A mathematical framework for measuring and tuning tempo in developmental gene regulatory networks.

Embryo development is a dynamic process governed by the regulation of timing and sequences of gene expression, which control the proper growth of the organism. Although many genetic programmes coordinating these sequences are common across species, the timescales of gene expression can vary significantly among different organisms. Currently, substantial experimental efforts are focused on identifying molecular mechanisms that control these temporal aspects. In contrast, the capacity of established mathematical models to incorporate tempo control while maintaining the same dynamical landscape remains less understood. Here, we address this gap by developing a mathematical framework that links the functionality of developmental programmes to the corresponding gene expression orbits (or landscapes). This unlocks the ability to find tempo differences as perturbations in the dynamical system that preserve its orbits. We demonstrate that this framework allows for the prediction of molecular mechanisms governing tempo, through both numerical and analytical methods. Our exploration includes two case studies: a generic network featuring coupled production and degradation, with a particular application to neural progenitor differentiation; and the repressilator. In the latter, we illustrate how altering the dimerisation rates of transcription factors can decouple the tempo from the shape of the resulting orbits. We conclude by highlighting how the identification of orthogonal molecular mechanisms for tempo control can inform the design of circuits with specific orbits and tempos.

Mutation of p53 increases the competitive ability of pluripotent stem cells.

During development, the rate of tissue growth is determined by the relative balance of cell division and cell death. Cell competition is a fitness quality-control mechanism that contributes to this balance by eliminating viable cells that are less fit than their neighbours. The mutations that confer cells with a competitive advantage and the dynamics of the interactions between winner and loser cells are not well understood. Here, we show that embryonic cells lacking the tumour suppressor p53 are 'super-competitors' that eliminate their wild-type neighbours through the direct induction of apoptosis. This elimination is context dependent, as it does not occur when cells are pluripotent and it is triggered by the onset of differentiation. Furthermore, by combining mathematical modelling and cell-based assays we show that the elimination of wild-type cells is not through competition for space or nutrients, but instead is mediated by short-range interactions that are dependent on the local cell neighbourhood. This highlights the importance of the local cell neighbourhood and the competitive interactions within this neighbourhood for the regulation of proliferation during early embryonic development.

Choice of friction coefficient deeply affects tissue behaviour in stochastic epithelial vertex models.

To understand the mechanisms that coordinate the formation of biological tissues, the use of numerical implementations is necessary. The complexity of such models involves many assumptions and parameter choices that result in unpredictable consequences, obstructing the comparison with experimental data. Here, we focus on vertex models, a family of spatial models used extensively to simulate the dynamics of epithelial tissues. Usually, in the literature, the choice of the friction coefficient is not addressed using quasi-static deformation arguments that generally do not apply to realistic scenarios. In this manuscript, we discuss the role that the choice of friction coefficient has on the relaxation times and consequently in the conditions of cell cycle progression and division. We explore the effects that these changes have on the morphology, growth rate and topological transitions of the tissue dynamics. These results provide a deeper understanding of the role that an accurate mechanical description plays in the use of vertex models as inference tools. This article is part of a discussion meeting issue 'Causes and consequences of stochastic processes in development and disease'.