The use of 4 grams for Protein Classification

The use of 4 -grams for Protein Classification and Sequence Comparison Dror Tobi, Shann. Ching Chen, Ivet Bahar

The 4 -gram Concept Each sequence or group of sequences is represented as a vector in the 204 -dimensional space of 4 -grams QLIR a AASD FGTY % of sequence identity between two sequences correlates with the cosine value of their vectors 4 -gram – a short sequence of four amino acids

Representation of Sequence(s) as 4 -gram Vector(s) Three steps: Ø Calculating 4 -gram frequencies in the examined DB Ø Calculating 4 -gram frequencies for a given sequence or a given family of sequences Ø Creating a 4 -gram vector using a weight function

1. Calculating 4 -gram frequencies in DB As a reference DB we chose the Swiss-Prot. A table of the # of occurrences of each 4 -gram was created AAAA AAAR. . VVVV 10929 2230 1402 The table enables us to calculate the database frequency of 4 -gram i as

2. Calculating 4 -gram frequencies of a sequence (or family) The 4 -gram frequencies for a given sequence or a family of sequences is done using a hash table. Each 4 -gram is entered into a hash table from which the 4 gram family frequency is calculated xxxx n

3. The 4 -gram weight function The weight defined as: of 4 -gram i for sequence/family f is where is the average number of times 4 -gram i appears in family f If > then Wi > 0 If = then Wi = 0 If < then Wi < 0 (no important contribution)

Building a 4 -gram Vector (cont’d) 4 -gram vector of length k is built from the k 4 -grams with the highest | Wi | values. These 4 -grams are referred to as the k most discriminative 4 -grams. The selection of the k most discriminative 4 -grams is done using a heap data structure. 1 Identity Weight 2 xxxx 1 w 1 xxxx 5 w 5 k xxxx 9 w 9 xxxx 1001 xxxx 1050 w 1001 w 1050 The vector elements are sorted according to their 4 gram identity using quick sort algorithm.

Comparing two Vectors Vector similarity is measured by the cosine of the angle between the two vectors a xxxx 1 w 1 xxxx 5 w 5 xxxx 9 w 9 xxxx 1001 xxxx 1050 w 1001 w 1050 xxxx 5 w 5 xxxx 6 w 6 xxxx 9 w 9 xxxx 1001 xxxx 1056 w 1001 w 1056

EC 4 family classification EC 4 Test 1769 families (containing a total of 10, 919 enzymes) defined at the EC level 4 classification (at Expasy) were considered (*). A 4 -gram vector (model, probe vector) was built for each EC 4 family. The cosine between the probe vector for a given EC 4 family and the 4 -gram vector of each sequence in the Swiss-Prot was calculated. All sequences were rankordered based on their cosine values. (*) out of a total of ~4000 in SWISS-PROT release 27. 7, excluding families that do not contain any sequences

Success Definition % success is defined as the % of family members having a cosine value higher then any non family sequence in the Swiss-Prot DB. Example: for a family (F 00 X) that has five members F 001 -5 A case of 80% success. Family members are colored blue. F 001 F 003 F 005 F 002 P 0 SD F 004 …. . 0. 567 0. 456 0. 354 0. 333 0. 301 0. 255

EC 4 Initial Results

EC 1. 14. 12. 3 a case of failure EC 1. 14. 12. 3 is a family of four proteins. When we tested this family against Swiss-Prot no family member had a higher cosine value than the highest cosine value of non-family members. EC 1. 14. 12. 3 Phylogenetic tree • THIS DIOXYGENASE SYSTEM CONSISTS OF FOUR PROTEINS: THE TWO SUBUNITS OF THE HYDROXYLASE COMPONENT (BEDC 1 AND BEDC 2), A FERREDOXIN (BEDB) AND A FERREDOXIN REDUCTASE (BEDA).

Sequence homogeneity is a prerequisite for successful 4 -gram classification Sub Family vector Sub Family

Preliminary Conclusions Ø 4 -gram classification is a fast way to classify/cluster sequences. 120, 000 comparisons take ~4 min on regular desktop. ØSequence homogeneity within a family is a prerequisite for successful classification. ØThe EC classification classifies enzymes according to their function, which does not necessarily correlate with classification based upon sequence similarity.

4 -grams uses in Sequence Search The 4 -gram vector “as is” measures “sequence identity” and therefore can easily detect close sequences ( >55% identity) But what about sequences with low sequence identity (30 -55%)?

Case of P 03579 / P 03581 43. 6% identity; Global alignment score: 414 10 20 30 40 50 60 P 03579 MPYTINSPSQFVYLSSAYADPVQLINLCTNALGNQFQTQQARTTVQQQFADAWKPVPSMT : : : . . . : : P 03581 MAYSIPTPSQLVYFTENYADYIPFVNRLINARSNSFQTQSGRDELREILIKSQVSVVSPI 10 20 30 40 50 60 70 80 90 100 110 P 03579 VRFPASD-FYVYRYNSTLDPLITALLNSFDTRNRIIEVDNQPAPNTTEIVNATQRVDDAT : : . : . . . : : : . : . : : : . P 03581 SRFPAEPAYYIYLRDPSISTVYTALLQSTDTRNRVIEVENSTNVTTAEQLNAVRRTDDAS 70 80 90 100 110 120 130 140 150 P 03579 VAIRASINNLANELVRGTGMFNQAGFETASGLVW--TTTPAT. : : . . . : . : : : . . . : : : : P 03581 TAIHNNLEQLLSLLTNGTGVFNRTSFESASGLTWLVTTTPRTA 130 140 150 160 Cos(P 03579, P 03581) = 0. 04

Improving Sensitivity using homology 4 -grams P 03579 MPYTINSPSQFVYLSSAY : : : . . : P 03581 MAYSIPTPSQLVYFTENY Identity 4 -grams Homology 4 -grams SPSQ APSQ NPSQ TPSQ … SPSK Identity Vector Homology Vector

Including homology in vector comparison Homology Vector Identity Vector ai Query Sequence ah Unknown Sequence Score = cos( ai ) + lcos( ah )

4 -gram Search Results

Correlation between cosine value and Sequence alignment % identity

Conclusions The use of homology 4 -grams improve detection of distant sequences (30 – 55% sequence identity). The 4 -gram based method seems to be suitable also for sequence search. After precalculation of the sequences’ 4 -gram vector it is possible to compare two sequences with time complexity of O(1).