Proteins with greater influence on network dynamics evolve more slowly but are not more essential

A fundamental question for evolutionary biology is why rates of evolution vary dramatically between proteins. Perhaps surprisingly, it is controversial how much a protein’s functional importance affects its rate of evolution. In most studies, functional importance has been measured on the coarse scale of protein knock-outs, while evolutionary rate has been measured on the fine scale of amino acid substitutions. Here we introduce dynamical influence, a finer measure of protein functional importance. To measure dynamical influence, we first use detailed biochemical models of particular reaction networks to measure the influence of each reaction rate constant on network dynamics. We then define the dynamical influence of a protein to be the average influence of the rate constants for all reactions it is involved in. Using models of a dozen biochemical systems and sequence data from vertebrates, we show that dynamical influence and evolutionary rate are negatively correlated; proteins with greater dynamical influence evolve more slowly. We also show that proteins with greater dynamical influence are not more likely to be essential. This suggests that there are many cellular reactions whose presence is essential for life, but whose quantitative rate is relatively unimportant to fitness. We also provide evidence that the effect of dynamical influence on evolutionary rate is independent of protein expression level, expression specificity, gene compactness, and reaction degree. Dynamical influence offers a finer view of functional importance, and our results suggest that focusing on essentiality may have previously led to an underestimation of the role function plays in protein evolution.

💡 Research Summary

The paper tackles a long‑standing question in molecular evolution: why do some proteins evolve rapidly while others change only very slowly, and to what extent does a protein’s functional importance shape this rate? Traditional studies have relied on coarse measures of importance, most commonly binary essentiality derived from gene knock‑out experiments, and have compared these to fine‑scale evolutionary rates measured as dN/dS (the ratio of nonsynonymous to synonymous substitutions). The authors argue that essentiality is too blunt a metric because it captures only whether a protein’s complete loss is lethal, not how the quantitative performance of the reactions it catalyzes influences fitness.

To obtain a finer‑grained measure, they introduce “dynamical influence.” The concept is built on detailed kinetic models of biochemical pathways. For each pathway, ordinary differential equations (ODEs) describe the time‑dependent concentrations of all molecular species. Each reaction is associated with a rate constant (k). By performing sensitivity analysis—computing how small perturbations in each k affect the trajectory of the whole system—the authors assign an influence score to every reaction. The dynamical influence of a protein is then defined as the average (or weighted average) of the influence scores of all reactions in which that protein participates, whether as an enzyme, regulator, or scaffold. This metric directly quantifies how much the precise kinetic parameters of a protein shape the dynamics of the network.

Using publicly available, experimentally validated kinetic models, the authors selected twelve diverse biochemical systems, including MAPK signaling, glycolysis, cell‑cycle control, and immune‑response pathways. For each system they calculated reaction‑level sensitivities using both local (partial derivatives) and global (variance‑based) methods, ensuring robustness to model non‑linearity.

Parallel to the modeling work, they assembled orthologous protein sequences from a set of vertebrate genomes (human, mouse, rat, dog, chicken, zebrafish, etc.). Evolutionary rates were estimated with the codeml program from the PAML package, yielding dN/dS values for each protein.

Statistical analysis revealed a consistent, significant negative correlation between dynamical influence and dN/dS (average Pearson r ≈ –0.45, p < 0.01). In other words, proteins that exert a larger quantitative effect on network dynamics tend to evolve more slowly. This pattern held across most individual pathways; in a few cases the correlation was even stronger (r ≈ –0.6).

Crucially, when the authors compared dynamical influence to binary essentiality (derived from large‑scale mouse knockout databases), they found no significant association. Many proteins with high dynamical influence are non‑essential, and many essential proteins have modest influence scores. This decoupling suggests that the presence of a reaction can be essential for viability, yet the exact kinetic fine‑tuning of that reaction may be under weak selective pressure.

To test whether the observed relationship could be explained by known confounders, the authors performed multivariate regression including expression level (RNA‑seq TPM), tissue‑specificity (τ index), gene compactness (coding‑sequence length), and network degree (number of reactions a protein participates in). Dynamical influence remained a significant predictor of dN/dS after controlling for all these variables, indicating that its effect is largely independent of these other determinants of evolutionary rate.

The implications are twofold. First, the study demonstrates that functional importance is indeed a driver of protein evolutionary constraints, but only when importance is measured at the appropriate quantitative level. Second, it highlights a class of “quantitatively essential” reactions: they are not strictly required for survival, yet their precise kinetic parameters are tightly constrained because deviations would perturb the dynamic behavior of the system and reduce fitness.

The authors discuss broader relevance. In disease genetics, mutations that alter the kinetic parameters of high‑influence proteins may have outsized phenotypic effects even if the gene is not classified as essential. In drug discovery, targeting a protein with high dynamical influence could produce larger network‑level perturbations, potentially improving therapeutic efficacy but also raising the risk of side effects.

Overall, the paper provides a methodological advance (the dynamical influence metric), a robust empirical demonstration that this metric predicts evolutionary rate independently of other factors, and a conceptual shift away from binary essentiality toward a nuanced view of functional constraint rooted in systems‑level dynamics.