# Connectome

Post-publication activity

Curator: Olaf Sporns

The connectome is the complete description of the structural connectivity (the physical wiring) of an organism’s nervous system. The field of science dealing with the assembly, mapping and analysis of data on neural connections is called connectomics.

## Structural connectivity as a basis for function

It may seem obvious that the function of a network is critically dependent on the pattern of its interconnections. The brain is an example of such a complex network, but despite the intense effort that has gone into elucidating the structure and function of neural systems we do not currently have a comprehensive map of the network connectivity structure of the brain of any species, with the notable exception of the nematode C. elegans (White et al., 1986). In principle, it should be possible to compile such data sets, at least at some level of resolution, for all organisms that have a nervous system. It has been suggested, simultaneously and independently by Sporns and Hagmann, to call the full connectivity structure (the connection set) of an organism’s brain the connectome (Sporns et al., 2005, Hagmann, 2005), in deliberate analogy to an organism’s full complement of genetic information, the genome. Connectomics (Hagmann, 2005) has been defined as the science concerned with assembling and analyzing connectome data sets.

In the human brain, the significance of the connectome stems from the realization that the structure (connectivity) and function of the human brain are intricately linked, through multiple levels and modes of brain connectivity. The connectome naturally places strong constraints on which neurons or neural populations can interact, or how strong or direct their interactions are. The pattern of dynamic interactions shaped by the connectome underlies the operations and processes of human cognition. Structure-function relationships in the brain are unlikely to reduce to simple one-to-one mappings. This is immediately evident since the connectome can evidently support a great number of variable dynamic states at each time, depending on current sensory inputs, global brain state, learning and development. Potential for very rapid changes of structural connectivity has been afforded by two-photon imaging experiments showing the rapid (dis-)appearance of dendritic spines (Bonhoeffer and Yuste, 2002). Despite such complex and variable structure-function mappings, the connectome is an indispensable basis for the mechanistic interpretation of dynamic brain data, from single-cell recordings to functional neuroimaging.

## The connectome at multiple scales

Brain networks can be defined at different levels of scale, corresponding to levels of spatial resolution (Kötter, 2007, Sporns, 2010). Connectomics is directed at providing descriptions of brain connectivity at different scales, which can be roughly categorized as microscale, mesoscale and macroscale. Ultimately, connectomic maps obtained at different levels may be joined into a single hierarchical map of the neural organization of a given species that ranges from cells to populations to systems, although it is unclear to what extent such a mapping might remain probabilistic (Sporns et al., 2005). At the microscale (micrometer resolution), neural systems are composed of interconnected neurons. In more highly evolved organisms, the number of neurons comprising the brain easily ranges into the billions. According to various estimates, the human cerebral cortex alone contains at least $$10^{10}$$ neurons linked by $$10^{14}$$ synaptic connections. Mapping such a network at cellular resolution poses unique challenges, which are discussed in more detail below. At the mesoscale, corresponding to a spatial resolution of hundreds of micrometers, many anatomical structures of the brain contain anatomically and/or functionally distinct neuronal populations, formed by local circuits (e.g. cortical columns) linking hundreds or thousands of individual neurons. At the macroscale (millimeter resolution), large brain systems may be parcellated into anatomically distinct modules or areas that maintain specific patterns of interconnectivity. Connectomic data bases at the mesoscale and macroscale will be significantly more compact than those at cellular resolution but they require sensible strategies for anatomical or functional partitioning of the neural volume into network nodes (for complexities see, e.g., Wallace et al., 2004).

## The connectome at cellular resolution

Traditional histological circuit-mapping approaches have included light-microscopic techniques for cell staining, injection of labeling agents for tract tracing, or reconstruction of serially sectioned tissue blocks via electron microscopy (EM). Each of these classical approaches has specific drawbacks when it comes to deploying these techniques for connectomics. The staining of single cells, e.g. with the Golgi stain, to trace cellular processes and connectivity suffers from the limited resolution of light-microscopy as well as difficulties in capturing long-range projections. Tract tracing, often described as the gold standard of neuroanatomy for detecting long-range pathways across the brain, generally only allows the tracing of fairly large cell populations and single axonal pathways. EM reconstruction was successfully used for the compilation of the C. elegans connectome (White et al., 1986). However, applications to larger tissue blocks of entire nervous systems have difficulty with identification of corresponding structures in tissue slices, which are usually distorted and of low contrast (Fiala, 2005).

