The system was developed largely from the experimental studies of Atwater and his colleagues in the later part of the 19th century and the early years of the 20th at Wesleyan University in Middletown, Connecticut.
As with the calculation of protein from total nitrogen, the Atwater system is a convention and its limitations can be seen in its derivation.
The gross energy (GE) of a food, as measured by bomb calorimetry is equal to the sum of the heats of combustion of the components – protein (GEp), fat (GEf) and carbohydrate (GEcho) (by difference) in the proximate system.
By measuring coefficients of availability or in modern terminology apparent digestibility, Atwater derived a system for calculating faecal energy losses.
where Dp, Df, and Dcho are respectively the digestibility coefficients of protein, fat and carbohydrate calculated as
Atwater collected values from the literature and also measured the heat of combustion of proteins, fats and carbohydrates.
These vary slightly depending on sources and Atwater derived weighted values for the gross heat of combustion of the protein, fat and carbohydrate in the typical mixed diet of his time.
It has been argued that these weighted values are invalid for individual foods and for diets whose composition in terms of foodstuffs is different from those eaten in the US in the early 20th century.
Atwater measured a large number of digestibility coefficients for simple mixtures, and in substitution experiments derived values for individual foods.
The energy/nitrogen ratio in urine shows considerable variation and the energy/organic matter is less variable, but the energy/nitrogen value provided Atwater with a workable approach although this has caused some confusion and only applies for subjects in nitrogen balance.
Based on the work of Atwater, it became common practice to calculate energy content of foods using 4 kcal/g for carbohydrates and proteins and 9 kcal/g for lipids.
This system relies on having measured heats of combustion of a wide range of isolated proteins, fats and carbohydrates.
This approach is based on the assumption that there are no interactions between foods in a mixture in the intestine, and from a practical view point, such studies with humans are difficult to control with the required accuracy.
The unavailable carbohydrates (dietary fibre) are degraded to a variable extent in the large bowel.
The products of this microbial digestion are fatty acids, CO2 (carbon dioxide), methane and hydrogen.
The fatty acids (acetate, butyrate and propionate) are absorbed in the large intestine and provide some metabolisable energy.
Whether the increased fat loss is due to an effect on small intestinal absorption is not clear.
Both these effects however lead to reductions in apparent digestibility, and therefore the Atwater system warrants small changes in the proper energy conversion factors for those diets.
It is difficult to calculate expected values for a protein from amino-acid data, as some of the heats of combustion are not known accurately.
The heat of hydrolysis is very small and these values are essentially equivalent when calculated on a monosaccharide basis.
The human digestive tract is a very efficient organ, and the faecal excretion of nitrogenous material and fats is a small proportion (usually less than 10%) of the intake.
Atwater recognised that the faecal excretion was a complex mixture of unabsorbed intestinal secretions, bacterial material and metabolites, sloughed mucosal cells, mucus, and only to a small extent, unabsorbed dietary components.
wherever faecal excretion is small, will approximate to unity and thus these coefficients have a low variance and have the appearance of constants.
These inaccuracies arise for a number of reasons The theoretical and physiological objections to the assumptions inherent in the Atwater system are likely to result in errors much smaller than these practical matters.
Conversion factors were derived from experimental studies with young infants, but these produced values for metabolisable energy intake that were insignificantly different from those obtained by direct application of the modified Atwater factors.