title: Delayed self-regulation and time-dependent chemical drive leads to novel states in epigenetic landscapes.
abstract: The epigenetic pathway of a cell as it differentiates from a stem cell state to a mature lineage-committed one has been historically understood in terms of Waddington's landscape, consisting of hills and valleys. The smooth top and valley-strewn bottom of the hill represent their undifferentiated and differentiated states, respectively. Although mathematical ideas rooted in nonlinear dynamics and bifurcation theory have been used to quantify this picture, the importance of time delays arising from multistep chemical reactions or cellular shape transformations have been ignored so far. We argue that this feature is crucial in understanding cell differentiation and explore the role of time delay in a model of a single-gene regulatory circuit. We show that the interplay of time-dependent drive and delay introduces a new regime where the system shows sustained oscillations between the two admissible steady states. We interpret these results in the light of recent perplexing experiments on inducing the pluripotent state in mouse somatic cells. We also comment on how such an oscillatory state can provide a framework for understanding more general feedback circuits in cell development.
authors.affiliation: Department of Physics, I.I.T. Bombay, Mumbai 400076, India.
authors.forename: Mithun K
authors.initials: MK
authors.lastname: Mitra
authors.affiliation: Systems Biology Doctoral Training Centre, University of Oxford, Oxford OX1 3QU, UK.
authors.forename: Paul R
authors.initials: PR
authors.lastname: Taylor
authors.affiliation: School of Biological and Biomedical Sciences, Durham University, Durham DH1 3LE, UK.
authors.forename: Chris J
authors.initials: CJ
authors.lastname: Hutchison
authors.affiliation: Department of Physics and Astronomy, Durham University, Durham DH1 3LE, UK.
authors.forename: T C B
authors.initials: TC
authors.lastname: McLeish
authors.affiliation: Department of Mathematical Sciences, Durham University, Durham DH1 3LE, UK The Isaac Newton Institute of Mathematical Sciences, University of Cambridge, Cambridge CB3 0EH, UK buddhapriya.chakrabarti@durham.ac.uk.
authors.forename: Buddhapriya
authors.initials: B
authors.lastname: Chakrabarti
mesh_terms: D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D002454:Cell Differentiation / Q000502:physiology*; D044127:Epigenesis, Genetic / Q000502:physiology*; D053263:Gene Regulatory Networks / Q000502:physiology*; D051379:Mice; D008954:Models, Biological; D039904:Pluripotent Stem Cells / Q000166:cytology / Q000502:physiology*
keywords: epigenetics; gene regulatory networks; mathematical modelling