# How to estimate the Phe content of a food from its protein content: Part 2

*This blog entry is the second in a series of four posts that introduce this simple web app which estimates the phenylalanine (Phe) content of a food from its protein content.*

*https://engineering.purdue.edu/brl/PKU/method_0.html*

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In the previous post, I explained how the 20-64.5 multipliers can be used to obtain an upper bound (i.e., a maximum) and a lower bound (i.e., a minimum) for the Phe content of a food from its protein content. However, in the previous computation, we assumed that the protein content was known exactly. Unfortunately, on the Nutrition Fact Label, the protein content is rounded up to the nearest gram. This means that, if the protein content listed is 1g, then the true protein content can be anywhere between 0.5g and 1.5g.

In that case, one can find out a lower bound on the Phe content by multiplying the minimum possible protein content, namely 0.5g in our example, by the multiplier 20. So we have 0.5g x 20=10, and thus the Phe content cannot be less than 10mg.

Now to find an upper bound on the Phe content, you have to multiply the maximum possible protein content, namely 1.5g in our example, by the multiplier 64.5. So we have 1.5 x 64.5= 96.75m and thus the Phe content cannot be more than 96.75mg.

Now image that the protein content listed in the nutrition fact label is 0g. Because the number is rounded up to the nearest gram, then the true protein content can be anywhere between 0g and 0.5g. In that case, we find the minimum Phe by multiplying zero by 20, which gives zero, and thus it is possible that the food contains zero Phe. To find the maximum Phe, we multiply 0.5 by 64.5, which gives 32.25, and thus the maximum Phe content is 32.25mg.

If you want to to this automatically, you can use our app at *https://engineering.purdue.edu/brl/PKU/method_0.html**. Just enter the protein content in grams in the first box, and click “no” and “no” for Question 1 and Question 2. (I will explain why we ask Question 2 in a future post.) Then click “show results” and a box will pop up with the minimum and maximum Phe value. *

To be continued in Part 3.

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