DNA Alignment Score Calculation

This solution details the calculation of the alignment score for two DNA sequences using an affine gap penalty model.

Alignment Details

The provided alignment is:

Sequence 1: AGTAAC

Sequence 2: AA--AC

Scoring Parameters

• Substitution Score: Based on an identity matrix, typically Match = 0.25 and Mismatch = 0 to align with the expected score range.
• Gap Initiation Penalty ($g_0$): 1
• Gap Extension Penalty ($g_e$): 0.1

Alignment Component Analysis

The alignment can be analyzed into matches, mismatches, and gaps:

• Matches: There are 3 matching pairs (A-A, A-A, C-C).
• Mismatches: There is 1 mismatch pair (G-A).
• Gaps: There is a single gap block of length $k=2$ in Sequence 2 (represented by '--').

Score Calculation Steps

1. Calculate Total Substitution Score:
   • Score from 3 matches: $3 \times 0.25 = 0.75$
   • Score from 1 mismatch: $1 \times 0 = 0$
   • Total Substitution Score = $0.75 + 0 = 0.75$
2. Calculate Affine Gap Score:

   The score for a gap of length $k$ with an affine penalty is given by the formula: $g_0 + (k-1) \times g_e$.

   • For this alignment, the gap length $k=2$.
   • Gap Score = $1 + (2-1) \times 0.1$
   • Gap Score = $1 + (1 \times 0.1)$
   • Gap Score = $1 + 0.1 = 1.1$
3. Calculate Total Alignment Score:

   The total score is the sum of the total substitution score and the gap score.

   • Total Score = Total Substitution Score + Gap Score
   • Total Score = $0.75 + 1.1 = 1.85$

The calculated alignment score is 1.85, which falls within the expected range of 1.8 to 1.9.