Noisy Random Boolean Networks and Cell Differentiation

We propose a modification of the Random Boolean Network model where noise is allowed, in such a way that in its asymptotic state the system can visit several attractors of the deterministic dynamics. The notion of Threshold Ergodic Sets (TES) is introduced, and it is proposed that they represent cell types. The degree of differentiation of a cell is related to the number of attractors which belong to its TES, and it shown that this leads to a meaningful description of cell differentiation. By coupling the threshold, which is related to the level of noise, to mutations which may interfere with the control mechanisms of the cell, a description of the the process of cell transformation, from normal to malignant, is provided. This description, albeit abstract, is consistent with several known experimental facts.