What is Motifs and information content? — Biology

Definition 5.12 University Biology — Year 3 · Chapter 5 — Bioinformatics and Sequence Analysis

A motif is a short pattern — a transcription-factor site, a splice signal, a phosphorylation site — represented by a position weight matrix of the frequency $f_{i}(b)$ of each base or residue $b$ at each position $i$ . The information content of position $i$ is $R_{i} = 2 - H_{i}$ bits for DNA, where $H_{i} = -\sum_{b} f_{i}(b)\log_{2} f_{i}(b)$ is its entropy: $2$ bits for an invariant base, $0$ for a position where all four are equally likely. The total $R = \sum_{i} R_{i}$ is drawn as a sequence logo, each position a stack of letters whose total height is $R_{i}$ and whose letters are sized by frequency.

A sequence logo of a TATA-box-like promoter motif. The height of each stack is the information content of that position,

2 - H_{i}

bits; the first four positions are nearly invariant and carry most of the motif’s

12

bits or so.

Examples

Example 5.14 (Expected chance matches)

A restriction site of six fixed bases has $R = 12$ bits and matches a random position with probability $4^{-6} = 2^{-12}$ : about $1100$ times in an E. coli genome of $4.6\,\mathrm{Mb}$ read on both strands (the site is palindromic, so once per position), and $7\times 10^{5}$ times in the human genome. A eukaryotic factor whose motif carries $10$ bits matches $3\times 10^{9}\times 2^{-10} \approx 3$ million positions in the human genome, several thousand times more than the genes it regulates. A motif alone is a weak predictor in a large genome; the chromatin state, the neighbouring motifs and the conservation of the site across species are what make a prediction.

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