotic. Robustness of the developmental process against microscopic and macroscopic perturbations is shown to be a natural consequence of such intra-inter dynamics, while irreversibility in developmental process is discussed in terms of the gain of stability, loss of diversity and chaotic instability.

nt.ntnu.no

Preprint, 2013

A Simple Mathematical Model Explaining Deterministic Cellular Reprogramming Using External Stimulus: Non-binary simultaneous decision network of gene regulation represents a cell differentiation process that involves more than two possible cell lineages. The simultaneous decision network is an alternative to the hierarchical models of gene regulation and it exhibits possible presence of multistable master switches. To investigate the qualitative behavior of the dynamics of the simultaneous decision network, we employ geometric techniques in the analysis of the network's corresponding system of ordinary differential equations (ODE). We determine the location and the maximum number of equilibrium points given a set of parameter values. Varying the values of some parameters, such as the degradation rate and the amount of exogenous stimulus, can decrease the size of the basin of attraction of an undesirable steady state as well as increase the size of the basin of attraction of a desirable steady state. A sufficient change in some parameter values can silence or reactivate gene transcription that results to cell fate switching without the aid of stochastic noise. We further show that increasing the amount of exogenous stimulus can shutdown multistability of the system such that only one stable equilibrium point remains.

SIAM Journal on Applied Mathematics, 2011

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 equations of transport type. Specifically, it consists of a structured population equation with a nonlinear feedback loop. This models the signaling process due to cytokines, which regulate the differentiation and proliferation process. We compare the continuous model to its discrete counterpart, a multi-compartmental model of a discrete collection of cell subpopulations recently proposed by to investigate the dynamics of the hematopoietic system. We obtain uniform bounds for the solutions, characterize steady state solutions, and analyze their linearized stability. We show how persistence or extinction might occur according to values of parameters that characterize the stem cells self-renewal. We also perform numerical simulations and discuss the qualitative behavior of the continuous model vis a vis the discrete one.

Biophysical Journal, 2012