# What calculation provided the amino acid profile of a complete protein?

A complete protein is defined by the Food and Nutrition Board of the National Academy of Medicine as having all nine amino acids essential for human health in sufficient concentration. What were the factors that went into calculating this profile that separates proteins into groups of "complete" vs. "incomplete"?

Foods are labelled as "complete proteins" if that food, consumed in isolation and only just enough to meet the estimated average requirement for protein, is able to meet human requirements for all essential amino acids.

### Amino Acid Requirements

Wide differences in requirements for amino acids have been observed among similar individuals, so two different values are provided in the literature. Estimated Average Requirement (EAR) is an intake expected to be sufficient for an average (median) individual. By definition 50% of the population are above the median, and thus the intake would be insufficient. The Recommended Daily Allowance (RDA) is an intake expected to be sufficient for about 97% of the population.

Here are the EAR and RDA amino acid intake levels for adults aged 19 and older. Requirements for children are slightly higher.

Amino Acid                 EAR (mg/kg/d)   RDA (mg/kg/d)
------------------------   -------------   -------------
Histidine                  11              14
Isoleucine                 15              19
leucine                    34              42
lysine                     31              38
Methionine + Cysteine      15              19
Phenylalanine + Tyrosine   27              33
Threonine                  16              20
Tryptophan                  4               5
Valine                     19              24


The methods used to determine adequate intake for individual amino acids are too complex to summarize here. For more details, see the chapter on protein and amino acids in Dietary Reference Intakes for Energy, Carbohydrate, Fiber, Fat, Fatty Acids, Cholesterol, Protein, and Amino Acids (2005).

### The Reference Protein

In order to generate scores for different foods, we need a reference profile to compare against. The reference profile is generated by dividing the EAR for each amino acid by the overall EAR for protein (0.66 g/kg/d). If the reference profile was computed by dividing amino acid RDA by total protein RDA the results would be very similar. The reference profile is shown below.

Note: I observed a modest discrepancy between the presented values and what was expected based on the formula, so I have provided a second column showing the expected values based on the formula.

Amino Acid                 mg/g protein   EAR ÷ 0.66
------------------------   ------------   ----------
Histidine                  18             16.7
Isoleucine                 25             22.7
leucine                    55             51.5
lysine                     51             47.0
Methionine + Cysteine      25             22.7
Phenylalanine + Tyrosine   47             40.9
Threonine                  27             24.2
Tryptophan                  7              6.0
Valine                     32             28.8


This is the standard profile used to define a complete protein. Note however, that because the EAR for amino acids is variable on several factors (eg. age, body composition) the definition of a complete protein is also variable.

### Complete Nutrition with Incomplete Proteins

Even the so-called incomplete proteins can provide all essential amino acids in sufficient quantities, provided a larger amount of food is consumed.

For example, lentils (USDA SR28 Food #16069) is considered an incomplete protein because it has a lower methionine+cysteine (sulfur-containing amino acids, or SAA) content (21.6 mg/g) than the reference protein (25 mg/g). However, lentils alone could satisfy the SAA requirement if the total protein obtained from lentils was 16% higher than the total protein requirement.

Consider the example of a 70 kg person. The RDA for total protein would be 88 grams (based on 0.80 g/kg) and the RDA for SAA would be 1.33 grams. The SAA requirement could be met by consuming 900 kcal worth of lentils. Therefore even lentils in isolation, which are commonly considered an incomplete protein, can satisfy all amino acid requirements.

For further reading, the Food and Nutrition Board of the National Academy of Medicine publishes a freely-available book about dietary reference intakes for various nutrients, and this book contains 179 pages about protein and amino acids.