How adaptations of substrate utilization regulate body composition

Implication of lipid turnover for the control of energy balance

The ongoing obesity epidemic is a consequence of a progressive energy imbalance. The energy-balance model (EBM) posits that obesity results from an excess in food intake and circulating fuels. A reversal in causality has been proposed recently in the form of the carbohydrate-insulin model (CIM), according to which fat storage drives energy imbalance. Under the CIM, dietary carbohydrates shift energy use in favour of storage in adipose tissue. The dynamics of lipid storage and mobilization could, therefore, be sensitive to changes in carbohydrate intake and represent a measurable component of the CIM. To characterize potential changes in lipid dynamics induced by carbohydrates, mathematical models were used. Here, we propose a coherent mathematical implementation of the CIM-energy deposition model (CIM-EDM), which includes lipid turnover dynamics. Using lipid turnover data previously obtained by radiocarbon dating, we build two cohorts of virtual patients and simulate lipid dynamics during ageing and weight loss. We identify clinically testable lipid dynamic parameters that discriminate between the CIM-EDM and an energy in, energy out implementation of the EBM (EBM-IOM). Using a clinically relevant two-month virtual trial, we additionally identify scenarios and propose mechanisms whereby individuals may respond differently to low-carbohydrate diets. This article is part of a discussion meeting issue 'Causes of obesity: theories, conjectures and evidence (Part II)'.

The energy balance model of obesity: beyond calories in, calories out

A recent Perspective article described the "carbohydrate-insulin model (CIM)" of obesity, asserting that it "better reflects knowledge on the biology of weight control" as compared with what was described as the "dominant energy balance model (EBM)," which fails to consider "biological mechanisms that promote weight gain." Unfortunately, the Perspective conflated and confused the principle of energy balance, a law of physics that is agnostic as to obesity mechanisms, with the EBM as a theoretical model of obesity that is firmly based on biology. In doing so, the authors presented a false choice between the CIM and a caricature of the EBM that does not reflect modern obesity science. Here, we present a more accurate description of the EBM where the brain is the primary organ responsible for body weight regulation operating mainly below our conscious awareness via complex endocrine, metabolic, and nervous system signals to control food intake in response to the body's dynamic energy needs as well as environmental influences. We also describe the recent history of the CIM and show how the latest "most comprehensive formulation" abandons a formerly central feature that required fat accumulation in adipose tissue to be the primary driver of positive energy balance. As such, the new CIM can be considered a special case of the more comprehensive EBM but with a narrower focus on diets high in glycemic load as the primary factor responsible for common obesity. We review data from a wide variety of studies that address the validity of each model and demonstrate that the EBM is a more robust theory of obesity than the CIM.

The energy balance model of obesity: beyond calories in, calories out

A recent Perspective article described the "carbohydrate-insulin model (CIM)" of obesity, asserting that it "better reflects knowledge on the biology of weight control" as compared with what was described as the "dominant energy balance model (EBM)," which fails to consider "biological mechanisms that promote weight gain." Unfortunately, the Perspective conflated and confused the principle of energy balance, a law of physics that is agnostic as to obesity mechanisms, with the EBM as a theoretical model of obesity that is firmly based on biology. In doing so, the authors presented a false choice between the CIM and a caricature of the EBM that does not reflect modern obesity science. Here, we present a more accurate description of the EBM where the brain is the primary organ responsible for body weight regulation operating mainly below our conscious awareness via complex endocrine, metabolic, and nervous system signals to control food intake in response to the body's dynamic energy needs as well as environmental influences. We also describe the recent history of the CIM and show how the latest "most comprehensive formulation" abandons a formerly central feature that required fat accumulation in adipose tissue to be the primary driver of positive energy balance. As such, the new CIM can be considered a special case of the more comprehensive EBM but with a narrower focus on diets high in glycemic load as the primary factor responsible for common obesity. We review data from a wide variety of studies that address the validity of each model and demonstrate that the EBM is a more robust theory of obesity than the CIM.

Design of a randomised controlled trial: does indirect calorimetry energy information influence weight loss in obesity?

