Linking Structure and Function in Macroscale Brain Networks
Authors: Laura E. Suárez, Ross D. Markello, Richard F. Betzel, Bratislav Misic
Journal: Trends in Cognitive Sciences (2020)

The emergence of network neuroscience allows researchers to quantify the link between the organizational features of neuronal networks and the spectrum of cortical functions.Current models indicate that structure and function are significantly correlated, but the correspondence is not perfect because function reflects complex multisynaptic interactions in structural networks.Function cannot be directly estimated from structure, but must be inferred by models of higher-order interactions. Statistical, communication, and biophysical models have been used to translate brain structure to brain function.Structure–function coupling is regionally heterogeneous and follows molecular, cytoarchitectonic, and functional hierarchies. Structure–function relationships are a fundamental principle of many naturally occurring systems. However, network neuroscience research suggests that there is an imperfect link between structural connectivity and functional connectivity in the brain. Here, we synthesize the current state of knowledge linking structure and function in macroscale brain networks and discuss the different types of models used to assess this relationship. We argue that current models do not include the requisite biological detail to completely predict function. Structural network reconstructions enriched with local molecular and cellular metadata, in concert with more nuanced representations of functions and properties, hold great potential for a truly multiscale understanding of the structure–function relationship. Structure–function relationships are a fundamental principle of many naturally occurring systems. However, network neuroscience research suggests that there is an imperfect link between structural connectivity and functional connectivity in the brain. Here, we synthesize the current state of knowledge linking structure and function in macroscale brain networks and discuss the different types of models used to assess this relationship. We argue that current models do not include the requisite biological detail to completely predict function. Structural network reconstructions enriched with local molecular and cellular metadata, in concert with more nuanced representations of functions and properties, hold great potential for a truly multiscale understanding of the structure–function relationship. The relationship between structure and function is a central concept in natural sciences and engineering. Consider how the conformation of a protein determines its chemical properties and, ultimately, its biological function. The folding of the protein into a 3D structure promotes interactions among amino acids, allowing the protein to chemically interact with other molecules and endowing it with function. Conversely, disruption of the protein's structure results in loss of function. Tellingly, the protein is said to be denatured, highlighting the idea that changing its structure has fundamentally altered its natural function. The function of the nervous system is analogously shaped by the structure and arrangement of neurons and neuronal populations. The complex network of synaptic projections forms a hierarchy (see Glossary) of nested and increasingly polyfunctional neural circuits that support perception, cognition, and action. Modern imaging technology permits high-throughput reconstruction of neural circuits across spatiotemporal scales and across species (Box 1). Through extensive international data sharing efforts, increasingly detailed reconstructions of the nervous system's connection patterns are available in humans and in multiple model organisms, including invertebrate [1.Chiang A-S. et al.Three-dimensional reconstruction of brain-wide wiring networks in Drosophila at single-cell resolution.Curr. 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Inter-regional projections promote signaling and synchrony among distant neuronal populations, giving rise to coherent neural dynamics, measured as regional time series of electromagnetic or hemodynamic neural activity. Systematic coactivation among pairs of regions can be used to map functional connectivity (FC) networks. Over the past decade, these dynamics are increasingly recorded without task instruction or stimulation; the resulting 'intrinsic' or ' resting-state' FC is thought to reflect spontaneous neural activity [18.Biswal B. et al.Functional connectivity in the motor cortex of resting human brain using echo-planar MRI.Magn. Reson. Med. 1995; 34: 537-541Crossref PubMed Scopus (5503) Google Scholar]. Intrinsic FC patterns are highly organized [19.Damoiseaux J. et al.Consistent resting-state networks across healthy subjects.Proc. Natl. Acad. Sci. 