Statistical analysis of mutant proteins sequences

Question

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.

Thanks in advance.

Answer 1

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.