Solving the influence maximization problem reveals regulatory organization of the yeast cell cycle

Abstract

AbstractThe Influence Maximization Problem (IMP) aims to discover the set of nodes with the greatest influence on network dynamics. The problem has previously been applied in epidemiology and social network analysis. Here, we demonstrate the application to cell cycle regulatory network analysis of Saccharomyces cerevisiae.Fundamentally, gene regulation is linked to the flow of information. Therefore, our implementation of the IMP was framed as an information theoretic problem on a diffusion network. Utilizing all regulatory edges from YeastMine, gene expression dynamics were encoded as edge weights using a variant of time lagged transfer entropy, a method for quantifying information transfer between variables. Influence, for a particular number of sources, was measured using a diffusion model based on Markov chains with absorbing states. By maximizing over different numbers of sources, an influence ranking on genes was produced.The influence ranking was compared to other metrics of network centrality. Although ‘top genes’ from each centrality ranking contained well-known cell cycle regulators, there was little agreement and no clear winner. However, it was found that influential genes tend to directly regulate or sit upstream of genes ranked by other centrality measures. This is quantified by computing node reachability between gene sets; on average, 59% of central genes can be reached when starting from the influential set, compared to 7% of influential genes when starting at another centrality measure.The influential nodes act as critical sources of information flow, potentially having a large impact on the state of the network. Biological events that affect influential nodes and thereby affect information flow could have a strong effect on network dynamics, potentially leading to disease.Code and example data can be found at: https://github.com/Gibbsdavidl/miergolfAuthor SummaryThe Influence Maximization Problem (IMP) is general and is applied in fields such as epidemiology, social network analysis, and as shown here, biological network analysis. The aim is to discover the set of regulatory genes with the greatest influence in the network dynamics. As gene regulation, fundamentally, is about the flow of information, the IMP was framed as an information theoretic problem. Dynamics were encoded as edge weights using time lagged transfer entropy, a quantity that defines information transfer across variables. The information flow was accomplished using a diffusion model based on Markov chains with absorbing states. Ant optimization was applied to solve the subset selection problem, recovering the most influential nodes.The influential nodes act as critical sources of information flow, potentially affecting the network state. Biological events that impact the influential nodes and thereby affecting normal information flow, could have a strong effect on the network, potentially leading to disease.