Modelling the Delta1/Notch1 pathway: in search of the mediator(s) of neural stem cell differentiation

The Notch1 signalling pathway has been shown to control neural stem cell fate through lateral inhibition of mash1, a key promoter of neuronal differentiation. Interaction between the Delta1 ligand of a differentiating cell and the Notch1 protein of a neighbouring cell results in cleavage of the trans-membrane protein, releasing the intracellular domain (NICD) leading to the up regulation of hes1. Hes1 homodimerisation leads to down regulation of mash1. Most mathematical models currently represent this pathway up to the formation of the HES1 dimer. Herein, we present a detailed model ranging from the cleavage of the NICD and how this signal propagates through the Delta1/Notch1 pathway to repress the expression of the proneural genes. Consistent with the current literature, we assume that cells at the self renewal state are represented by a stable limit cycle and through in silico experimentation we conclude that a drastic change in the main pathway is required in order for the transition from self-renewal to differentiation to take place. Specifically, a model analysis based approach is utilised in order to generate hypotheses regarding potential mediators of this change. Through this process of model based hypotheses generation and testing, the degradation rates of Hes1 and Mash1 mRNA and the dissociation constant of Mash1-E47 heterodimers are identified as the most potent mediators of the transition towards neural differentiation.