In conventional disorder-order phase transitions, a system shifts from a highly symmetric state, where all states are equally accessible (disorder) to a less symmetric state with a limited number of available states (order). This transition may occur by varying a control parameter that represents the intrinsic noise of the system. It has been suggested that stem cell differentiation can be considered as a sequence of such symmetry-breaking events. Pluripotent stem cells, with their capacity to develop into any specialized cell type, are considered highly symmetric systems. In contrast, differentiated cells have lower symmetry, as they can only carry out a limited number of functions. For this hypothesis to be valid, differentiation should emerge collectively in stem cell populations. Additionally, such populations must have the ability to self-regulate intrinsic noise and navigate through a critical point where spontaneous symmetry breaking (differentiation) occurs. This study presents a mean-field model for stem cell populations that considers the interplay of cell-cell cooperativity, cell-to-cell variability, and finite-size effects. By introducing a feedback mechanism to control intrinsic noise, the model can self-tune through different bifurcation points, facilitating spontaneous symmetry breaking. Standard stability analysis showed that the system can potentially differentiate into several cell types mathematically expressed as stable nodes and limit cycles. The existence of a Hopf bifurcation in our model is discussed in light of stem cell differentiation.
Keywords: bifurcation theory; cell differentiation; mean field theory; phase transitions; self-tuned criticality; symmetry breaking.