We have the following interests. John R.B. Lighton, PhD, is the President and Chief Scientist of Sable Systems International (SSI), and formerly adjunct professor of biological science at the University of Nevada at Las Vegas. SSI manufactured and loaned the calorimeter system used in this study (Promethion metabolic phenotyping system) at UNLV. Dr. Lighton participated in manuscript conceptualization, study design and data collection, was involved in the initial analysis of data, and contributed to manuscript preparation. Dr. Lighton/SSI did not provide any salary or other compensation to either of the other authors of this work (KJK, BEW). Thomas Foerster, PhD, an employee of SSI assisted in carrying out the metabolic measurements at UNLV but had no other role. Brent E. Wisse, MD, Associate Professor of Medicine at the University of Washington, provided funding (National Institutes of Health DK074758, DK090320, and DK076126) that supported animal and supply costs associated with the studies. There are no further patents, products in development or marketed products to declare. This does not alter our adherence to all the PLOS ONE policies on sharing data and materials, as detailed online in the guide for authors.
Energy expenditure (EE) calculated from respirometric indirect calorimetry is most accurate when based on oxygen consumption (VO2), carbon dioxide production (VCO2) and estimated protein metabolism (PM). EE has a substantial dependence of ~7% on the respiratory quotient (RQ, VCO2/VO2) and a lesser dependence on PM, yet many studies have instead estimated EE from VO2 only while PM has often been ignored, thus reducing accuracy. In 1949 Weir proposed a method to accurately calculate EE without using RQ, which also adjusts for estimated PM based on dietary composition. This RQ- method utilizes the calorimeter airflow rate (FR), the change in fractional O2 concentration (ΔFO2) and the dietary protein fraction. The RQ- method has not previously been empirically validated against the standard RQ+ method using both VO2 and RQ. Our aim was to do that.
VO2 and VCO2 were measured repeatedly in 8 mice fed a high protein diet (HPD) during exposure to different temperatures (n = 168 measurements of 24h gas exchange). The HPD-adjusted RQ+ equation was: EE [kcal/time] = VO2 [L/time]×(3.853+1.081RQ) while the corresponding RQ- equation was: EE = 4.934×FR×ΔFO2. Agreement was analyzed using the ratios of the RQ- to RQ+ methods along with regression and Bland-Altman agreement analyses. We also evaluated the standard equation using the dietary food quotient (FQ) of 0.91 as a proxy for RQ (FQ+ method).
Ratio analysis revealed that the mean error of the RQ- method was only 0.11 ± 0.042% while the maximum error was only 0.21%. Error using the FQ+ method was 4 -and 10-fold greater, respectively. Bland-Altman analysis demonstrated that the RQ- method very slightly overestimates EE as RQ decreases. Theoretically, this error can be eliminated completely by imposing an incurrent fractional oxygen concentration at a value only slightly greater than the atmospheric level.
The Weir ‘RQ-free’ method for calculating EE is a highly valid alternative to the ‘gold standard’ method that requires RQ. The RQ- approach permits reduced cost and complexity in studies focused on EE and provides a way to rescue EE measurement in studies compromised by faulty CO2 measurements. Practitioners of respirometry should consider adjusting EE calculations for estimated protein metabolism based on dietary composition.
Animal life is powered by catalytic combustion, the intricate “Fire of Life” [
The ratio of VCO2 to VO2, termed the respiratory quotient (RQ), normally ranges between ~0.7 and ~1.0 depending largely on the proportions of carbohydrate, fat and protein being combusted. EE is commonly calculated by multiplying VO2 times a linear transform of the form (A+B×RQ), where A and B are coefficients whose ‘most accurate’ values have a modest inverse dependence on the rate of protein metabolism as estimated from nitrogen excretion or diet composition [
One of the most widely employed equations for calculating EE from respirometric data was introduced in 1949 by Weir in a paper focused principally on adjusting the EE calculation for protein metabolism [
In the same paper [
It is important to emphasize that the constant term in
The RQ- method is all but unknown, likely overshadowed by Weir’s canonical EE equation [
If the RQ- method in fact agrees very well with the standard RQ+ method, its adoption could confer a number of important advantages (discussed below). Accordingly, our major aim was to validate the RQ- method. We also present a new and hopefully more rigorous and transparent explanation for why the method should work, and demonstrate that, theoretically, the agreement between the RQ- and RQ+ methods can be made perfect by imposing an incurrent oxygen fraction that is only slightly greater than the normal atmospheric value. Finally, our analysis suggests that protein metabolism should get wider consideration in the application of respirometry.
