Matthew Ricci: Data-Driven Modeling of Bifurcations in Systems Biology

Dynamical systems can undergo qualitative, topological changes in their orbit structure called bifurcations when underlying parameters cross a threshold: the "shape" of their behavior alters fundamentally. The development of data-driven tools for modeling these changes holds special promise in the life sciences, from the design of gene regulatory networks to the prediction of catastrophic oscillations in neural circuits. In this talk, I describe an ongoing research program which tackles this challenge by focusing on the realistic case where governing equations are unknown and dynamical behavior must be predicted from prior knowledge given noisy, sparse data. Building on classical work in so-called model manifold theory, our approach learns a shared feature landscape where diverse systems coalesce within a unified embedding space, revealing their underlying qualitative structure. I first describe work which uses such learned universal embeddings of low-dimensional dynamical systems to classify circuits by their function. Next, I demonstrate how a simple autoencoder can learn an implicit notion of topological conjugacy which functions as a robust detector of Hopf bifurcations in single-cell RNA sequencing data from the pancreas. Finally, we generalize to the case of spatiotemporal dynamics, where I outline recent work on building reduced-order parametric models ofpartial differential equations with applications to spatial patterning in the ocellated lizard. We conclude with some future directions, notably extensions to high-dimensional systems and applications to synthetic biology, where engineered organisms and tissues could be designed for stable, predictable functions in dynamic environments.