Reference

Rahayel, Shady, et al. "Differentially targeted seeding reveals unique pathological alpha-synuclein propagation patterns." Brain (2021). [webpage]

Zheng, Ying-Qiu, et al. "Local vulnerability and global connectivity jointly shape neurodegenerative disease propagation." PLoS biology 17.11 (2019): e3000495. [webpage]

Overview

This project contains the MATLAB source code for an agent-based Suspectible-Infectious-Recovered/Removed (SIR) model to predict spreading of pathogenous proteins and atrophy progression in Parkinson's Disease (PD). It contains:

• SIRsimulator.m: a function to simulate the spread of misfolded alpha-synuclein

• main.m: a demo script to simulate neuronal loss

• data folder contains the connectivity and gene expression data required by the model

• results contains the scripts to generate the figures.

Getting Started

The code does not need installation; users have to install MATLAB to run the code. Typically, the model is not computational expensive, but this depends on the size of networks (e.g., number of nodes and edges). For a network of ~100 nodes with 30% connection density, it typically takes less than 5s.

• Specify number of regions N_regions, velocity v, time increment dt, total number of steps T_total, transmission rate trans_rate, seed region seed, mobility parameter prob_stay. For example, the parameters used in Zheng et al., 2019

N_regions = 42;
v = 1;
dt = 0.01;
T_total = 20000;
init_number = 1;
syn_control = ROIsize;
prob_stay = 0.5;
trans_rate = 1;
seed = N_regions;

• Load gene expressions, atrophy, region size, functional and structural connectivity on your local system. To use the data in this repository

% load gene expressions, real atrophy, ROIsize, functional connectivity...
load('data/42regions/workspace.mat');
% load structural connectivity
load('data/42regions/sc35.mat');

This will load GBA and SNCA expressions (GBA and SNCA), connectivity length sconnLen, connectivity strength sconnDen, region size ROIsize to your workspace

• Run the model

[Rnor_all, Rmis_all, Rnor0] = SIRsimulator(N_regions, v, dt, T_total, GBA, SNCA, sconnLen, sconnDen, ROIsize, seed, syn_control, init_number, prob_stay, trans_rate);

The region-wise numbers of normal and misfolded proteins are stored in Rnor_all and Rmis_all, with Rnor0 being the number of normal proteins at healthy state.

• Simulate regional atrophy growth. This involves another two parameters to control contribution of deafferentation and endogenous neuronal death. For example, if the two factors have equal contribution:

k1 = 0.5;
k2 = 1 - k1;
% input weigths of deafferentation (scaled by structrual connectivity)
weights = sconnDen ./ repmat(sum(sconnDen, 2), 1, N_regions);

% neuronal loss caused by lack of input from neighbouring regions
ratio_cum = weights * (1-exp(-ratio * dt));
% one time step back
ratio_cum = [zeros(N_regions, 1), ratio_cum(:, 1:end-1)];
ratio_cum = k2 * ratio_cum + k1 * (1-exp(-ratio * dt));

% add all the increments across t
simulated_atrophy = cumsum(ratio_cum, 2);

Bugs and Questions

Please contain Ying-Qiu Zheng at [email protected]