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.

Dynamical phase diagram of an auto-regulating gene in fast switching conditions

“…As we have seen, working with the total protein number is analytically convenient because unlike the free protein number, it is conserved under fast binding-unbinding reactions (see Ref. 31 for a related application). However, in single-cell experiments, we typically obtain data for the statistics of free protein numbers.…”

An appreciation of the prescience of Don Gilbert (1930–2011): master of the theory and experimental unravelling of biochemical and cellular oscillatory dynamics

“…For other recent reviews, see Brodsky (2014); Poon (2016); Ahn et al (2017); Palmisano et al (2017); Papagiannakis et al (2017); Murray et al (2019); Bokes and King (2019).…”

A robust method for designing multistable systems by embedding bistable subsystems

“…In addition, mathematical models have been proposed to achieve bistability in gene regulatory networks without any high cooperativity coefficients 39 , 40 . Bifurcation theory is also an efficient method to explore the mechanisms of GATA1-PU.1 module 41 . We have proposed a mathematical model to realise the mechanisms of GATA-switching and designed an effective algorithm to realise tristability of mathematical models 42 .…”