Part I Mutation Model

Hypothesis

The mutation efficiency from the initial gene to the target gene should remain a continuous curve along reproduction, or along time. Here we discrete the mutation rate to be linear function according to the replication time (), which in fact create several discontiguous point.
DNA lesion repair rate appears high enough in replication than other cell activities, so that the DNA lesion repair rate can be conformed to background mutations except in replication process.
The whole yeast is large enough to obey the statistics rules

Probability Model
For each DNA sequence status, we take down a probability matrix for the coding sequence, which gives out each base appearance possibility on every site. The structure on each site is 5*1 matrix,(P_a,P_t,P_c,P_g,P_u), and ΣP=1. Therefore, the whole sequence status is recorded as 5*length matrix.E.g. For the Gal4 DNA, with a length of 2646, one status is a 5*2646 matrix.
Scanning Model
The hotbox appearance rate on a specific site i is calculated as below.

W: a, t; R: a, g; H: a, c, g;
Hotbox appearrance rate P_H=P_W^(i-2)P_R^(i-2)P_C^(i-2)P_H^(i-2), and here (i) refers to the site i.

As reviewed by the paper, the U:G mismatch DNA lesion will be repaired in three pathways.

VH Odegard, DG Schatz. Targeting of somatic hypermutation. Nat Rev Immunol. 2006 Aug;6(8):573-83