From Genes to Patterns: A Framework for Modeling the Emergence of Embryonic Development from Transcriptional Regulation

Jimena Garcia-Guillen Ezzat El-Sherif ^*

• The University of Texas Rio Grande Valley, Edinburg, United States

Understanding embryonic patterning, the process by which groups of cells are partitioned into distinct identities defined by gene expression, is a central challenge in developmental biology. This complex phenomenon is driven by precise spatial and temporal regulation of gene expression across many cells, resulting in the emergence of highly organized tissue structures. While similar emergent behavior is well understood in other fields, such as statistical mechanics, the regulation of gene expression in development remains less clear, particularly regarding how molecular-level gene interactions lead to the large-scale patterns observed in embryos. In this study, we present a modeling framework that bridges the gap between molecular gene regulation and tissue-level embryonic patterning. Beginning with basic chemical reaction models of transcription at the single-gene level, we progress to model gene regulatory networks (GRNs) that mediate specific cellular functions. We then introduce phenomenological models of pattern formation, including the French Flag and Temporal Patterning/Speed Regulation models, and integrate them with molecular/GRN realizations. To facilitate understanding and application of our models, we accompany our mathematical framework with computer simulations, providing intuitive and simple code for each model. A key feature of our framework is the explicit articulation of underlying assumptions at each level of the model, from transcriptional regulation to tissue patterning. By making these assumptions clear, we provide a foundation for future experimental and theoretical work to critically examine and challenge them, thereby improving the accuracy and relevance of gene regulatory models in developmental biology. As a case study, we explore how different strategies for integrating enhancer activity affect the robustness and evolvability of GRNs that govern embryonic pattern formation. Our simulations suggest that a two-step regulation strategy, enhancer activation followed by competitive integration at the promoter, ensures more standardized integration of new enhancers into developmental GRNs, highlighting the adaptability of eukaryotic transcription. These findings shed new light on the transcriptional mechanisms underlying embryonic patterning, while the overall modeling framework serves as a foundation for future experimental and theoretical investigations.