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.

Reprogramming, oscillations and transdifferentiation in epigenetic landscapes

“…While we predicted the presence of sustained oscillations in the one gene network reported previously [12], this study conclusively highlights the importance of these oscillations for a more realistic twogene network. Additionally, oscillations in the concentrations of transcription factors show different characteristics, (a) oscillations between the differentiated and undifferentiated state in one regime (IIA), and (b) oscillations between the two differentiated states in a different regime (IIB).…”

“…Finally there is a decay term with the strength of the degradation process controlled by the decay parameter k. This model has been studied extensively [11,13,16] as a representation of the cell differentiation process and has yielded insights into the epigenetic landscape as a cell differentiates. In order to model the reverse differentiation process, we incorporate a time dependent chemical drive (along the lines of our earlier work [12]) as in experiments [18]. The feedback regulation depend on the concentrations of the TFs at some previous times, to account for the finite timescales of chromosome reorganisation and other epigenetic state markers.…”

“…In a previous work [12], we argued that modeling of the underlying gene regulatory network requires careful consideration of the time delays associated with the feedback regulation of the transcription factors. The reverse differentiation process can take place over a duration of weeks, and is accompanied by a host of changes in the epigenetic markers that characterize the state of the cell, such as changes in histone protein expression levels [19,20], as well as changes in the chromatin compaction characteristics [21][22][23][24][25][26][27][28][29].…”

“…The discovery of the reprogramming pathway has led to an interest in mathematically modeling the epigenetic landscape though the underlying Gene Regulatory Networks (GRN). Initial studies using a toy single gene regulatory network studied the properties of cellular differentiation using a selfactivating gene [8][9][10][11][12]. Later studies have expanded this work to model more realistic two gene networks, that are self-activating and mutually inhibiting [11,[13][14][15][16][17].…”

Designing a blueprint for next‐generation stem cell bioprocessing development

“…When the ball is on the mountaintop, it can roll down through any of the valleys below; this represents the process of cell development through differentiation into different cell types. Cells “switch” during development in an almost discontinuous manner between cell fates, giving rise to discrete developmental stages, as well as discrete lineages and terminally‐differentiated cell types (Hemberger et al, ; Mitra et al, ). All these processes are tightly controlled and regulated via coordinated activation or repression of target genes, which depend on the orchestrated action of key regulatory transcription factors, in combination with changes in epigenetic marks such as DNA methylation, histone modifications, and chromatin state (Kim et al, ; Martinez Arias & Brickman, ; Rouhani et al, ).…”