Séance Séminaire

Colloquium de Mathématiques

Modelling and calibrating depolymerising systems

Shrinkage of large particles, either through depolymerisation (i.e., progressive shortening) or through fragmentation (breakage into smaller pieces) are dynamical phenomena which appear in many applications - our own focus being protein fibrils depolymerisation and/or fragmentation, which are thought to be a key mechanism for many diseases (Parkinson's, Alzheimer's...) as well as many functional biomolecular mechanisms (actin filaments). The dynamic nature of the experiments, as well as their nanoscale, makes it very challenging to estimate their features. We will review some results, new progresses and open questions in their estimation. More specifically, in many cases, the fragmentation kernel, i.e. the place where the individuals break down into pieces, is neither known a priori nor may be inferred by direct observations on the dividing population. In this talk, we will address this estimation problem and propose several approaches, studying and making use either of the long-term, the transient or the short-term behaviour.