UBC Math Bio Seminar: Ulysse Herbach

Inferring graphs of interactions between genes has become a textbook case for high-dimensional statistics, while models describing gene expression at the molecular level have come into their own with the advent of single-cell data. Linking these two approaches seems crucial today, but the dialogue is far from obvious: statistical models often suffer from a lack of biological interpretability, and mechanistic models are known to be difficult to calibrate from real data.

In this talk, I will show that it is possible to obtain a statistical framework that is both mathematically well-posed and realistic in terms of current biological knowledge, from a stochastic biochemical model—whose master equation forms a hyperbolic PDE system—describing the expression over time of an arbitrary number of interacting genes. More precisely, the idea is to view the invariant probability distribution of the Markov process as a statistical likelihood: this distribution turns out to admit a simple expression for a whole class of parameters, and can then be interpreted as a Markov random field with interesting properties.

This work is in collaboration with Elias Ventre, Thibault Espinasse, Gérard Benoit and Olivier Gandrillon.