Variable-length Intervals in Homology Search

Abstract

Fast, accurate, and scalable search techniques for homology searching of large genomic collections are becoming an increasingly important requirement as genomic sequence collections continue to double in size almost yearly. Almost all homology search techniques rely on extracting fixed-length overlapping sequences from queries and database sequences, and comparing these as the first step in query evaluation; this is a feature of well-known tools such as fasta, blast, and our own cafe technique. In this paper we discuss a novel, variable-length approach to extracting subsequences that is based on homology scoring matrices. Our motivation is to achieve a balance between the speed and accuracy of fixed-length choices, that is, to encapsulate the speed of longer subsequence lengths and the accuracy of shorter ones. We show that incorporating this approach into our cafe technique leads to a good compromise between accuracy and retrieval e#ciency when searching with blosum matrices sensitive to distant evolutionary relationships. We expect the same results would be achieved with other homology search techniques.

Full text

Variable-length Intervals in Homology Search
Abhijit Chattaraj Hugh E. Williams
School of Computer Science and Information Technology
RMIT University, GPO Box 2476V
Melbourne, Australia
{abhijit,hugh}@cs.rmit.edu.au
Abstract
Fast, accurate, and scalable search techniques for ho-
mology searching of large genomic collections are be-
coming an increasingly important requirement as ge-
nomic sequence collections continue to double in size
almost yearly. Almost all homology search techniques
rely on extracting fixed-length overlapping sequences
from queries and database sequences, and comparing
these as the first step in query evaluation; this is a fea-
ture of well-known tools such as fasta,blast, and
our own cafe technique. In this paper we discuss a
novel, variable-length approach to extracting subse-
quences that is based on homology scoring matrices.
Our motivation is to achieve a balance between the
speed and accuracy of fixed-length choices, that is, to
encapsulate the speed of longer subsequence lengths
and the accuracy of shorter ones. We show that in-
corporating this approach into our cafe technique
leads to a good compromise between accuracy and
retrieval efficiency when searching with blosum ma-
trices sensitive to distant evolutionary relationships.
We expect the same results would be achieved with
other homology search techniques.
Keywords Homology search, Scoring matrices, Ef-
ficiency, Effectiveness
1 Introduction
Homology search techniques are used by biologists to
investigate evolutionary relationships. Such searches
are often made on the data contributed through
world-wide collaborations of biologists that have
helped determine complete genomes, including the
human genome. The data is stored in large reposito-
ries of nucleotide and protein sequence data (Benson
et al. 2002, Wu et al. 2002).
The primary structure of nucleotide sequences is
represented by strings drawn from a four-letter alpha-
bet, while protein sequences are strings over a twenty-
letter alphabet. The linear string representation of
genomic sequences allows the use of text retrieval and
Copyright c
2004, Australian Computer Society, Inc. This
paper appeared at the 2nd Asia-Pacific Bioinformatics Con-
ference (APBC2004), Dunedin, New Zealand. Conferences in
Research and Practice in Information Technology, Vol. 29. Yi-
Ping Phoebe Chen, Ed. Reproduction for academic, not-for
profit purposes permitted provided this text is included.
string matching techniques to be applied in searching
genomic data (Setubal & Meidanis 1997).
Conventional genomic search techniques evaluate
queries using a several step process. In the first step
of this process — which is common to almost all tech-
niques — fixed-length overlapping subsequences or
intervals are extracted from a query and compared
to intervals from database sequences. In the pop-
ular blast and fasta techniques, this comparison
is exhaustive, that is, the query intervals are com-
pared to the intervals extracted from all database se-
quences (Altschul et al. 1990, Altschul et al. 1997, Lip-
man & Pearson 1985, Pearson & Lipman 1988).
To speed up this process, exhaustive search tech-
niques are often adapted to run on specialised high-
end hardware1or parallelised to permit greater
throughput2. Hardware and parallelisation provides
one solution. However, an entirely different approach
is to use text indexing structures (Witten et al. 1999)
that are commonly used in web search engines to de-
termine the subset of the sequences in the collection
that are similar to the query. One such successful
approach to indexing genomic collections is our cafe
technique (Williams & Zobel 2002). However, regard-
less of whether the approach is exhaustive or index-
based, intervals are the key to determining coarse sim-
ilarity in the first step of the retrieval process.
