CMX Lunch Seminar
Quantitative models in biology largely partition into either classical mechanistic (e.g., differential equations) or statistical/machine-learned. The former tend to fail to faithfully incorporate noisy, heterogeneous data, whereas the latter struggle to extract underlying interpretable mechanisms. In this talk, I will share a humble case study in the pursuit of bridging these techniques in the context of a specific biological problem. Advances in microscopy have provided snapshot images of individual RNA molecules within a nucleus. Decoding the underlying spatiotemporal dynamics is important for understanding gene expression, but challenging due to the static, heterogeneous, and stochastic nature of the data. I will write down a stochastic reaction-diffusion model and show that observations of this process follow a spatial point (Cox) process constrained by a reaction-diffusion PDE. Inference on this data resembles a classical "inverse problem" but differs in the observations of individual particles rather than concentrations. We perform inference using variational Bayesian Monte Carlo with promising results. However, a number of seemingly open computational challenges remain in the development of scalable and extendable techniques for this inverse problem.
This work is in collaboration with the Fangyuan Ding lab of Biomedical Engineering at UCI.