Male C57Bl/6J mice (N = 8, age ~8 weeks; Jackson Laboratories (Bar Harbor, ME)) were housed in a constant temperature walk-in room housed within the AAALAC-accredited animal care facility at the University of Nevada at Las Vegas. Mice were individually housed within live-in, unsealed, pull-mode metabolic measurement cages (see [
All study procedures were approved by the Institutional Animal Care and Use Committee (IACUC) at the University of Nevada at Las Vegas. The program is fully accredited by the Association for the Assessment and Accreditation for Laboratory Animal Care International (AAALAC).
A valid expression for VO2, easily derived from equation 11.2 on p.126 in [
(We emphasize that the flow rate and fractional gas concentrations must be mathematically corrected for or scrubbed of water vapor).
Next, to compute EE in accordance with
Note that we intentionally placed the RQ+ transform over the denominator of
Remarkably, the numerator and denominator of the ratio in
It can be shown that the RQ- minus RQ+ EE difference in kcal/h calculated as the simplified version of
Thus, for a given RQ <1.0, the EE difference is predicted to scale directly but only slightly with VO2, and for a given VO2, the difference is predicted to increase linearly, but again only slightly, as RQ decreases.
Metabolic rates were measured using an 8-cage Promethion-C continuous, parallel metabolic phenotyping system (Sable Systems International (SSI), Las Vegas, NV; SSI). This system imposes minimal stress due to handling or other disruptive influences because it uses live-in cages of ~8 L STP internal volume that are transferred from the housing colony to the testing room for studies. Air was pulled from the cages at a controlled mass flow rate of 2 L/min STP. This yielded a time constant of ~4 min. The flow from each cage was sampled by a gas analysis chain consisting of a water vapor analyzer a CO2 analyzer, an O2 analyzer, a barometric pressure sensor, and a subsampling flow control system, all integrated into one gas analysis system (GA3m4: SSI) per bank of 4 cages. Gas flow for each bank was generated by a FR-4b mass flow controlled pull flow generator (SSI). The calorimeter room also incorporated a fluorescent light source controlled by a timer set to a 12:12 light:dark cycle.
The system acquired data on fractional O2 and CO2 concentrations, water vapor pressure (WVP), barometric pressure (BP), ambient temperature and light levels, flow rates, food and water dispenser masses (to 1 mg), body masses (to 1 mg via a weighed enrichment habitat), running wheel revolutions, and X, Y and Z locations together with beam-breaks. Measurements were acquired at a sample rate of 1 sample/sec for all sensors and cages simultaneously via an error-correcting control area network (CAN). The provision for exercise increased variability in EE and RQ, important goals of our study design, but the primary strategy for achieving that end was to systematically vary the temperature of the testing room from 19 to 29°C. Specifically, the 8 mice were each tested at 19°C (total of 3 d), 21°C (9 d), 23°C (3 d), 25°C (2 d), 27°C (1 d), and 29°C (4 d) for a total of N = 168 measurements. Note that the maintenance of thermal homeostasis in mice requires EE to be exquisitely sensitive to even the seemingly mild cold stress imposed by typical laboratory temperatures of ~21°C while thermoneutrality in mice is achieved at ~30–32°C [
We corrected for water vapor dilution of fractional gas concentrations using Dalton's law of partial pressures, an application of elementary chemistry based on measurement of BP and WVP in the gas stream. The equation is simply:
The calorimeter system switched from measuring the excurrent air pulled from each cage to measuring incurrent air pulled from the cages’ environment for 30 sec every 20 min. This permitted periodic re-spanning of the O2 analyzers to WVP-corrected FiO2 = 0.2094, effectively eliminating O2 drift; this also allowed measurement of FiCO2. During data analysis these brief and infrequent interruptions–each lasting only ~15% of the cage time constant, thus minimizing their effect on the underlying data -were removed by linear interpolation, which rendered them effectively invisible.
