Predicting Changes of Body Weight, Body Fat, Energy Expenditure and Metabolic Fuel Selection in C57BL/6 Mice

Citation: Guo J, Hall KD ( Predicting Changes of Body Weight, Body Fat, Energy Expenditure and Metabolic Fuel Selection in C57BL/6 Mice Juen Guo 0 1 Kevin D. Hall 0 1 0 Editor: Pere-Joan Cardona, Fundacio Institut Germans Trias i Pujol, Universitat Auto` noma de Barcelona, CibeRES, Corporate Research Program on Tuberculosis , Spain 1 Laboratory of Biological Modeling, National Institute of Diabetes and Digestive and Kidney Diseases , Bethesda, Maryland , United States of America The mouse is an important model organism for investigating the molecular mechanisms of body weight regulation, but a quantitative understanding of mouse energy metabolism remains lacking. Therefore, we created a mathematical model of mouse energy metabolism to predict dynamic changes of body weight, body fat, energy expenditure, and metabolic fuel selection. Based on the principle of energy balance, we constructed ordinary differential equations representing the dynamics of body fat mass (FM) and fat-free mass (FFM) as a function of dietary intake and energy expenditure (EE). The EE model included the cost of tissue deposition, physical activity, diet-induced thermogenesis, and the influence of FM and FFM on metabolic rate. The model was calibrated using previously published data and validated by comparing its predictions to measurements in five groups of male C57/BL6 mice (N = 30) provided ad libitum access to either chow or high fat diets for varying time periods. The mathematical model accurately predicted the observed body weight and FM changes. Physical activity was predicted to decrease immediately upon switching from the chow to the high fat diet and the model coefficients relating EE to FM and FFM agreed with previous independent estimates. Metabolic fuel selection was predicted to depend on a complex interplay between diet composition, the degree of energy imbalance, and body composition. This is the first validated mathematical model of mouse energy metabolism and it provides a quantitative framework for investigating energy balance relationships in mouse models of obesity and diabetes. - Funding: This research 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. The mouse has become the most popular model organism for investigating the molecular mechanisms regulating energy metabolism and body weight (BW). However, a quantitative understanding of energy expenditure in mice remains lacking as highlighted by recent articles addressing problems with the interpretation of indirect calorimetry measurements [14]. Indeed, it is often unclear whether an observed BW change in mice is a result of altered energy intake (EI), energy expenditure (EE), or both. While we know that diet and EE impact metabolic fuel selection and body fat change over time, their quantitative relationship is uncertain. From a physiological perspective, a proper understanding of the metabolic phenotypes of various mouse models requires quantitative integration of these variables and how they change over time. To begin addressing these issues, we present a mathematical model of EE and metabolic fuel selection in male C57BL/6 mice. Our EE model incorporated the influence of body fat mass (FM), fat-free mass (FFM), the energy cost of tissue deposition, physical activity, and dietinduced thermogenesis (DIT). We combined the EE model with a mathematical model of energy partitioning to predict changes of BW, FM, and respiratory quotient (RQ) in response to measured changes of food intake. The model was validated by accurately predicting the BW and FM data from an independent set of experiments in C57BL/6 mice without adjusting any model parameters. The mathematical model demonstrates the complex relationships between metabolic fuel selection, diet composition, energy imbalance, and body composition change and provides a quantitative framework for investigation of murine energy metabolism. Modeling Energy Expenditure and Body Composition Change We begin with the law of energy conservation, also known as the energy balance equation: where rFM = 9.4 kcal/g and rFFM = 1.8 kcal/g are the energy densities for changes in FM and FFM, respectively [5]. EI is the total metabolizable energy intake rate corrected for spillage. We assumed that the calculated metabolizable energy intake based on food intake measurements adequately accounted for any differences of digestibility between the diets. We did not directly measure the energy content of the feces to confirm this assumption. We previously showed that there is a well-defined, timeinvariant function, a, that describes the relationship between changes of FFM and FM in adult male C57BL/6 mice: Using equation 6 to rescale the human values of cFFM = 22 kcal/kg/d and cFM = 3.6 kcal/kg/d [13] results in mouse values of cFFM = 0.15 kcal/g/d and cFM = 0.03 kcal/g/d. Data for Model Calibration The calibration data were obtained from a previously described study, the results of which are depicted in Figure 1 [14]. Briefly, we studied 47 three-month-old male C57BL/6 mice that were individually housed at a temperature of 22uC and randomly assigned to five groups: 1) C group (N = 12) on a chow diet (24% protein, 12% fat, and 64% carb.); 2) HF group (N = 12) on a high fat diet (14% protein, 59% fat, 27% carb.); 3) EN group (N = 11) on a high fat diet plus liquid EnsureH (14% protein, 22% fat, 64% carb.); 4) HF-C group (N = 6) switched from high fat to chow after 7 weeks; 5) EN-C group (N = 6) switched from high fat plus EnsureH to chow after 7 weeks. All animals received free access to water and food throughout the study. The high fat diet was provided using Rodent CAFE feeders (OYC International, Inc., MA), and liquid Ensure was provided in a 30-ml bottle with a rodent sip tube (Unifab Co., MI) and liquid intake was measured every day. Solid food intake was corrected for any visible spillage and was measured every day for the high fat diet and every other day for the chow diet using a balance with a precision of 0.01 g (Ohaus model SP402). Body composition was measured using 1H NMR spectroscopy (EchoMRI 3-in-1, Echo Medical Systems LTD, Houston, TX) and was recorded longitudinally throughout the study along with food intake and BW. The BW and FM at the ~czd expk|FM where the parameters c = 0.1, d = 1.8961024, and k = 0.45 g21 specify the shape of the empirically measured function a [6]. This function allows us to write equation 1 as a pair of differential equations specifying the rates of change of FM and FFM [6,7]: Given measurements of EI, solving equation 3 requires a model of EE which was adapted from published human models [810]: EE~KzbDEI zlBW zcFFM FFMzcFM FM ~K zbDEI zcFFM zlFFMzcFM zlFM where K is a thermogenesis parameter which was assumed to be cons (...truncated)