INTRODUCTION

Respiratory quotient (RQ) provides an indication of the relative balance of carbohydrate and fat oxidation. RQ could serve as an early biomarker of negative energy balance during weight loss. Restriction of energy intake relative to total daily energy requirements produces a negative energy balance which can lead to a fall in RQ, accompanied by a decrease in resting energy expenditure (REE). However, the net change in body weight does not usually match predicted weight change due to intraindividual metabolic adaptations. Our aim is to determine the effectiveness of utilising EE information from indirect calorimetry during weight loss intervention.

METHODS AND ANALYSIS

We will undertake an assessor-blinded, parallel-group randomised controlled trial of 105 adults with obesity randomised in 1:1 ratio to receive either standard weight management care (SC) or EE information plus SC (INT) during a 24-week multicomponent weight management programme. The primary outcome is difference in weight loss between INT and SC group at 24 weeks. Secondary outcomes include: change in RQ, REE, glycaemic variability, and appetite-relating gut hormones (glucagon-like peptide 1, gastric inhibitory polypeptide, peptide YY). Generalised linear mixed models (intention to treat) will assess outcomes for treatment (INT vs SC), time (baseline, 24 weeks) and the treatment-by-time interaction. This will be the first study to evaluate impact of utilising measured REE and RQ on the lifestyle-based intensive intervention programme.

ETHICS AND DISSEMINATION

Ethics approval was obtained from the Health Research Authority and the North West Research Ethics Committee (18/NW/0645). Results from this trial will be disseminated through publication in peer-reviewed journals, national and international presentations.

TRIAL REGISTRATION NUMBERS

NCT03638895; UoL001379.

A mathematical model of the effects of resistance exercise-induced muscle hypertrophy on body composition

PURPOSE

Current diet and exercise methods used to maintain or improve body composition often have poor long-term outcomes. We hypothesize that resistance exercise (RE) should aid in the maintenance of a healthy body composition by preserving lean mass (LM) and metabolic rate.

METHOD

We extended a previously developed energy balance model of human metabolism to include muscle hypertrophy in response to RE. We first fit model parameters to a hypothetical individual to simulate an RE program and then compared the effects of a hypocaloric diet only to the diet with either cardiovascular exercise (CE) or RE. We then simulated a cohort of individuals with different responses to RE by varying the parameters controlling it using Latin Hypercube Sampling (LHS). Finally, we fit the model to mean data from an elderly population on an RE program.

CONCLUSION

The model is able to reproduce the time course of change in LM in response to RE and can be used to generate a simulated cohort for in silico clinical studies. Simulations suggest that the additional LM generated by RE may shift the body composition to a healthier state.

UCP1 and UCP3 Expression Is Associated with Lipid and Carbohydrate Oxidation and Body Composition

BACKGROUND/OBJECTIVE

Uncoupling proteins (UCPs) are located in the inner membrane of mitochondria. These proteins participate in thermogenesis and energy expenditure. This study aimed to evaluate how UCP1 and UCP3 expression influences substrate oxidation and elicits possible changes in body composition in patients submitted to bariatric surgery.

SUBJECTS/METHODS

This is a longitudinal study comprising 13 women with obesity grade III that underwent bariatric surgery and 10 healthy weight individuals (control group). Body composition was assessed by bioelectrical impedance. Carbohydrate and fat oxidation was determined by indirect calorimetry. Subcutaneous adipose tissue was collected for gene expression analysis. QPCR was used to evaluate UCP1 and UCP3 expression.

RESULTS

Obese patients and the control group differed significantly in terms of lipid and carbohydrate oxidation. Six months after bariatric surgery, the differences disappeared. Lipid oxidation correlated with the percentage of fat mass in the postoperative period. Multiple linear regression analysis showed that the UCP1 and UCP3 genes contributed to lipid and carbohydrate oxidation. Additionally, UCP3 expression was associated with BMI, percentage of lean body mass, and percentage of mass in the postoperative period.

CONCLUSIONS

UCP1 and UCP3 expression is associated with lipid and carbohydrate oxidation in patients submitted to bariatric surgery. In addition, UCP3 participates in body composition modulation six months postoperatively.

