Department of Physics, University of California Santa Barbara, Santa Barbara, California, United States of America.
PLoS Comput Biol. 2010 Apr 22;6(4):e1000748. doi: 10.1371/journal.pcbi.1000748.
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.
神经系统是通过自然选择进化而来的信息处理网络，而超大规模集成电路 (VLSI) 计算机电路则是通过商业驱动的技术发展而进化的。在这里，我们遵循历史直觉，即所有物理信息处理系统都将共享关键的组织属性，例如模块化，这通常赋予功能的适应性。长期以来，人们一直观察到模块化 VLSI 电路在处理元素数量和连接数量之间表现出等距缩放关系，称为伦茨定律，这与电路的互连拓扑的维度及其逻辑容量有关。我们表明，人类大脑结构网络和线虫 C. elegans 的神经系统也遵守伦茨定律，并表现出一定程度的层次模块化。我们进一步表明，从 MRI 数据得出的人类大脑网络的估计伦茨指数可以解释在广泛的哺乳动物物种中灰质和白质体积之间的异速缩放关系，这再次表明这些神经系统设计原则具有高度的保守性。对于这些分形模块化网络中的每一个，互连拓扑的维度都大于其嵌入的空间的二维或三维欧几里得维度。这种相对较高的复杂性需要额外的物理布线成本：尽管所有网络都经过经济或成本效益布线，但它们并没有严格地最小化布线成本。人工和生物信息处理系统都可能进化到优化物理成本和拓扑复杂性之间的权衡，从而导致在许多不同种类的神经和计算网络中出现同源的经济、分形和模块化设计原则。
