# i don't understand: mice ate 30% less calories but ate the equivalent amount of protein

#### genekuli

##### New member
In a scientific study they say that the low energy diet mice ate 30% less calories but ate the same amount of protein as the high energy diet mice, but the protein intake was in the same proportions in the low and high energy diets so I don't see how it's possible to eat 30% less calories and have the same amount of protein because you either eat 30% less calories and therefore have 30% less protein or you eat the same amount of protein and you end up with the same amount of calories?
I don't understand how it is possible for the following 3 statements to all be correct:

“The % of protein (P), carbohydrate (C) and fat (F) (as a % of total energy). Each diet was replicated at 8 kJ g-1 (low energy), 13 kJ g-1 (medium energy) and 17kJ g-1 (high energy).”

“ Mice fed experimental diets containing 50% nondigestible cellulose ate a greater bulk of food (3.6 ± 0.4 versus 2.5 ± 0.4 g/day) but ingested about 30% less total energy than mice provided with food containing higher energy content...”

“mice on the low-energy diets were able to achieve their protein target through increasing chronic food intake (protein intake: 9.6 ± 4.3 kJ/day with low-energy diets versus 9.6 ± 6.3 kJ/day with high-energy diets)”

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#### JeffM

##### Elite Member
Well I cannot get to the article.

Your first citation does not have a complete first sentence. What I think it is saying is that the three mixtures had the same proportion of types of nutrient to total energy content, but the mixtures had different quantities of energy per mass. What is obscure about that? It is saying that (for example) if 20% of the energy in one diet came from protein, then 20% of the energy in every mixture tested came from protein. (They say "diet" but mean "mixture.")

Your second citation says that mice eating the mixture with low-energy relative to mass ate more mass than did the mice eating the mixture with high-energy relative to mass. Nevertheless, they did not eat enough extra mass to achieve the same level of calories.

Your third citation says that the low-energy mice did achieve the desired level of protein.

All that is consistent because energy is derived from fat and carbohydrates as well as protein. You are assuming that protein is the only source of calories. That assumption is wrong. Why do people who are dieting stay away from carbs and fat?

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#### genekuli

##### New member
Well I cannot get to the article.

Your first citation does not have a complete first sentence. What I think it is saying is that the three mixtures had the same proportion of types of nutrient to total energy content, but the mixtures had different quantities of energy per mass. What is obscure about that? It is saying that (for example) if 20% of the energy in one diet came from protein, then 20% of the energy in every mixture tested came from protein. (They say "diet" but mean "mixture.")

Your second citation says that mice eating the mixture with low-energy relative to mass ate more mass than did the mice eating the mixture with high-energy relative to mass. Nevertheless, they did not eat enough extra mass to achieve the same level of calories.

Your third citation says that the low-energy mice did achieve the desired level of protein.

All that is consistent because energy is derived from fat and carbohydrates as well as protein. You are assuming that protein is the only source of calories. That assumption is wrong. Why do people who are dieting stay away from carbs and fat?
thank you for your answer, could you please please explain though how one can have the same amount of protein but have 30% less calories when the mixtures are all of the same ratios of protein carbs fat?

#### JeffM

##### Elite Member
Let's try a numerical example.

In mixture 1, 10 units of weight of weight contain 1 unit in weight of protein, 2 units in weight of fat, 2 units in weight of carbohydrate, and 5 units in weight of indigestible material. Each unit of weight in protein provides 2 units of energy; each unit of weight of fat or carbohydrate provides 3 units of energy. Therefore 10 units in weight generate 1 * 2 + 2 * 3 + 2 * 3 + 5 * 0 = 14 units of energy. Or 1.4 units of energy per unit of weight. The proportion of energy derived from protein 2/14 = 1/7; the proportion of energy derived from carbohydrates and fats is 6/14 = 3/7 each.

In mixture 2, 10 units of weight of weight contain 2 units in weight of protein, 4 units in weight of fat, 4 units in weight of carbohydrate, and no units in weight of indigestible material. Therefore 10 units in weight generate 2 * 2 + 4 * 3 + 4 * 3 + 0 * 0 = 28 units of energy. Or 2.8 units of energy per unit of weight. In other words, mixture 2 provides 100% more energy per unit of weight than does mixture 1. The proportion of energy derived from protein 4/28 = 1/7; the proportion of of energy derived from carbohydrates and fats is 12/28 = 3/7 each.

In short, mixture 2 is more energy rich than mixture 1, but the proportion of energy coming from each kind of energy source is the same.

With me so far?

Now suppose that, each week, a mouse will forage for and consume 15 units of weight in food unless that does not provide at least 18 units of weight in protein each week, in which case it will forage and eat just enough to meet a target of 18 units in weight of protein. (Remember that protein provides many essential nutrients not found in fats or carbohydrates and that foraging incurs risk of predation from cats and takes work and time that could be more enjoyably spent taking safe naps in a den and making baby mice).

So a mouse eating mixture 1 will eat 18 units in weight. From that, the mouse will derive 18 units of weight in protein and 18 * 1.4 = 25.2 units of energy.

A mouse eating mixture 2 will eat 15 units in weight . From that, the mouse will derive 30 units in protein and 15 * 2.8 = 42 units of energy.

That means that (1) both mice receive AT LEAST the minimum required weight of protein although the mouse eating mixture 2 gets more than that minimum, (2) the mouse eating mixture 2 actually eats less in weight of its energy-rich diet than the mouse eating mixture 1, and (3) the mouse eating mixture 2 receives 67% more energy in total.

The problem in reading the snippets of article is that the discussion requires jumping from units of energy to units of mass and units of food eaten per unit of time in a way that is extremely opaque.