The choice of interval length in the first step of
the search process is crucial to efficiency. Short inter-
val lengths are more sensitive to matches between se-
quences, but are less selective and, therefore, require
more processing and result in slower searches. Long
interval lengths are less sensitive, but more selective
and permit faster processing. A related issue is the
use of main-memory for the matching process: there
are less unique short intervals, which allows a more
compact main-memory model than for longer inter-
val lengths. In practice, an interval length of n= 2
to n= 4 is used for protein databank searches, and
n= 9 to n= 12 for nucleotide searches.
In this paper, we explore a novel variable-length
interval extraction technique. Our aim in propos-
ing this approach is to develop techniques that com-
bine both the fast query evaluation property of longer
fixed-length intervals and the accuracy characteristics
of shorter fixed-length intervals. Our variable-length
technique uses alignment scoring matrices to extract
intervals that score equally: under this approach a
1For example, TeraBlast at http://www.timelogic.com/
2For example, TurboBlast at http://www.turbogenomics.com/

rare amino-acid that is likely to be strongly indica-
tive of homology contributes to a short interval, while
a common amino-acid contibutes to a longer interval.
In protein databank searching, we show that variable-
length intervals can reduce query evaluation costs
compared to a short fixed-length choice by around
30% with only a small accuracy penalty. We con-
clude that variable-length intervals are a useful tool
for fast and accurate genomic homology search.
2 Background
The basic requirement for understanding the func-
tion of both nucleotide and amino-acid sequences is
establishing homology between two sequences. Ho-
mology means “possessing a common evolutionary
origin” (Reeck et al. 1987), and it is often in-
ferred by sequence comparison when it is found that
two sequences share significant statistical similar-
ity (Setubal & Meidanis 1997).
By establishing that homology exists, researchers
can often infer the structure, function, role, and evo-
lutionary history of an unknown sequence. Indeed,
sequence comparison techniques for homology search-
ing have been crucial in the discovery of many useful
homologous relationships between sequences. Such
discoveries have then led to advancements in critical
areas such as cancer research.
The homology search process typically requires
that a query sequence be compared to the candidate
sequences in a genomic collection. The conventional
approach to comparison is sequence alignment using
a variant of Smith-Waterman local alignment (1981)
that identifies the region of highest similarity between
the query and each of the collection sequences. In
this process, sequences are compared as a sequence of
characters, and each possible alignment of characters
is assigned a score. For example, when two identical
characters are aligned — an identity — the score is
usually a positive integer weight. In contrast, when
two characters are different — or a insertion or dele-
tion of a character is chosen — the score may be neg-
ative. We describe these scoring schemes in the next
section, and return to homology search techniques in
the following section.
2.1 Alignment Matrices
Precomputed alignment or scoring matrices that tab-
ulate integer scores associated with character pair-
ings are used for scoring in the amino-acid alignment
process (Dayhoff 1978, Henikoff & Henikoff 1992),
along with a function to compute the cost of inserting
or deleting a character (Altschul & Erickson 1986).
Alignment matrices are based on observations of the
frequency of conservation and mutation of amino-
acids in protein sequences. For nucleotide alignment,
simple scores of +5 for an identity and −4 for a mis-
match are most often used (Altschul et al. 1990);
schemes to derive matrices based on observations of
mutations have been proposed (States et al. 1991) but
are not in widespread use.
The well-known pam (Dayhoff 1978) matrices are
derived from observed alignments of closely related
sequences and tabulate the probability of each of the
twenty amino-acids changing to another during an
evolutionary interval. A pam distance of one corre-
sponds to a 1% change in an amino-acid sequence,
that is, to the mutation on average of one amino-acid
in a hundred. For example, a pam0 matrix — which
tabulates an evolutionary interval of zero — has all
ones on the diagonal and zeros elsewhere. As pam
values increase — for example, in a pam10 matrix
— the values on the diagonal are close to one, while
values elsewhere in the matrix are close to zero.
