The energy cost of protein turnover is arbitrarily distributed between maintenance requirements and protein retention efficiency--comments by Hall

Estimating changes in free-living energy intake and its confidence interval

BACKGROUND

Free-living energy intake in humans is notoriously difficult to measure but is required to properly assess outpatient weight-control interventions.

OBJECTIVE

Our objective was to develop a simple methodology that uses longitudinal body weight measurements to estimate changes in energy intake and its 95% CI in individual subjects.

DESIGN

We showed how an energy balance equation with 2 parameters can be derived from any mathematical model of human metabolism. We solved the energy balance equation for changes in free-living energy intake as a function of body weight and its rate of change. We tested the predicted changes in energy intake by using weight-loss data from controlled inpatient feeding studies as well as simulated free-living data from a group of "virtual study subjects" that included realistic fluctuations in body water and day-to-day variations in energy intake.

RESULTS

Our method accurately predicted individual energy intake changes with the use of weight-loss data from controlled inpatient feeding experiments. By applying the method to our simulated free-living virtual study subjects, we showed that daily weight measurements over periods >28 d were required to obtain accurate estimates of energy intake change with a 95% CI of <300 kcal/d. These estimates were relatively insensitive to initial body composition or physical activity level.

CONCLUSIONS

Frequent measurements of body weight over extended time periods are required to precisely estimate changes in energy intake in free-living individuals. Such measurements are feasible, relatively inexpensive, and can be used to estimate diet adherence during clinical weight-management programs.

Mathematical modelling of energy expenditure during tissue deposition

Predicting the magnitude and rate of weight gain for a given increase of energy intake requires a model of whole-body energy expenditure that includes the energy cost of tissue deposition. Here, I introduce a mathematical framework for modelling energy expenditure that elucidates conceptual problems with the classical Kielanowski method for estimating the efficiencies of body fat and protein deposition. An alternative approach uses the theoretical biochemical efficiencies for protein and fat synthesis in combination with models of energy expenditure that include body fat and protein turnover costs. I illustrate this alternative approach using a simple mathematical model applied to previously published data from growing rats and human infants and compare the simple model results with the classical Kielanowski model. While both models fit the data reasonably well (R2>0.87 in rats and R2>0.67 in infants), the Kielanowski method resulted in parameter estimates that varied widely across experiments, had poor precision, and occasionally produced efficiency estimates greater than 1. In contrast, the new method provided precise parameter values and revealed consistencies across different experiments. The proposed mathematical framework has implications for interpreting studies of animal nutrition as well as providing a roadmap for future modelling efforts.

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.

The unrelenting obesity epidemic has resulted in intensive basic scientific investigation into the molecular mechanisms of body weight regulation—with 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 continuous-time 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.