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Network Neuroscience

BIOINF - MATH 540: Mathematics of Biological Networks

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The Human Connectome

https://www.humanconnectome.org/

https://alleninstitute.org/brain-science/connectomics

Sporns, O., Tononi, G., & Kötter, R. (2005). The human connectome: a structural description of the human brain. PLoS computational biology, 1(4), e42.

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Connectomics can track and predict patterns of disease spread

Mapping the human connectome

The Human Connectome

Fornito, A., Zalesky, A., & Breakspear, M. (2015). The connectomics of brain disorders. Nature reviews neuroscience, 16(3), 159-172.

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Adjacency Matrix

Graph

Unweighted

Weighted

Directed

Hybrid

The Human Connectome

Functional connectivity

Structural connectivity

Fornito, Alex, Andrew Zalesky, and Michael Breakspear. "Graph analysis of the human connectome: promise, progress, and pitfalls." Neuroimage 80 (2013): 426-444.

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The Human Connectome

Depression

Attention deficit hyperactivity disorder (ADHD)

Schizophrenia

Fornito, Alex, et al. "General and specific functional connectivity disturbances in first-episode schizophrenia during cognitive control performance." Biological psychiatry 70.1 (2011): 64-72.
Korgaonkar, Mayuresh S., et al. "Abnormal structural networks characterize major depressive disorder: a connectome analysis." Biological psychiatry 76.7 (2014): 567-574.

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Schematic of the modular organization of the brain, depicting overlapping module structure

The Human Connectome

Fornito, A., Zalesky, A., & Breakspear, M. (2015). The connectomics of brain disorders. Nature reviews neuroscience, 16(3), 159-172.

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The Human Connectome

From the Web

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The Human Connectome

Bullmore, E. T., & Bassett, D. S. (2011). Brain graphs: graphical models of the human brain connectome. Annual review of clinical psychology, 7(1), 113-140.

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Grid Cells: Global positioning system that helps people navigate

https://www.nobelprize.org/uploads/2018/06/edvard-moser-lecture.pdf

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Hypergraphs

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Motivation

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A Tensor is an 𝑑-way array

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Motivation

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Genomic Networks

Ecological Networks

Metabolic Networks

Many biological systems involve higher-order (multiway) interactions

Compared to graphs, hypergraphs allow each hyperlink (hyperedge) to connect more than two nodes.

Bairey, Eyal, Eric D. Kelsic, and Roy Kishony. "High-order species interactions shape ecosystem diversity." Nature communications 7, no. 1 (2016): 1-7.
Dotson, Gabrielle A., ……., Indika Rajapakse. "Deciphering Multi-way Interactions in the Human Genome." Nature Communications 13, no. 1 (2022): 5498.

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Motivation

Hypergraphs can represent multidimensional relationships unambiguously
For example, when using a graph model to represent metabolic networks, it is often unclear whether metabolites A, B, C, D, and E participate in the same reaction.

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