Cell differentiation in noisy random boolean networks.

The dynamics of genetic regulatory networks are often affected bystochastic noise, due to the small number of molecules involved in some reactions.The role of these fluctuations is analyzed in a discrete model of gene regulatorynetworks, i.e. that of noisy random Boolean networks. By relating the asymptoticstates of the noisy system to the different cell types, we show how the main featuresof the important process of cell differentiation can be described by assuming thatthe noise level changes as differentiation proceeds. Differentiation is seen as a seriesof transitions from an asymptotic state in which the system can wander amongmany states under the action of noise to other asymptotic states in which the systemcan reach fewer and fewer states. This model easily describes the fact that multipotentcells can stochastically differentiate along various routes.We show here thatthe process can also be controlled (as it happens in the embryo growth) so that it ispossible to determine the final fully differentiated state of the cell. This is achievedby forcing some genes, which are called here "swithces", to take constant values,in a way which mimicks the influence of external signals, and by simoultaneouslyvarying the noise level in the cell