Mathematical models of discrete and continuous cell differentiation

Abstract:

Cell differentiation is a multi-step process, in which a relatively

small population of stem cells undergo asymmetric cell divisions

leading to formation of more mature cells (differentiation process)

and subsequent replenishment of cells at different maturation stages.

Understanding of the mechanisms governing cell differentiation is of

central interest for stem cell biology, especially because of its

clinical impact. One established method of modeling of such

hierarchical cell systems is to use a discrete collection of ordinary

differential equations, each of which describes a well-defined

differentiation stage. However, there are indications that the

differentiation process is less rigid and that it involves transitions

which are continuous, along with discrete ones.

In this talk we compare the applicability of both the discrete and

continuous framework to describe dynamics of cell differentiation.

Multi-compartmental and structured populations models are formulated

to investigate the role of regulatory feedbacks in the process of

blood regeneration. Model results are compared to the clinical data.

Analysis of the model equations leads to a generalization of the

concept of self-renewal potential, which might be helpful to define

stem cells population.