December 3, 2020: the next Inria Paris Center Colloquium

The classical mathematical theory of chemical reaction networks (CRNs) views molecules as entities devoid of structure. At this level of abstraction, molecules are proper names represented by variables that track concentrations determined by mass action kinetics. Various refinements have arisen over time, such as stochastic CRNs, and formalizations emphasizing concurrency, like Petri nets. The past couple of decades saw the development of a fundamentally different formalization of reaction networks—one that views molecules as structured entities and interaction as the transformation of their graphical structure.Transformations are specified as rewrite rules of patterns contained in molecules.

This approach affects the type of network complexity that we can tackle and how we might reason about causality. The objective of my lecture is to illustrate this approach through its application to combinatorial aspects of assembly and aggregation in the context of a protein-mediated signaling system, known as the canonical Wnt pathway, which regulates cell proliferation. Although still in progress, our work suggests specific insights into the nature and biological role of large scaffolding aggregates and connects them with phenomena of phase separation.

Main contributors to this work include Hector Medina-Abarca, Andrés Ortiz, Pierre Boutillier, and Jérôme Feret.