A bi-monomeric, nonlinear Becker-Döring-type system to capture oscillatory aggregation kinetics in prion dynamics
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:
$$\left \{\!\!
\begin{array}{lclr}
{\cal V}+{\cal W}&\xrightarrow{k}&2{\cal W},\\
{\cal W}+{\cal C}_i&\xrightarrow{a_i} &{\cal C}_{i+1}, \quad & 1\leq i\leq n,\\
{\cal C}_i+{\cal V} &\xrightarrow{b_i} &{\cal C}_{i-1}+2{\cal V}, \quad & 2\leq i\leq n,\\
\end{array}
\right.
$$
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.
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