Article

A small-world of weak ties provides optimal global integration of self-similar modules in functional brain networks

Levich Institute and Physics Department, City College of New York, New York, NY 10031, USA.
Proceedings of the National Academy of Sciences (Impact Factor: 9.81). 02/2012; 109(8):2825-30. DOI: 10.1073/pnas.1106612109
Source: PubMed

ABSTRACT The human brain is organized in functional modules. Such an organization presents a basic conundrum: Modules ought to be sufficiently independent to guarantee functional specialization and sufficiently connected to bind multiple processors for efficient information transfer. It is commonly accepted that small-world architecture of short paths and large local clustering may solve this problem. However, there is intrinsic tension between shortcuts generating small worlds and the persistence of modularity, a global property unrelated to local clustering. Here, we present a possible solution to this puzzle. We first show that a modified percolation theory can define a set of hierarchically organized modules made of strong links in functional brain networks. These modules are "large-world" self-similar structures and, therefore, are far from being small-world. However, incorporating weaker ties to the network converts it into a small world preserving an underlying backbone of well-defined modules. Remarkably, weak ties are precisely organized as predicted by theory maximizing information transfer with minimal wiring cost. This trade-off architecture is reminiscent of the "strength of weak ties" crucial concept of social networks. Such a design suggests a natural solution to the paradox of efficient information flow in the highly modular structure of the brain.

Download full-text

Full-text

Available from: Lazaros K. Gallos, Jun 21, 2015
0 Followers
 · 
136 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: A matter of network topologyIt is commonly assumed that the brain is a small-world network (e.g., Sporns and Honey 2006). Indeed, one of the present authors claimed as much 15 years ago (Hilgetag et al. 2000). The small-worldness is believed to be a crucial aspect of efficient brain organization that confers significant advantages in signal processing (e.g., Lago-Fernández et al. 2000). Correspondingly, the small-world organization is deemed essential for healthy brain function, as alterations of small-world features are observed in patient groups with Alzheimer’s disease (Stam et al. 2007), autism (Barttfeld et al. 2011) or schizophrenia spectrum diseases (Liu et al. 2008; Wang et al. 2012; Zalesky et al. 2011).While the colloquial idea of a small, interconnected world has a long tradition (e.g., Klemperer 1938), the present concept of small-world features of networks is frequently associated with the Milgram experiment (Milgram 1967) that demonstrated surprisingly short paths across ...
    Brain Structure and Function 04/2015; DOI:10.1007/s00429-015-1035-6 · 4.57 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper we present a generative model for protein contact networks. The soundness of the proposed model is investigated by focusing primarily on mesoscopic properties elaborated from the spectra of the graph Laplacian. To complement the analysis, we study also classical topological descriptors, such as statistics of the shortest paths and the important feature of modularity. Our experiments show that the proposed model results in a considerable improvement with respect to two suitably chosen generative mechanisms, mimicking with better approximation real protein contact networks in terms of diffusion properties elaborated from the Laplacian spectra. However, as well as the other considered models, it does not reproduce with sufficient accuracy the shortest paths structure. To compensate this drawback, we designed a second step involving a targeted edge reconfiguration process. The ensemble of reconfigured networks denotes improvements that are statistically significant. As a byproduct of our study, we demonstrate that modularity, a well-known property of proteins, does not entirely explain the actual network architecture characterizing protein contact networks. In fact, we conclude that modularity, intended as a quantification of an underlying community structure, should be considered as an emergent property of the structural organization of proteins. Interestingly, such a property is suitably optimized in protein contact networks together with the feature of path efficiency.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: A modular small-world topology in functional and anatomical networks of the cortex is eminently suitable as an information processing architecture. This structure was shown in model studies to arise adaptively; it emerges through rewiring of network connections according to patterns of synchrony in ongoing oscillatory neural activity. However, in order to improve the applicability of such models to the cortex, spatial characteristics of cortical connectivity need to be respected, which were previously neglected. For this purpose we consider networks endowed with a metric by embedding them into a physical space. We provide an adaptive rewiring model with a spatial distance function and a corresponding spatially local rewiring bias. The spatially constrained adaptive rewiring principle is able to steer the evolving network topology to small world status, even more consistently so than without spatial constraints. Locally biased adaptive rewiring results in a spatial layout of the connectivity structure, in which topologically segregated modules correspond to spatially segregated regions, and these regions are linked by long-range connections. The principle of locally biased adaptive rewiring, thus, may explain both the topological connectivity structure and spatial distribution of connections between neuronal units in a large-scale cortical architecture.
    Cognitive Neurodynamics 12/2014; 8(6). DOI:10.1007/s11571-014-9288-y · 1.77 Impact Factor