An Efficient Kinetic Model for Assemblies of Amyloid Fibrils and Its Application to Polyglutamine Aggregation

Protein polymerization consists in the aggregation of single monomers into polymers that may fragment. Fibrils assembly is a key process in amyloid diseases. Up to now, protein aggregation was commonly mathematically simulated by a polymer size-structured ordinary differential equations (ODE) system, which is infinite by definition and therefore leads to high computational costs. Moreover, this Ordinary Differential Equation-based modeling approach implies biological assumptions that may be difficult to justify in the general case. For example, whereas several ordinary differential equation models use the assumption that polymerization would occur at a constant rate independently of polymer size, it cannot be applied to certain protein aggregation mechanisms. Here, we propose a novel and efficient analytical method, capable of modelling and simulating amyloid aggregation processes. This alternative approach consists of an integro-Partial Differential Equation (PDE) model of coalescence-fragmentation type that was mathematically derived from the infinite differential system by asymptotic analysis. To illustrate the efficiency of our approach, we applied it to aggregation experiments on polyglutamine polymers that are involved in Huntington's disease. Our model demonstrates the existence of a monomeric structural intermediate (c) over tilde (1) acting as a nucleus and deriving from a non polymerizing monomer (c(1)). Furthermore, we compared our model to previously published works carried out in different contexts and proved its accuracy to describe other amyloid aggregation processes.