If you posit that it’s unequal, then what do you think happens with the “extra” or “missing” atoms and molecules?
Wrong. We are just talking about physics here.
We don’t have to be bomb calorimeters, and we most certainly do consume units of energy. That is the way physics works.
Oh lord, Bob… But hey - good question.
Okay, let’s go with that - ‘predicted’ weight gain @3500 cals/lb:
LPD = 9.6 lbs
NPD = 16 lbs
HPD = 16 lbs
So then let’s compare that with the observed weight gain.
LPD gained ~3.6 kg = 7.92 lbs
NPD/HPD gained ~6 kg = 13.2 lbs.
At this point we have “missing calories” since the observed weight gain is less than the predicted.
LPD --> 9.6 - 7.92 = 1.68 lbs. Staying with the 3500 cals/lb deal, that’s 105 “missing” calories per day.
NPD --> 16 - 13.2 = 2.8 lbs or 175 “missing” calories per day.
HPD --> 16 - 13.2 = 2.8 lbs or 175 “missing” calories per day.
Increased energy expenditure as measured:
LPD = ~110 cals.
NPD = ~195 cals.
HPD = ~350 cals.
For the LPD, the observed weight gain left 105 cals/day to be ‘found.’ 110 were in the increased energy expenditure. Nearly perfect.
For the NPD, the observed weight gain left 175 cals/day to be ‘found.’ 195 were in the increased energy expenditure. Nearly perfect.
For the HPD, the observed weight gain left 175 calories to be ‘found.’ There were 350 in the increased energy expenditure, so a net of ~175 “extra.” Not perfect, but that’s only 5% of the daily calories, so not bad at all.
Across all three groups, the average accuracy is ~98%, which is really pretty astounding when you think about it. There is possible error every step of the way in the study, and we all (should) acknowledge that 3500 cals/lb begins as an estimate, despite how nearly perfect things worked out here.
How close would it have to be to satisfy?
I would think that within 20% would be pretty good. On a personal level most of us are not super-precise about weighing food, etc., if we’re even interested in counting stuff to start with.
Within 10% would be excellent. The 3500 calories/lb is a generalized estimate to begin with.
Confounding factors have to be controlled for. While the report on the study you linked to has a lot of stuff in it (almost to an eye-glazing-over stage), it does appear that they did a good job of it. They didn’t specifically set out to compare increased caloric intake with weight gain (rather, they were focused toward changes in energy expenditure as related to body size and the effect of protein ratios), yet the data is quite useful.
The single largest energy usage, by far, is normal body maintenance and metabolism. This is with no change in weight or energy expenditure.
That’s not what the study did, in the pursuit of its stated purpose. The isocaloric part was only determining how many calories would result in not gaining weight. This is not dealing with any weight gain or increased energy expenditure. The “eating more” part came later.
With increased caloric intake here’s what they found. Taking the ‘Normal Protein’ group:
71% of energy went for normal body maintenance and metabolism.
24% of energy went for weight gain.
5% of energy went for increased energy expenditure.
Does that make sense? I wouldn’t have known what to predict, beforehand, but this study’s numbers look very good.
They didn’t examine everything - for example, there is some energy in solid waste as well as liquid waste, and the only mention I see is that they didn’t find nitrogen loss in stools. The amount of fat in solid waste is one possible confounder. From the lower end of the normal human range to the upper end of it is ~350%, so it’s considerably variable. (Where an individual has an abnormal amount of fat going through undigested, it can be a very significant confounding factor; nothing in the study points toward that being the case with the study subjects.)
It’s reasonable to expect that the energy content of solid waste would not change appreciably from the baseline period to the study’s end. Even had they examined it, and found some change, it would likely amount to no more than a rounding error (the raw amount of fat is normally very low compared to the total energy intake) or the inherent limitations on accuracy already present in the study. “The math” here looks excellent, and very complete, really - even to an amazing extent. It’s good science, with a nice control of possibly confounding factors.
Going back to comments from May -
There’s no reason to throw away the science there. A changing energy output does not affect the caloric content of our body fat.
Certainly, and that makes a difference. Basically, the more carbon atoms, the higher the caloric density will be, and we definitely observe that with triglycerides. Human fat is a combination of triglycerides, but a quite consistent one across individuals. The average is just under 9 calories per gram. For comparison, long-chain triglycerides average to 9 cals per gram, while medium-chain triglycerides average 8.3.
Yes, and human fat tissue is not all fat. 
The science is actually better than that. The 3500 calories figure is not something just conjured up. This stuff is actually not very “mysterious.”
We do know about energy consumption and density at the basic levels where they operate in the human body. The ATP to ADP conversion is where essentially ALL our energy comes from. A mole of ATP thus used under physiological conditions gives us ~7.3 calories. At the level of a cell, we know the energy involved in the oxidation of carbon and hydrogen atoms - for decades we’ve known, to a level of accuracy that would not even swing a day’s energy usage for a person by one calorie.
That “mole of ATP” is 240.974 grams, so we’re getting only 3% of a calorie per gram. Not much, eh? But we’re not changing ATP very much, there - we’re only knocking off one phosphorus group. We’re also really good at “recharging” the ADP into ATP; we use this like a battery, and the recharging is quick - we’ve got these big-butt ATP synthase molecules, and each one can give us back more than 100 ATP molecules per second.
When we go ‘back’ or ‘up’ to our stored fat, we have our triglyceride mixture - at a little less than 9 cals per gram. Call it 9 if you want to. Our adipose tissue is 87% fat. 9 x 454 grams x 87% = 3555 calories. We’re already within 2% of the 3500 figure. Go with the actual human mix of triglycerides at slightly less and bingo, we’re right on it. This was found out quite a few decades ago.
So if we are talking about human fat tissue and there being ~3500 calories in there, it’s not just just a myth, it’s what is actually in there.
Yeah, that glazing thing… 
Most of the information given doesn’t affect the discussion here, but you have to consider it to make sure.
I really wish they would give us the weight and energy balance figures as a numerical table, rather than the somewhat rudimentary pictures. I assume we are seeing computer plots, so probably very accurate, but hard numbers would be better. Sometimes they have links to more tables or a study appendix toward the side or bottom of the webpage, but nothing there that I saw. Now that I know what to look for, I’m tempted to do it over, as exact as possible.
A look at the ‘hard science’ of it is good. This study gives us a lot to struggle through, but seems to be complete. What do you think is wrong with it?
