The universal properties of stem cells as pinpointed by a simple discrete model (original) (raw)
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There is a significant interest in studying stem cells, to learn about the biological functions during development and adulthood as well as to learn how to utilize them as new sources of specialized cells for tissue repair. Modeling of stem cells not only describes, but also predicts, how a stem cell's environment can control its fate. The first stem cell populations discovered were Hematopoietic Stem Cells (HSCs). In this paper, we present a biologically feasible deterministic model of bone marrow that hosts HSCs. Our model demonstrates that a single HSC can populate the entire bone marrow. It almost always produces sufficient number of differentiated cells (RBCs, WBCs, etc.). It also overcomes the biological feasibility limitations of previously reported models. We have performed agent-based simulation of the model of bone marrow system proposed in this paper. We have included the details and the results of this validation using simulation in the Appendix. The simulation also demonstrates that a large fraction of stem cells do remain in the quiescent state. The program of the agent-based simulation of the proposed model is made available on a public website.
A Dynamical-Systems View of Stem Cell Biology
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.
Theory of Robustness of Irreversible Differentiation in a Stem Cell System: Chaos Hypothesis
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.
On the dynamical properties of a model of cell differentiation
EURASIP Journal on Bioinformatics and Systems Biology, 2013
One of the major challenges in complex systems biology is that of providing a general theoretical framework to describe the phenomena involved in cell differentiation, i.e., the process whereby stem cells, which can develop into different types, become progressively more specialized. The aim of this study is to briefly review a dynamical model of cell differentiation which is able to cover a broad spectrum of experimentally observed phenomena and to present some novel results.
A Dynamical Model of Cell Differentiation
One of the major challenges in complex systems biology is that of providing a general theoretical framework to describe the phenomena involved in cell differentiation, i.e. the process whereby stem cells, which can develop into different types, become progressively more specialized. The aim of this work is that of describing a dynamical model of cell differentiation which is able to cover a broad spectrum of experimentally observed phenomena.
A delay differential-difference system of hematopoietic stem cell dynamics
Comptes Rendus Mathematique, 2015
All functionally blood cells are generated in the bone marrow through hematopoiesis from a small population of cells called hematopoietic stem cells (HSCs). HSCs have the capacity to self-renew and also the capacity to differentiate into any types of blood cells. We consider a system of two age-structured partial differential equations, describing the evolution of HSC population. By integrating this system over the age and using the characteristics method, we reduce it to a system composed with a differential equation and a delay difference equation. We investigate the asymptotic stability of steady states and the existence of a Hopf bifurcation. We conclude our work by numerical simulations. Résumé Equations différentielles et aux différencesà retard pour des modèles de dynamique des cellules souches hématopoïétiques. Toutes les cellules sanguines sont produites dans la moelle osseuse lors de l'hématopoïèseà partir d'une petite population de cellules appelées cellules souches hématopoïétiques (CSHs). Les CSHs ont la capacité de s'auto-renouveler etégalement de se différencier en tous types de cellules sanguines. Le sytème mathématique que nous considérons pour modéliser ces populations de CSHs est un système de deux equations aux dérivées partielles structurées enâge. Par intégration suivant les caractéristiques, le modèle est réduit a un système composé d'uneéquation différentielle et d'uneéquation aux différencesà retard. Nousétudions le comportement asymptotique desétats d'équilibre et l'existence d'une bifurcation de Hopf. Nous concluons notre travail par des simulations numériques.
Numerical integration of a mathematical model of hematopoietic stem cell dynamics
Computers & Mathematics with Applications, 2008
A mathematical model of hematopoiesis, describing the dynamics of stem cell population, is investigated. This model is represented by a system of two nonlinear age-structured partial differential equations, describing the dynamics of resting and proliferating hematopoietic stem cells. It differs from previous attempts to model the hematopoietic system dynamics by taking into account cell age-dependence of coefficients, that prevents a usual reduction of this system to an unstructured delay differential system. We prove the existence and uniqueness of a solution to our problem, and we investigate the existence of stationary solutions. A numerical scheme adapted to the problem is presented. We show the effectiveness of this numerical technique in the simulation of the dynamics of the solution. Numerical simulations show that long-period oscillations can be obtained in this model, corresponding to a destabilization of the system. These oscillations can be related to observations of some periodical hematological diseases (such as chronic myelogenous leukemia).
A Structured Population Model of Cell Differentiation
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.
Asymptotic behaviour of a mathematical model of hematopoietic stem cell dynamics
International Journal of Computer Mathematics, 2013
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Minimal model for stem-cell differentiation
Physical Review E, 2013
To explain the differentiation of stem cells in terms of dynamical systems theory, models of interacting cells with intracellular protein expression dynamics are analyzed and simulated. Simulations were carried out for all possible protein expression networks consisting of two genes under cell-cell interactions mediated by the diffusion of a protein. Networks that show cell differentiation are extracted and two forms of symmetric differentiation based on Turing's mechanism and asymmetric differentiation are identified. In the latter network, the intracellular protein levels show oscillatory dynamics at a single-cell level, while cell-to-cell synchronicity of the oscillation is lost with an increase in the number of cells. Differentiation to a fixed-point type behavior follows with a further increase in the number of cells. The cell type with oscillatory dynamics corresponds to a stem cell that can both proliferate and differentiate, while the latter fixed-point type only proliferates. This differentiation is analyzed as a saddle-node bifurcation on an invariant circle, while the number ratio of each cell type is shown to be robust against perturbations due to self-consistent determination of the effective bifurcation parameter as a result of the cell-cell interaction. Complex cell differentiation is designed by combing these simple two-gene networks. The generality of the present differentiation mechanism, as well as its biological relevance, is discussed.