Information theory for model reduction in stochastic dynamical systems

Model reduction is the construction of simple yet predictive descriptions of the dynamics of many-body systems in terms of a few relevant variables. A prerequisite to model reduction is the identification of these relevant variables, a task for which no general method exists. Here, we develop a systematic approach based on the information bottleneck to identify the relevant variables, defined as those most predictive of the future. We elucidate analytically the relation between these relevant variables and the eigenfunctions of the transfer operator describing the dynamics. Further, we show that in the limit of high compression, the relevant variables are directly determined by the slowest-decaying eigenfunctions. Our information-based approach indicates when to optimally stop increasing the complexity of the reduced model. Further, it provides a firm foundation to construct interpretable deep learning tools that perform model reduction. We illustrate how these tools work on benchmark dynamical systems and deploy them on uncurated datasets, such as satellite movies of atmospheric flows downloaded directly from YouTube.

Zyxin is all you need: machine learning adherent cell mechanics

Cellular form and function emerge from complex mechanochemical systems within the cytoplasm. No systematic strategy currently exists to infer large-scale physical properties of a cell from its many molecular components. This is a significant obstacle to understanding biophysical processes such as cell adhesion and migration. Here, we develop a data-driven biophysical modeling approach to learn the mechanical behavior of adherent cells. We first train neural networks to predict forces generated by adherent cells from images of cytoskeletal proteins. Strikingly, experimental images of a single focal adhesion protein, such as zyxin, are sufficient to predict forces and generalize to unseen biological regimes. This protein field alone contains enough information to yield accurate predictions even if forces themselves are generated by many interacting proteins. We next develop two approaches - one explicitly constrained by physics, the other more agnostic - that help construct data-driven continuum models of cellular forces using this single focal adhesion field. Both strategies consistently reveal that cellular forces are encoded by two different length scales in adhesion protein distributions. Beyond adherent cell mechanics, our work serves as a case study for how to integrate neural networks in the construction of predictive phenomenological models in cell biology, even when little knowledge of the underlying microscopic mechanisms exist.