The Problem Is Not How We Calculate Enzyme Stoichiometry Threshold—It Is That We Calculate It

A recent paper by Puissant (2025) appropriately raised concerns about the use of log-transformed data in determining enzymatic stoichiometry thresholds—an important and valid critique. However, this discussion gives the misleading impression that, if the thresholds are calculated without log-transformation, they would function accurately. In reality, the more fundamental issue lies in the validity of calculating thresholds based on enzyme data itself. Here, I first address the conceptual issues associated with calculating thresholds from regressions of enzyme activity data—even when the log-transformation problem is resolved. Furthermore, while Puissant (2025) suggests that addressing this issue would enable enzyme ratio calculations or vector analyses to serve as indicators of microbial nutrient limitation, I respectfully disagree with this conclusion. This is because multiple studies have shown that enzyme stoichiometry fails to reliably reflect nutrient limitation, and importantly, the enzyme stoichiometry framework has never been empirically validated.

Thresholds for carbon (C), nitrogen (N), and phosphorus (P) limitations were calculated using regression analyses of enzyme activity data measured under natural conditions. These analyses included: β-1,4-glucosidase (BG) versus N-acetylglucosaminidase (NAG) for C versus N limitation; BG versus acid or alkaline phosphatase (i.e., phosphomonoesterase, AP) for C versus P limitation; and NAG versus AP for N versus P limitation (Sinsabaugh et al. 2009). This approach assumes that the enzyme activities used to establish the thresholds represent either conditions of no nutrient limitation or equal limitation by all nutrients. Based on this assumption, deviations from these thresholds can be interpreted as indicators of C, N, or P limitation. However, this assumption lacks theoretical justification (Mori et al. 2023; Cui et al. 2024). Why should natural conditions be free from nutrient limitation? In fact, ecological understanding suggests that microbial activity is often constrained by one or more limiting nutrients (Kaspari et al. 2008). Furthermore, this underlying assumption—that typical or average natural conditions are nutrient-unlimited—is directly contradicted by how the thresholds are applied thereafter. In the application phase, the same type of enzyme data is used to test for nutrient limitations, based on the assumption that a specific nutrient is limiting. Consequently, the construction and application of the thresholds rest on fundamentally contradictory assumptions, leading to a methodological inconsistency.

Puissant (2025) suggested that enzymatic stoichiometry and vector analysis remain valid methods, provided that enzyme activity ratios are calculated without prior log transformation. However, I respectfully disagree with this conclusion. It is important to underscore that both approaches rest on questionable methodological assumptions. Notably, the enzyme stoichiometry framework has never been empirically validated, whereas multiple independent studies have demonstrated its limitations.

In particular, direct enzyme activity ratios have repeatedly been shown to inadequately represent microbial nutrient limitations. Several meta-analyses have revealed that the commonly used indicators—BG, NAG combined with leucine aminopeptidase (LAP), and AP—do not accurately represent microbial C, N, and P limitations, respectively (Mori et al. 2021; Mor 2024b). The enzymatic stoichiometry framework assumes that increasing C availability will lower BG:NAG(+LAP) and BG:AP ratios, while increasing N or P availability will raise these ratios. However, the observed patterns in meta-analyses often run counter to these predictions, calling into question the validity of the approach. It is worth noting that some of these meta-analyses addressed criticisms that short-term responses or fertilization treatments may be unsuitable for evaluating the enzyme stoichiometry approach (Moorhead et al. 2023). In response, these meta-analyses relied exclusively on long-term field experiments (Mor 2024a) or on C additions that naturally occur in the environment (Mor 2024b). Another clear piece of evidence for the inadequacy of the enzymatic stoichiometry approach is that microbial growth responses to fertilization do not correspond with predictions based on enzyme stoichiometry (Rosinger et al. 2019). This body of evidence highlights a fundamental limitation of the enzymatic stoichiometry approach: BG, NAG(+LAP), and AP represent only a subset of enzymes involved in microbial nutrient acquisition (Nannipieri et al. 2018) and are not the exclusive terminal enzymes specific to each nutrient. Furthermore, these enzymes often participate in the acquisition of multiple nutrients, making them unreliable as proxies for specific nutrient limitations (Mori et al. 2023; Cui et al. 2024). Therefore, although these enzymes can indicate microbial investment in the acquisition of C, N, and P to some extent, the use of their activity ratios as proxies for nutrient limitation is problematic.

Vector analysis—which calculates vector length as (x² + y²)^0.5 and angle (in degrees) as atan2(y, x), where x = BG/(BG + AP) and y = BG/(BG + LAP)—suffers from the same fundamental issue as the direct use of enzyme activity ratios (noting that alternative ratios, such as those including NAG, are also commonly used). In this framework, an increase in BG increases the vector length, while increases in AP and NAG respectively increase and decrease the vector angle. Thus, vector analysis is essentially a visual reformulation of the enzyme ratio approach and inherits its conceptual limitations.

Overall, while I fully agree with Puissant (2025)'s critique regarding the misuse of log-transformation in enzyme activity data, I argue that resolving this issue does not address the core problem. The fundamental limitations of the enzyme stoichiometry approach persist, even when the log-transformation concern is corrected.

The author declares no conflicts of interest.

This article is a Letter to the Editor regarding Jérémy Puissant https://doi.org/10.1111/gcb.70228. See also the Response to the Letter by Jérémy Puissant https://doi.org/10.1111/gcb.70517.