Monte-Carlo Simulation of a Multi-Dimensional Switch-Like Model of Stem Cell Differentiation

The process controlling the diferentiation of stem, or progenitor, cells into one specific functional direction is called lineage specification. An important characteristic of this process is the multi-lineage priming, which requires the simultaneous expression of lineage-specific genes. Prior to commitment to a certain lineage, it has been observed that these genes exhibit intermediate values of their expression levels. Multi-lineage differentiation has been reported for various progenitor cells [Hu et al., 1997, Akashi et al., 2003, Kim et al., 2005, Miyamoto et al., 2002, Swiers et al., 2006, Loose & Patient, 2006, Patient et al., 2007, Graf, 2002], and it has been explained through the bifurcation of a metastable state [Roeder & Glauche, 2006, Huang et al., 2007, Chickarmane et al., 2009]. During the differentiation process the dynamics of the core regulatory network follows a bifurcation, where the metastable state, corresponding to the progenitor cell, is destabilized and the system is forced to choose between the possible developmental alternatives. While this approach gives a reasonable interpretation of the cell fate decision process, it fails to explain the multi-lineage priming characteristic. Here, we describe a new multi-dimensional switch-like model that captures both the process of cell fate decision and the phenomenon of multi-lineage priming. We show that in the symmetrical interaction case, the system exhibits a new type of degenerate bifurcation, characterized by a critical hyperplane, containing an infinite number of critical steady states. This critical hyperplane may be interpreted as the support for the multi-lineage priming states of the progenitor. Also, the cell fate decision (the multi-stability and switching behavior) can be explained by a symmetry breaking in the parameter space of this critical hyperplane. These analytical results are confirmed by Monte-Carlo simulations of the corresponding chemical master equations.