Trends in Cognitive Sciences
ReviewSpatial Embedding Imposes Constraints on Neuronal Network Architectures
Section snippets
Network Topology versus Geometry in Neural Systems
In contemporary neuroscience, increasing volumes of data are being used to answer the question of how heterogeneous and distributed interactions between neural units might give rise to complex behaviors. Such interactions form characteristic patterns across multiple spatial scales, spanning molecules and cells to brain regions and lobes [1]. An intuitive language in which to describe such interactions is network science, which elegantly represents interconnected systems as sets of nodes (see
Physical Constraints on Network Topology and Geometry
Diverse processes guide the formation of structural connections in neural systems 6, 7. Evidence from genetics suggests that neurons with similar functions, as operationalized by similar patterns of gene expression, tend to have more similar connection profiles than neurons with less similar functions 6, 8, 9, with the greatest similarity appearing at highly interconnected, metabolically demanding hubs [10]. Of course, it is important to note that some spatial similarity in expression profiles
Reflections of Physical Constraints in Local, Mesoscale, and Global Network Topology
Across species, the brain consistently exhibits a set of topological features at local (single regions), meso (neural circuits), and global (entire connectome) scales that can be simply explained by a few spatial wiring rules 29, 36, 37. At the local scale, multiple modalities have been used to demonstrate that a key conserved topological feature is the existence of hubs, or nodes of an unexpectedly high degree 38, 39. Such hubs emerge naturally in computational models in which the location of
Relevance of Network Geometry for Dynamics and Cognition
Pressures for wiring minimization and communication efficiency can exist alongside developmental processes that produce non-isotropically structured organs that result in patterning across multiple overlapping signaling gradients [27]. It is intuitively possible that such processes could also explain the observed differences in the network topologies of different sectors of the brain 55, 56, which can impinge on the functions that those sectors are optimized to perform (Box 3). Indeed, prior
Relevance of Network Geometry for Disease
The spatial architecture of brain networks not only impacts our understanding of dynamics and cognition but also our understanding of neurological disease and psychiatric disorders. Mounting evidence suggests that many diseases and disorders of mental health can be thought of fruitfully as network disorders, where the anatomy and physiology of crossregional communication can go awry [70]. Intuitively, spatial anisotropies of developmental processes, or the spatial specificity of pathology,
Statistics, Null Models, and Generative Models
In the previous sections we outlined developmental rules for efficient wiring, and we discussed the reflections of these rules in spatial patterns of healthy and diseased brain dynamics. Collectively, the studies reviewed motivate the broader use and further development of sophisticated and easily implementable tools for the analysis of the spatial embedding of a network [83]. We outline here the current state of the field in developing effective network statistics, network null models, and
Concluding Remarks and Future Directions
The spatial embedding of the brain is an important driver of its connectivity, which in turn directly constrains neural function and by extension behavior. Emerging tools from network science can be used to assess this spatial architecture, thereby allowing investigators to test more specific hypotheses about brain network structure and dynamics. While we envisage that the use of these tools will significantly expand our understanding, it is also important to acknowledge their limitations. In
Acknowledgments
We would like to thank Ann Sizemore for valuable input in the construction of Box 2 – Applied Algebraic Topology. D.S.B. and J.S. acknowledge support from the John D. and Catherine T. MacArthur Foundation, the Alfred P. Sloan Foundation, the ISI Foundation, the Paul Allen Foundation, the Army Research Laboratory (W911NF-10-2-0022), the Army Research Office (Bassett-W911NF-14-1-0679, Grafton-W911NF-16-1-0474, DCIST-W911NF-17-2-0181), the Office of Naval Research, the National Institute of Mental
Glossary
- Adjacency matrix
- an N × N matrix of a graph, where N is the number of nodes. Each element Aij of the matrix gives the strength of the edge between nodes i and j.
- Allometric scaling
- in biology this term refers to the differential (compared to isometric scaling) growth of different aspects of physiology with respect to body size. We discuss here the allometric scaling of gray matter volume with respect to white matter volume, which is described with a power law.
- Cycle
- in applied algebraic topology, this
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