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posted 31. October 2004 08:26
PLoS Biology, October 26, 2004
From the PLoS synopsis:
Only Connect: The Functional Architecture of Brain Connectivity
Published October 26, 2004
Copyright: © 2004 Public Library of Science. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citation: (2004) Only Connect: The Functional Architecture of Brain Connectivity. PLoS Biol 2(11): e411.
Imagine three cities, A, B, and C, splayed across the landscape to form a triangle, with each connected to the other two by two-lane roads. Such an arrangement of cities and roads constitutes a structural network. On any given day traffic may flow, say, only from A to B to C, or in both directions between A and B but from C only to A, or in both directions between all three, or any one of ten other arrangements. Within this structural network, then, there are 13 possible functional networks. If these cities are embedded within a larger network of routes and destinations, their particular triangular traffic pattern represents a “motif” of connectivity, akin to a recurring musical motif within a larger symphony.
Such connectivity networks are central to information processing in the brain, and understanding the recurring structural and functional motifs they contain is one way to begin to dissect how the symphony of brain function is composed. In this issue, Olaf Sporns and Rolf Kötter identify several common motifs in real brain networks, and show that brains tend to maximize the number of functional motifs while keeping the number of structural motifs relatively low.
The authors began with the frequency of motifs of different sizes (two, three, four, or five nodes) found in the visual cortex and whole cortex of the macaque monkey, the cat cortex, and the nervous system of the nematode Caenorhabditis elegans. For comparison, they generated matrices that contained an equivalent number of components (nodes and connections), but whose connections were either random or lattice-like, in which all nearest neighbors were connected. They found that, compared to the artificial networks, the biological ones were relatively low in structural diversity. For instance, macaque visual cortex contained instances of 3,697 different motifs with five nodes, versus 8,887 for equivalent random networks. Functionally, however, unlike the artificial systems, the biological systems were maximally diverse, with the maximum functional motif diversity (e.g., 13 for three vertices and 9,364 for five vertices) observed in all motif sizes they investigated.
The researchers also found some intriguing patterns within this maze of connectivity. For instance, not all motifs were found in equal numbers. A common functional motif for three vertices was for both A and C to communicate back and forth with B, but not with each other. This structure allows B to function as an integrator of signals from A and C, while keeping the activities of A and C distinct from one another. This kind of structure is widespread throughout the nervous system.
The authors then ran an evolutionary algorithm on their artificial networks. They showed that by selecting for maximal functional motif number, the structure of the artificial systems quickly came to resemble the structure of the real ones, with dense local connections and relatively fewer long-distance ones. Such a structure, termed “ small world” connectivity, promotes cooperation between functional units, and efficient information exchange. Taken together, these results suggest that one factor that may drive the evolution of neural architecture is the maximization of functional connectivity within a network of relatively few neural actors.
From the paper:
Motifs in Brain Networks
Olaf Sporns , Rolf Kötter
Complex brains have evolved a highly efficient network architecture whose structural connectivity is capable of generating a large repertoire of functional states. We detect characteristic network building blocks (structural and functional motifs) in neuroanatomical data sets and identify a small set of structural motifs that occur in significantly increased numbers. Our analysis suggests the hypothesis that brain
networks maximize both the number and the diversity of functional motifs, while the repertoire of structural motifs remains small. Using functional motif number as a cost function in an optimization algorithm, we obtain network topologies that resemble real brain networks across a broad spectrum of structural measures, including small-world attributes. These results are consistent with the hypothesis that highly evolved neural architectures are organized to maximize functional repertoires and to support highly efficient integration of information.
Received April 14, 2004; Accepted August 26, 2004; Published October 26, 2004
Copyright: © 2004 Sporns and Kötter. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abbreviations: ID, motif identity number; K, number of edges; M, motif size; N, number of vertices
Academic Editor: Karl J. Friston, University College London
*To whom correspondence should be addressed. E-mail: firstname.lastname@example.org, E-mail: email@example.com
Citation: Sporns O, Kötter R (2004) Motifs in Brain Networks. PLoS Biol 2(11): e369.
The complex vertebrate brain has evolved from simpler networks of neurons over a time span of many millions of years. Brain networks have increased in size and complexity (Jerison 1973; Butler and Hodos 1996; Kaas 2000; Krubitzer 2000), as have the flexibility of interactions with the environment and the range of potential behaviors that can be generated (Changizi 2003). Most of the rules governing the evolutionary process toward more complex brains are still unknown, although the central roles of modularization (Kaas 2000), conservation of wiring length (Cherniak 1994; Chklovskii et al. 2002), and of the elaboration of network connectivity (Laughlin and Sejnowski 2003) are becoming increasingly evident.
