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

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 continuous-time 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

Estimation of Activity Related Energy Expenditure and Resting Metabolic Rate in Freely Moving Mice from Indirect Calorimetry Data

Physical activity (PA) is a main determinant of total energy expenditure (TEE) and has been suggested to play a key role in body weight regulation. However, thus far it has been challenging to determine what part of the expended energy is due to activity in freely moving subjects. We developed a computational method to estimate activity related energy expenditure (AEE) and resting metabolic rate (RMR) in mice from activity and indirect calorimetry data. The method is based on penalised spline regression and takes the time dependency of the RMR into account. In addition, estimates of AEE and RMR are corrected for the regression dilution bias that results from inaccurate PA measurements. We evaluated the performance of our method based on 500 simulated metabolic chamber datasets and compared it to that of conventional methods. It was found that for a sample time of 10 minutes the penalised spline model estimated the time-dependent RMR with 1.7 times higher accuracy than the Kalman filter and with 2.7 times higher accuracy than linear regression. We assessed the applicability of our method on experimental data in a case study involving high fat diet fed male and female C57Bl/6J mice. We found that TEE in male mice was higher due to a difference in RMR while AEE levels were similar in both groups, even though female mice were more active. Interestingly, the higher activity did not result in a difference in AEE because female mice had a lower caloric cost of activity, which was likely due to their lower body weight. In conclusion, TEE decomposition by means of penalised spline regression provides robust estimates of the time-dependent AEE and RMR and can be applied to data generated with generic metabolic chamber and indirect calorimetry set-ups