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How does one calculate the information content of DNA sequence like ATCGGCT where mutation rate of G's is 10% and the most common mutation product binds with C and A with equal frequency.

I know that the individual information of a sequence is the dot product of the sequence and the weights matrix for each base. Essentially I = sum (base1xweight + base2xweight + ...)

What I can't figure out is how to determine the the weight of each base so as to incorporate the 10% probability of mutation of G's.. Can anyone help me figure that out

EDITED since wording may be confusing: Original problem says: " Spontaneous deamination of exocyclic amine is dG (deoxyguanosine) can occur occasionally in DNA strand. Given probability of this occurring during the time it takes DNA polymerase to copy DNA is 20% per dG in a particular DNA. Given that most common deamination product pairs with dC and dA with equal frequency calculate information content during DNA replication in the given sequence. " As an example I choose ATCGGCT and changed it to 10% deamination of dG.

PROPOSED SOLUTION: For sequence ATCGGCT, I am only consider the initial strand bases A,T,C are 2 bits a base, given by I=-1/ln(2)ln(n_before/n_after) ,where n_before = 1, and n_after = 4 In the case of mutated G (Gm) , I say, I = -1/ln(2)ln(1/3)= 1.58 bits , n_after=3 since A,C are equivalent to Gm

Perfect copy would give us 7 bases x 2 bits each = 14 bits content of strand. Since there are 2 G's, with 10% change of mutating --> 0.02 of G in strand will mutate.

Thus I content during replication, Information content I(ideal) - I(inc. mutation) = 14-0.03 = 13.97 bits during time of replication

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    $\begingroup$ Sounds like a homework question. Have you already tried to solve this yourself? If so then it would help if you show what you have tried and why you think it is incorrect (or correct). $\endgroup$ – mdperry Apr 16 '16 at 19:11
  • $\begingroup$ "the mutation rate of G's is 10 %" what does this phrase mean? For example, are you saying that for every cell division a G residue has a 1/10 chance of mutating (and that the other bases have a 0/10 chance of mutating?)? In this model, what base does a G mutate into? One of the other 3 bases, randomly? "The most common mutation product binds with C and A" this phrase does not have a clear sense to me. Since there are only 3 choices, G could mutate into A or C or T, but none of those will bind with C and A with equal frequency, do you see what I mean? $\endgroup$ – mdperry Apr 17 '16 at 5:42
  • $\begingroup$ Since DNA is double-stranded, if the sense strand is 5'-ATCGGCT-3' then the antisense strand (or reverse complement) will be 5'-AGCCGAT-3', so there are two G's on the top strand and two more G's on the bottom strand, did you take that into account? $\endgroup$ – mdperry Apr 17 '16 at 5:45
  • $\begingroup$ This sounds like computing science/statistics rather than biology. Where does this mathematical formula you quote for information content come from? I've never heard of it and I can't see how it relates to anything 'real' in genetic information. $\endgroup$ – David Apr 17 '16 at 10:14
  • $\begingroup$ I think I have a solution.. I am only considering 1 strand based on original problem wording, however mdperry I did consider the second strand. I am glad you also brought that up. David the formulas come largely from (schneider.ncifcrf.gov/paper/ri/latex ) So my soluion $\endgroup$ – SciEnt Apr 17 '16 at 19:14

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