Modeling body mass variation: incorporating social influence into calculations of caloric intake and energy expenditure

Variations in individual body mass and composition have long been a key focus in the health sciences, particularly now that overweight and obesity are considered as public health problems. We study a mathematical model that describes body mass variations which are determined by the energy balance between caloric intake and total energy expenditure. To calculate the change in caloric intake and energy expenditure over time, we proposed a relationship for each of these quantities, and we used measured values that are reported in the literature for the initial conditions. To account for small variations in the daily energy balance of an individual, we include social interactions as the multiplication of two terms: social proximity and social influence. We observe that social interactions have a considerable effect when the body mass of an individual is quite constant and social interactions take random values. However, when an individual's mass value changes (either increases or decreases), social interactions do not have a notable effect. In our simulation, we tested two different models that describe the body mass composition, and it resulted that one fits better the data.

A mathematical model of the human metabolic system and metabolic flexibility

In healthy subjects some tissues in the human body display metabolic flexibility, by this we mean the ability for the tissue to switch its fuel source between predominantly carbohydrates in the postprandial state and predominantly fats in the fasted state. Many of the pathways involved with human metabolism are controlled by insulin and insulin-resistant states such as obesity and type-2 diabetes are characterised by a loss or impairment of metabolic flexibility. In this paper we derive a system of 12 first-order coupled differential equations that describe the transport between and storage in different tissues of the human body. We find steady state solutions to these equations and use these results to nondimensionalise the model. We then solve the model numerically to simulate a healthy balanced meal and a high fat meal and we discuss and compare these results. Our numerical results show good agreement with experimental data where we have data available to us and the results show behaviour that agrees with intuition where we currently have no data with which to compare.

Modeling metabolic adaptations and energy regulation in humans

Mathematical modeling of human energy regulation and body weight change has recently reached the level of sophistication required for accurate predictions. Mathematical models are beginning to provide a quantitative framework for integrating experimental data in humans and thereby help us better understand the dynamic imbalances of energy and macronutrients that give rise to changes in body weight and composition. This review provides an overview of the various approaches that have been used to model body weight dynamics and energy regulation in humans, highlights several insights that these models have provided, and suggests how mathematical models can serve as a guide for future experimental research.

Quantification of the effect of energy imbalance on bodyweight

Obesity interventions can result in weight loss, but accurate prediction of the bodyweight time course requires properly accounting for dynamic energy imbalances. In this report, we describe a mathematical modelling approach to adult human metabolism that simulates energy expenditure adaptations during weight loss. We also present a web-based simulator for prediction of weight change dynamics. We show that the bodyweight response to a change of energy intake is slow, with half times of about 1 year. Furthermore, adults with greater adiposity have a larger expected weight loss for the same change of energy intake, and to reach their steady-state weight will take longer than it would for those with less initial body fat. Using a population-averaged model, we calculated the energy-balance dynamics corresponding to the development of the US adult obesity epidemic. A small persistent average daily energy imbalance gap between intake and expenditure of about 30 kJ per day underlies the observed average weight gain. However, energy intake must have risen to keep pace with increased expenditure associated with increased weight. The average increase of energy intake needed to sustain the increased weight (the maintenance energy gap) has amounted to about 0·9 MJ per day and quantifies the public health challenge to reverse the obesity epidemic.

Imaging body composition in obesity and weight loss: challenges and opportunities

Obesity is a threat to public health worldwide primarily due to the comorbidities related to visceral adiposity, inflammation, and insulin resistance that increase risk for type 2 diabetes and cardiovascular disease. The translational research portfolio that originally described these risk factors was significantly enhanced by imaging techniques, such as dual-energy X-ray absorptiometry (DEXA), computed tomography (CT), and magnetic resonance imaging (MRI). In this article, we briefly review the important contributions of these techniques to understand the role of body composition in the pathogenesis of obesity-related complications. Notably, these imaging techniques have contributed greatly to recent findings identifying gender and racial differences in body composition and patterns of body composition change during weight loss. Although these techniques have the ability to generate good-quality body composition data, each possesses limitations. For example, DEXA is unable to differentiate type of fat, CT has better resolution but provides greater ionizing radiation exposure, and MRI tends to require longer imaging times and specialized equipment for acquisition and analysis. With the serious need for efficacious and cost-effective therapies to appropriately identify and treat at-risk obese individuals, there is greater need for translational tools that can further elucidate the interplay between body composition and the metabolic aberrations associated with obesity. In conclusion, we will offer our perspective on the evolution toward an ideal imaging method for body composition assessment in obesity and weight loss, and the challenges remaining to achieve this goal.

