Sequence logo

A sequence logo consists of a stack of letters at each position. The relative sizes of the letters indicate their frequency in the sequences. The total height of the letters depicts the information content of the position, in bits.

To create sequence logos, related DNA, RNA or protein sequences, or DNA sequences that have common conserved binding sites, are aligned so that the most conserved parts create good alignments. A sequence logo can then be created from the conserved multiple sequence alignment. The sequence logo will show how well residues are conserved at each position: the higher the number of residues, the higher the letters will be, because the better the conservation is at that position. Different residues at the same position are scaled according to their frequency. The height of the entire stack of residues is the information measured in bits. Sequence logos can be used to represent conserved DNA binding sites, where transcription factors bind.

The information content (y-axis) of position ${\displaystyle i}$ is given by:[2]

for amino acids, ${\displaystyle R_{i}=\log _{2}(20)-(H_{i}+e_{n})}$

for nucleic acids, ${\displaystyle R_{i}=\log _{2}(4)-(H_{i}+e_{n})}$

where ${\displaystyle H_{i}}$ is the uncertainty (sometimes called the Shannon entropy) of position ${\displaystyle i}$

${\displaystyle H_{i}=-\sum _{b=a}^{t}f_{b,i}\times \log _{2}f_{b,i}}$

Here, ${\displaystyle f_{b,i}}$ is the relative frequency of base or amino acid ${\displaystyle b}$ at position ${\displaystyle i}$, and ${\displaystyle e_{n}}$ is the small-sample correction for an alignment of ${\displaystyle n}$ letters. The height of letter ${\displaystyle a}$ in column ${\displaystyle i}$ is given by

${\displaystyle {\text{height}}=f_{b,i}\times R_{i}}$

The approximation for the small-sample correction, ${\displaystyle e_{n}}$, is given by:

${\displaystyle e_{n}={\frac {1}{\ln {2}}}\times {\frac {s-1}{2n}}}$

where ${\displaystyle s}$ is 4 for nucleotides, 20 for amino acids, and ${\displaystyle n}$ is the number of sequences in the alignment.

A consensus logo is a simplified variation of a sequence logo that can be embedded in text format. Like a sequence logo, a consensus logo is created from a collection of aligned protein or DNA/RNA sequences and conveys information about the conservation of each position of a sequence motif or sequence alignment[1][3] . However, a consensus logo displays only conservation information, and not explicitly the frequency information of each nucleotide or amino acid at each position. Instead of a stack made of several characters, denoting the relative frequency of each character, the consensus logo depicts the degree of conservation of each position using the height of the consensus character at that position.

A sequence logo for the LexA-binding motif of several Gram-positive species.

A consensus logo for the LexA-binding motif of several Gram-positive species.

Hidden Markov models (HMMs) not only consider the information content of aligned positions in an alignment, but also of insertions and deletions. In an HMM sequence logo used by Pfam, three rows are added to indicate the frequencies of occupancy (presence) and insertion, as well as the expected insertion length.[5]

A sequence logo for TALE-likes. Note the reduced occupancy (blue) at the position one and the occasional insertion at position 19 (red).

• Sequence motif
• Position-specific scoring matrix
• DNA binding site

• How to read sequence logos.
• Recommendations for Making Sequence Logos.
• Erill, I., "A gentle introduction to information content in transcription factor binding sites", Eprint
• What is (in) a sequence logo?