Abstract
During development, cells gradually assume specialized fates via changes of transcriptional dynamics, sometimes even within the same developmental stage. For anterior-posterior (AP) patterning in metazoans, it has been suggested that the gradual transition from a dynamic genetic regime to a static one is encoded by different transcriptional modules. In that case, the static regime has an essential role in pattern formation in addition to its maintenance function. In this work, we introduce a geometric approach to study such transition. We exhibit two types of genetic regime transitions, respectively arising through local or global bifurcations. We find that the global bifurcation type is more generic, more robust, and better preserves dynamical information. This could parsimoniously explain common features of metazoan segmentation, such as changes of periods leading to waves of gene expressions, “speed/frequency-gradient” dynamics, and changes of wave patterns. Geometric approaches appear as possible alternatives to gene regulatory networks to understand development.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
A new subsection "Relation to existing networks" was added to the Model section to emphasize the connection of the model to biology and experiments. The last section of the Results was rewritten to include a discussion of three different metrics that could possibly help distinguish experimentally Hopf and SNIC bifurcations in the context of metazoan segmentation. A new supplementary figure for Figure 7 was added to the Results to illustrate one of these metrics: the distribution of positions as a function of the control parameter. A new subsection "Experimental evidence" was added to the Discussion to review the current experimental evidence associated to each of the three metrics. A new subsection "Evolution and developmental plasticity" was added to the Discussion to connect our results with the gene networks obtained via in silico evolution in previous studies. A new supplementary figure for Figure 4 was added to the Results to emphasize the role of the non-linearity in the weights of the dynamic and static modules for getting a Hopf bifurcation in our framework. Two new supplemental figures and two new movies for Figure 4 were added to the Results to evaluate the robustness to noise of pattern formation models based on subcritical Hopf bifurcations. The schematic of Figure 7 was modified to include the results from a Van der Pol model that provides a better visualisation of an asymmetric wave profile. The explanation of the difference between local and global bifurcations was modified to make it more pedagogical.
https://github.com/laurentjutrasdube/Dual-Regime_Geometry_for_Embryonic_Patterning
