The Mathematics of Phenotypic State Transition: Paths and Potential

Abstract

Change in the phenotype of a cell is considered as a transition
of a cell from one cellular state to another. Cellular state transition
can be driven by an external cue or by the noise in molecular processes.
Over the years, generalized physical principles, and associated mathematical models have been developed to understand phenotypic state
transition. Starting with Waddington’s epigenetic landscape, phenotypic
state transition is seen as a movement of cells on a potential landscape.
Though the landscape model is close to the thermodynamic principles of
state change, it is difficult to envisage it from experimental observations.
Therefore, phenotypic state transition is often considered as a discrete
state jump process. This approach is particularly useful to estimate the
paths of state transition from experimental observations. In this review,
we discuss both of these approaches and the associated mathematical
formulations. Furthermore, we explore the opportunities to connect these
two approaches and the limitations of our current understanding and
mathematical methods.