Conservation of Energy -- Biophysicist Style

Here's one paper by Hall and Chow, or the duo my readers might recognize as those young biophysicists.  This link is to the free full text.

Abstract:  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.
General Model of Macronutrient and Energy Flux Balance:  The human body obeys the law of energy conservation [20], which can be expressed as ∆U= ∆Q - ∆W  (1), where ∆U is the change in stored energy in the body, ∆Q is a change in energy input or intake, and ∆W is a change in energy output or expenditure. The intake is provided by the energy content of the food consumed. Combustion of dietary macronutrients yields chemical energy and Hess’s law states that the energy released is the same regardless of whether the process takes place inside a bomb calorimeter or via the complex process of oxidative phosphorylation in the mitochondria. Thus, the energy released from oxidation of food in the body can be precisely measured in the laboratory. However, there is an important caveat. Not all macronutrients in food are completely absorbed by the body. Furthermore, the dietary protein that is absorbed does not undergo complete combustion in the body, but rather produces urea and ammonia. In accounting for these effects, we refer to the metabolizable energy content of dietary carbohydrate, fat, and protein, which is slightly less than the values obtained by bomb calorimetry. The energy expenditure rate includes the work to maintain basic metabolic function (resting metabolic rate), to digest, absorb and transport the nutrients in food (thermic effect of feeding), to synthesize or break down tissue, and to perform physical activity, together with the heat generated. The energy is stored in the form of fat as well as in lean body tissue such as glycogen and protein. The body need not be in equilibrium for Equation 1 to hold.   
Nothing about insulin or other hormones to this point, which makes sense to me.  The article goes on to explain how they relate ∆U to changes in body mass by determining the energy density of the body.  Then the math and computer modeling gets quite complex (and I get special nightmares when I see partial derivatives LOL).    

They are interested in long term changes in weight, not short term fluctuations due to variation in dietary intake.  They discuss how their model can treat glycogen (carbohydrate) storage/mass as a constant because of the limited and relatively constant (over the long term) nature of this contribution to body mass.  Therefore when looking at body composition, a two-compartment model is used:  Fat and Lean mass where M = L + F, or, as they put it L = M - F.  

Body Composition is described by a p-ratio = 1/(1+α) ... Exerpts:
Forbes found that his general relationship (14) was similar whether weight loss is induced by diet or exercise [27]. It is possible that resistance exercise or a significant change in the protein content of the diet may result in a different relationship for a [28–30].
Previous uses of the energy partition model often considered p to be a constant [6,12–18], which implies that the partitioning of energy is independent of current body composition and macronutrient composition. This is in contradiction to weight loss data that finds that the fraction of body fat lost does depend on body composition with more fat lost if the body fat is initially higher [26,32,33]. However, if a is a weak function of body composition then a constant p-ratio may be a valid approximation for small changes. 

This is what we, especially the body building contingency of the diet/fitness world, are all trying to manipulate with diet, and/or are hoping to do so.  Whether it is trying to gain lean mass, or lose more fat mass when reducing total body mass.  
Perturbations that move the body composition off the fixed trajectory can be done by altering body composition directly or by altering the fat utilization fraction f. For example, body composition could be altered directly through liposuction and f could be altered by administering compounds such as growth hormone. Resistance exercise may cause an increase in lean muscle tissue at the expense of fat. Exogenous hormones, compounds, or infectious agents that change the propensity for fat versus carbohydrate oxidation (for example, by increasing adipocyte proliferation and acting as a sink for fat that is not available for oxidation [42–44]), would also perturb the body composition off of a fixed F vs. L curve by altering f. If the body composition returned to its original state after such a perturbation then there is a unique fixed point. If it does not then there could be an invariant manifold although multiple fixed points are also possible.  We found an example of one clinical study that bears on the question of whether humans have a fixed point or an invariant manifold. Biller et al. investigated changes of body composition pre- and post-growth hormone therapy in forty male subjects with growth hormone deficiency [45]. Despite significant changes of body composition induced by 18 months of growth hormone administration, the subjects returned very closely to their original body composition 18 months following the removal of therapy.  However, there was a slight (2%) but significant increase in their lean body mass compared with the original value. Perhaps not enough time had elapsed for the lean mass to return to the original level. Alternatively, the increased lean mass may possibly have been the result of increased bone mineral mass and extracellular fluid expansion, both of which are known effects of growth hormone, but were assumed to be constant in the body composition models. Therefore, this clinical study provides some evidence in support of a fixed point, but it has not been repeated and the result was not conclusive.
Note that I underlined exogenous ... meaning hormones added at artificial levels, not produced by our own bodies in response to differing macronutrient composition of dietary intake.

