Wiring Between Close Nodes in Molecular Networks Evolves More Quickly Than Between Distant Nodes

Abstract

As species diverge, a wide range of evolutionary processes lead to changes in protein-protein interaction (PPI) networks and metabolic networks. The rate at which molecular networks evolve is an important question in evolutionary biology. Previous empirical work has focused on interactomes from model organisms to calculate rewiring rates, but this is limited by the relatively small number of species and sparse nature of network data across species. We present a proxy for variation in network topology: variation in drug-drug interactions (DDIs), obtained by studying drug combinations (DCs) across taxa. Here, we propose the rate at which DDIs change across species as an estimate of the rate at which the underlying molecular network changes as species diverge. We computed the evolutionary rates of DDIs using previously published data from a high-throughput study in gram-negative bacteria. Using phylogenetic comparative methods, we found that DDIs diverge rapidly over short evolutionary time periods, but that divergence saturates over longer time periods. In parallel, we mapped drugs with known targets in PPI and cofunctional networks. We found that the targets of synergistic DDIs are closer in these networks than other types of DCs and that synergistic interactions have a higher evolutionary rate, meaning that nodes that are closer evolve at a faster rate. Future studies of network evolution may use DC data to gain larger-scale perspectives on the details of network evolution within and between species.

Keywords: biological network evolution; drug–drug interactions; gram-negative bacteria; phylogenetic comparative methods.

Fig. 1.

DDI score distance diverges nonlinearly over time. Species and strain abbreviations are shown in the top left box. a) Bayesian phylogeny and divergence time estimates based on an alignment of 27 highly conserved protein sequences. b) Hierarchical clustering of strains based on average Euclidean distances across DDIs (i.e. “DDI score distance”); drug combination (DC) data are from Brochado et al. (2018). c) Heatmap of DDI scores across strains. Along top, hierarchical clustering of DCs is shown based on Euclidean distances across strains, but these clusters were constrained by t-SNE cluster membership (see text). The heatmap displays synergistic interactions (close to −1), antagonistic interactions (close to 1), and additivities (close to 0; measured in Bliss score units). The bars below indicate whether the two drugs involved in the interaction are the same or different in terms of: belonging to the same drug category, targeting the same cellular process, or having the same use. d) Evolutionary rate of DDI score change, calculated for each cluster. e) Pairwise DDI score distances between strains as a function of divergence time between strains. Intraspecific comparisons, comparisons between Salmonella and Escherichia, and comparisons with Pseudomonas are each labeled. f) First two axes of a phylomorphospace-PCA for the DDI score data. The percent of variance explained for principal components 1 and 2 are shown.

Fig. 2.

a) Graphical representations of the cofunctional gene pair network of E. coli (EcoliNet: EcoCyc/GO-BP). This network contains 1,835 nodes with an average path length of 4.8 and contains 20 proteins targeted by 36 drugs in our analysis. b) Graphical representations of the PPI network of E. coli, as determined by small and medium-scale experiments (EcoliNet: LC. Small/medium-scale PPI). This network contains 764 nodes with an average path length of 4.9, with 18 proteins targeted by 27 drugs in our analysis. In a and b, each node represents a unique protein (KEGG ID) in E. coli; the red nodes are target proteins identified as participating in DCs in our analysis.

Fig. 3.

Pairs of protein targets with synergistic DDIs have lower path length and higher connectivity and centrality measures in E. coli cofunctional (a, c, e, g, i) and PPI (b, d, f, h, j) networks. DDI types examined are synergies, additivities, and antagonisms (“nontargets” are a background sample of nondrug target proteins in the network). The number of interactions in each category is in parentheses. Network metrics are: a and b: path length between two targets, c and d: K-edge connectivity between two targets, e and f: mean node degree of the two targets, g and h: mean betweenness centrality of the two targets, i and j: mean eigenvector centrality of the two targets. In all plots, significance of Wilcoxon test P-values are given for differences in the mean between all pairwise comparisons: P-value < *0.05, **0.0001, ***0.00001. For all plots, Kruskal−Wallis test for difference among groups is P < 1 × 10⁻⁷.

Fig. 4.

Evolutionary rates of DDI scores as a function of DDI type and network connectivity of targets. a) DCs resulting in only synergy or synergy↔antagonism DDIs across strains have faster evolutionary rates. b) Aggregated interaction types reveal that more synergistic DCs have higher evolutionary rates. The x axis value is the sum, per DC, across strains, where DDIs are scored as −1 for synergies, 0 for additive, and +1 for antagonistic interactions. c) Rate of DDI evolution as a function of DDI type, for DCs with protein targets in the cofunctional and small/medium-scale PPI networks. Synergistic DCs have higher evolutionary rates than additive and antagonistic DCs (combination types and networks from E. coli). d) Rate of DDI evolution as a function of the minimum distance between DC target proteins reveals that wiring between close nodes in molecular networks evolves more quickly than between distant nodes. See supplementary table S2, Supplementary Material online for statistical tests for differences among groups shown here. For all plots, the error bars represent the standard error of the mean.