# Statistical analysis of mutant proteins sequences

Let's say that there is a table like the one below, where for each mutant (A, B, C, etc.) protein or peptide we have a binding and a functional information (true/false) column, and for each amino acid in that protein, we have some kind of amino acid property like hydrophobicity:

Protein Binding Functional     1  2  3  4  5  6  7  8  9 10
A          0         0        13 96 39 77 70 94 96 29 22 82
B          0         1        94 45  2  2 11 46 50 77  7 99
C          0         1        66 71 97 37 14 77 89 92 12 72
D          1         1        11  8 94 73 16 53  2 27 54 97
E          1         1        31 62 49 51  2 86 91 49 61  7
F          1         0         2 42 65 42 54 41 45  9 71 20
G          0         0        26 44 56 65 61 43 56 90 70 86
H          0         1        54 99 68 64 94 81 85  0 50 84
I          1         1        27 52 76 12 46 38 24 74 11 90
J          1         1         1 58 77 50 72 51 87 99 47 67


What statistical tests would you recommend to:

1. See if the difference between means for each mutant is statistically significant.
2. See if the the aminoacid property can somewhere be related to binding and functional properties.

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It is also a pretty good topic for machine learning, especially if linear methods would fail/be too general. –  mbq Feb 2 '11 at 23:26
Thanks for the hint. –  SwatchPuppy Feb 11 '11 at 0:00
For your first question, it's not clear what is to be compared. Are you considering each mutant one at a time? In the phrase "difference between means": "means" of what? "difference" between which and which? –  Karl Aug 21 '11 at 13:49

I would use a random intercept model for the data that is given. The numbers (amino acid property) as the level 1 dependent variable; the proteins as level 2; and the binding and functional as level 2 explanatory variables.

The codes in R should look something like this(I would probably also transform the data to long form first):

lmer(amino~binding+functional+(1|protein))


Then, to answer question 1, you would check that if the variance of the random intercept is statistically significant by likelihood ratio test.

The coefficients of the binding and functional and their standard errors should answer question 2 for you.

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Unfortunately that completely ignores locality information, which is the critical thing in biological sequence analysis –  biofreezer Oct 20 '11 at 1:46
What is locality information? I'm sorry for ignoring it in my answer because I know very little about biological sequence... –  King Oct 20 '11 at 8:12