It has long been recognised that cellular differentiation could result from epigenetic memory, controlled by the dynamical properties of the same system, present with an identical structure in all cells (Delbrück, 1949), rather than from a progressive, irreversible loss of differentiation potential; a fundamental property of such a control system would be the presence of positive feedback circuits (Gouzé, 1998, Plahte et al., 1995, Cinquin and Demongeot, 2002, Snoussi, 1998, Soulé, 2003, Thomas, 1981). Indeed, pioneer experiments showed that the genomes of some differentiated cell types retain the capacity to regenerate a whole organism (Gurdon et al., 1975, Gurdon, 1962), and more recent experiments have strengthened the view that there is extensive plasticity in cell-fate determination (reviewed by Blau and Baltimore, 1991, Blau and Blakely, 1999, and Theise and Krause, 2002).
Bistable switches have been given a thorough theoretical investigation (Cherry and Adler, 2000), and have been constructed de novo (Gardner et al., 2000) or modified (Ozbudak et al., 2004). There is evidence, discussed in section 2.1, that cells undergoing differentiation sometimes face commitment decisions which involve more than two possible outcomes, but switches involving more than two variables have not been given extensive attention (we are not aware of any generic mathematical model that addresses cellular differentiation, with more than two possible outcomes). In the following, we discuss the relevance of these high-dimensional switches to the modeling of cellular differentiation, and investigate the properties of different molecular models, evaluating them with the current knowledge of the mechanisms of cellular differentiation. In particular, we test whether these models are able to display a coexistence of antagonistic factors at low levels, as decision-making with increased expression levels could be a relevant model of differentiation.