Reply to Guo and Hall

response: we appreciate the attention Guo and Hall (4a) have given our paper (5). We view their letter as an opportunity for clarification, to demonstrate further the utility of our work for mouse calorimetry analysis and to stress the importance of “cross-pollination” between computational and empirical researchers in this area. In preparation for this rebuttal, we performed a comprehensive review of all of the original data and statistical analyses (Table 1).

Table 1.

Corrected measurements of fat mass and fat-free mass

	Lean	STDIO	LTDIO
Unadjusted, mean (SD)
Fat mass, g	13.18 (1.55)	14.55 (2.34)	21.93 (1.43)†‡
Fat-free mass, g	19.00 (0.54)	19.82 (1.00)	23.93 (0.96)†‡
Adjusted for ΔMb, mean ± SE
Fat mass, g	13.77 ± 0.51	13.64 ± 0.69	22.25 ± 0.40†‡
Fat-free mass, g	19.29 ± 0.24	19.36 ± 0.32	24.10 ± 0.19†‡

We here report an error in our original computations of fat mass and fat-free mass; a linear correction was not performed on the raw data. The corrected measurements are shown as per original Table 1 (see Ref. 5). None of our original interpretations has been changed as a result of these corrections. The number in each group is 32 mice. ΔM_b, change in body mass. STDIO, 4-day, short-term diet-induced obesity; LTDIO, 17-wk, long-term DIO.

^†P < 0.001, STDIO vs. LTDIO;

^‡P < 0.001, lean vs. LTDIO.

Our original paper investigated whether the change in body weight in mice during indirect calorimetry (Δbody wt) was a useful linear covariate. Unlike humans, mice are uniquely suited for this type of adjustment, precisely because their body weights are known to fluctuate so widely during calorimetry (2). While the relationship between 24-h respiratory quotient (RQ) and energy intake has been long understood (3), we tested whether this could be modeled with an obesigenic diet and the extent to which Δbody wt influenced this relationship.

With regard to the authors' major criticism, we believe that they have framed our conclusions incorrectly due to their misinterpretation of the variance components of our analysis. Stated simply, Δbody wt significantly explained a major portion of variance in the relationship between 24-h RQ and caloric intake; an additional much smaller portion of variance that was independent of Δbody wt also significantly explained this relationship. To demonstrate this here, we present again the case of the lean chow-fed group (the pertinent data are shown in Figure 3 and Table 4 of Rev. 5). The Δbody wt explained 71% of variance in the relationship between 24-h RQ and caloric intake. Of the 29% residual “unexplained” variance, 13.4% was explained significantly by some unknown covariate(s) other than Δbody wt (see Fig. 3D of Ref. 5), leaving 15.6% of the variance in the relationship completely unexplained. In other words, we were able to model correctly ∼71% of this relationship with Δbody wt alone, and 84% with Δbody wt and some unknown factor(s). This explains why adjusting the daily energy intake for Δbody wt (see Table 2 of Ref. 5) trended in the right direction but did not completely offset energy expenditure. (The average correction of 82% is remarkably in line with our model's 84% prediction of “explained” variance. These percentages and variance components can be directly observed in or deduced from Tables 2 and 4 of Ref. 5.) To the extent that Δbody wt did not account for 100% of the variance in the relationship between RQ and energy intake, authors Guo and Hall (4a) correctly question its power as a covariate. However, we have unquestionably demonstrated that Δbody wt significantly explained most of the variance in this relationship; this proposed model can reduce the error in RQ and energy intake measurements through an understanding of their covariance with an easily obtained measurement, Δbody wt.

The “challenge” Guo and Hall (4a) have articulated should not be with indirect calorimetry alone, but with identifying potential sources of error in, and reconciling disagreements between, calorimetric and computational models. For example, the Δbody wt covariate needs further refinement; its use assumes that the amount of food transitioning in the gut at any point in time is constant, but in certain circumstances this is demonstrably false. Computational methods to correct for this would likely improve the power of this covariate. Conversely, the computational model is complex and relies on inflexible assumptions and constants, many derived from the literature or from other species, that may not always hold true for the mouse; performing well-designed and controlled calorimetry experiments would allow for more rigorous testing and validation of their computational model.

Does Guo and Hall's model (4a) correctly predict the changes in RQ and energy expenditure observed from mice in calorimetry chambers? Such long-term calorimetry experiments would be arduous, but are nonetheless possible (1) and arguably necessary. Validation experiments were not presented in their recent publication (4); interestingly, the authors reported an attempt to do so, but stated that the loss of body weight by mice in the calorimetry chambers produced data that disagreed with their model. Consequently, they concluded that their computational model had helped them to “… diagnose a technical problem with the indirect calorimetry equipment” (4). We propose that Guo and Hall reflect on the axiom “the animal is always right” and revisit their data using Δbody wt as a covariate; they can then make linear adjustments of RQ based on body weight estimates of mice in typical home cages where they would be expected to maintain/gain weight over time.

Until the computational and empirical components are reconciled, it will be difficult to ascertain whether all elements of the computational model are reliably inferential; in statistical terms, predictions of RQ made by their present model may be over-fitted. We hope that Guo and Hall succeed in validating their model; if so, it would be a significant advancement for the field of mouse energetics.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).