Some commitments are irreducible to binary steps

Cellular differentiation is often envisioned as a temporal cascade of decisions, by which cells restrict their potential fate further and further, until they reach a unique fate. It has been argued that each of these decisions is binary (Kaletta et al., 1997, Brown et al., 1988, Sternberg and Horvitz, 1989, Lin et al., 1998). However, recent studies of hematopoeisis strongly suggest otherwise (Rothenberg et al., 1999), and point to models in which many cross-antagonising factors compete with each other (see below), receiving activation or inhibition from extracellular signals, leading to the progressive up-regulation of one specific factor, and down-regulation of all others. The hypothesis that decisions are more complex than binary is also supported by the fact that the same cell type can be obtained by different developmental pathways (Rothenberg et al., 1999).

Apart from hematopoiesis, two systems have been described which seem to clearly involve a 3-outcome decision, irreducible to a sequence of 2 binary decisions: cells in the C. elegans hemaphrodite germline are directed to mitosis, differentiation as sperm, or differentiation as oocyte (Ellis and Kimble, 1995), and founder cells of Drosophila mesoderm are directed to specific dorsal muscle or pericardial cell phenotypes by 3 mutually-repressive genes (Jagla et al., 2002).

Finally, in at least two instances of neural development, fate choices between a great diversity of possible outcomes have been shown, and are unlikely to be mediated by a series of binary commitments. This is the case of olfactory development (Serizawa et al., 2000, Ebrahimi et al., 2000), which does not involve genetic rearrangements (Eggan et al., 2004), and of the regulation of hundreds of alternatively-spliced transcripts of a single gene in the Drosophila brain (Neves et al., 2004).

Thus, it appears that model a, depicted in Figure 1, is not the only possibility, and that model b of Figure 1 should also be taken into account.

Figure 1: Arrows represent activation, and squares inhibition. Adapted from Cinquin and Demongeot (2002).

Having shown that high-dimensional switches are necessary for the mathematical modeling of some developmental decisions, we now turn to the way their structure should be modeled: differentiation factors are often antagonistic (section 2.1.2), which doesn't prevent them from being sometimes coexpressed (section 2.1.3), and modulation of the interaction strength is a way differentiation is regulated (section 2.1.4). The basis for a mathematical formulation of the models is provided in section 2.2.