Recent advances in mapping neural connectivity at the cellular level offer significant new hope for overcoming the limitations of classical techniques and for compiling cellular connectome data sets (Livet et al., 2007; Lichtman et al., 2008). Using a combinatorial color labeling method based on the stochastic expression of several fluorescent proteins, called Brainbow, Lichtman and colleagues were able to mark individual neurons with one of over 100 distinct colors. The labeling of individual neurons with a distinguishable hue then allows the tracing and reconstruction of their cellular structure including long processes within a block of tissue. While the labeling and tracing of all neurons in a complete mammalian brain may still represent an overly ambitious goal, more restricted components of a cellular connectome, for example the wiring of a cortical column or of the layered structure of the retina have come within reach.

## The connectome at the large scale

There are several established empirical approaches that allow the construction of connectome data sets at the level of macroscopic connectivity, i.e. at the level of anatomically segregated brain regions connected by inter-regional pathways. Cerebral white matter architecture can be mapped by histological dissection and staining, by degeneration methods and by axonal tracing (see above). Axonal tracing methods have formed the basis for the systematic collection of white matter pathways into comprehensive and species-specific anatomical connection matrices. Landmark studies have included the areas and connections of the macaque visual cortex (Felleman and Van Essen, 1991) and the cat thalamo-cortical system (Scannell et al., 1999). The development of neuroinformatics data bases for anatomical connectivity, for example the online macaque cortex connectivity tool CoCoMac (Kötter, 2004), allow for continual updating and refinement of such anatomical connection maps.

A promising new avenue for the noninvasive in vivo mapping of white matter fiber pathways is diffusion magnetic resonance imaging. In recent years, a wide spectrum of diffusion imaging paradigms and computational tractography algorithms has been explored. While different methods have different strengths and weaknesses, the goal of constructing comprehensive maps of brain connectivity requires spatially homogeneous signal registration and computational processing in order to remove as much as possible systematic volume or connectional artifacts. Ideally, connectome maps acquired through the use of diffusion imaging should allow for cross-validation with anatomical data collected by more classical histologic techniques. Particularly desirable would be the cross-validation of diffusion imaging and anatomical tract tracing in the same species, for example the macaque monkey.

Over the past few years, several investigators have attempted to map the large-scale structural architecture of the human cortex. One attempt exploited cross-correlations in cortical thickness or volume across individuals (He et al., 2007). Such gray-matter thickness correlations have been postulated as indicators for the presence of structural connections. A drawback of the approach is that it provides highly indirect information about cortical connection patterns and requires data from large numbers of individuals to derive a single connection data set across a subject group.

Other investigators have attempted to build whole-brain connection matrices from diffusion imaging data. One group of researchers (Iturria-Medina et al., 2008) has constructed connectome data sets using diffusion tensor imaging (DTI) followed by the derivation of average connection probabilities between 70-90 cortical and basal brain gray matter areas. All networks were found to have small-world attributes and “broad-scale” degree distributions. An analysis of betweenness centrality in these networks demonstrated high centrality for the precuneus, the insula, the superior parietal and the superior frontal cortex. Another group (Gong et al. 2008) has applied DTI to map a network of anatomical connections between 78 cortical regions. This study also identified several hub regions in the human brain, including the precuneus and the superior frontal gyrus.

Figure 1: The human connectome. Images show the fiber architecture of the human brain as revealed by diffusion imaging (left), a reconstructed structural brain network (middle) and the location of the brain's core, its most highly and densely interconnected hub (right). Image on the left courtesy of Patric Hagmann, University of Lausanne; middle and right panels are from Hagmann et al. (2008).