From the tabulation of probabilities in the pam
matrices, a log-odds matrix is derived so that scores
can be summed and are integer values. In this deriva-
tion, the elements of the probability matrix are each
divided by the frequency of the replacement amino-
acid, so that each element is the probability of re-
placement of amino-acid awith amino-acid bper
occurrence of amino-acid b. In general-purpose ex-
ploratory searching, the pam250 matrix — which is
sensitive to an evolutionary change of 2.5 amino-acids
in each 100 — is often used.
The blosum matrices are in most widespread use
and are derived from ungapped local alignments of
distantly related sequences (Henikoff 1993, Henikoff
& Henikoff 1992). All matrices are calculated directly
and, unlike the pam matrices where approximations
were used for rare events, no extrapolations are used.
The frequently-used log-odds blosum62 matrix is,
for example, derived from sequences within families
that display a 62% similarity.
The choice of alignment matrix is crucial to the
outcome of an investigation. The pam matrices
were originally developed for global alignments, but
have also been found to be useful in local align-
ment (Altschul 1991). However, the blosum62 ma-
trix has been shown to work well for general-purpose
exploration and the blosum matrices have been
shown to be more useful for finding homologous se-
quences than the pam matrices (Henikoff 1993). Re-
cently, the phat and slim matrices (Muller et al.
2001, Ng et al. 2000) have been shown to outper-
form the blosum matrices for specific tasks. How-
ever, overall, the blosum matrices are the popular
choice for most homology searching tasks and we use
these in our experiments.
2.2 Homology Search
There are three popular techniques for general-
purpose homology search with large genomic col-
lections: exhaustive local alignment (Smith &
Waterman 1981), fasta (Lipman & Pearson 1985,
Pearson & Lipman 1988), and blast (Altschul et al.
1990, Altschul et al. 1997). Of these techniques,
blast is the most popular, with the US NCBI
web search service processing around 120,000 queries
per day on the large GenBank nucleotide collec-
tion (Madden 2003). Moreover, the GenBank collec-
tion is doubling in size almost yearly, query lengths
are steadily increasing, and user numbers continue to
grow (Williams 2003). However, despite this, users
expect fast accurate answers to queries.
Heuristics are essential to fast and scalable ho-
mology search. Smith-Waterman local alignment is
impractical on general-purpose hardware; the algo-
rithm is O(n2) in both time and space, and would
take several days to evaluate a query of moderate

length on the GenBank collection on modern general-
purpose hardware. Therefore, both fasta and blast
use a several step process to identify a small set of
candidate sequences that display broad similarity to
a query before continuing with an heuristic, compu-
tationally expensive local alignment. However, even
with these heuristics, both approaches take minutes
to evaluate a single query using general-purpose hard-
ware.
The first step in fasta and blast is to pre-process
the query sequence using a variant of the Wilbur &
Lipman (1983) approach. Through this technique,
fixed-length overlapping subsequences — we refer to
these as intervals, and they are also known as n-mers,
n-grams, or words — are stored in a fast lookup struc-
ture, along with the offset of the interval within the
sequence. Consider the sequence attaatt and an in-
terval length of n= 3. For this sequence, the intervals
and their offsets with the sequence are att (1,5), tta
(2), taa (3), and aat (4).
After pre-preprocessing the query, each database
sequence from the genomic collection is sequentially
retrieved and parsed into its consituent intervals. The
intervals are looked-up in the query search structure
and, if the interval is present, then an initial match
region is recorded by computing the difference in the
query and database sequence offsets, and storing the
identity of the matching interval. After the first step,
the steps used in fasta and blast diverge but the
goal is the same: initial match regions that are likely
to be indicative of homology are locally aligned, and
results returned to the user.
We have previously proposed an alternative to the
exhaustive approaches used in the popular homology
search tools. The cafe homology search technique
uses an inverted index to support fast and scalable
querying of large genomic collections (Williams &
Zobel 2002). Inverted indexes (Witten et al. 1999)
are used to support almost all information retrieval
applications and, most prominently, are the search
structures used by web search engines such as Google.