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U.S.A. 2009; 106: 13040-13045Crossref PubMed Scopus (2684) Google Scholar,25.Cole M.W. et al.Intrinsic and task-evoked network architectures of the human brain.Neuron. 2014; 83: 238-251Abstract Full Text Full Text PDF PubMed Scopus (516) Google Scholar. The persistent and reproducible nature of brain activity during rest makes resting-state FC an ideal starting point to study structure–function relationships [26.Honey C.J. et al.Can structure predict function in the human brain?.NeuroImage. 2010; 52: 766-776Crossref PubMed Scopus (291) Google Scholar,27.Damoiseaux J.S. Greicius M.D. Greater than the sum of its parts: a review of studies combining structural connectivity and resting-state functional connectivity.Brain Struct. Funct. 2009; 213: 525-533Crossref PubMed Google Scholar. Here we synthesize the current state of knowledge linking structure and function in macroscale brain networks. We first show that direct one-to-one links between structure and function are limited and inherently obscured by the networked nature of the brain. We survey modern quantitative methods that move away from direct correlations between structure and function by conceptualizing function as emerging from higher-order interactions among multiple neuronal populations, with a focus on strengths, limitations, and commonalities. We posit that the next steps in understanding network-level structure–function relationships must take into account regional heterogeneity by enriching network reconstructions with microscale attributes, including transcriptomic, cytoarchitectonic, and neuromodulatory information. We close by highlighting emerging theories that macroscale structure–function relationships are not uniform across the brain, but vary in parallel with cytoarchitectonic and representational hierarchies. Early studies emphasized correlations between structural and functional connection weights. Structural weights are correlated with functional weights [28.Honey C. et al.Predicting human resting-state functional connectivity from structural connectivity.Proc. Natl. Acad. Sci. U.S.A. 2009; 106: 2035-2040Crossref PubMed Scopus (1543) Google Scholar], and nodes that are central to structural networks also tend to be central in functional networks [28.Honey C. et al.Predicting human resting-state functional connectivity from structural connectivity.Proc. Natl. Acad. Sci. U.S.A. 2009; 106: 2035-2040Crossref PubMed Scopus (1543) Google Scholar]. Furthermore, structurally connected pairs of neural elements display greater FC than structurally unconnected pairs [28.Honey C. et al.Predicting human resting-state functional connectivity from structural connectivity.Proc. Natl. Acad. Sci. 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A particularly salient example is the case of homotopic functional connections between corresponding structures in the two hemispheres. These are typically the strongest subset of functional connections [32.Mišić B. et al.The functional connectivity landscape of the human brain.PLoS One. 2014; 9: e111007Crossref PubMed Scopus (14) Google Scholar], but not all homotopic functional connections are supported by a direct underlying callosal projection [33.Shen K. et al.Stable long-range interhemispheric coordination is supported by direct anatomical projections.Proc. Natl. Acad. Sci. 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The discordance between structure and function is particularly pronounced at the mesoscopic scale. Intrinsic networks commonly observed in resting-state FC and meta-analytic coactivation cannot be recovered from structural networks [37.Mišić B. et al.Cooperative and competitive spreading dynamics on the human connectome.Neuron. 2015; 86: 1518-1529Abstract Full Text Full Text PDF PubMed Google Scholar,38.Betzel R.F. et al.Diversity of meso-scale architecture in human and non-human connectomes.Nat. Commun. 2018; 9: 346Crossref PubMed Scopus (21) Google Scholar (Figure 1C). While intrinsic networks can be reproducibly defined using independent component analysis [19.Damoiseaux J. et al.Consistent resting-state networks across healthy subjects.Proc. Natl. Acad. Sci. U.S.A. 2006; 103: 13848-13853Crossref PubMed Scopus (2665) Google Scholar], community detection [39.Power J.D. et al.Functional network organization of the human brain.Neuron. 