Seminar on Qualitative Theory of Differential Equations - Pavol Bokes (27.2.2020)
Thursday 27.2.2020 at 14:00, Lecture room M/223
Pavol Bokes:
Limit-cycle oscillatory coexpression of cross-inhibitory transcription factors: a model mechanism for lineage promiscuity
Abstract:
Lineage switches are genetic regulatory motifs that govern and maintain the commitment of a developing cell to a particular cell fate. A canonical example of a lineage switch is the pair of transcription factors PU.1 and GATA-1, of which the former is affiliated with the myeloid and the latter with the erythroid lineage within the hematopoietic system. On a molecular level, PU.1 and GATA-1 positively regulate themselves and antagonise each other via direct protein--protein interactions. Here we use mathematical modelling to identify a novel type of dynamic behaviour that can be supported by such a regulatory architecture. Guided by the specifics of the PU.1--GATA-1 interaction, we formulate, using the law of mass action, a system of differential equations for the key molecular concentrations. After a series of systematic approximations, the system is reduced to a simpler one, which is tractable to phase-plane and linearisation methods. The reduced system formally resembles, and generalises, a well-known model for competitive species from mathematical ecology. However, in addition to the qualitative regimes exhibited by a pair of competitive species (exclusivity, bistable exclusivity, stable-node coexpression) it also allows for oscillatory limit-cycle coexpression. A key outcome of the model is that, in the context of cell-fate choice, such oscillations could be harnessed by a differentiating cell to prime alternately for opposite outcomes; a bifurcation-theory approach is adopted to characterise this possibility.
This is a joint work with John R. King.