Can the lack of fibrillar form of alpha-synuclein in Lewy bodies be explained by its catalytic activity?

Abstract

Finding the causative pathophysiological mechanisms for Parkinson's disease (PD) is important for developing therapeutic interventions. Until recently, it was believed that Lewy bodies (LBs), the hallmark of PD, are mostly composed of alpha-synuclein (α-syn) fibrils. Recent results (Shahmoradian et al. (2019)) demonstrated that the fibrillar form of α-syn is lacking from LBs. Here we propose that this surprising observation can be explained by the catalytic activity of the fibrillar form of α-syn. We assumed that α-syn fibrils catalyze the formation of LBs, but do not become part of them. We developed a mathematical model based on this hypothesis. By using the developed model, we investigated the consequences of this hypothesis. In particular, the model suggests that the long incubation time of PD can be explained by a two-step aggregation process that leads to its development: (i) aggregation of monomeric α-syn into α-syn oligomers and fibrils and (ii) clustering of membrane-bound organelles, which may cause disruption of axonal trafficking and lead to neuron starvation and death. The model shows that decreasing the rate of destruction of α-syn aggregates in somatic lysosomes accelerates the formation of LBs. Another consequence of the model is the prediction that removing α-syn aggregates from the brain after the aggregation of membrane-bound organelles into LBs has started may not stop the progression of PD because LB formation is an autocatalytic process; hence, the formation of LBs will be catalyzed by aggregates of membrane-bound organelles even in the absence of α-syn aggregates. The performed sensitivity study made it possible to establish the hierarchy of model parameters with respect to their effect on the formation of vesicle aggregates in the soma.

Keywords: Alpha-synuclein; Axon; Mathematical modeling; Neuron; Parkinson’s disease.

Fig. 1.

A diagram of a neuron showing transport of a-syn monomers and misfolded aggregates in the axon and catalytic effect of α-syn aggregates leading to the formation of aggregates of membrane-bound organelles (which later become LBs and LNs). Demand sites are numbered starting with the most proximal (#1) to the most distal (#N) [96].

Fig. 2.

Kinetic diagrams showing various kinetic states in the following sub-models: (a) in the sub-model of slow axonal transport of α-syn monomers from the soma to the synapse. The diagram is based on the model of SCa transport of neurofilaments [25], which was modified in [26,27] to extend it to SCb transport of cytosolic proteins. (b) in the sub-model simulating transitions between various states of α-syn in the presynaptic terminal: α-syn monomers suspended in the cytosol, α-syn monomers bound to the membrane, and α-syn aggregated in the cytosol; (c) in the sub-model of fast axonal transport of α-syn aggregates from the presynaptic terminal to the soma; (d) in the sub-model of fast axonal transport of various vesicles from the soma to the presynaptic terminal and their aggregation that is presumably catalyzed by α-syn aggregates; (e) in the sub-model simulating vesicle aggregation in the soma, which is presumably catalyzed by α-syn aggregates, and also simulating the destruction of α-syn aggregates in the somatic lysosomes. The above sub-models interact with each other. For example, α-syn -monomers (Fig. 2a) enter the presynaptic terminal and form aggregates (Fig 2b). α-syn aggregates formed in the presynaptic terminal are transported to the soma (Fig. 3c). En route, the α-syn aggregates catalyze aggregation of membrane fragments from damaged vesicles that later become LNs (Fig. 2d). After exiting the axon α-syn aggregates accumulate in the soma and also catalyze aggregation of membrane fragments that later become LBs (Fig 2e). The model thus connects all the subsystems shown in Fig. 2a-e.

Fig. 3.

(a) Various linear concentrations (per unit length of the axon) of α-syn monomers in the axon, including the total concentration, which is the sum of α-syn concentrations in motor-driven, pausing, and diffusing states. (b) Total flux of α-syn monomers due to active transport, powered by molecular motors, and diffusion in the cytosol. $T_{B,1/2,s}^{\ast }=2.59\times {10}^5\text{s}.k_{10}^{\ast }=3\times {10}^{-7}{\text{s}}^{-1}$. .

Fig. 3.

(a) Various linear concentrations (per unit length of the axon) of α-syn monomers in the axon, including the total concentration, which is the sum of α-syn concentrations in motor-driven, pausing, and diffusing states. (b) Total flux of α-syn monomers due to active transport, powered by molecular motors, and diffusion in the cytosol. $T_{B,1/2,s}^{\ast }=2.59\times {10}^5\text{s}.k_{10}^{\ast }=3\times {10}^{-7}{\text{s}}^{-1}$. .

Fig. 4.

(a) Volumetric concentrations of α-syn monomers and α-syn aggregates in the presynaptic terminal and surface concentration of α-syn monomers bound to the presynaptic membrane. (b) Volumetric concentration of α-syn aggregates in the presynaptic terminal (same as in (a), but on the enlarged scale). $T_{B,1/2,s}^{\ast }=2.59\times {10}^5\text{s}.k_{10}^{\ast }=3\times {10}^{-7}{\text{s}}^{-1}$. .