2011; 72: 665-678Abstract Full Text Full Text PDF PubMed Scopus (1499) Google Scholar], or data-driven clustering [20.Bellec P. et al.Multi-level bootstrap analysis of stable clusters in resting-state fMRI.NeuroImage. 2010; 51: 1126-1139Crossref PubMed Scopus (170) Google Scholar,21.Thomas Yeo B. et al.The organization of the human cerebral cortex estimated by intrinsic functional connectivity.J. Neurophysiol. 2011; 106: 1125-1165Crossref PubMed Scopus (2040) Google Scholar, both in resting state recordings and in meta-analytic coactivation [24.Smith S.M. et al.Correspondence of the brain's functional architecture during activation and rest.Proc. Natl. Acad. Sci. U.S.A. 2009; 106: 13040-13045Crossref PubMed Scopus (2684) Google Scholar], application of comparable methods to diffusion-weighted SC or anatomical covariance networks yields networks that are more spatially contiguous [37.Mišić B. et al.Cooperative and competitive spreading dynamics on the human connectome.Neuron. 2015; 86: 1518-1529Abstract Full Text Full Text PDF PubMed Google Scholar,40.Betzel R.F. et al.The modular organization of human anatomical brain networks: accounting for the cost of wiring.Net. Neurosci. 2017; 1: 42-68Crossref Scopus (33) Google Scholar. For example, clustering or community detection methods typically fail to identify a default mode-like structural network, perhaps because not all parts of the network are anatomically inter-connected [26.Honey C.J. et al.Can structure predict function in the human brain?.NeuroImage. 2010; 52: 766-776Crossref PubMed Scopus (291) Google Scholar]. Structural and functional networks also show global organizational differences. For example, structural networks show evidence of extensive assortative mixing, whereby nodes with similar properties (e.g., degrees) are more likely to be connected, whereas the same is not true of functional networks [50.Lim S. et al.Discordant attributes of structural and functional brain connectivity in a two-layer multiplex network.Sci. Rep. 2019; 9: 2885Crossref PubMed Scopus (2) Google Scholar]. At the mesoscopic scale, communities or modules recovered from structural networks are assortative, while communities recovered from functional networks are disassortative [38.Betzel R.F. et al.Diversity of meso-scale architecture in human and non-human connectomes.Nat. Commun. 2018; 9: 346Crossref PubMed Scopus (21) Google Scholar]. In other words, in functional networks there is a pronounced affinity among nodes with dissimilar attributes. As a result, tuning community detection algorithms to be sensitive to disassortative structures improves the match between structural and functional modules [38.Betzel R.F. et al.Diversity of meso-scale architecture in human and non-human connectomes.Nat. Commun. 2018; 9: 346Crossref PubMed Scopus (21) Google Scholar]. Altogether, a rich body of work demonstrates discordance between SC and FC that spans multiple scales, from the embedding of individual nodes and edges to their global arrangement. Why the discrepancy between SC and FC? Functional interactions may arise via indirect structural connections, resulting in coherent time courses among regions that are two or more synapses removed from each other. In other words, the propensity of two regional time courses to correlate is driven not only by direct signaling between them, but also by the common inputs they receive from sensory organs and from the entire network [27.Damoiseaux J.S. Greicius M.D. Greater than the sum of its parts: a review of studies combining structural connectivity and resting-state functional connectivity.Brain Struct. Funct. 2009; 213: 525-533Crossref PubMed Google Scholar,51.Bettinardi R.G. et al.How structure sculpts function: unveiling the contribution of anatomical connectivity to the brain's spontaneous correlation structure.Chaos. 2017; 27: 047409Crossref PubMed Scopus (12) Google Scholar. A corollary is that functional interactions are much less distance-dependent than structural connections. Anatomical wiring is subject to material, spatial, and metabolic constraints [14.Bullmore E. Sporns O. The economy of brain network organization.Nat. Rev. Neurosci. 2012; 13: 336Crossref PubMed Scopus (1282) Google Scholar]; these pressures manifest in reduced connection probability and connection weight with increasing spatial separation [15.Horvát S. et al.Spatial embedding and wiring cost constrain the functional layout of the cortical network of rodents and primates.PLoS Biol. 2016; 14: e1002512Crossref PubMed Google Scholar,16.Roberts J.A. et al.The contribution of geometry to the human connectome.NeuroImage. 