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

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.

SUBMITTER: Gallos LK

PROVIDER: S-EPMC3286928 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Modular organization in biological networks has been suggested as a natural mechanism by which a cell coordinates its metabolic strategies for evolving and responding to environmental perturbations. To understand how this occurs, there is a need for developing computational schemes that contribute to integration of genomic-scale information and assist investigators in formulating biological hypotheses in a quantitative and systematic fashion. In this work, we combined metabolome data and constraint-based modeling to elucidate the relationships among structural modules, functional organization, and the optimal metabolic phenotype of Rhizobium etli, a bacterium that fixes nitrogen in symbiosis with Phaseolus vulgaris. To experimentally characterize the metabolic phenotype of this microorganism, we obtained the metabolic profile of 220 metabolites at two physiological stages: under free-living conditions, and during nitrogen fixation with P. vulgaris. By integrating these data into a constraint-based model, we built a refined computational platform with the capability to survey the metabolic activity underlying nitrogen fixation in R. etli. Topological analysis of the metabolic reconstruction led us to identify modular structures with functional activities. Consistent with modular activity in metabolism, we found that most of the metabolites experimentally detected in each module simultaneously increased their relative abundances during nitrogen fixation. In this work, we explore the relationships among topology, biological function, and optimal activity in the metabolism of R. etli through an integrative analysis based on modeling and metabolome data. Our findings suggest that the metabolic activity during nitrogen fixation is supported by interacting structural modules that correlate with three functional classifications: nucleic acids, peptides, and lipids. More fundamentally, we supply evidence that such modular organization during functional nitrogen fixation is a robust property under different environmental conditions.

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

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