A longstanding idea in evolutionary physiology holds that an enzyme cannot jointly optimize performance at high and low temperatures because catalytic activity requires local flexibility that costs thermodynamic stability. Miller's 2017 appraisal of comparative and directed-evolution data found that this stability-activity trade-off is not imposed by any physical-chemical constraint, that negative stability-activity correlations among orthologous enzymes appear mainly at high sequence divergence, and that they may often reflect long-term degeneration of unselected function rather than a direct pleiotropic constraint of thermal adaptation. The problem is to determine, for natural enzyme systems, whether reported negative stability-activity correlations reflect a direct mechanistic constraint of thermal adaptation or may in some cases instead be a consequence of the degeneration over time of enzyme function in unselected environments, what molecular processes could generate the reported divergence-dependent pattern, how generally each explanation holds across enzyme systems and families, and whether comparisons of recently diverged populations or species can cleanly discriminate the two explanations. Later work has resolved pieces (single-enzyme mutational trade-off structure, flexibility trends across one enzyme family, absence of general cold-activity rate compensation), but the mechanism-versus-history question in its original generality remains open.

Background

Enzymes are catalysts whose rates and thermal stability are tuned by evolution to an organism's environment. In evolutionary physiology, the 'stability-activity trade-off' is the hypothesis that a protein cannot simultaneously maximize catalytic activity and thermodynamic stability: the active site needs enough local flexibility (molecular motion) to perform catalysis, while a stable, rigid fold resists thermal denaturation, so gains in one property are expected to cost the other. The hypothesis is invoked to explain why psychrophilic enzymes (from cold-adapted organisms) tend to be flexible, marginally stable, and highly active at low temperature, while thermophilic enzymes are rigid and stable but sluggish in the cold. 'Orthologous' enzymes are the same enzyme in different species, descended from a common ancestral gene, so their properties can be compared across known evolutionary distances.

Miller (2017) assembled comparative biochemical studies of purified orthologous enzymes and surveys of directed evolution (laboratory mutation-selection experiments on enzymes) and reported three key observations. First, the stability-activity relationship varies greatly among studies; a trade-off 'is not imposed by any physical chemical constraint'. Second, studies of enzymes with low mean synonymous nucleotide divergence (differences at synonymous codon sites, a standard proxy for divergence time since two sequences shared a common ancestor) were less likely to show the predicted negative correlation between stability and activity. Third, directed-evolution studies often show the two traits uncoupled among nearly identical but phenotypically divergent enzymes. Miller therefore proposed that the negative correlations often reported for highly diverged enzymes may in some cases be a consequence of the gradual degeneration of enzyme function in environments where it is not under selection — for example via conditionally deleterious mutations (mutations that are harmful in one context but tolerable or neutral in another) — rather than a direct effect of thermal adaptation.

Several unresolved issues follow from that appraisal, and they define one coherent scientific objective: deciding the explanatory status of the trade-off. (i) It is still unclear whether the trade-off acts as a direct mechanistic constraint in any particular enzyme system, or whether the reported negative correlations are better explained by long-term divergence and mutation accumulation. (ii) The specific molecular processes that would generate a negative correlation appearing mainly at higher sequence divergence are not identified; conditionally deleterious mutation accumulation is only one candidate. (iii) The comparative evidence is thin — many studies examine few enzymes or small samples — so the breadth of any conclusion across enzyme families is unknown. (iv) The strategy of studying recently diverged populations or species, where historical degeneration has had little time to act, has not been shown to consistently separate true pleiotropic trade-offs (one mutation affecting both traits) from indirect historical effects.

The neighboring literature frames why this is hard and what tools exist. Deep mutational scanning (DMS) methods, which use sequencing to read out the effects of thousands of mutations at once, can now measure mutation-level effects on both stability proxies and activity in a single enzyme, as in the enzyme proximity sequencing study of a D-amino acid oxidase (Vanella et al. 2024), which found direct evidence of trade-off regions near the active site alongside distal positions where activity improves without stability cost. Ancestral sequence reconstruction (ASR), which infers and experimentally resurrects ancient protein sequences, can in principle date a trade-off to specific historical events, as demonstrated for an activity-resistance trade-off in the enzyme IMPDH (inosine monophosphate dehydrogenase, a nucleotide-biosynthesis enzyme; Sarkis et al. 2026) and reviewed for temperature adaptation by Akanuma (2026). Meta-analysis of thousands of enzyme kinetic constants (Stark et al. 2022) finds that stability, but not catalytic rates, broadly tracks organismal growth temperature, and computational modeling (Echave 2019) shows that site-wise evolutionary rate patterns require selection on activity as well as on stability. None of these, however, directly implements the mechanism-versus-history discrimination across natural ortholog sets that Miller's appraisal left open.

