Spreading of pathologenic proteins through the brain connectome

Mathieu Bourdenx - Thomas Paul (@Thomas-Paul-Fr) - 2021

Code to model the spread of pathogenic proteins through the mouse brain connectome. This is a replication from by Henderson et al. Nat. Neurosci, 2019. The original code has been developped using RStudio 3.3.3 and can be found here. The code has been here replicated in Python.

This ReadMe is subdivided into different sections and aimed at clarifying the main inputs required and the main outputs obtained after running the code.

Requirements

This code has been written for Python 3.6/3.7 and successfully tested on Microsoft Windows 10 and MacOS 11.2.3 (BigSur). It requires the following packages:

• numpy
• matplotlib
• seaborn
• pandas
• scipy
• tqdm
• statsmodels

Datasets

All data are contained in the folder Data83018. The essential files are the following ones:

• data.csv [37rowsx118columns]
• connectivity_ipsi.csv [58rowsx58columns]
• connectivity_contra.csv [58rowsx58columns]
• SncaExpression.csv [116rowsx2columns]

Scripts

Pipeline.py This is the main file allowing to control and run the model. Several functions have been implemented to allow to run the model it is simple version or combining expression values. It also allows to run some robustness tests.

Main inputs:

• exp_data: Quantification of alpha-synuclein pathology (values from data.csv)
• timepoints: by default [1,3,6]. Can be modified when changing the experimental data set.
• connectivity_ipsi.csv & connectivity_contra.csv: connectivity matrices obtained from Oh et al. 2014
• synuclein: Energy (i.e. expression) values found in SncaExpression.csv. By defaut use_expression_values= False.
• seed: seeding region. By default: iCPu. If the seed is not found in seed list returns [ERROR in make_Xo].
• nb_of_region: by default: 58 (maximum value). Used the compute the robustness of the model.

Main outputs: The main outputs are saved in two main folders. In the folder "output":

• predicted_pathology{seed}.csv: CSV table with the predicted pathology values for each timepoint.
• model_output_MPI{timepoint}{seed}.csv: CSV table that contains the results of the linear regression for a specific timepoint.
• stats{seed}.csv: Contains for each timepoint the Pearson's r coefficient, the p-value and the corrected p-value. (Bonferroni's correction)

In the folder "plots"

• Predicted_VS_Path_MPI{timepoint}{seed}.png/.pdf: lollipop plots showing the predicted vs pathology data.
• density_VS_residual{seed}.png/.pdf: Density plots of the residuals for a specific seed.
• predicted_pathology{seed}.csv: Heatmap with normalized values of predicted pathology. By default Drop_seed : False. If True then it drops the seed region from the Heatmap and plots to allow a better dynamic range in visualization. Predictions_{seed}_excluded{seed}.png/.pdf.
• plot_r_(c)_MPI{timepoint}{seed}.png/.pdf: Plots of the evolution of r with respect to c for a specific timepoint.
• Random_Seed/Random_patho/Random_Adja.png/.pdf: Plots of the the fits obtained when we used different controls.
• Stability_MPI{timepoint}{seed}.png/.pdf: Graph used to compute the minimal regions needed to obtain a stable fit r
• Mean_MPI{timepoint}_SW{Sliding_number}{seed}.png/.pdf: Same as before but when computing a mean with a Sliding window.
• SD_MPI{timepoint}_SW{Sliding_number}{seed}.png/.pdf: Same as before but when computing a Standard Deviation with a Sliding window.

The same tables and figures are also produced when running the scripts for the Iterative model or considering each mouse individually.

process_files.py Processes the data inputs (Quantified pathology matrix, ipsilateral connectivity matrix, and contralateral connectivity matrix). Its main outputs are the adjacency matrix, a pathology matrix, and the list of regions of interest shaped as panda DataFrames. More information on each of the functions defined in process_files.py can be found in the code.

Laplacian.py Computes from the adjacency matrix the out-degree Laplacian matrix. Computes the Laplacian adjacency matrix weighted with the energy value of snca gene expression when use_expression_values=True.

fitfunctions.py Set of functions with different roles. "make_Xo" has been reproduced as described in Henderson's code and produces of a column vector (here shaped as a Pandas DataFrame) that contains 0 for non-seed regions or 1 for the seed region. "predict_Lout" predicts the regional alpha-synuclein pathology when given the Laplacian, the seed, a timepoint of prediction, and the tuning constant c. "c_fit" returns the value of the best fit c and the best correlation coefficient using "predict_Lout" and Pearson's correlation test.

Robustness_Stability.py Breaks the matrices into pieces to compute different test of stability. Confere the definition of the functions for more information.

summative_model.py Iterative model. The main modifications from the original code resides in the prediction function that uses a different equation.