Controlling body weight is a simple matter of balancing how much you eat against how much you burn, right? For some, maybe, but HMS researchers have devised a mathematical model of energy balance and body weight that suggests a more complicated equation.
The model predicts that mice susceptible to developing resistance to the metabolic regulator leptin have multiple stable body weights. Simulated mice based on the model grow obese after overeating, eventually hitting a high stable weight. But losing this weight and returning to a lower stable weight can be extraordinarily difficult. Though the model blends two competing theories of body weight, it departs from their predictions that body weight gravitates to one stable weight or weight range. If the model proves correct, it may point to new interventions to help ease weight loss even in the most intractable cases.
It may seem odd that this model of metabolism comes from the lab of a tumor biologist, Rakesh Jain, the A. Werk Cook professor of radiation oncology (tumor biology) at Massachusetts General Hospital. But to Jain, a chemical engineer trained to think in terms of systems and controls, it is perfectly natural. In fact, his career in tumor biology began with a mathematical model of pressure differentials in tumors. Jain got into obesity research when he learned that leptin, in addition to regulating body weight, may also regulate blood vessel formation.
Joshua Tam, a doctoral student in the Harvard–MIT Division of Health Sciences and Technology and also a chemical engineer, picked up on Jain’s interest. He saw parallels between engineering control systems and the body’s system to regulate weight, so he wanted to see if the engineering tools fit. Tam is first author of the January Cell Metabolism paper that describes the resulting model.
Weight Regulation
Drawing on decades of experiments in mice, Tam defined a set of equations that simulates their collective results. He began by creating two models, each aligned with one of the two prevailing theories of body weight regulation. One, the set point model, works much like the cruise control system in a car. The leptin system in the body aims to maintain a constant body weight by adjusting the desire for food and the burn rate. The other, the settling point model, is a more open-ended system. Tam likened it to a water faucet; adjusting the hot and cold taps results in a water temperature that settles in a given range.
Though Tam built both models on experimental evidence, neither fit perfectly with all the evidence. Simulated mice representing the set point model never remained obese; their weights always returned to the set point. This contradicted evidence of diet-induced obesity in live mice. The settling point model contradicted evidence in the case of starvation.
So Tam decided to combine the two models. The unified model uses the set point theory to simulate the case of starvation, but when leptin levels in the brain cross a certain threshold, the settling point dynamics take over. This kind of combination, said Jain, is very common in thermodynamics. “You develop it based on one phase, then another phase, then you mix it together.”
It is not, however, common in biology. Co-author Dai Fukumura, HMS associate professor of radiation oncology at MGH, played a large role in this work by acting as a translator. He helped Tam and Jain ground their model in biology and also helped them change their engineering-centric (and, to them, “common sense”) explanations into more accessible terms.
Another element Tam added to the models was a way to simulate leptin resistance. Leptin is a hormone produced by fat tissue. It crosses the blood–brain barrier and signals the body to stop eating. In its absence, the body craves food. A decreased sensitivity to leptin results in unnecessarily high food intake, so it is thought to be a cause of diet-induced obesity. It is also thought to be a consequence of obesity because, as fat stores increase, leptin concentrations also increase, eventually triggering the development of resistance.
The model predicts that mice susceptible to developing resistance to the metabolic regulator leptin have multiple stable body weights. Simulated mice based on the model grow obese after overeating, eventually hitting a high stable weight. But losing this weight and returning to a lower stable weight can be extraordinarily difficult. Though the model blends two competing theories of body weight, it departs from their predictions that body weight gravitates to one stable weight or weight range. If the model proves correct, it may point to new interventions to help ease weight loss even in the most intractable cases.
It may seem odd that this model of metabolism comes from the lab of a tumor biologist, Rakesh Jain, the A. Werk Cook professor of radiation oncology (tumor biology) at Massachusetts General Hospital. But to Jain, a chemical engineer trained to think in terms of systems and controls, it is perfectly natural. In fact, his career in tumor biology began with a mathematical model of pressure differentials in tumors. Jain got into obesity research when he learned that leptin, in addition to regulating body weight, may also regulate blood vessel formation.
Joshua Tam, a doctoral student in the Harvard–MIT Division of Health Sciences and Technology and also a chemical engineer, picked up on Jain’s interest. He saw parallels between engineering control systems and the body’s system to regulate weight, so he wanted to see if the engineering tools fit. Tam is first author of the January Cell Metabolism paper that describes the resulting model.
Weight Regulation
Drawing on decades of experiments in mice, Tam defined a set of equations that simulates their collective results. He began by creating two models, each aligned with one of the two prevailing theories of body weight regulation. One, the set point model, works much like the cruise control system in a car. The leptin system in the body aims to maintain a constant body weight by adjusting the desire for food and the burn rate. The other, the settling point model, is a more open-ended system. Tam likened it to a water faucet; adjusting the hot and cold taps results in a water temperature that settles in a given range.
Though Tam built both models on experimental evidence, neither fit perfectly with all the evidence. Simulated mice representing the set point model never remained obese; their weights always returned to the set point. This contradicted evidence of diet-induced obesity in live mice. The settling point model contradicted evidence in the case of starvation.
So Tam decided to combine the two models. The unified model uses the set point theory to simulate the case of starvation, but when leptin levels in the brain cross a certain threshold, the settling point dynamics take over. This kind of combination, said Jain, is very common in thermodynamics. “You develop it based on one phase, then another phase, then you mix it together.”
It is not, however, common in biology. Co-author Dai Fukumura, HMS associate professor of radiation oncology at MGH, played a large role in this work by acting as a translator. He helped Tam and Jain ground their model in biology and also helped them change their engineering-centric (and, to them, “common sense”) explanations into more accessible terms.
Another element Tam added to the models was a way to simulate leptin resistance. Leptin is a hormone produced by fat tissue. It crosses the blood–brain barrier and signals the body to stop eating. In its absence, the body craves food. A decreased sensitivity to leptin results in unnecessarily high food intake, so it is thought to be a cause of diet-induced obesity. It is also thought to be a consequence of obesity because, as fat stores increase, leptin concentrations also increase, eventually triggering the development of resistance.
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