Lewy body radius growth: The hypothesis of the cube root of time dependency

This paper presents a model for the growth of Lewy bodies (LBs), which are pathological hallmarks of Parkinson's disease (PD). The model simulates the growth of classical LBs, consisting of a core and a halo. The core is assumed to comprise lipid membrane fragments and damaged organelles, while the halo consists of radiating alpha-synuclein (α-syn) fibrils. The Finke-Watzky model is employed to simulate the aggregation of lipid fragments and α-syn monomers. Analytical and numerical exploration of the governing equations yielded approximate solutions applicable for larger times. The application of these approximate solutions to simulate LB radius growth led to the discovery of the cube root hypothesis, which posits that the LB radius is proportional to the cube root of its growth time. Sensitivity analysis revealed that the LB radius is unaffected by the kinetic rates of nucleation and autocatalytic growth, with growth primarily regulated by the production rates of lipid membrane fragments and α-syn monomers. The model indicates that the formation of large LBs associated with PD is dependent on the malfunction of the machinery responsible for the degradation of lipid membrane fragments, α-syn monomers, and their aggregates.