Sequence motif

The notation [XYZ] means X or Y or Z, but does not indicate the likelihood of any particular match. For this reason, two or more patterns are often associated with a single motif: the defining pattern, and various typical patterns.

For example, the defining sequence for the IQ motif may be taken to be:

[FILV]Qxxx[RK]Gxxx[RK]xx[FILVWY]

where x signifies any amino acid, and the square brackets indicate an alternative (see below for further details about notation).

Usually, however, the first letter is I, and both [RK] choices resolve to R. Since the last choice is so wide, the pattern IQxxxRGxxxR is sometimes equated with the IQ motif itself, but a more accurate description would be a consensus sequence for the IQ motif.

Several notations for describing motifs are in use but most of them are variants of standard notations for regular expressions and use these conventions:

• there is an alphabet of single characters, each denoting a specific amino acid or a set of amino acids;
• a string of characters drawn from the alphabet denotes a sequence of the corresponding amino acids;
• any string of characters drawn from the alphabet enclosed in square brackets matches any one of the corresponding amino acids; e.g. [abc] matches any of the amino acids represented by a or b or c.

The fundamental idea behind all these notations is the matching principle, which assigns a meaning to a sequence of elements of the pattern notation:

a sequence of elements of the pattern notation matches a sequence of amino acids if and only if the latter sequence can be partitioned into subsequences in such a way that each pattern element matches the corresponding subsequence in turn.

Thus the pattern [AB] [CDE] F matches the six amino acid sequences corresponding to ACF, ADF, AEF, BCF, BDF, and BEF.

Different pattern description notations have other ways of forming pattern elements. One of these notations is the PROSITE notation, described in the following subsection.

The PROSITE notation uses the IUPAC one-letter codes and conforms to the above description with the exception that a concatenation symbol, '-', is used between pattern elements, but it is often dropped between letters of the pattern alphabet.

PROSITE allows the following pattern elements in addition to those described previously:

• The lower case letter 'x' can be used as a pattern element to denote any amino acid.
• A string of characters drawn from the alphabet and enclosed in braces (curly brackets) denotes any amino acid except for those in the string. For example, {ST} denotes any amino acid other than S or T.
• If a pattern is restricted to the N-terminal of a sequence, the pattern is prefixed with '<'.
• If a pattern is restricted to the C-terminal of a sequence, the pattern is suffixed with '>'.
• The character '>' can also occur inside a terminating square bracket pattern, so that S[T>] matches both "ST" and "S>".
• If e is a pattern element, and m and n are two decimal integers with m <= n, then:
  • e(m) is equivalent to the repetition of e exactly m times;
  • e(m,n) is equivalent to the repetition of e exactly k times for any integer k satisfying: m <= k <= n.

Some examples:

• x(3) is equivalent to x-x-x.
• x(2,4) matches any sequence that matches x-x or x-x-x or x-x-x-x.

The signature of the C2H2-type zinc finger domain is:

• C-x(2,4)-C-x(3)-[LIVMFYWC]-x(8)-H-x(3,5)-H

A matrix of numbers containing scores for each residue or nucleotide at each position of a fixed-length motif. There are two types of weight matrices.

• A position frequency matrix (PFM) records the position-dependent frequency of each residue or nucleotide. PFMs can be experimentally determined from SELEX experiments or computationally discovered by tools such as MEME using hidden Markov models.
• A position weight matrix (PWM) contains log odds weights for computing a match score. A cutoff is needed to specify whether an input sequence matches the motif or not. PWMs are calculated from PFMs.

An example of a PFM from the TRANSFAC database for the transcription factor AP-1:

The first column specifies the position, the second column contains the number of occurrences of A at that position, the third column contains the number of occurrences of C at that position, the fourth column contains the number of occurrences of G at that position, the fifth column contains the number of occurrences of T at that position, and the last column contains the IUPAC notation for that position. Note that the sums of occurrences for A, C, G, and T for each row should be equal because the PFM is derived from aggregating several consensus sequences.

The sequence motif discovery process has been well-developed since the 1990s. In particular, most of the existing motif discovery research focuses on DNA motifs. With the advances in high-throughput sequencing, such motif discovery problems are challenged by both the sequence pattern degeneracy issues and the data-intensive computational scalability issues.

There are software programs which, given multiple input sequences, attempt to identify one or more candidate motifs. One example is the Multiple EM for Motif Elicitation (MEME) algorithm, which generates statistical information for each candidate.[2] There are more than 100 publications detailing motif discovery algorithms; Weirauch et al. evaluated many related algorithms in a 2013 benchmark.[3] The planted motif search is another motif discovery method that is based on combinatorial approach.

Motifs have also been discovered by taking a phylogenetic approach and studying similar genes in different species. For example, by aligning the amino acid sequences specified by the GCM (glial cells missing) gene in man, mouse and D. melanogaster, Akiyama and others discovered a pattern which they called the GCM motif in 1996.[4] It spans about 150 amino acid residues, and begins as follows:

WDIND*.*P..*...D.F.*W***.**.IYS**...A.*H*S*WAMRNTNNHN

Here each . signifies a single amino acid or a gap, and each * indicates one member of a closely related family of amino acids. The authors were able to show that the motif has DNA binding activity.

A similar approach is commonly used by modern protein domain databases such as Pfam: human curators would select a pool of sequences known to be related and use computer programs to align them and produce the motif profile, which can be used to identify other related proteins. A phylogenic approach can also be used to enhance the de novo MEME algorithm, with PhyloGibbs being an example.[5]

In 2017, MotifHyades has been developed as a motif discovery tool that can be directly applied to paired sequences.[6]

In 2018, a Markov random field approach has been proposed to infer DNA motifs from DNA-binding domains of proteins.[7]

The E. coli lactose operon repressor LacI (PDB: 1lcc​ chain A) and E. coli catabolite gene activator (PDB: 3gap​ chain A) both have a helix-turn-helix motif, but their amino acid sequences do not show much similarity, as shown in the table below. In 1997, Matsuda, et al. devised a code they called the "three-dimensional chain code" for representing the protein structure as a string of letters. This encoding scheme reveals the similarity between the proteins much more clearly than the amino acid sequence (example from article):[8] The code encodes the torsion angles between alpha-carbons of the protein backbone. "W" always corresponds to an alpha helix.