2016; 124: 379-393Crossref PubMed Scopus (60) Google Scholar. Although similar distance-dependence is observed for FC, its effect is weaker, ensuring systematic differences between structural and functional configurations. In the next section we consider models that translate structure to function by conceptualizing function as an emergent property of multiple structural links. As we have seen so far, there exists a nontrivial link between SC and FC, but the two are not perfectly aligned. A number of models have emerged that embody this link, including statistical models [41.Mišić B. et al.Network-level structure-function relationships in human neocortex.Cereb. Cortex. 2016; 26: 3285-3296Crossref PubMed Scopus (153) Google Scholar,42.Messé A. et al.Relating structure and function in the human brain: relative contributions of anatomy, stationary dynamics, and non-stationarities.PLoS. Comput. Biol. 2014; 10: e1003530Crossref PubMed Scopus (90) Google Scholar, communication models [37.Mišić B. et al.Cooperative and competitive spreading dynamics on the human connectome.Neuron. 2015; 86: 1518-1529Abstract Full Text Full Text PDF PubMed Google Scholar,43.Graham D. Rockmore D. The packet switching brain.J. Cogn. Neurosci. 2011; 23: 267-276Crossref PubMed Scopus (18) Google Scholar, 44.Goñi J. et al.Resting-brain functional connectivity predicted by analytic measures of network communication.Proc. Natl. Acad. Sci. 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Though different in their implementation and assumptions, the common idea is to emphasize collective, higher-order interactions among neural elements that transcends the strong local clustering and geometric dependence of dyadic structural relationships. Here we briefly review each of these analytic strategies, with a focus on their biological interpretation and predictive utility, and most importantly, what they teach us about the nature of the structure–function relationship in the brain. Perhaps the simplest way to link structure and function is statistically. Varying forms of reduced rank regression have emerged as particularly useful, including canonical correlation [52.Deligianni F. et al.NODDI and tensor-based microstructural indices as predictors of functional connectivity.PLoS One. 2016; 11: e0153404Crossref PubMed Scopus (13) Google Scholar] and partial least squares [41.Mišić B. et al.Network-level structure-function relationships in human neocortex.Cereb. Cortex. 2016; 26: 3285-3296Crossref PubMed Scopus (153) Google Scholar]. In these data-driven models the objective is to simultaneously identify weighted combinations of structural and functional connections that are maximally correlated across individuals [53.McIntosh A.R. Mišić B. Multivariate statistical analyses for neuroimaging data.Annu. Rev. Psychol. 2013; 64: 499-525Crossref PubMed Scopus (73) Google Scholar] (Figure 2). An appealing feature of such models is that they embody multiple structure–function modes. In other words, a particular structural configuration or subnetwork may give rise to distinct patterns of functional interactions [41.Mišić B. et al.Network-level structure-function relationships in human neocortex.Cereb. Cortex. 2016; 26: 3285-3296Crossref PubMed Scopus (153) Google Scholar]. Taking this idea further, artificial neural networks can be used to learn functional networks from structural networks. For example, a recent study used a variant of the word2vec algorithm to build a low-dimensional embedding representation of the connectome and used it to train a deep neural network to predict edge-wise FC [54.Rosenthal G. et al.Mapping higher-order relations between brain structure and function with embedded vector representations of connectomes.Nat. Commun. 2018; 9: 2178Crossref PubMed Scopus (3) Google Scholar]. Altogether, statistical models offer a data-driven way to associate combinations of structural and functional connections without assuming a specific mode of interaction among neuronal populations. Communication models emerging from network science and telecommunication engineering conceptualize functional interactions as the superposition of elementary signaling events on the underlying anatomical network [43.Graham D. Rockmore D. The packet switching brain.J. Cogn. 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