We also contrasted the performance of the RQ- equation with the standard Weir equation using the mouse diet’s FQ of 0.91 as a proxy for RQ, denoted the FQ+ method.
Data were stored in raw, unprocessed form for later analysis using analysis scripts run on ExpeData analytical software (SSI). This allowed complete and traceable control of the analytical process, the equations used, the baselining algorithms employed, and all other aspects of data transformation and final data extraction.
For the major analyses in this paper, calorimeter outcomes were averaged (mean) across each 24h circadian cycle of each day of exposure at the 6 ambient temperatures. A separate time series analysis binned the 1 Hz continuous data into 30 sec bins across a 24h study to make the data and graphical analyses more tractable to analysis.
Agreement between the RQ- and RQ+ equations was analyzed in several ways. One simply involved analysis of the N = 168 ratios of RQ-:RQ+ EE calculations. We also employed the Tukey mean-difference method (widely known as the Bland-Altman technique [
All statistical and graphical analyses were performed using R (R: A Language and Environment for Statistical Computing. R Core Team. R Foundation for Statistical Computing. Vienna, Austria, 2018. url =
Data are reported as means ± SEM unless reported otherwise.
Mean ± SD EE outcomes in kcal/h for the three computational methods were essentially the same: RQ+ = 0.421 ± 0.0651, RQ- = 0.421 ± 0.0652, FQ+ = 0.423 ± 0.0667. The mean ± SD ratios were: (RQ-/RQ+) = 1.0011 ± 0.00042, (FQ+/RQ+) = 1.0044 ± 0.0092. The most extreme ratios were: (RQ-/RQ+) = 1.0021, (FQ+/RQ+) = 1.0265. Accordingly, the largest relative errors compared to the ‘gold standard’ RQ+ method were 0.21% for the RQ- method and 2.65% for the FQ+ method.
Scatterplots relating the alternative EE equations are depicted in
(A) Substituting the FQ of the mouse chow for RQ in the standard Weir equation (y-axis) versus the standard Weir RQ+ equation. (B) Comparison of the Weir RQ- equation to the standard Weir RQ+ method.
Data consist of 168 measurements of 24h EE in n = 8 mice. EE, energy expenditure; RQ, Respiratory Quotient; FQ, Food Quotient.
Note in
In panels A and B the x-axis depicts the mean of two methods being compared and the y-axis depicts the difference; the standard Weir RQ+ method was subtracted from the other method (refer to text or
The performance of the RQ- method was strikingly superior to that of the FQ+ method; indeed, the ± 2 SD range of agreement was 18.8-fold greater for the FQ+ equation than for the RQ- method. This is notable, in part, because the data involve 24h averages for which one expects RQ and FQ to be equivalent in unstressed weight stable animals (as was the case in our study). The increased error reflects the fact that RQ is very labile in fed animals (example below).
The RQ- equation exhibited a very slight positive bias (mean bias = 0.00047 kcal/h, representing just 0.11% of the overall mean of the two methods (and 0.11% of the mean RQ+ EE since the overall means were equal); this simply indicates that, as expected, the RQ- method exhibited a very slight tendency to overestimate EE compared to the RQ+ method. The upper bound for agreement (mean bias + 2 SD) was 0.00088 kcal/h and equates to an error of just 0.21% of the mean. Indeed, of the entire data vector, just 5 of the 168 (RQ- minus RQ+) difference values (3%) exceeded the 0.21% limit. Thus agreement between the RQ- and RQ+ equations was highly satisfactory.
