Fig 1.
Boolean dynamics are implemented on the networks, wherein the activation state of nodes undergoes changes determined by the cumulative sum of edge weights from their direct neighbors, taking into account the signs of connections as indicated by the Pearson coefficient: if the total sum is positive, the node becomes active, otherwise it becomes inactive. In this example, node A starts out inactive. Node B is active and is linked to node A by an edge with a negative contribution of 0.3. On the other hand, node C, which is also active, contributes to the activation of A positively with a weight of 0.5. In total, the contribution is 0.2, so node A is activated. In the next step, A is active and contributes positively to the activation of C, so C remains active. However, the contribution to node B is negative, so it becomes inactive.
Fig 2.
Impact of noise on the cross-correlation coefficient of signals between nodes in a combined network.
In the absence of noise (0%), the majority of cross-correlation values approached 1, making it challenging to rank node pairs based on connection strength. However, with 5% noise, the cross-correlation values exhibited greater variation, enabling easier identification of paths between a selected source and target.
Fig 3.
Calculation of the path score.
The cross-correlation coefficient is computed by assessing the signals for each connected node pair. A path score is then determined for all possible paths, defined as the sum of the reciprocals of the cross-correlation coefficients between consecutive node pairs along a specific path.
Fig 4.
Network permutation for negative controls.
In this example, in the first permutation, the edges (b,c) and (d,e) were exchanged with the edges (b,d) and (c,e). For the second permutation, the edges (a,e), (b,c) were swapped with the edges (a,c) and (b,e). In the third permutation, the top network’s edge swap was applied first, followed by the middle network’s edge swap: (a,b), (b,c) and (d,e) were exchanged for (a,c), (b,d) and (b,e). Three possibilities were considered when determining if the paths from the original network appeared in the permuted networks. In the first permutation, the path existed in the permuted network and was also identified as a top path. In the second permutation, the original path existed in the permuted network but was not identified as a top path. Finally, in the third permutation, the original path did not exist in the permuted network at all.
Fig 5.
Illustration of the multilayer network construction.
Icons were adapted from freely available resources at Openclipart and Wikimedia Commons, under Creative Commons licenses.
Fig 6.
The data from each layer is taken from the ADNI cohort and used to create networks, with nodes representing the dataset’s elements (genetics, molecular, PET, MRI, risk factors, and phenotype) and edges representing the mutual information between element pairs across all subjects. For clarity, nodes are labeled numerically in the figure, and the corresponding variable names are provided in S1–S6 Tables. See high resolution networks at https://dsb-lab.github.io/networks/
Table 1.
Characteristics of the ADNI cohort
Fig 7.
Following a hierarchy that connects each layer successively, starting with the genomics layer and working up to the phenotypic (clinical) layer, individual networks are created and linked together using mutual information once again. The risk factors nodes are shown in the periphery of the network, as well as being external to the biological hierarchy, for visualization purposes. For clarity, nodes are labeled numerically in the figure, and the corresponding variable names are provided in S1–S6 Tables. See high resolution image at https://dsb-lab.github.io/multilayer_net/.
Fig 8.
Network densities within and between layers.
The connectance matrix was calculated using the expression in (7).
Fig 9.
Path analysis from the genetic layer in ADNI participants.
Depictions of the multilayer paths identified through Boolean simulations with the genetic layer as the starting point. The top paths, meeting criteria for negative controls, are presented for each input (genetic) - output (clinical phenotype) pair. Nodes within each layer are color-coded to reflect the node’s degree, indicating the frequency of its appearance in a path as a percentage of the total paths. For clarity, nodes are labeled numerically in the figure, and the corresponding variable names are provided in S1–S6 Tables. For detailed high-resolution paths, please refer to https://dsb-lab.github.io/network_paths/.
Fig 10.
Path analysis from the molecular layer in ADNI participants.
Depictions of the multilayer paths identified through Boolean simulations with the molecular layer as the starting point. The top paths, meeting criteria for negative controls, are presented for each input (molecular) - output (clinical phenotype) pair. Nodes within each layer are color-coded to reflect the node’s degree, indicating the frequency of its appearance in a path as a percentage of the total paths. For clarity, nodes are labeled numerically in the figure, and the corresponding variable names are provided in S1–S6 Tables. For detailed high-resolution paths, please refer to https://dsb-lab.github.io/network_paths/.
Fig 11.
Path analysis from the PET layer in ADNI participants.
Depictions of the multilayer paths identified through Boolean simulations with the PET layer as the starting point. The top paths, meeting criteria for negative controls, are presented for each input (PET) - output (clinical phenotype) pair. Nodes within each layer are color-coded to reflect the node’s degree, indicating the frequency of its appearance in a path as a percentage of the total paths. For clarity, nodes are labeled numerically in the figure, and the corresponding variable names are provided in S1–S6 Tables. For detailed high-resolution paths, please refer to https://dsb-lab.github.io/network_paths/.
Fig 12.
Path analysis from the MRI layer in ADNI participants.
Depictions of the multilayer paths identified through Boolean simulations with the MRI layer as the starting point. The top paths, meeting criteria for negative controls, are presented for each input (MRI) - output (clinical phenotype) pair. Nodes within each layer are color-coded to reflect the node’s degree, indicating the frequency of its appearance in a path as a percentage of the total paths. For clarity, nodes are labeled numerically in the figure, and the corresponding variable names are provided in S1–S6 Tables. For detailed high-resolution paths, please refer to https://dsb-lab.github.io/network_paths/.
Fig 13.
Path analysis from the risk factors layer in ADNI participants.
Depictions of the multilayer paths identified through Boolean simulations with the risk factors layer as the starting point. The top paths, meeting criteria for negative controls, are presented for each input (risk factors) - output (clinical phenotype) pair. Nodes within each layer are color-coded to reflect the node’s degree, indicating the frequency of its appearance in a path as a percentage of the total paths. For clarity, nodes are labeled numerically in the figure, and the corresponding variable names are provided in S1–S6 Tables. For detailed high-resolution paths, please refer to https://dsb-lab.github.io/network_paths/.
Table 2.
Summary of FDG PET connectivity across network layers.
Fig 14.
Selection of the top paths when the source is a risk factor node.
The top 20 shortest paths are presented for each input (risk factors) - output (clinical phenotype) pair. Nodes in the risk factor layer are shown in yellow and those in the phenotype layer in blue. The paths for a particular source out of the five chosen are shown in red: drowsiness, hypertension, crying, cardiovascular history and musculoskeletal pain. For clarity, nodes are labeled numerically in the figure, and the corresponding variable names are provided in S6 Table. For detailed high-resolution paths, please refer to https://dsb-lab.github.io/risk_paths/.