Automated Design and Analysis of Gene Regulatory Networks (GRNs)

Gene Regulatory Networks (GRNs) are essential frameworks for understanding complex gene interactions and regulatory mechanisms in biological systems. Traditional GRN modeling approaches often rely on deterministic or probabilistic frameworks to simulate gene expression dynamics, but they typically overlook the critical role of spatially heterogeneous initial conditions. Synthetic developmental biology has focused on constructing GRNs to replicate specific spatial patterns, yet most models assume simplified, uniform distributions of gene products, limiting biological realism. This work addresses this limitation by introducing an approach that incorporates variable initial conditions, simulating diverse spatial distributions of gene activity in a two-dimensional environment.

We developed the GRN-Designer algorithm, an end-to-end hybrid optimization framework that combines evolutionary algorithms with gradient-based methods to construct GRNs capable of replicating predefined spatial patterns. By treating the initial expression levels and spatial activation potential of genes as adjustable parameters, the algorithm designs GRN structure and optimizes regulatory parameters to achieve target diffusion patterns. Multiple distinct spatial patterns were tested, each simulated through partial differential equations (PDEs) to model gene expression dynamics.

The algorithm successfully designed GRNs for all target patterns, ranging from simple gradients to intricate shapes, demonstrating flexibility in managing diverse spatial configurations. The constructed GRNs adaptively balanced complexity, tailoring the number of genes and regulatory interactions to match the intricacies of each target pattern. Results indicate that our approach effectively combines computational efficiency with biological realism, producing spatial patterns that closely resemble their intended designs.

This work establishes a robust framework for GRN design, with promising applications in synthetic biology and tissue engineering. By integrating heterogeneous spatial initial conditions, our model advances the realism of GRN simulations. Future enhancements may explore stochastic simulation techniques to account for biological variability, extend the framework to three-dimensional environments, and improve optimization performance to address more complex biological systems.