Building an inverted index requires terms to be ex-
tracted from the collection to be searched — in the
case of English text, this is usually words — and the
creation of a list for each term that records, for ex-
ample, a list of documents that the term appears in.
Query evaluation proceeds by looking-up each term
in the search structure, retrieving the lists associated
with each term, and then retrieving the documents
that contain the terms.
Similar to blast and fasta, our cafe approach is
an interval based scheme. The search terms stored in
the inverted index are the intervals extracted from the
database sequences and, at query time, intervals are
extracted from the query and matched against the in-
dex in the first step. Again, the motivation is to find
a subset of sequences that have broad similarity to
the query sequence, and then more computationally-
intensive local alignment is used. Williams and Zobel
showed that in 1997 their implementation of cafe
was more than eight times faster the the popular
blast search system, and more scalable with increas-
ing collection size.
In general, for all homology search techniques,
short interval lengths permit slow, sensitive search-
ing and longer intervals allow fast, selective searching.
For example, for an interval of length n= 1, almost
all sequences in a collection share similarity with the
query; the search process is therefore sensitive and
slow — almost all sequences are locally-aligned — but
not selective in determining a subset of sequences. In
contrast, for an interval length of n= 10, only a small
fraction of the sequences in the collection contain a
specific interval, and therefore only that fraction of
sequences are locally-aligned; the process is therefore
fast because it is selective, but less sensitive to distant
similarity. For protein databank searching, interval
lengths of n= 2, n= 3, or n= 4 are preferred.
3 Variable-Length Intervals
In this section, we propose a novel technique for ex-
tracting intervals from amino-acid sequences. Our
aim in proposing this approach is to permit a com-
promise between the fast query evaluation of longer
fixed-length intervals and the accurate query evalu-
ation of short fixed-length intervals. Our approach
uses alignment matrices to guide the interval extrac-
tion process, leading to variable-length intervals.
Codons are three-base nucleotide sequences that
code for an amino-acid. Since there are 64 possible
codons — there are 4 bases and therefore 64 possible
three-base combinations — and only 20 amino-acids,
there is redundancy in the coding process. For ex-
ample, the amino-acid arginine is coded for by six
codons; in contrast, tryptophan is coded by only one.
By using fixed-length intervals as index terms, the
initial step in the heuristic homology search process
described in the previous section neglects that some
amino-acids may be better indicators of possible ho-
mology than others. To continue our example, a
match between two tryptophan residues using the
blosum62 alignment matrix scores 11 in the align-
ment process, while an arginine scores only 5. We
therefore might conclude that a single tryptophan
identity is more than twice as strong an indicator of
homology as an arginine identity.
Based on this observation, we propose a variable-
length interval scheme where the interval length is
dependent on the sum score of its composite amino-
acids. In this approach, we set a threshold kas the
minimum identity score of each interval. To extract
intervals, we then set a score s= 0 prior to parsing the
interval from the sequence. As an amino-acid residue
is added to the interval, we use an alignment matrix
to determine the identity score for that amino-acid
and add the score to s. When sis greater than or
equal to k, the interval is complete, and the process
continues with the next overlapping interval.
To illustrate our approach, consider this technique
applied to the sequence fragment agvewaept. Ta-
ble 1 lists the identity scores from a blosum62 ma-
trix for each of the amino-acids in the fragment. The
highest score awarded by this matrix is 11 for a tryp-
tophan identity and, by default, we use this as the
value of k; by setting k= 11, the minimum interval
length is 1, that is, when the interval consists of a
single tryptophan residue. For agvewaept, the first
interval is agv, since the scores of an aand giden-
tity total s= 10, and the addition of vis required to

Amino Acid Single Three blosum62 Score blosum40 Score
Letter Code Letter Code
Alanine A Ala 4 5
Glutamic Acid E Glu 5 7
Glycine G Gly 6 8
Proline P Pro 7 11
Threonine T Thr 5 6
Valine V Val 4 5
Tryptophan W Trp 11 19
Table 1: Selected amino-acid identity scores from blosum matrices.
exceed k= 11. The second interval is gve and scores
s= 15, the third is vew with s= 20, and the fourth
ew with s= 16. At the completion of processing the
fragment, the following intervals — with scores shown
in brackets — are index terms: agv (14), gve (15),
vew (20), ew (16), w(11), aep (16), ep (12), and
pt (12).
