From worms to humans:common principles of large-scale organization

in the nervous system G. Zamora-López1,2*, C.S. Zhou3, J. Kurths1,2,4

1Bernstein Center for Computational Neuroscience, Berlin, Germany2Department of Physics, Humboldt University, Berlin, Germany

3Center for Nonlinear Studies, Hong Kong Baptist University, Hong Kong, China4Potsdam Institute for Climate Impact Research, Potsdam, Germany

*gorka.zamora@ymail.com

Despite the significant differences in the number of neurons and structures observed in the brains across the animal kingdom, the nervous systems of all animals suffer of similar limitations to aquire reliable information from the environment and serve the same functional purpouses. These limitations and goals are the main driving forces shaping the large-scale architecture of the neuronal connectivity. We review knowledge gained in the recent years by means of complex network analysis on the organization of both anatomical and functional connectivity of few species. They share a few fundamental architectural features: (i) neural systems posses short but abundant alternative processing paths, (ii) neurons and cortical regions form clusters of densely interconnected elements, and (iii) neural systems contain few network hubs. This architecture supports the idea that brain function is to be understood as emerging from the collective working of its constituents without a single coordinating center. The modular organization is a consequence of the specialization of different parts, and the highly interconnected hubs help in the integration and/or coordination of multisensory information.

MOTIVATIONThe neurons in a nervous system form a vast and complex network of communication, whose architecture has been shaped during evolution as a trade to overcome limita-tions (poor computational capacity of neurons, energy consumption, etc.) and to serve its functional necessities (collect and process sensory information).

Comprehensive data of anatomical connectivity is scarce and difficult to obtain. A complete map ef every neuron and their axonal projections in a brain is out of technological reach. Tract-tracing experiments permit to identify long-range fibers by following the dispersion of chemical dyes. For humans, non-invasive neuroimaging and electro-physiological techniques are a window to connectivity.

CAT CORTICAL CONNECTIVITYThe cat cortico-cortical connectivity data of cats was first published by [Scannell, 1993] as a collation of tract-tracing experiemental reports. Graph analysis of this corticocorti-cal network has revealed striking topological properties:

Figure–1: CORTICAL NETWORK OF CATS

The network consists of a parcellation of the cortex (a) into 53 cortical areas which are connected by 826 long-range fibers. (b) Adjacency matrix of the network.

1) Modular organization: Clustering analysis of the net-work reveals four network modules (groups of densely in-terconnected areas) which contain areas involved in either visual, auditory or somatosensory functions, and a fourth module composed of frontolimibic areas [Hilgetag, 2000].

2) Short processing paths. Average pathlength is of only L ~ 1.83. Areas influence each other either by direct pro-jections or are separated by only two processing steps.

3) Multiple routes of information. Statistical analysis of the corticocortical communication paths reveals several al-ternative paths between pairs of cortical areas [Zamora-López, 2009].

4) Cortical hubs. Few cortical areas are largely con-nected to other areas. Two major implications of the pres-ence of these hubs are the following:

• Communication paths between different modules are not random but centralised, they go through the cortical hubs [Zamora-López, 2009].

• Cortical hubs are densely interconnected, forming a rich-club structure [Zamora-López, 2010].

The network is organised into a modular architecture with centralised hierarchy, whose top level is formed by the cortical hubs. This architecture represents the physical substrate that permits the brain to simultaneously process information of different modalities (parallel processing) and to integrate that information toward the generation of a coherent, global representation of the reality.

11 1

1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1

1 1 1 1 1 1 11 1 1 1 1 1 1

1 1 1 1 1 1 11 1 1 1

11 1 1 1

1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1

1 1 1 1 11 1 1

1 1

11 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 11 1 1 11 1 1 1 1 1 1

1 11 1

1 1 1 1 1 1 11 1 1 1

1 1 1 1 11 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 11 1 1 1 1

1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 11

1 1 1 1 1 1

22 2 2 2

2 22 2 2

2 2 2 22 2

2 2 2 22 2 2 2

2 2 2 2 2 22 2 2 22 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 22 2 2 2