Mechanisms of metabolic fuel selection: modeling human metabolism and body-weight change

Casual observation of any magazine rack or browsing the diet section of any bookshop provides convincing evidence that weight loss is of great interest to the U.S. population. Americans spend more than US$30 billion/year on weight-loss products, and the health cost of obesity was recently estimated to be as high as US$147 billion/year. Understanding the development of obesity and how excess weight can be lost requires knowledge of the physiological mechanisms by which the body uses food to provide fuel for metabolism and how the body copes with imbalances between fuel delivery and utilization.

Nutritional systems biology modeling: from molecular mechanisms to physiology

The use of computational modeling and simulation has increased in many biological fields, but despite their potential these techniques are only marginally applied in nutritional sciences. Nevertheless, recent applications of modeling have been instrumental in answering important nutritional questions from the cellular up to the physiological levels. Capturing the complexity of today's important nutritional research questions poses a challenge for modeling to become truly integrative in the consideration and interpretation of experimental data at widely differing scales of space and time. In this review, we discuss a selection of available modeling approaches and applications relevant for nutrition. We then put these models into perspective by categorizing them according to their space and time domain. Through this categorization process, we identified a dearth of models that consider processes occurring between the microscopic and macroscopic scale. We propose a "middle-out" strategy to develop the required full-scale, multilevel computational models. Exhaustive and accurate phenotyping, the use of the virtual patient concept, and the development of biomarkers from "-omics" signatures are identified as key elements of a successful systems biology modeling approach in nutrition research--one that integrates physiological mechanisms and data at multiple space and time scales.

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.

Energy metabolism and body composition in long-term recovery from anorexia nervosa

OBJECTIVE

The aim of this study was to determine if energy metabolism and body composition differ between women recovered from anorexia nervosa for 2 or more years (RAN) and control (C) women.

METHOD

Using a cross-sectional design, 16 RAN and 18 C women were studied. Respiratory quotient (RQ) and resting energy expenditure (REE) were measured using indirect calorimetry and body composition using dual energy X-ray absorptiometry.

RESULTS

The REE between RAN and C women was not significantly different, even when adjusted for body composition. However, RAN women had a higher rate of fat oxidation (p = .015), controlling for diet and body composition. There were no significant differences between the groups for body composition, percent body fat, or percent truncal fat mass.

DISCUSSION

Although RAN women have a higher rate of fat oxidation, there were no significant differences in REE or body composition when compared with C women.

Modeling transitions in body composition: the approach to steady state for anthropometric measures and physiological functions in the Minnesota human starvation study

Background

This study evaluated whether the changes in several anthropometric and functional measures during caloric restriction combined with walking and treadmill exercise would fit a simple model of approach to steady state (a plateau) that can be solved using spreadsheet software (Microsoft Excel^®). We hypothesized that transitions in waist girth and several body compartments would fit a simple exponential model that approaches a stable steady-state.

Methods

The model (an equation) was applied to outcomes reported in the Minnesota starvation experiment using Microsoft Excel's Solver^® function to derive rate parameters (k) and projected steady state values. However, data for most end-points were available only at t = 0, 12 and 24 weeks of caloric restriction. Therefore, we derived 2 new equations that enable model solutions to be calculated from 3 equally spaced data points.

Results

For the group of male subjects in the Minnesota study, body mass declined with a first order rate constant of about 0.079 wk^-1. The fractional rate of loss of fat free mass, which includes components that remained almost constant during starvation, was 0.064 wk^-1, compared to a rate of loss of fat mass of 0.103 wk^-1. The rate of loss of abdominal fat, as exemplified by the change in the waist girth, was 0.213 wk^-1.

