A reaction-diffusion model for the progression of Parkinsons disease

📝 Abstract

The temporal and spatial development of Parkinson’s disease has been characterised as the progressive formation of {\alpha}-synuclein aggregations through susceptible neuronal pathways. This article describes a new model for this progression mechanism in which Parkinsonian damage moves over time through the nervous system by the combined effect of the reaction kinetics of pathogenesis and molecular diffusion. In the reaction-diffusion model, the change from a healthy state to the disease state advances through the nervous system as a wave front of Parkinsonian damage, marking its path by accumulations of damaged {\alpha}-synuclein and neurotoxic levels of oxidative species. Progression according to this model follows the most vulnerable routes through the nervous system as described by Braak’s staging theory and predicts that damage will advance at differing speeds depending upon the level and number of risk factors, in a manner that gives new insights into the variations with which Parkinson’s disease develops.

💡 Analysis

The temporal and spatial development of Parkinson’s disease has been characterised as the progressive formation of {\alpha}-synuclein aggregations through susceptible neuronal pathways. This article describes a new model for this progression mechanism in which Parkinsonian damage moves over time through the nervous system by the combined effect of the reaction kinetics of pathogenesis and molecular diffusion. In the reaction-diffusion model, the change from a healthy state to the disease state advances through the nervous system as a wave front of Parkinsonian damage, marking its path by accumulations of damaged {\alpha}-synuclein and neurotoxic levels of oxidative species. Progression according to this model follows the most vulnerable routes through the nervous system as described by Braak’s staging theory and predicts that damage will advance at differing speeds depending upon the level and number of risk factors, in a manner that gives new insights into the variations with which Parkinson’s disease develops.

📄 Content

• In memorial to Prof. Peter Wellstead. This was his last piece of work. † Deceased 24th June 2016.

A reaction-diffusion model for the progression of Parkinson’s disease*

Míriam R. García1 , Mathieu Cloutier 2, Peter Wellstead3†

1 Bioprocess Engineering Group. IIM-CSIC, Vigo Spain. To whom correspondence should be addressed (miriam@iim.csic.es) 2Ecole Polytechnique de Montreal, Montreal, QC, Canada 3NUIM, Maynooth, Ireland

The temporal and spatial development of Parkinson’s disease has been characterised as the progressive formation of α-synuclein aggregations through susceptible neuronal pathways. This article describes a new model for this progression mechanism in which Parkinsonian damage moves over time through the nervous system by the combined effect of the reaction kinetics of pathogenesis and molecular diffusion. In the reaction-diffusion model, the change from a healthy state to the disease state advances through the nervous system as a wave front of Parkinsonian damage, marking its path by accumulations of damaged α-synuclein and neurotoxic levels of oxidative species. Progression according to this model follows the most vulnerable routes through the nervous system as described by Braak’s staging theory and predicts that damage will advance at differing speeds depending upon the level and number of risk factors, in a manner that gives new insights into the variations with which Parkinson’s disease develops.

I. INTRODUCTION The pathology of Parkinson’s disease is characterised by the progressive appearance in the nervous system of aggregations (consisting principally of damaged α-synuclein) that follow ‘an ascending course with little inter-individual variations’ [Braak, 2003a]. The same authors have suggested that this spatially progressive sequence could be achieved [Braak, 2003b] by an invading pathogen which enters the enteric nervous system (ENS) and proceeds by backward projection to the brain stem and hence the brain itself. The Braak progression theory concerns the long term development of Parkinson’s disease, and is therefore highly important in building an overall understanding of Parkinson’s from beginning to end.
The idea that an invading pathogen can itself propagate through the nervous systems has been thrown into question by the finding [Pan-Montojo, 2010] that Parkinsonian damage an animal model caused by intragastrically administered toxin is not accompanied by traces of the toxin. This paper describes an explanation of progression that overcomes this problem. Specifically, we propose that, while an invading pathogen may initiate Parkinsonian damage locally, it is the endogenous pathogenesis mechanism of the disease, rather than the pathogen, that causes subsequent transmission and progression.
In particular, we describe a model for the spread of Parkinsonian damage by a combination of (i) the reaction kinetics of pathogenesis which cause the local growth of α- synuclein misfolds (αSYNmis) and the rise of reactive oxidative species (ROS) to neuro-toxic levels, plus (ii) molecular diffusion of these pathogenic products. We envisage the process as operating as follows: an initial trigger mechanism (e.g. an external pathogen or other stress factor) overthrows the homeostatic neurochemical balance within a localised compartment somewhere in the nervous system. This causes local pathogenesis whereby levels of α-synuclein increase and reactive oxidative species (ROS) rise to neurotoxic levels that create the disease state.
In this model it is the neurochemical reaction dynamics of pathogenesis, combined with molecular diffusion, which communicates the elevated ROS and protein damage to neighbouring compartments. This causes the effected compartments themselves undergo pathogenesis, such that Parkinsonian damage spreads sequentially from compartment to compartment. The rate of progression of the disease state depends upon the kinetics of the pathogenic reaction and this, in turn, is determined by the severity of the risk factors and the vulnerability of individual neurons.
II. A MODEL FOR THE PATHOGENESIS OF PARKINSON’S DISEASE A. Pathogenesis as a critical transition within a neuronal compartment. Despite being a well-known phenomenon in biology [Murray, 2002, Volpert, 2009], the spread of chemical species and concentrations by reaction-diffusion (R-D) has not previously been considered as a progression mechanism for Parkinson’s disease. This is probably because the neurochemical kinetics of Parkinson’s pathogenesis has not previously been understood (see, for example, [Lotharius, 2002, Hattori, N, 2004, Shin, 2009, Schapira, 2011]). However, a recently developed mathematical model [Cloutier, 2012a] of α-synuclein and oxidative metabolism simulates the pathogenesis of Parkinson’s within a neuronal compartment, and gives an analytical picture of the pathogenic process [Cloutier, 201

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