Calculating the predicted replacement mutability of a sequence

I will use an empirical mutability model, that was inferred from a database of 520 unselected mutations found in 28511 nucleotides sequenced from J_H-C_H and $J_\kappa-C_\kappa$ introns (1996). Cowell et al. (1998) showed that these data are efficiently described by a mechanism that operates on triplets of nucleotides, the probability that a nucleotide mutates being conditioned on the two flanking nucleotides. Cowell and Kepler (in preparation) inferred from these data the probability of any nucleotide mutating given its identity and the identity of the two nucleotides that flank it in the sequence. For each position in the gene sequence, one can retrieve, from this empirical mutability model, the predicted mutability under somatic hypermutation. In general I will be interested in the replacement mutability, defined as the probability that a nucleotide undergoes a substitution that leads to an amino acid replacement. Silent substitutions may only contribute to CDR or FR functional diversity through second order effects, such as subsequently affecting the mutability of the neighboring nucleotides. Although the mutability of a nucleotide is essentially a probability, I will still use the term mutability for historical reasons (see Kepler (1997)).

The procedure that I designed for calculating an average replacement mutability per nucleotide in a sequence is the following:

• From the empirical mutability matrix I retrieve the mutability of the nucleotide, given its identity and the identity of its two neighboring nucleotides.
• From the empirical transition matrix given in Cowell and Kepler I retrieve the probability of each of the three possible substitutions of the nucleotide.
• Each substitution of the original nucleotide by another has a probability 0 or 1 to lead to an amino acid replacement.
• Then the predicted replacement mutability at a given site is given by the product of the mutability of the nucleotide found in the germline sequence at that position, and the sum, over all three possible substitutions, of the product of the probability of the specific substitution and the probability that the given nucleotide substitution leads to an amino acid replacement.
• I then calculate the predicted average replacement mutability of a nucleotide in the sequence is calculated by taking the average over all sites in the sequence of the replacement mutability per site.

To compare FR and CDR mutabilities, I separately determine the mutability of FR and CDR sites. I will use the same procedure to determine the predicted mutability of artificially-constructed sequences.