Anna Marciniak-Czochra (Université de Heidelberg)

Mathematical models of discrete and continuous cell differentiation

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.