Modeling and analysis of modular structure in diverse biological networks

Abstract

Biological networks, like most engineered networks, are not the product of a singular design but rather are the result of a long process of refinement and optimization. Many large real-world networks are comprised of well-defined and meaningful smaller modules. While engineered networks are designed and refined by humans with particular goals in mind, biological networks are created by the selective pressures of evolution. In this paper, we seek to define aspects of network architecture that are shared among different types of evolved biological networks. First, we developed a new mathematical model, the Stochastic Block Model with Path Selection (SBM-PS) that simulates biological network formation based on the selection of edges that increase clustering. SBM-PS can produce modular networks whose properties resemble those of real networks. Second, we analyzed three real networks of very different types, and showed that all three can be fit well by the SBM-PS model. Third, we showed that modular elements within the three networks correspond to meaningful biological structures. The networks chosen for analysis were a proteomic network composed of all proteins required for mitochondrial function in budding yeast, a mesoscale anatomical network composed of axonal connections among regions of the mouse brain, and the connectome of individual neurons in the nematode C. elegans. We find that the three networks have common architectural features, and each can be divided into subnetworks with characteristic topologies that control specific phenotypic outputs.