The choice of scoring matrix and threshold k
are important parameters in our variable-length ap-
proach. The diversity of identity scores correlates
with the range of lengths of the variable-length in-
tervals: for matrices that are sensitive to close evolu-
tionary events, the range of scores varies, for exam-
ple, from 4 to 20 in a blosum30 matrix, but only
from 6 to 16 for blosum80. Similarly, the choice
of kaffects the minimum and maximum lengths: if
kexceeds the maximum score (usually for a trypto-
phan identity), then the minimum interval length is
two; similarly, kdivided by the minimum score (usu-
ally for arginine) defines the maximum interval length
We expect, therefore, that kshould be carefully cho-
sen with consideration to the matrix, and the desired
range of interval lengths; as we show later, choosing
values of kso that the minimum interval length is
n= 2 works well in practice.
In addition to the twenty amino-acids, three wild-
cards z,x, and bare used to represent the possible
substitutions of more than one amino-acid. For exam-
ple, the wildcard brepresents dor n. The wildcard x
represents any amino-acid and, in almost all matrices,
scores negatively when aligned with itself. We tried
several methods for handling a negative contribution
to the value of sin creating variable-length intervals.
However, since the collection we used contained only
1,701 wildcard occurrences across only 0.2% of the se-
quences, we found that the choice of approach had no
significant impact on our results. We therefore chose a
simple approach of replacing negative identity scores
with a constant score of +1.
4 Experiments
In this section, we describe the test collection and
query sets used in our experiments, and the measures
we used for evaluating the accuracy of our approach.
4.1 Test Collection
To compare the retrieval effectiveness of different in-
terval extraction approaches, we use a subset of the
Protein Identification Resource–International Pro-
tein Sequence Database (PIR), a collection of well-
classified amino-acid sequences (Barker et al. 2000).
The PIR collection is divided into a set of four smaller
databases, pir1 to pir4. Entries in pir1 are an-
notated and fully classified, pir2 entries are well-
classified, sequences in the pir3 collection are largely
unclassified, and those in pir4 are unclassified.
We used an approach similar to that used by
Williams and Zobel (2002) in creating a collection for
accuracy assessment, where we formed a collection
based on the pir1 and pir2 databases. Sequences
from pir1 and pir2 — in addition to being classified
and annotated — are usually also assigned a super-
family (sf) number. A super-family is a group of
sequences that have the same domains in the same or-
der, that is, they can reasonably be inferred as being
homologous. We extracted from pir1 and pir2 those
sequences with an sf number, and this resulted in a
database of 67,543 sequences. The collection contains
22,675,479 residues, with a mean sequence length of
335.
4.2 Queries
The query set was compiled by selecting the first-
occurring member sequence in the database from
each super-family. Super-families with single mem-
bers were excluded from the query set; there were
1,175 single member sequences. Sequences of lengths
exceeding 500 bases were also removed, based on the
assumption that amino-acid queries rarely tend to ex-
ceed this limit. After the above filtering process, the
query set consisted of 4,021 queries.
We also compiled a smaller query set of 403 queries
by selecting every tenth query from the larger query
set. We used this smaller set in selected initial exper-
iments that we describe later.
4.3 Measuring Accuracy
A common method of measuring relative retrieval
effectiveness of information retrieval techniques are
the measures of precision and recall (Bollmann 1983,
Raghavan et al. 1989, Salton 1989, Witten et al.
1999). Recall is the proportion of the known relevant
answers that have been retrieved, while precision is
the proportion of relevant answers retrieved in the
set of answers.