22 2 2 2 2 22

2 2 2 2 2 2 2 22 2 2

2 2 2 2 2 2 2 2 2 2 2 22

2 22 22 22 22 2 2 2

2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 2

2 2 2 2 22 2 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2

2 2 22 2 2 2 2 2 2

2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 22 2 2 2 2

2 2 2 2 22 2 2 22 2 2 2

2

3 3 3 3 3 33 3 3 33 3 3 3 3

3 3 33 3 3 3 3 33

33

3

3 3 3 33

333 3

3 3 33

3

33 3 3 3

3 3 3 33 3 3 33 3 3 33 3 3 3

3 33

33 3 3

3 3 3 3 33 3 3 3 3

3 33

3

3 3 3 33 3 3 3 3

333

3 3 33 3 3

3 3 33 3 3

3 3 33

17

18

19

PL

LS

PM

LS

AM

LS

AL

LS

VL

SD

LS

21

a2

1b

20

a2

0b 7

AE

SP

SA

IA

IIA

AF P

VP

EP

p

Tem 3

a3

b 1 2S

IIS

IV 4g 4 6l

6m

5A

m5

Al

5B

m5

Bl

SS

SA

iS

SA

oP

FC

Mil

PF

CM

dP

FC

L Ia Ig

CG

aC

Gp

RS

35

36

pS

b

Sb

En

rH

ipp

17 - 118 - 219 - 3

PLLS - 4PMLS - 5AMLS - 6ALLS - 7

VLS - 8DLS - 9

21a - 1021b - 1120a - 1220b - 13

7 - 14AES - 15

PS - 16AI - 17

AII - 18AAF - 19

P - 20VP - 21

EPp - 22Tem - 23

3a - 243b - 251 - 262 - 27

SII - 28SIV - 294g - 30

4 - 316l - 32

6m - 335Am - 345Al - 35

5Bm - 365Bl - 37

SSSAi - 38SSAo - 39

PFCMil - 40PFCMd - 41

PFCL - 42Ia - 43Ig - 44

CGa - 45CGp - 46

RS - 4735 - 4836 - 49

pSb - 50Sb - 51

Enr - 52Hipp - 53

Visual Auditory Somato-motor Frontolimbic

Fig-2: DISTRIBUTED “CENTER OF CONTROL”

Cortical hubs form a functional module on top of the modular architecture of the cat cortical network, giving rise to a modular structure with centralized hierarchy. Contrary to typical rules of cortical organization, the module formed by the cortical hubs is distributed all along the cortex.

Beyond integration, cross-modal connections can be associated to modulation of the neuronal activity in other modalities [Driver, 2000]. A detailed analysis of the multisensory connectivity in the cat reveals: 1) most corti-cal areas have afferent and efferent projections to areas of other sensory modality and 2) we can classify cortical ar-eas into three categories: unimodal, multimodal and su-pramodal [Zamora-López, 2011].

Figure-3: MULTISENSORY CONNECTIVITY

(A) Number of cross-modal connections of each corti-cal area in the cat. (B) Mapping of the multisensory importance of cortical areas. The ascending trend is a particular characteristic of the modular organization with centralised heirarchy of the network.

CAENORHABDITIS ELEGANS

Figure-4: CAENORHABDITIS ELEGANS

The nervous system of the nematode C. elegans has been fully mapped by reconstruction of electron micro-graphs of sectioned specimens [Durbin, 1987; Varsh-ney, 2011] . It contains 302 neurons and approximately 6400 chemical synapses and 900 gap junctions.

Clustering analysis of the network shows that its neurons are arranged into a modular hierarchical architecture [Pan, 2010]. The modules contain neural circuits which play a vital role in performing different functions: chemo-sensation, thermotaxis, mechanosensation, feeding, etc. [Arenas, 2008].

The network is characterised by short processing paths (L ~ 4.0). Hub neurons have been found [Varshney et al., 2011] which are central in information processing. In par-ticular, command interneurons (responsible for worm lo-comotion) have high degree centrality.

A Segregation (specialization) Integration

Lateral Medial

C

Lateral MedialB D

A BVisual Audit. Som.-motor Frontol.

HUMAN BRAINData of human brain connectivity is obtained by non-invasive methods which lack the accuracy of methods for animal models. Tractography, based on neuroimaging have revealed human large connectivity networks (white matter). Functional imaging and electroencephalography permit to reconstruct functional networks as correlated dynamical inferences between brain regions or sensors.