Problem Statement

For sets of orthologous enzymes spanning a graded range of sequence divergence, determine whether the negative correlations reported between catalytic activity and thermodynamic stability reflect a direct mechanistic (pleiotropic) effect of thermal adaptation or may in some cases instead be a consequence of the degeneration over time of enzyme function in unselected environments — for example through the historical accumulation of conditionally deleterious mutations that degrade whichever trait is not under selection in each lineage — and how generally each explanation holds across enzyme systems and families. An admissible outcome is that the reported negative correlations, and their apparent dependence on divergence, are not robust once phylogenetic non-independence, small samples and cross-assay heterogeneity are controlled, in which case neither explanation need be affirmed. Where a divergence-dependent pattern is robust, the molecular processes that could generate it — at the level of residue positions, structural flexibility, and mutation types — remain to be identified, and the discriminating power of particular comparative designs is itself part of the question: whether any comparative design separates the two explanations cleanly has not been established. The problem follows Miller (2017): it asks for the mechanism-versus-history discrimination and generality assessment that the appraisal left unresolved, not merely for additional single-enzyme case studies. Resolving the question therefore requires the mechanism-versus-history discrimination to be decided for a bounded, explicitly enumerated set of orthologous enzyme systems under phylogenetic control — a stated bound, not coverage of all such systems — with the trade-off affirmed, rejected, or left undecided for each member of that set; identifying the molecular processes that generate a robust divergence-dependent pattern and establishing the discriminating power of a given comparative design are conditional, bearing only where such a pattern is established, and a demonstration that the reported negative correlations are not robust is itself an admissible completion.

References

  1. Miller, Scott R. (2017). An appraisal of the enzyme stability-activity trade-off. Evolution 71(7):1876-1887. doi:10.1111/evo.13275, https://doi.org/10.1111/evo.13275
  2. Klesmith, Justin R.; Bacik, John-Paul; Wrenbeck, Emily E.; Michalczyk, Ryszard; Whitehead, Timothy A. (2017). Trade-offs between enzyme fitness and solubility illuminated by deep mutational scanning. Proceedings of the National Academy of Sciences 114(9):2265-2270. doi:10.1073/pnas.1614437114, https://doi.org/10.1073/pnas.1614437114
  3. Echave, Julian (2019). Beyond stability constraints: a biophysical model of enzyme evolution with selection on stability and activity. Molecular Biology and Evolution 36(3):613-620. doi:10.1093/molbev/msy244, https://doi.org/10.1093/molbev/msy244
  4. Stark, Catherine; Bautista-Leung, Teanna; Siegfried, Joanna; Herschlag, Daniel (2022). Systematic investigation of the link between enzyme catalysis and cold adaptation. eLife 11:e72884. doi:10.7554/eLife.72884, https://doi.org/10.7554/eLife.72884
  5. Vanella, Rosario; Küng, Christoph; Schoepfer, Alexandre A.; Doffini, Vanni; Ren, Jin; Nash, Michael A. (2024). Understanding activity-stability tradeoffs in biocatalysts by enzyme proximity sequencing. Nature Communications 15:1807. doi:10.1038/s41467-024-45630-3, https://doi.org/10.1038/s41467-024-45630-3
  6. Kontopoulos, Dimitrios-Georgios; Patmanidis, Ilias; Barraclough, Timothy G.; Pawar, Samraat (2025). Changes in flexibility but not in compactness underlie the thermal adaptation of prokaryotic adenylate kinases. Evolution Letters 9(5):598-609. doi:10.1093/evlett/qraf026, https://doi.org/10.1093/evlett/qraf026
  7. Akanuma, Satoshi (2026). Learning about protein stability and functional activity from ancestral reconstruction. Journal of Molecular Biology 438(4):169435. doi:10.1016/j.jmb.2025.169435, https://doi.org/10.1016/j.jmb.2025.169435
  8. Sarkis, Alexander W.; Sørensen, Jens Laurids; Sondergaard, Teis Esben; Nielsen, Kåre Lehmann; Frisvad, Jens C.; Theobald, Douglas L.; Hedstrom, Lizbeth (2026). An activity-resistance trade-off constrains enzyme evolution. Proceedings of the National Academy of Sciences 123(30):e2602068123. doi:10.1073/pnas.2602068123, https://doi.org/10.1073/pnas.2602068123