Why are my calculations for O2 requirements of daily metabolism so far off?

Question

When I attempt to calculate the O2 necessary for a day of metabolism at rest (for an imaginary average human) and compare it with the expected O2 consumed per day my results differ by a factor of 3. I don't expect it to be 1 to 1, but a factor of 3 makes me think that I am missing a fundamental concept.

For our fictional human, I'm starting with the values for 1 MET. Specifically:

• RMR (kcal / kg / hr) = 1
• VO2 (mL / kg / min) = 3.5

I then define the weight of my human:

• weight (kg) = 70
• RMR (kcal / hr) = 70
• VO2 (mL / min) = 245

And convert to more useful units:

• RMR (kcal / day) = 70 * 24 = 1680
• VO2 (L / day) = 245 * 60 * 24 / 1000 = 352.8

At this point, my understanding is that consuming 352.8 L of oxygen should produce somewhere in the ballpark of 1680 kcal at rest. My next assumption is going to be that aerobic respiration of glucose is accounting for all of the energy throughout this day of rest. I'm aware this isn't reality, but I wouldn't expect it to be 3x off. I'd guess that either this assumption is wrong or I'm misunderstanding something in the following math.

Let's start with some more constants regarding cellular respiration.

• ATP creates 7.3 kcal / mol
• An average of 30 ATP are generated per glucose (glycolysis, krebs, etc)
• 6 O2 are required to aerobically metabolize 1 glucose

Given the energy to ATP ratio, we can compute the ATP necessary per day. I should note that the result here is about twice as high as reference numbers I've seen so I am suspicious.

• ATP (mol / day) = 1680 / 7.3 = 230.1369863
• Glucose (mol / day ) = 230.1369863 / 30 = 7.671232877
• O2 (mol / day) = 7.671232877 * 6 = 46.02739726

To convert the O2 requirements for our ATP from moles to liters, we use Avogadro's law at standard pressure (100 kPa) to conclude there are 22.712 liters per mole in a gas.

• O2 (L / day) = 46.02739726 * 22.712 = 1045.374247

And finally, we can see that my calculation says that you need 1045.37 liters of oxygen to produce 1680 kcal of energy through aerobic respiration, but earlier I computed that you should only need 352.8 liters using 1 MET as my basis. There were assumptions made in there, but these results make me think that I am still misunderstanding a fundamental concept.

Answer 1

The math was correct, but there was a misunderstanding in what some of the numbers represent. The energy expenditures listed for RMR include resting dietary thermogenesis in addition to the actual ATP energy used for work. You can see that the same is done for reporting Calories in food (e.g. 4 per carb) at http://www.fao.org/docrep/006/Y5022E/y5022e04.htm

When this is taken into account, we use 686 kcal/mole of glucose to get similar oxygen numbers. This includes the energy for the ATP and the energy from heat.

Answer 2

Your 1680kcal/day estimate for a resting human of 70kg sounds about right.

Pages around the web agree to about 11000 L of air inhaled and 550 L of oxygen consumed from it per day. I'd guess that includes resting + activity, so the 350 L estimate for resting metabolism sounds roughly accurate.

At 7.3 kcal / mol ATP and 30 ATP / glucose, you arrive at 219 kcal / mol glucose.

Wikipedia lists -2880kJ/mol of glucose (https://en.wikipedia.org/wiki/Cellular_respiration). That's 688.3 kcal/mol glucose. Unfortunately, the page doesn't cite a source, but continuing your calculation from there: For 1680 kcal you then only need 2.44 mol of glucose per day, 14.64 mol of O2 and therefore 332.6 L of O2. So 688.3 kcal/mol glucose fits the expected O2 consumption roughly.

The molecular weight of glucose is 180.16 g/mol. For 219 kcal/mol, you would arrive at 1.22 kcal/g. Conversely, 688.3 kcal/mol gives you 3.82 kcal/g. Again, the latter value is definitely closer to nutritional information found for glucose from different generally accepted references (3.75-4kcal/g).

The only explanation I can offer for this is that the ATP generated from glucose metabolism accounts only for about 35% of the energy contained in the glucose - which implies that the remaining energy is wasted.