  Parkinson's disease (PD) is the second most common neurodegenerative disorder
worldwide, yet there is no disease-modifying therapy up to this date. The
biological complexity underlying PD hampers the investigation of the principal
contributors to its pathogenesis. In this context, mechanistic models grounded
in molecular-level knowledge provide virtual labs to uncover the primary events
triggering PD onset and progression and suggest promising therapeutic targets.
Multiple modeling efforts in PD research have focused on the pathological role
of $\alpha$-synuclein ($\alpha$syn), a presynaptic protein that emerges from
the intricate molecular network as a crucial driver of neurodegeneration. Here,
we collect the advances in mathematical modeling of $\alpha$syn homeostasis,
focusing on aggregation and degradation pathways, and discussing potential
modeling improvements and possible implications in PD therapeutic strategy
design.