On average, 0.77 kg was lost per cm of waist girth. Other girths showed rates of loss between 0.085 and 0.131 wk^-1. Resting energy expenditure (REE) declined at 0.131 wk^-1. Changes in heart volume, hand strength, work capacity and N excretion showed rates of loss in the same range. The group of 32 subjects was close to steady state or had already reached steady state for the variables under consideration at the end of semi-starvation.

Conclusion

When energy intake is changed to new, relatively constant levels, while physical activity is maintained, changes in several anthropometric and physiological measures can be modeled as an exponential approach to steady state using software that is widely available. The 3 point method for parameter estimation provides a criterion for testing whether change in a variable can be usefully modelled with exponential kinetics within the time range for which data are available.

The dynamics of human body weight change

An imbalance between energy intake and energy expenditure will lead to a change in body weight (mass) and body composition (fat and lean masses). A quantitative understanding of the processes involved, which currently remains lacking, will be useful in determining the etiology and treatment of obesity and other conditions resulting from prolonged energy imbalance. Here, we show that a mathematical model of the macronutrient flux balances can capture the long-term dynamics of human weight change; all previous models are special cases of this model. We show that the generic dynamic behavior of body composition for a clamped diet can be divided into two classes. In the first class, the body composition and mass are determined uniquely. In the second class, the body composition can exist at an infinite number of possible states. Surprisingly, perturbations of dietary energy intake or energy expenditure can give identical responses in both model classes, and existing data are insufficient to distinguish between these two possibilities. Nevertheless, this distinction has important implications for the efficacy of clinical interventions that alter body composition and mass.

Understanding the dynamics of human body weight change has important consequences for conditions such as obesity, starvation, and wasting syndromes. Changes of body weight are known to result from imbalances between the energy derived from food and the energy expended to maintain life and perform physical work. However, quantifying this relationship has proved difficult, in part because the body is composed of multiple components and weight change results from alterations of body composition (i.e., fat versus lean mass). Here, we show that mathematical modeling can provide a general description of how body weight will change over time by tracking the flux balances of the macronutrients fat, protein, and carbohydrates. For a fixed food intake rate and physical activity level, the body weight and composition will approach steady state. However, the steady state can correspond to a unique body weight or a continuum of body weights that are all consistent with the same food intake and energy expenditure rates. Interestingly, existing experimental data on human body weight dynamics cannot distinguish between these two possibilities. We propose experiments that could resolve this issue and use computer simulations to demonstrate how such experiments could be performed.

Dynamic coordination of macronutrient balance during infant growth: insights from a mathematical model

BACKGROUND

Complex dynamic changes in body composition, dietary intake, energy expenditure, and macronutrient oxidation occur during infant growth. Although previous investigators have focused on energy requirements for normal growth, little is known about the dynamic coordination of macronutrient balance.

OBJECTIVE

Our objective was to develop a mathematical model of the dynamic relations between diet, macronutrient oxidation, and energy expenditure during normal infant growth.

DESIGN

We developed a mathematical model that integrates longitudinal data on changes of body composition and carbon dioxide production determined with the doubly labeled water method to calculate both energy intake requirements and macronutrient oxidation rates during normal infant growth.

RESULTS

The calculated fat oxidation rate was initially <20 kcal x kg(-1) x d(-1), despite the consumption of >60 kcal x kg(-1) x d(-1) of dietary fat. This discrepancy was maintained until approximately 6 mo, after which fat intake was only slightly greater than fat oxidation. Nonfat oxidation closely followed nonfat dietary intake for the duration of the period studied. Model calculations of the energy intake requirements for normal growth were slightly lower than previous estimates. The calculations were robust to variations of body weight, body composition, and diet composition input data, but depended sensitively on variations of carbon dioxide production data.

CONCLUSIONS

Our model presents a dynamic picture of how macronutrient oxidation adapts in concert with dietary changes and energy expenditure to give rise to normal tissue deposition. The model integrates a variety of data in a self-consistent way, simulating the complex metabolic adaptations occurring during normal growth while extracting important physiologic information from the data that would otherwise be unavailable.