Seminar 27.2.2020: Pavol Bokes

Seminar on Qualitative Theory of Differential Equations
organized by P.Quittner, M.Fila and R.Kollar

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Seminar 27.2.2020: Pavol Bokes

Postby quittner » Wed Feb 19, 2020 8:08 am

Seminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations

Štvrtok 27.2.2020 o 14:00, poslucháreň M-223

Pavol Bokes (KAMŠ FMFI UK):
Limit-cycle oscillatory coexpression of cross-inhibitory transcription factors:
a model mechanism for lineage promiscuity

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.
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