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Limit cycles, multistability, and bifurcations - Applications to circadian rhythms and to embryonic cell fate specification
(Université Libre de Bruxelles)
Salle de séminaire 4ième étage (Bâtiment CEI-2 Antenne Inria Lyon)
Salle de séminaire 4ième étage
Bâtiment CEI-2 Antenne Inria Lyon
INRIA- antenne Lyon- La Doua Batiment CEI-2 56 Boulevard Niels Bohr 6960 Villeurbanne cedex France
Numerical simulations and bifurcation analyses are widely used in computational biology to unravel dynamical properties of biological systems. This will be illustrated here through two examples.
Circadian clocks are usually modeled by limit cycle oscillators. These models account for the emergence of oscillations at the level of single cells and allow theoretical analyses of the dynamical properties of circadian oscillations, including their entrainment by light-dark cycles and resetting by light pulses. Recent single cell experiments however revealed a great cell-to-cell heterogeneity in the oscillatory behaviour, with many cells displaying damped oscillations. Numerical and analytical investigation of the circadian Goodwin model shows that damped oscillators can be entrained over larger ranges of period of the light-dark cycle.
During embryonic development, the specification of different cell fates results from interactions between transcription factors. These regulatory networks often exhibit multiple stable steady states (multistability), providing a common dynamical basis for differentiation. I will present here a model for early murine embryogenesis which describes the specification of cells from the inner cell mass (ICM) into epiblast (Epi) or primitive endoderm (PrE). The model incorporates the intracellular gene regulatory network as well as the intercellular interactions involving Erk/Fgf4 signaling pathway. The results are analyzed by means of bifurcation diagrams. The model displays tristability in a range of Fgf4 concentrations, accounts for the self-organized specification process observed in vivo, and predicts that heterogeneities in extracellular Fgf4 concentration play a primary role in the spatial arrangement of the Epi/PrE cells in a salt-and-pepper pattern.