Estimating the Continuous-Time Dynamics of Energy and Fat Metabolism in Mice

Citation: Guo J, Hall KD ( Estimating the Continuous-Time Dynamics of Energy and Fat Metabolism in Mice Juen Guo 0 Kevin D. Hall 0 Jorg Stelling, ETH Zurich, Switzerland 0 Laboratory of Biological Modeling, National Institute of Diabetes and Digestive and Kidney Diseases , Bethesda, Maryland , United States of America The mouse has become the most popular organism for investigating molecular mechanisms of body weight regulation. But understanding the physiological context by which a molecule exerts its effect on body weight requires knowledge of energy intake, energy expenditure, and fuel selection. Furthermore, measurements of these variables made at an isolated time point cannot explain why body weight has its present value since body weight is determined by the past history of energy and macronutrient imbalance. While food intake and body weight changes can be frequently measured over several weeks (the relevant time scale for mice), correspondingly frequent measurements of energy expenditure and fuel selection are not currently feasible. To address this issue, we developed a mathematical method based on the law of energy conservation that uses the measured time course of body weight and food intake to estimate the underlying continuoustime dynamics of energy output and net fat oxidation. We applied our methodology to male C57BL/6 mice consuming various ad libitum diets during weight gain and loss over several weeks and present the first continuous-time estimates of energy output and net fat oxidation rates underlying the observed body composition changes. We show that transient energy and fat imbalances in the first several days following a diet switch can account for a significant fraction of the total body weight change. We also discovered a time-invariant curve relating body fat and fat-free masses in male C57BL/6 mice, and the shape of this curve determines how diet, fuel selection, and body composition are interrelated. - Funding: This work was supported by the Intramural Research Program of the NIH/NIDDK. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. Mouse models of obesity have become critically important research tools for discovering molecular mechanisms of body weight regulation. But understanding these mechanisms in the context of whole-body physiology requires knowledge of food intake, energy output, and fuel selection [1]. Furthermore, measurements made at an isolated time point cannot explain why body weight has its present value since body weight is determined by the past history of energy and macronutrient imbalance [2]. While food intake and body weight changes can be measured frequently over several weeks (the relevant time scale for mice), correspondingly frequent measurements of energy output and fuel selection are not currently feasible. Expensive indirect calorimetry systems can be used to measure energy expenditure and respiratory exchange over periods of a few days and most systems require removing mice from their normal environment which can alter their behavior [3]. Alternatively, the doubly labeled water method can give an estimate of average energy expenditure, but this method requires specialized equipment for sample analysis as well as prior knowledge of fuel selection as measured by the respiratory quotient (RQ) [4]. Furthermore, significant quantities of blood need to be collected which could impact the behavior of the mouse and makes repeat measurements untenable [4]. Here, we present a mathematical method that quantitatively relates food intake, body weight and body fat to calculate the dynamic changes of energy output and net fat oxidation rates during the development of obesity and weight loss in male C57BL/6 mice. The mathematical model is based on the law of energy conservation, makes very few assumptions, and provides the first continuous-time estimates of energy output and fuel selection over periods lasting many weeks. Our methodology also revealed the relationship between diet, fuel selection, and body composition change in male C57BL/6 mice by identifying a timeinvariant curve relating body fat and fat-free masses. Body Composition and the Relationship between Body Fat and Fat-Free Mass As previously described [5], male C57BL/6 mice were given ad libitum access to standard chow (C), high fat diet (HF), or high fat diet plus liquid Ensure (EN) for 19 weeks, while some mice were fed the high fat or the high fat plus Ensure for 7 weeks before being switched back to chow for the remaining 12 weeks (HF-C and ENC, respectively). Figure 1A shows the body weight changes of the various groups during the development of obesity on the HF and EN diets as well as the weight loss and persistent obesity of the HFC and EN-C groups following a switch back to the chow diet at 7 weeks (error bars have been omitted for clarity). A single curve was able to describe the adjusted fat-free mass as a function of body fat mass for all groups at all time points (Figure 1B) and is analogous to the curve discovered by Forbes describing human body The unrelenting obesity epidemic has resulted in intensive basic scientific investigation into the molecular mechanisms of body weight regulationwith the mouse being the organism of choice for such studies. We know that any mechanism of body weight regulation must exert its effect by influencing food intake, energy output, fuel selection, or some combination of these factors over extended time scales (,weeks for mice). While food intake and body weight can be frequently measured in mice, current methods prohibit corresponding measurements of energy output or fuel selection on such long time scales. We address this deficiency by developing a mathematical method that quantitatively relates measurements of food intake, body weight and body fat to calculate the dynamic changes of energy output and net fat oxidation rates during the development of obesity and weight loss in male C57BL/6 mice. The mathematical model is based on the law of energy conservation, makes very few assumptions, and provides the first continuoustime estimates of energy output and fuel selection over periods lasting many weeks. Application of our methodology to various mouse models of obesity will improve our understanding of body weight regulation by placing molecular mechanisms in their whole-body physiological context. composition change [6]. Our mathematical model used this fitted curve along with the body weight data to compute the body fat mass changes (Figure 1C). Without adjusting any parameters, the model also accurately predicted the fat mass changes measured in a separate experiment with high-fat feeding of C57BL/6 mice followed by a switch to chow after 20 weeks (Figure 1D). Continuous-Time Estimates of Energy Output Our model calculated the first continuou (...truncated)