Novel generic models for differentiating stem cells reveal oscillatory mechanisms

Abstract

Understanding cell fate selection remains a central challenge in developmental biology. We present a class of simple yet biologically motivated mathematical models for cell differentiation that generically generate oscillations and hence suggest alternatives to the standard framework based on Waddington’s epigenetic landscape. The models allow us to suggest two generic dynamical scenarios that describe the differentiation process. In the first scenario, gradual variation of a single control parameter is responsible for both entering and exiting the oscillatory regime. In the second scenario, two control parameters vary: one responsible for entering, and the other for exiting the oscillatory regime. We analyse the standard repressilator and four variants of it and show the dynamical behaviours associated with each scenario. We present a thorough analysis of the associated bifurcations and argue that gene regulatory networks with these repressilator-like characteristics are promising candidates to describe cell fate selection through an oscillatory process.

Cell Fate Decisions in the Neural Crest, from Pigment Cell to Neural Development

“…This 'double-repressilator' circuit has three natural modes of response: an equilibrium in which all TF levels are equal (Figure 4d, left), oscillatory expression levels (Figure 4d, center), and novel equilibria in which one TF is expressed at a much higher level than the other two (Figure 4d, right). As reported in Farjami et al (2021), the two different kinds of equilibrium state appear at low and high levels of parameters that describe the overall level of interaction between the three genes, with the oscillatory regime providing a natural intermediate regime that mediates between them. This has a natural interpretation in terms of dynamical evolution from a highly multipotent state, through an oscillatory state in which the cell makes repeated transitions between transient "sub-states" in which it is biased in favor of a specific fate, but has not yet made a fate selection, through to stable acquisition of a single fate.…”

“…In the course of formulating the CFR hypothesis, we asked whether a molecular mechanism could be envisaged that would exhibit the cyclical behavior required; our modelling investigations generated some striking observations that show interesting parallels to the biology [120]. Of course, it is important to remember that, like most mathematical models, the system is highly simplified and thus must be interpreted cautiously; nevertheless, the outputs of the modelling showed several striking features that at least provide some support for the possibility of the behavior the CFR model requires.…”

“…However, it turns out that a simple and natural modification of the standard repressilator GRN does allow the emergence of multiple fates, and moreover provides a robust pathway between highly multipotent and fate-specialized states [120]. The key modification of the standard repressilator is to incorporate mutual repression between every pair of TFs, with potentially unequal strengths in the repressions that act in one cyclic direction compared to those that act in the opposite direction around the circuit, as illustrated in Figure 4c.…”

“…Where the cross-repression strengths are set equal, oscillatory behavior shows symmetrical cycling of each transcription factor, so that sub-states biased to each of the derivative fates are equally weighted (Figure 4d), and as the external signal increases, the specific fate stably adopted is determined by the transcription factor expression levels at the time when the external signal exceeds the oscillatory boundary [120]. Our modeling also revealed that exit from the oscillatory regime to a stable state (fate) can also be driven by a second external signaling factor that is fate-specific, e.g., Ltk signaling for iridophores.…”

Parameterising Translational Feedback Models of Autoregulatory RNA-Binding Proteins in Saccharomyces cerevisiae

“…Furthermore, transcriptional feedback loops have also been extended to complex topological scenarios, leading to rich dynamical behaviours. Interlocked feedback loops, for instance, have been shown to be relevant in bacterial quorum sensing mechanisms, while variants of the repressilator were incorporated into model cell differentiation [48,49]. Noise control and propagation has also been largely investigated in both negative and positive feedback loops [50,51].…”