DNA Sequence Alignment Explorer

Scoring Scheme

Match score +1.0

Mismatch penalty -1.0

Gap penalty -2.0

Alignment

match mismatch gap

Alignment score

Identity

Gaps

Matrix cells

How it works

The Needleman-Wunsch algorithm finds the best global alignment between two sequences by filling an (m+1)×(n+1) dynamic-programming matrix F, where F(i,j) is the best score for aligning the first i letters of sequence A against the first j letters of sequence B:

F(i,0) = i · gap
F(0,j) = j · gap
F(i,j) = max{
  F(i-1,j-1) + s(A[i], B[j])   (diagonal: align A[i] with B[j])
  F(i-1,j)   + gap             (up: A[i] aligned to a gap)
  F(i,j-1)   + gap             (left: B[j] aligned to a gap)
}
where s(x,y) = match score if x = y, else mismatch penalty

Every column of boxes in the 3D grid is one cell of F, with height and color mapped to its score. Once the full matrix is filled, F(m,n) — the corner cell — holds the optimal alignment score, and tracing back from that corner to the origin along whichever rule produced each value (gold markers and line) recovers the actual best alignment shown in the sequence panel.

Match / Mismatch / Gap sliders — change the scoring scheme s(x,y) and gap cost; the whole matrix and the optimal traceback path recompute live.
New Sequences — draws two fresh random 10-base DNA strands (A, C, G, T).
Mutate — flips one random base in sequence B, showing how a single substitution reshapes the optimal path and drops percent identity.

This exact recurrence (Needleman & Wunsch, 1970) underlies real global-alignment tools used to compare genes, proteins and genomic reads in bioinformatics pipelines; local alignment (Smith-Waterman) uses the same matrix with a floor of zero instead of negative gap runouts.

low score high score traceback path

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