Efficient Physical Embedding of Topologically Complex Information Processing Networks in Brains and Computer Circuits

Abstract

Nervous systems are information processing networks that evolved by natural selection, whereas very large scale integrated (VLSI) computer circuits have evolved by commercially driven technology development. Here we follow historic intuition that all physical information processing systems will share key organizational properties, such as modularity, that generally confer adaptivity of function. It has long been observed that modular VLSI circuits demonstrate an isometric scaling relationship between the number of processing elements and the number of connections, known as Rent's rule, which is related to the dimensionality of the circuit's interconnect topology and its logical capacity. We show that human brain structural networks, and the nervous system of the nematode C. elegans, also obey Rent's rule, and exhibit some degree of hierarchical modularity. We further show that the estimated Rent exponent of human brain networks, derived from MRI data, can explain the allometric scaling relations between gray and white matter volumes across a wide range of mammalian species, again suggesting that these principles of nervous system design are highly conserved. For each of these fractal modular networks, the dimensionality of the interconnect topology was greater than the 2 or 3 Euclidean dimensions of the space in which it was embedded. This relatively high complexity entailed extra cost in physical wiring: although all networks were economically or cost-efficiently wired they did not strictly minimize wiring costs. Artificial and biological information processing systems both may evolve to optimize a trade-off between physical cost and topological complexity, resulting in the emergence of homologous principles of economical, fractal and modular design across many different kinds of nervous and computational networks.

The modular and integrative functional architecture of the human brain

“…Brain regions also exhibit cytoarchitectonic differences (12). A modular structural wiring network (i.e., white matter tracts), with dense connectivity within modules and weak connectivity between modules, has also been consistently found in human brain imaging data (5,6,13,14). Finally, the brain's functional architecturehow the brain's modules interact to produce cognition-appears modular (7,(15)(16)(17).…”

“…Moreover, a double dissociation was found between two modules, such that, for both modules, damage to a node in one module only caused dysfunction (i.e., a decrease in functional connectivity) in the damaged module, suggesting their autonomy (78). Finally, empirical functional connectivity studies have shown that modules are weakly functionally connected to each other, likely because their computations are predominantly distinct, suggesting modular function (6,7,16,36,79). However, connections do occur between modules that transfer information between the modules and influence local activity in the modules, potentially increasing the modules' computational loads (6,7,16,27,28,36,(80)(81)(82)(83).…”

“…Finally, empirical functional connectivity studies have shown that modules are weakly functionally connected to each other, likely because their computations are predominantly distinct, suggesting modular function (6,7,16,36,79). However, connections do occur between modules that transfer information between the modules and influence local activity in the modules, potentially increasing the modules' computational loads (6,7,16,27,28,36,(80)(81)(82)(83). Thus, to validate the autonomous nature of modules, it is necessary to demonstrate that, as more modules are engaged simultaneously and more information is generated across the network and transferred between the modules, the modules' computational loads do not increase (50,51,53) (Fig.…”

“…modularity | hubs | cognition | graph theory | network T he principle of modularity, in which a system or process is mostly decomposable into distinct units or "modules," explains the architecture of many complex systems. Biological systems, including the human brain, are particularly well explained by the principle of modularity (1)(2)(3)(4)(5)(6)(7). For example, gene expression in the brain is modular; the transcriptomes of human brain regions are robustly organized into modules of coexpressed genes that reflect the underlying cellular composition of brain tissue (8), and the spatial topography of cortex is also strongly reflected in its genetic topography-the closer two cortical regions, the more similar their transcriptomes (9).…”

Energy and time determine scaling in biological and computer designs

“…This hierarchical scaling of communication is a well-known pattern in circuit design called Rent's rule [4], where p ¼ 1/D w is Rent's exponent. 1 This pattern is not unique to circuits and has been shown to occur in many biological networks [12][13][14][15]. Vascular systems correspond to a special case, where w i ¼ 1 for all i.…”