From The Introduction
What rules underlie the organization of the particular types of networks that we see in complex brains? It is likely that, as networks become more complex, already existing simpler networks are largely preserved, extended, and combined, while it is less likely that complex structures are generated entirely de novo. One hypothesis states that complex and highly evolved networks arise from the addition of network elements in positions where they maximize the overall processing power of the neural architecture. This could be achieved by increasing the number of existing processing configurations or by introducing new processing configurations that add to the robustness or range of cognitive and behavioral repertoires. We may gain insight into the rules governing the structure of complex networks by investigating their composition from smaller network building blocks. Those building blocks are called “motifs” (in analogy to driving elements that are elaborated in a musical theme or composition), and they have been examined in the context of gene regulatory, metabolic, and other biological and artificial networks (Milo et al. 2002; Milo et al. 2004). Motifs occur in distinct motif classes that can be distinguished according to the size (M) of the motif, equal to the number of nodes (vertices), and the number and pattern of interconnections. For a more formal definition of motifs and related concepts, see Materials and Methods.
While the most common definition of network motifs is based on their structural characteristics (Milo et al. 2002), structural motifs of neuronal networks form the physical substrate for a repertoire of distinct functional modes of information processing. In brain networks, a structural motif may consist of a set of brain areas and pathways that can potentially engage in different patterns of interactions depending on their degree of activation, the surrounding neural context or the behavioral state of the organism. Thus, we propose a distinction between structural and functional motifs. Structural motifs quantify anatomical building blocks, whereas functional motifs represent elementary processing modes of a network (Figure 1). In this paper, functional motifs refer to specific combinations of nodes and connections (contained within structural motifs) that may be selectively recruited or activated in the course of neural information processing. Sorting all possible structural motifs within a network as a function of motif class yields a motif frequency spectrum that records the number of distinct motifs in each structural motif class. Given the motif frequency spectrum, one can easily obtain the motif number, defined as the total number of distinct occurrences of any motif of size M, and the motif diversity, defined as the number of classes that are represented within the network by at least one example.
Clearly, the number of vertices (N) and edges (K) within a large network has a strong effect on the motif number and diversity of its constituent structural and functional motifs. But even if N and K are held constant, different connection patterns will result in different repertoires of such network motifs, expressed in terms of both number and diversity. These considerations lead us to formulate hypotheses concerning the rules for brain network organization in terms of network motifs. We hypothesize that neuronal networks have evolved such that their repertoire of potential functional interactions (functional motifs) is both large and highly diverse, while their physical architecture is constructed from structural motifs that are less numerous and less diverse. A large functional repertoire facilitates flexible and dynamic processing, while a small structural repertoire promotes efficient encoding and assembly.
We investigate this hypothesis first by performing an analysis of structural and functional motifs in various brain networks. We compare the motif properties of real brain networks with random networks and with networks that follow specific connection rules such as neighborhood connectivity (lattice networks). We identify some motif classes that occur more frequently in real brain networks, as compared to random or lattice topologies. Second, by rewiring random networks and imposing a cost function that maximizes functional motif number, network topologies are generated that resemble real brain networks across a broad spectrum of structural measures, including small-world attributes. The results of our analyses are consistent with the hypothesis that complex brain networks maximize functional motif number and diversity while maintaining relatively low structural motif number and diversity.
From the Results
We obtained complete structural motif frequency spectra for large-scale connection matrices of macaque visual cortex, macaque cortex, and cat cortex, for motifs sizes of M = 2, 3, 4, and 5 (estimations). In addition, we obtained motif frequency spectra for the matrix of interneuronal connections (“chemical synapses”) of C. elegans, for motif sizes M = 2, 3, and 4 (estimations). For each neural connectivity matrix we generated equivalent (N, K) random and lattice matrices, preserving degree distributions (n = 100; see Materials and Methods), and we obtained their structural motif frequency spectra for comparison. Thus, statistical significance of a motif can only be reached if it occurs in significantly increased proportions with respect to both random and lattice reference cases.
…Large-scale connection matrices exhibit a consistent statistical trend. Their structural motif number is relatively low, and their functional motif number is relatively high, with both measures approaching the corresponding values of lattice networks. All of these brain networks contain a very high proportion of connected motifs (e.g., 53.2% for M = 3 in macaque visual cortex versus 24.6% in corresponding random networks). All neuronal networks (all cortical networks and C. elegans) showed maximal functional motif diversity for all motif sizes examined (values of 2, 13, 199, and 9,364 for M = 2 to 5)…
…We hypothesized that high functional motif number and diversity represent important ingredients in the global organization of cortical networks, and that a selective advantage for these two properties might contribute to the generation of other significant structural properties. To test this hypothesis we applied an evolutionary algorithm (Sporns et al. 2000) that selects for networks with high functional motif number, while rewiring their connectivity…
… To further characterize these networks, we calculated their clustering coefficient and their path length to determine if they exhibited small-world properties (Figure 5). We found that networks that maximized functional motif number also had clustering coefficients that were much higher than those of random networks (γ = 0.5288 ± 0.0201 for optimized networks; γ = 0.4323 ± 0.0073 for random networks), while their path lengths remained relatively short (λ = 1.7891 ± 0.0275 for optimized networks; λ = 1.9300 for a nearest-neighbor lattice network). Both measures closely approximated those of macaque visual cortex (γ = 0.5313, λ = 1.7256)…
Emphases added by ISCID News editor
See full paper at PLoS biology
[ 03. December 2004, 20:48: Message edited by: ISCID News Editor ]