Although they differ in terms of experimental methodology and cortical parcellation, most studies reveal highly clus-tered networks, with most pathways existing between ar-eas that are spatially close and functionally related. These modules are interlinked by hub regions, ensuring that overall path lengths across the network are short [Bull-more, 2009; Meunier, 2010].

Figure-5: HIERARCHICAL MODULARITY

Clustering analysis of functional brain networks reveal hierarchical modularity, i.e, modules which can be de-composed in further submodules.

DISCUSSIONAll neural connectivity studies report the following: 1) short and abundant processing paths, 2) hierarchical / modular organization, and 3) the presence of highly connected hubs. These common principles of organisa-tion arise because the nervous system of all animals serve the same functional purpouses and suffer from similar limi-tations to collect and processe sensory information. Com-bined together, these characteristics imply that the neural networks are highly interactive systems.

SPECIALIZATION LEADS TO MODULARITYSensory neurons collect only one type of sensory informa-tion. Therefore, the paths of sensory processing of differ-ent modal information remain segregated of each other giving rise to groups of neurons specialised in the process-ing one modal information (parallel processing).

HUBS LEAD TO INTEGRATIONBut, a collection of specialized functional modules alone cannot give rise to a coherent perception of the reality. For that, information of different modalities needs to be com-bined. Cortical and neural hubs play a crucial role by cen-tralizing the paths of information between modalities.

REFERENCESArenas, Fernández et al.. Lect. Notes Comput. Sci. 515, 9 (2008).Bullmore & Sporns Nat. Rev. Neurosci. 10, 1 (2009).Driver & Spence, Curr. Biol. 57, 11 (2000).Durbin. Ph.D Thesis, Kings College, Oxford (1987).Hilgetag et al. Phil. Trans. R. Soc. London, 355, 71 (2000).Meunier, Lambiotte & Bullmore, Front. Neurosci. 4, 200 (2010).Pan, Chatterjee & Sinha, PLoS ONE 5, e940 (2010).Scannell & Young, Curr. Biol 3, 191-200 (1993).Varshney, Chen et al. PLoS Comput. Biol. 7, e1001066 (2011).Zamora-López, Zhou & Kurths, Chaos 19, 015117 (2009).Zamora-López, Zhou & Kurths, Front. Neuroinf. 4, 1 (2010)Zamora-López, Zhou & Kurths. Front. Neurosci. 5, 83 (2011).

Meunier et al. Modularity of brain networks

Frontiers in Neuroscience www.frontiersin.org December 2010 | Volume 4 | Article 200 | 9

important to explore how topological modular-ity of large-scale brain networks might be related to concepts of psychological modularity. For example, Fodor (1983) built on prior ideas from phrenology and faculty psychology to argue that some, relatively low-level, cognitive, or perceptual processes – such as visual perception of motion – can be described as psychologically modular because they are domain-specific, informationally encapsulated, fast, automatic, and anatomically localized. Whereas relatively high-level, inte-grated, effortful, and conscious cognitive proc-esses have often been linked to an anatomically

processes of modularization might be disrupted in the pathogenesis of neuropsychiatric disor-ders such as autism or schizophrenia, supporting abnormal modularity of brain network organiza-tion as a diagnostic biomarker. In support of this expectation, some evidence for dysmodularity, or abnormal modular organization, has already been reported in the brain functional networks of patients with childhood-onset schizophrenia (Alexander-Bloch et al., 2010).

Since one of the fundamental drivers of human cognitive neuroscience is to understand the brain basis for mental functions, it will also be

Central module Medial occipital moduleParieto!frontal module

Fronto!temporal moduleLateral occipital module

A

C

B

FIGURE 4 | Hierarchical modularity of a human brain functional network. (A) Cortical surface mapping of the community structure of the network at the highest level of modularity; (B) anatomical representation of the connectivity between nodes in color-coded modules. The brain is viewed from the left side with the frontal cortex on the left of the panel and occipital cortex on the right.

Intra-modular edges are colored differently for each module; inter-modular edges are drawn in black; (C) sub-modular decomposition of the five largest modules (shown centrally) illustrates, for example, that the medial occipital module has no major sub-modules whereas the fronto-temporal module has many sub-modules. Reproduced with permission from Meunier et al. (2009a).