Recall is often said to be an impractical measure,
because it is not always possible to judge all sequences
in a collection as being relevant or irrelevant to each
query. However, using the pir collection and queries,
it is possible to approximate recall if super-family se-
quences are deemed as relevant to a query drawn from

a super-family, and non super-family sequences are
deemed as irrelevant. For example, using this ap-
proach the members of sf 12 are deemed as the only
relevant answers to the query that was extracted from
sf 12; this approach has limitations, which are dis-
cussed in detail by Williams & Zobel (2002), but the
approach has been shown to offer a reasonable guide
to the relative effectiveness of search techniques.
In our work, precision is therefore the fraction of
relevant sequences retrieved:
Precision = Relevant sequences retrieved
Total sequences retrieved
Recall measures the proportion of total relevant se-
quences retrieved:
Recall = Relevant sequences retrieved
Total relevant sequences
We report accuracy as 11-point average interpolated
precision. Interpolated precision is the highest pre-
cision achieved at a particular recall level, and all
subsequent levels of recall. We calculate average in-
terpolated precision for all queries at eleven standard
recall levels — from 0% to 100% in increments of 10%
— and these precision values are then averaged into
a single value.
Each recall level reflects the fraction of relevant
answers reported, while the corresponding precision
value is the fraction of reported answers that are rel-
evant. The 0% recall level is treated as a special case
and is assigned the highest precision achieved at any
recall level (Witten et al. 1999).
5 Results
In this section, we describe the results of our exper-
iments with fixed and variable-length intervals. We
use our cafe retrieval technique to evaluate accu-
racy and speed; however, we believe that the relative
results are indicative of the tradeoffs that would oc-
cur in all interval-based homology search tools. All
experiments were conducted on an Intel Pentium IV
system under light-load, that is, where no other sig-
nificant tasks were running.
5.1 Overall Results
Table 2 shows our overall results using a blosum62
matrix and 4,021 queries on our pir collection. The
first three rows show the effect of choosing fixed in-
terval lengths of n= 3 through to n= 5. As ex-
pected, with increasing fixed interval length, average
11-point precision declines and, as expected, accuracy
is highest when the interval length is most sensitive
at n= 3. In addition — and again as expected —
average query time falls and index size increases from
n= 3 to n= 5.
As more intervals are stored in the index structures
of cafe, the number of locations of the intervals falls,
and therefore the index becomes less compressible.
However, as the amount of information per interval
decreases, less information is retrieved from disk per
query, and query evaluation speed improves. Overall,
the benefit of n= 3 is the 2.6% absolute improve-
ment in accuracy over n= 4 but with a three-fold
increase in average query time; these are similar re-
sults to those we have observed in blast.
The fourth and fifth lines of Table 2 show the ef-
fect of using variable-length intervals with two score
thresholds of k= 13 and k= 14. For a threshold
of k= 13, accuracy is around 0.7% less than n= 3
but speed improves by 0.09 seconds per query. For
k= 14, the speed improvement is a substantial 0.65
seconds per query, with a penalty of an 1.05% reduc-
tion in absolute precision. Both variable-length re-
sults offer accuracy at least 1.5% better than n= 4,
but are slower by a factor of two. Overall, our results
show that variable-length intervals permit a compro-
mise between the speed of fixed-length intervals of
length n= 4 and the accuracy of n= 3.
5.2 Choosing the Threshold k
The choice of the interval score threshold kis crucial
to the performance of variable-length intervals. Ta-
ble 3 shows the effect of varying kfor a blosum62
matrix on accuracy, the number of intervals found
in the collection, and interval length statistics; the
trends are typical of the blosum matrices we tested
in the range blosum30 to blosum100.
Overall, our results show that accuracy peaks
when kis the maximum identity score — in this case,
11 for tryptophan — or slightly higher. We therefore
conclude that the value of kshould be chosen so that
the minimum interval length is 2, and the mean is
close to 3.5; this is again not an unexpected result,
since variable-length intervals have been proposed to
offer a compromise between fixed-length intervals of
n= 3 and n= 4.
5.3 Choosing a Matrix
Figure 1 shows how query evaluation speed and ac-
curacy are affected by the choice of blosum matrix.