I searched the article for any mention of insulin, in case I missed it.  No mention.  That is not to mean that this model is infallible, but these researchers have obviously given extensive consideration into what factors to include in their models.  That insulin is not among the factors, even those cited as potentially altering p or f. 

Therefore carbs drives insulin drives fat accumulation is a theory this dynamic duo seem to have dismissed on the basis of modern research.


Sanjeev said…
Your link's not working for me, I get "file not found"

or as PDF (just to the right of the article's title in that html page);jsessionid=C840A584A19CDBEC03F311D1EA5F6A09.ambra01?uri=info%3Adoi%2F10.1371%2Fjournal.pcbi.1000045&representation=PDF
Sanjeev said…
Sorry about that

EDIT: to fix the links - these work on the "preview" page, hopefully they'll work after posting

as html

or as PDF (also just to the right of the article's title in that html page)
Sanjeev said…
Don't know if you've noticed this

Carson Chow has a blog of sorts
CarbSane said…
Thanks Sanjeev! I fixed mine too.
Christian said…
Your only concern with that paper seems to be that they didn't include include insulin as some sort of driving force and you feel content that they didn't. The thing is of course that the reasearchers invested A COMPLETELY DIFFERENT SCENARIO. After deriving their dynamic control model the authors state:

"To simplify the analysis, we consider the intake rates to be clamped to constant values or set to predetermined functions of time. We do not consider the control and variation of food intake rate that may arise due to feedback from the body composition or from exogenous influences."

With other words, they fixed a predetermined food intake and looked what happened to their model. That is of course a totally valid scenario to study and I don't critize them for doing so. But it has virtually nothing to do with a theory of reverse causality. This model doesn't refute it, it doesn't confirm it, it simply doesn't deal with it at all. The "causality" is fixed: they make their virtual model lean by semi-starving.
Matter of fact is that in order to study the effect of variation in food intake aka fat storage driving overeating you would have to model the intake rate as a random variable with some mean and variance. Then you would have to introduce feedback loops that modifiy this mean, i.e. any hormones that induce hunger like ghrelin or leptin and and and ... and besides that they would have to include exogenous factors as well which is all pretty much impossible to quantify on any level.

The question that remains then is: Did you simply overlook their statement?? Because in this light your last sentence "Therefore carbs drives insulin drives fat accumulation is a theory this dynamic duo seem to have dismissed on the basis of modern research." sounds even absurd. The authors clearly state that they didn't investigate anything that would relate to this because they already fixed the food intake "to simplify analysis".

In your profile you state that "science should be correct! Otherwise it is counterproductive and possibly harmful." It is simply beyond me how someone with this noble goal in mind can let a blog post deteriorate into a simple "what-Taubes-says-is-nonsense" statement without any critical reflection.
CarbSane said…
As to your last statement, that's not what this blog is about. This post was made back near the time Taubes claimed H&C said something like that the G3P thing didn't matter b/c insulin so fundamentally determined fat accumulation. Do please tell me how insulin is "feedback from the body composition". If we're talking about dysfunctional fat we're already talking about those who get fat having already gotten there.
Christian said…
Why should insulin be "feedback from the body composition"?? I addressed non of the issues you mention in my comment. G3P is also not mentioned once.

I addressed what this study or their dynamic model is about and what it is not about ...