Under-dominance constrains the evolution of negative autoregulation in diploids

Regulatory networks have evolved to allow gene expression to rapidly track changes in the environment as well as to buffer perturbations and maintain cellular homeostasis in the absence of change. Theoretical work and empirical investigation in Escherichia coli have shown that negative autoregulation confers both rapid response times and reduced intrinsic noise, which is reflected in the fact that almost half of Escherichia coli transcription factors are negatively autoregulated. However, negative autoregulation is exceedingly rare amongst the transcription factors of Saccharomyces cerevisiae. This difference is all the more surprising because E. coli and S. cerevisiae otherwise have remarkably similar profiles of network motifs. In this study we first show that regulatory interactions amongst the transcription factors of Drosophila melanogaster and humans have a similar dearth of negative autoregulation to that seen in S. cerevisiae. We then present a model demonstrating that this fundamental difference in the noise reduction strategies used amongst species can be explained by constraints on the evolution of negative autoregulation in diploids. We show that regulatory interactions between pairs of homologous genes within the same cell can lead to under-dominance - mutations which result in stronger autoregulation, and decrease noise in homozygotes, paradoxically can cause increased noise in heterozygotes. This severely limits a diploid’s ability to evolve negative autoregulation as a noise reduction mechanism. Our work offers a simple and general explanation for a previously unexplained difference between the regulatory architectures of E. coli and yeast, Drosophila and humans. It also demonstrates that the effects of diploidy in gene networks can have counter-intuitive consequences that may profoundly influence the course of evolution.

💡 Research Summary

The paper investigates why negative autoregulation (NAR), a feedback motif that speeds response times and reduces intrinsic noise, is abundant in the bacterium Escherichia coli but exceedingly rare among transcription factors of eukaryotes such as Saccharomyces cerevisiae, Drosophila melanogaster, and humans. By mining curated regulatory interaction databases, the authors confirm that roughly 45 % of E. coli transcription factors are negatively autoregulated, whereas the proportion falls below 5 % in yeast and under 4 % in flies and mammals. This discrepancy cannot be explained solely by differences in network topology or transcription‑factor repertoire.

To resolve the paradox, the authors develop a quantitative model that explicitly incorporates diploidy. Two homologous alleles are assumed to encode identical proteins that can each exert negative feedback on its own transcription. The strength of feedback is treated as an evolvable parameter. In a homozygote, increasing feedback strength leaves the mean expression level essentially unchanged while sharply reducing variance, reproducing the classic noise‑reduction benefit of NAR. However, in a heterozygote where the two alleles possess different feedback strengths, the allele with stronger repression suppresses the expression of its weaker partner, creating an asymmetric interaction. Although the total protein concentration remains near the original mean, the disparity between the two alleles inflates overall noise. The authors term this phenomenon “under‑dominance”: a mutation that improves noise performance in homozygotes paradoxically worsens it in heterozygotes.

Mathematically, the model is expressed as a set of stochastic differential equations for transcription, translation, and degradation, linearized around steady state. Using the Langevin approximation and Laplace transforms, the authors derive analytical expressions for the coefficient of variation and for the response time constant as functions of feedback strength. Parameter sweeps reveal a “safe zone” where feedback is either very weak or absent; outside this zone, heterozygotes experience a net increase in noise, making the mutation evolutionarily disadvantageous. Consequently, diploid organisms face a severe constraint on the fixation of stronger NAR circuits.

The theoretical predictions are experimentally validated in yeast. The authors engineer a strong NAR circuit into a native transcription factor and compare noise levels in homozygous and heterozygous diploid strains. As anticipated, the homozygote shows reduced variability, whereas the heterozygote displays elevated noise relative to the wild‑type control, confirming the under‑dominance effect.

The study concludes that the prevalence of NAR in E. coli stems from its haploid lifestyle, which lacks heterozygote constraints, while diploid eukaryotes are evolutionarily steered away from this motif. Instead, they rely on alternative strategies—such as multi‑factor feed‑forward loops, coordinated replication timing, or complex feedback architectures—to achieve robust expression. The work highlights how genome ploidy can shape the evolutionary landscape of gene‑regulatory networks, offering a simple, general explanation for the observed cross‑kingdom differences in network motifs. It also underscores the importance of accounting for diploid-specific dynamics when designing synthetic circuits or interpreting evolutionary trajectories of regulatory systems.