Hagmann et al. (2007) constructed a connection matrix from fiber densities measured between homogeneously distributed and equal-sized regions of interest (ROIs) numbering between 500 and 4000. A quantitative analysis of connection matrices obtained for approximately 1000 ROIs and approximately 50,000 fiber pathways from two subjects demonstrated an exponential (one-scale) degree distribution as well as robust small-world attributes for the network. The data sets were derived from diffusion spectrum imaging (DSI) (Wedeen, 2005), a variant of diffusion-weighted imaging that is sensitive to intra-voxel heterogeneities in diffusion directions caused by crossing fiber tracts and thus allows more accurate mapping of axonal trajectories than other diffusion imaging approaches (Wedeen, 2008).

The combination of whole-head DSI datasets acquired and processed according to the approach developed by Hagmann et al. (2007) with the graph analysis tools conceived initially for animal tracing studies (Sporns, 2006; Sporns, 2007) allow a detailed study of the network structure of human cortical connectivity (Hagmann et al., 2008; Figure 1). The human brain network was characterized using a broad array of network analysis methods including core decomposition, modularity analysis, hub classification and centrality. Hagmann et al. presented evidence for the existence of a structural core of highly and mutually interconnected brain regions, located primarily in posterior medial and parietal cortex. The core is comprised of portions of the posterior cingulate cortex, the precuneus, the cuneus, the paracentral lobule, the isthmus of the cingulate, the banks of the superior temporal sulcus, and the inferior and superior parietal cortex, all located in both cerebral hemispheres.

The studies outlined in this section represent only a first step towards creating comprehensive structural connection data sets for the human brain. We should expect to soon see more refined datasets and analyses as imaging and network methodologies become more sophisticated. Future analyses will likely include more comprehensive coverage of subcortical regions and pathways and may aim at achieving higher spatial resolution to capture smaller fiber bundles and anatomical subdivisions. In addition, other schemes for defining ROIs may be used, for example based on functional criteria, or on the detection of boundaries in functional connectivity patterns. A particularly promising avenue is the combination of structural and functional imaging in the same participants, including the use of functionally defined regional boundaries for deriving whole-brain connection matrices.

## The future of the connectome

While the full connectome at cellular resolution seems presently out of reach, at least for the human brain, a decoupled multiresolution approach is more feasible. On one side the human brain can be studied at the large- or macro-scale with MRI. Such a large-scale connectome will provide a structural substrate for observed manifestations of large-scale brain dynamics recorded by electrophysiological and neuroimaging techniques. Admittedly, this goal falls short of a complete description of the cellular architecture of the human brain, for which current techniques are still insufficient. Also none of the imaging methods so far provides directional information, although this could be achieved with the development of better in vivo MR detectable tracers (see, e.g., Murayama et al., 2006). Nonetheless, the large-scale connectome will provide valuable insight into how structural brain connectivity gives rise to functional and effective connectivity. On the other hand the detailed mapping of cortical mammalian microcolumns is becoming feasible giving a generic idea of the micro-scale architecture. The intelligent combination of heterogeneous data coming from different scales will potentially provide the solution for mapping a good estimate of the full connectome thanks to the fact that brain connectivity is highly generic and redundant.

Increasingly, connectome maps will be used to inform computational models of whole-brain dynamics. Perhaps the most sophisticated large-scale model based on DTI-derived whole-head cortical connectivity to date (2008) was introduced by Izhikevich and Edelman (2008) and showed complex patterns of spike dynamics in spontaneous neural activity. Other models will follow in due time, opening the way towards building a global brain simulator that integrates across human brain structure and function. Further approaches could include systematic tracer injections in animal models using a regular voxel grid and an automated processing pipeline, a high-throughput anatomy approach, as was initiated by the Allen Brain Institute for the mapping of gene expression data in the rat brain. Furthermore, studying diseased connectomes and its related dynamics is certainly going to significantly increase our understanding of the related pathophysiologies and potential therapeutic effects.

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Internal references

• Olaf Sporns (2007) Complexity. Scholarpedia, 2(10):1623.
• William D. Penny and Karl J. Friston (2007) Functional imaging. Scholarpedia, 2(5):1478.
• Almut Schüz (2008) Neuroanatomy. Scholarpedia, 3(3):3158.
• Rodolfo Llinas (2008) Neuron. Scholarpedia, 3(8):1490.
• John Dowling (2007) Retina. Scholarpedia, 2(12):3487.