Antagonistic Coevolution Drives Whack-a-Mole Sensitivity in Gene Regulatory Networks

Abstract

Robustness, defined as tolerance to perturbations such as mutations and environmental fluctuations, is pervasive in biological systems. However, robustness often coexists with its counterpart, evolvability--the ability of perturbations to generate new phenotypes. Previous models of gene regulatory network evolution have shown that robustness evolves under stabilizing selection, but it is unclear how robustness and evolvability will emerge in common coevolutionary scenarios. We consider a two-species model of coevolution involving one host and one parasite population. By using two interacting species, key model parameters that determine the fitness landscapes become emergent properties of the model, avoiding the need to impose these parameters externally. In our study, parasites are modeled on species such as cuckoos where mimicry of the host phenotype confers high fitness to the parasite but lower fitness to the host. Here, frequent phenotype changes are favored as each population continually adapts to the other population. Sensitivity evolves at the network level such that point mutations can induce large phenotype changes. Crucially, the sensitive points of the network are broadly distributed throughout the network and continually relocate. Each time sensitive points in the network are mutated, new ones appear to take their place. We have therefore named this phenomenon "whack-a-mole" sensitivity, after a popular fun park game. We predict that this type of sensitivity will evolve under conditions of strong directional selection, an observation that helps interpret existing experimental evidence, for example, during the emergence of bacterial antibiotic resistance.

Fig 1. Host-parasite model and alternating phenotype dynamics.

A) Schematic overview of the host-parasite model. B) To compare host and parasite phenotypes, here in a typical simulation, gene expressions are rescaled from [0,1] to [−1,+1] so that for each gene the sign of their multiplied gene expression indicates whether their expressions are similar or different. Host and parasite phenotypes are compared, here in a typical simulation, by multiplying the expression of each gene, rescaled from [0,1] to [−1,+1], from one host and one parasite at each generation. In the horizontal direction, the leftmost block of columns represents the comparative expression (by multiplication of rescaled expressions) level of gene 1 for 200 host-parasite pairs (the pairings themselves are random). Similar gene expression between host and parasite is shown in yellow (parasite winning) and divergent expression in blue (host winning).

Fig 2. Emergence of sensitivity.

A) As coevolution proceeds, the sensitivity score (SS) increases monotonically reaching a plateau in both host and parasite. B) Robustness in the remaining (non-sensitive) part of the network was defined as the fraction of mutations that leave the phenotype unchanged if we exclude phenotype inversions (see main text). Both plots show mean values for 100 simulations with the error bars indicating standard error of the mean (SEM).

Fig 3. Lability of sensitive interactions and network diversity.

A) Comparison of the sensitivity network interactions from a single individual in a population at generation 2000 with its ancestors using the Jaccard index to quantify the overlap in sensitivity (see Methods). (B) Time course of network diversity, defined as the number of distinct networks, simplified to sign (-1/0/+1) form, and expressed as a fraction of the population (green line: host population of single simulation). Apart from the green line in (B), both plots show mean values for 100 simulations with the error bars indicating SEM.

Fig 4. Distribution of sensitivity throughout the network.

A) Frequency of being a sensitive interaction in the N×N matrix of interactions (with N = 10) in a typical simulation. From generation 500 onwards we identified the sensitive gene interactions w _ij (SS _ij>0), then measured the frequency for each w _ij being sensitive within the population, at intervals of 50 generations. We sum the frequencies over time and normalize to the interval [0,1] as indicated by the colors. Generally there are no interactions that appear to dominate within each population over many generations. B) Detailed progression of sensitivity over time for two particular interactions in (A). These interactions had the lowest (blue) and highest (pink) overall sensitivity, as indicated by the black squares in (A). C) Distribution of the frequency of being sensitive in all N×N interactions for all host individuals (green dashed line: the host population of (A), red solid line: mean of 100 simulations). Since distributions are mostly right-skewed there are no interactions that dominate in terms of sensitivity. Error bars indicate one SD.