As predicted by
Another view of the impact of RQ on the Weir RQ- minus Weir RQ+ EE difference is depicted in
The foregoing data indicate that the Weir RQ- method works very well for analyzing EE data averaged over longer time durations, but we also wanted to confirm that this method holds up for continuous time series data in single mice. The data depicted in
The thick solid lines indicate the dark photoperiod. (A) EE as computed by the RQ- equation (see text or
Of particular note in
We also performed the time series analysis using the standard Weir equation assuming the mouse diet’s FQ of 0.91; the difference between the upper and lower agreement limits was more than 30-fold greater than for the RQ- method (0.0275 vs. 0.0009 kcal/h). This emphasizes the fact that the difference between FQ and RQ in ad-lib fed animals varies markedly across the circadian cycle and so reduces the accuracy of EE calculations when using FQ in place of measured RQ.
It is important to emphasize the importance of correcting fractional gas concentrations for WV dilution.
Data consist of 168 measurements of 24h EE in n = 8 mice.
The present work demonstrates clearly, and to our knowledge for the first time, that the ‘RQ-free’ method published seven decades ago by Weir [
Because the RQ- approach constitutes a method rather than a single equation, we should stress how easy it is to adapt it for use with a different RQ+ equation, for instance the equation derived by Hall and associates [
Note that
When Eqs
Protein oxidation has been widely ignored in research involving respirometric EE estimation. Depending on study design and goals, the potential impact of protein metabolism may or may not be significantly problematic. To illustrate, we note that the predicted ‘error’ in EE calculated from the RQ+ or RQ- methods
One reason that protein metabolism has been ignored is the assumed need to measure nitrogen excretion (6.25 g of protein metabolized per g of excreted nitrogen [
Our findings do more than simply validate the use of the RQ- method for research involving the need to compute only EE. In particular, measuring VCO2 is technically problematic and adds cost. CO2 calibration gases of <1% accuracy are not widely available and most are accurate to only ±2–5%. CO2 is generally measured using an optical absorption method with non-linear properties [
By contrast, it is considerably easier to accurately measure fractional O2 concentrations within a range narrowly centered on the normal atmospheric value. One reason whose importance is hard to overstate is that O2 calibration is anchored to the atmosphere’s near-constant FO2 of 20.939 ± 0.0003% after correcting for WVP and variations in BP [
Our results and comments regarding CO2 should make it obvious that the RQ- method provides an excellent means by which to rescue high accuracy EE data in studies compromised by faulty CO2 sensing. Moreover, the RQ- method may also be developed to provide a way to determine whether CO2 sensing is potentially compromised. Specifically, if CO2 sensing is accurate, then mean EE as calculated by the RQ- method will be only very slightly higher than EE calculated by the RQ+ method (0.11% in the present study), whereas if, for example, CO2 sensing is too low and therefore results in artifactually low RQ values, then mean EE as calculated by the RQ- method may be notably higher than EE calculated by the RQ+ method. To take advantage of this quality control approach, it would be important to first determine typical RQ- to RQ+ EE ratios in studies where the gas sensors are known to be functioning well.
Another potentially important application of the RQ- approach is that eliminating the CO2 sensor and related components would help minimize the weight, volume and expense of small ‘wearable’ calorimeters designed to measure human EE during occupational, recreational and ‘everyday living’ tasks.
Finally, our study also lends credence to the use of the Weir RQ- method in previous research involving measurement of EE during exposure to nitrous oxide, a gas that interferes with CO2 sensing [
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We thank Thomas Foerster PhD for assistance with carrying out the metabolic measurements at UNLV. We thank Douglas S. Ramsay, DMD, PhD, Katherine Rafferty, PhD, Stephan Guyenet, PhD, and Stephen C. Woods for their very helpful comments during internal review.