Co-expression properties

Of the models proposed here, if the cooperativity of activation is considered to be constant, only the model with bHLH dimerisation is capable both of exclusive expression of an arbitrary number of switch elements, and coexpression at similar levels of all elements. This behaviour is finely tunable with the key competition parameter deriving from the availability of the bHLH hetero-dimerisation partner, with lower availability being unfavourable to co-expression of the antagonistic factors (see below for a further discussion).

The model with mutual inhibition, autocatalysis, and leak can express no more than one switch element at a level higher than the other ones, and is thus less amenable to progressive elimination of unwanted factors in the course of differentiation. In order for coexpression to occur at a significantly-higher level than the leak, the cooperativity of the system must be close to 1. If differentiation was controlled by a network of this kind, initial coexpression could be maintained either by a low transcriptional strength in the system (which is consistent with antagonistic factors being expressed at a lower level in the un-differentiated state), or, as has been suggested, by regulated degradation of mRNAs.

Interestingly, the multistability behaviours of a switch based on bHLH-like dimerisation and that of a switch based on direct cross-repression are qualitatively different: the former can maintain many variables on at an equilibrium only if those variables are sufficiently high (compared to the transcription strength), while the reverse is true of the latter.

We previously studied networks of cross-repressing factors, in which the factors do not enhance their own expression (Cinquin and Demongeot, 2002). We did not include this kind of model in the present study, because for one factor to be able to dominate all the others, it had to be assumed that the cooperativity of the network was very high, an assumption which is possibly not realistic.