Fig. 4.

(a) Volumetric concentrations of α-syn monomers and α-syn aggregates in the presynaptic terminal and surface concentration of α-syn monomers bound to the presynaptic membrane. (b) Volumetric concentration of α-syn aggregates in the presynaptic terminal (same as in (a), but on the enlarged scale). $T_{B,1/2,s}^{\ast }=2.59\times {10}^5\text{s}.k_{10}^{\ast }=3\times {10}^{-7}{\text{s}}^{-1}$. .

Fig. 5.

Linear concentrations (per unit length of the axon) of retrogradely transported α-syn aggregates and free a-syn aggregates in the axon. $T_{B,1/2,\text{s}}^{\ast }=2.59\times {10}^5\text{s}.k_{10}^{\ast }=3\times {10}^{-7}{\text{s}}^{-1}$. .

Fig. 6.

Total area of membrane in all membrane-bound organelles that are actively anterogradely transported in the axon and in all membrane-bound organelles that are detached from MTs, per unit length of the axon. Also, the anterograde flux of membrane due to transport of membrane-bound organelles. $T_{B,1/2,s}^{\ast }=2.59\times {10}^5\text{s}.k_{10}^{\ast }=3\times {10}^{-7}{\text{s}}^{-1}$.

Fig. 7.

(a) Total area of the membrane in all vesicle aggregates in the axon, per unit length of the axon, vs x*, at t*=3.17 years. (b) Total area of the membrane in all vesicle aggregates in the axon, per unit length of the axon, vs time, at $x^{\ast }=L^{\ast }/2$. $T_{B,1/2,s}^{\ast }=2.59\times {10}^5\text{s}.k_{10}^{\ast }=3\times {10}^{-7}{\text{s}}^{-1}$.

Fig. 7.

(a) Total area of the membrane in all vesicle aggregates in the axon, per unit length of the axon, vs x*, at t*=3.17 years. (b) Total area of the membrane in all vesicle aggregates in the axon, per unit length of the axon, vs time, at $x^{\ast }=L^{\ast }/2$. $T_{B,1/2,s}^{\ast }=2.59\times {10}^5\text{s}.k_{10}^{\ast }=3\times {10}^{-7}{\text{s}}^{-1}$.

Fig. 8.

(a) Volumetric concentration of α-syn aggregates in the cytosol of the soma. (b) Volumetric concentration of membrane surrounding membrane-bound vesicles in the soma, and membrane contained in fragments and fragmented organelles in the soma. $T_{B,1/2,s}^{\ast }=2.59\times {10}^5\text{s}$ and $T_{B,1/2,s}^{\ast }=2.59\times {10}^{10}\text{s}.k_{10}^{\ast }=3\times {10}^{-7}{\text{s}}^{-1}$. The curves marked by “no α-syn 1 year” are computed under the assumption that all α-syn aggregates are removed (by enhancing their destruction via autophagosomes) 1 year after the beginning of the α-syn aggregation process.

Fig. 8.

(a) Volumetric concentration of α-syn aggregates in the cytosol of the soma. (b) Volumetric concentration of membrane surrounding membrane-bound vesicles in the soma, and membrane contained in fragments and fragmented organelles in the soma. $T_{B,1/2,s}^{\ast }=2.59\times {10}^5\text{s}$ and $T_{B,1/2,s}^{\ast }=2.59\times {10}^{10}\text{s}.k_{10}^{\ast }=3\times {10}^{-7}{\text{s}}^{-1}$. The curves marked by “no α-syn 1 year” are computed under the assumption that all α-syn aggregates are removed (by enhancing their destruction via autophagosomes) 1 year after the beginning of the α-syn aggregation process.

Fig. 9.

(a) Volumetric concentration of α-syn aggregates in the cytosol of the soma. (b) Volumetric concentration of membrane surrounding membrane-bound vesicles in the soma, and membrane contained in fragments and fragmented organelles in the soma. $T_{B,1/2,s}^{\ast }=2.59\times {10}^5\text{s}$ and $T_{B,1/2,s}^{\ast }=2.59\times {10}^{10}\text{s}.k_{10}^{\ast }=3\times {10}^{-10}{\text{s}}^{-1}$.

Fig. 9.

(a) Volumetric concentration of α-syn aggregates in the cytosol of the soma. (b) Volumetric concentration of membrane surrounding membrane-bound vesicles in the soma, and membrane contained in fragments and fragmented organelles in the soma. $T_{B,1/2,s}^{\ast }=2.59\times {10}^5\text{s}$ and $T_{B,1/2,s}^{\ast }=2.59\times {10}^{10}\text{s}.k_{10}^{\ast }=3\times {10}^{-10}{\text{s}}^{-1}$.