A bi-monomeric, nonlinear Becker–Döring-type system to capture oscillatory aggregation kinetics in prion dynamics. (7th November 2019) - Doumic, Marie; Fellner, Klemens; Mezache, Mathieu; Rezaei, Human
Highlights: A new class of polymerisation-depolymerisation reaction systems is proposed, which are nonlinear variants of Becker–Döring system. The model may explain experimentally observed periodic oscillations in protein aggregation. In the case of a simplest two-polymer model, an exponential convergence towards a positive steady state, together with damped oscillations, is proved. The infinite dimensional system features two explicit links to perturbed Lotka–Volterra models. Abstract: In this article, in order to understand the appearance of oscillations observed in protein aggregation experiments, we propose, motivate and analyse mathematically the differential system describing the kinetics of the following reactions: { V + W → k 2 W, W + C i → a i C i + 1, 1 ≤ i ≤ n, C i + V → b i C i − 1 + 2 V, 2 ≤ i ≤ n, with n finite or infinite. This system may be viewed as a variant of the seminal Becker–Döring system, and is capable of displaying sustained though damped oscillations.