Our results show that for matrices in the range blo-
sum30 to blosum50, variable-length intervals permit
both accurate and fast query evaluation; for example,
with a blosum40 matrix and threshold of k= 21, ac-
curacy is only around 0.7% less than fixed-length in-
tervals of length n= 3, while being almost 30% faster.
In contrast, for matrices above blosum70, searching
using variable-length intervals is unacceptably slow
and accuracy falls.
Figure 2 shows on the x-axis the number of se-
quences that contain an interval plotted against the
frequency of such intervals for two matrices. For ex-
ample, there are just under 100 different intervals ex-
tracted using a blosum40 matrix that occur in only
10 sequences. The distribution of intervals explains
the improved speed for lower-numbered blosum ma-
trices: there are more intervals that occur fewer times
for the blosum40 than the blosum62 and, therefore,
the average number of initial match regions created in
the query evaluation process is likely to be lower. This
is perhaps unsurprising, given our observations previ-
ously that the diversity of scores affects the diversity
of intervals, and that matrices sensitive to close evo-
lutionary events are those that have score diversity.
Variable-length intervals are therefore both accurate
and fast for blosum matrices sensitive to distant evo-
lutionary events.

Scheme Interval Average Average Query Total Index
Parameter Precision Time (sec) Size (Mb)
Fixed n= 3 91.86 2.43 68.65
Fixed n= 4 89.21 0.81 83.21
Fixed n= 5 86.59 0.59 140.63
Variable k= 13 91.10 2.34 70.15
Variable k= 14 90.81 1.78 72.99
Table 2: Speed, accuracy, and index size for the fixed and variable-length schemes. Results are averaged for
4,021 queries using the blosum62 matrix.
Interval 11-pt Average Distinct Interval Length
Threshold kPrecision Intervals Maximum Minimum Mean Median
4 75.43 257 5 1 2.40 2
6 81.57 1,113 7 1 2.93 3
8 86.93 2,600 9 1 3.23 3
9 88.76 4,707 10 1 3.35 3
10 90.25 7,589 11 1 3.45 3
11 91.69 10,360 12 2 3.52 3
12 91.50 15,303 13 2 3.67 4
13 91.06 26,317 14 2 3.83 4
14 91.09 44,747 15 2 3.93 4
15 90.19 67,930 16 2 3.98 4
20 89.12 932,651 21 2 4.92 5
25 85.37 6,062,082 26 3 5.77 6
30 79.48 11,898,501 31 3 6.50 7
Table 3: 11-point average precision, and interval statistics from searches using variable-length intervals. These
experiments use the small 403 query set and the blosum62 matrix.
6 Conclusion
With genomic sequence collections rapidly growing
in size, there is a need for fast, accurate, and scalable
homology search techniques. In this paper, we have
investigated a novel technique for extracting intervals
that are used to discover promising matches between
queries and database sequences. In our approach, in-
tervals have a variable length that is determined by
the alignment matrix used in the search process. Our
aim in proposing this approach is to offer a compro-
mise between the accuracy of short fixed-length inter-
vals and the speed of longer fixed-length intervals.
We have shown that our variable-length scheme
works well for matrices sensitive to distant evolu-
tionary events. For example, when searching with
ablosum40 matrix, our variable-length schemes are
up to 30% faster than the most accurate fixed-length
scheme with less than a 1% reduction in accuracy.
Therefore, variable-length indexes offer a good com-
promise between accuracy and speed for index-based
homology searching.
In future work, we plan to investigate the use of
variable-length intervals in the initial phases of ex-
haustive techniques such as blast and fasta. We
also aim to further develop our techniques in order
to apply variable-length intervals on nucleotide data.
In addition, we plan to explore techniques that are
accurate for closely related sequences.
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40 60 80 100
Blosum Matrices
80
85
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100
Average Precision
Varlen Accuracy
0
2
4
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8
10
Average Query Time (sec)
Varlen Time
Figure 1: Impact of blosum matrix choice on the accuracy and query evaluation speed using variable-length
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1 10 100
Number of sequences containing interval
1
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