K-mer Frequency Explorer

What Are K-mers?

A k-mer is a substring of length k extracted from a longer sequence. For a DNA sequence of length L, there are L − k + 1 overlapping k-mers. Despite their simplicity, k-mer counts are the foundation of many modern bioinformatics tools — from genome assemblers to metagenomic classifiers.

This simulation lets you paste or generate a DNA sequence, choose a value of k, and immediately see the resulting frequency spectrum.

What You’ll Explore

• Adjust k from 1 to 12 and watch how the frequency histogram changes shape. Small values of k produce few distinct k-mers with high counts; large values produce many distinct k-mers that mostly appear once.
• Load different sequences — a bacterial genome, a human exon, or a random string — and compare their k-mer spectra. Real genomes have distinctive spectral shapes due to codon usage bias and repetitive elements.
• Identify repeats by looking for k-mers with unexpectedly high frequency. Transposable elements, tandem repeats, and low-complexity regions all leave signatures in the spectrum.
• Explore GC content through dinucleotide (k = 2) frequencies, which vary dramatically across species and even within a single chromosome.

Key Concepts

The K-mer Spectrum

A k-mer frequency spectrum plots the number of distinct k-mers (y-axis) that occur exactly f times (x-axis). In a typical genome, the spectrum has a large peak near the average sequencing depth, a smaller peak at double that depth (representing diploid heterozygosity or repeats), and a long tail of high-frequency repetitive k-mers. Sequencing errors appear as a spike at frequency 1.

Applications

Genome assembly. De Bruijn graph assemblers (Velvet, SPAdes, MEGAHIT) build a graph where each node is a k-mer and edges connect k-mers that overlap by k − 1 bases. The choice of k is a trade-off: smaller k values give better connectivity but more ambiguity; larger values resolve repeats but require higher coverage.

Taxonomic classification. Tools like Kraken2 assign each read to a taxon by looking up its k-mers in a reference database. Because k-mer lookup is an O(1) hash operation, this is orders of magnitude faster than alignment-based approaches.

Sequence comparison. The Jaccard index or cosine similarity between two k-mer frequency vectors provides an alignment-free estimate of sequence similarity, useful for building rough phylogenies or detecting contamination.

Background Reading

1. Compeau, P. E. C., Pevzner, P. A. & Tesler, G. (2011). How to apply de Bruijn graphs to genome assembly. Nature Biotechnology, 29(11), 987–991.
2. Marçais, G. & Kingsford, C. (2011). A fast, lock-free approach for efficient parallel counting of occurrences of k-mers. Bioinformatics, 27(6), 764–770.
3. Wood, D. E., Lu, J. & Langmead, B. (2019). Improved metagenomic analysis with Kraken 2. Genome Biology, 20, 257.