How to compute a p-value for the similarity measurement of two DNA sequences/contigs?

Question

I'm attempting to come up with a statistical model to determine the p-value for the similarity value $ 0 \le s \le 1 $ of two DNA contigs. The idea is to get a numerical measure to estimate if two contigs are homologous.

I want to account for base composition (and/or other structural features) if possible, but not necessarily because I might want to do the analysis only from the information about the length of the sequences/contigs and largest overlaps. Maybe something inspired from other statistical significance in bioinformatics .

Assume we have two DNA sequences: $a$ and $b$ with the basepair lengths $a_{\text{len}}$, $b_{\text{len}}$. Their overlap $o_{a-b}$ is the number of contiguous bases that appears in both sequences. If we define the similarity $s = \frac{o_{a-b}}{\min{(a_{\text{len}}, b_{\text{len}})}}$ how can we define a p-value for $s$?

Answer 1

Well, here my thoughts:

The equation $s$ somehow tries to represent the ratio $\frac{equality}{equality+inequality}$. But $s$ returns only a value. And to assing the p-value to a single value... is complicated.

How could you approach this?

• Using some kind of Hamming distance for each base pair at the position $n$ ($1 \leqslant n \leqslant len$) between the sequence i ($s_{i}$) and sequence j ($s_{j}$) in order to get a set of binary data:

$$s_{ij} = \begin{Bmatrix} 1\ if\ seq_{i_{n}}=seq_{j_{n}} \\ 0\ if\ seq_{i_{n}}\neq seq_{j_{n}} \end{Bmatrix}$$

With this, you get a set of binomial data (eg $\{0,1,0,1,0,1,1,1,0,1,1,1,0,...\}$). Now, you should be able to perform some (Binary?) test and get the p-value.

PD: Consider aligning the two sequences if there is interest in discussing base pair homology.