Editor's note: Aaron Mackey discovered bioinformatics during the second year of his Ph.D. program in Immunology at Washington University in St. Louis. After taking a class in computational molecular biology, Aaron realized that it was possible to combine an aptitude for mathematics and computer science with non-theoretical biological research, and was hooked. Aaron will be giving a tutorial on Relational Databases for Bioinformatics at O'Reilly's upcoming Bioinformatics Technology Conference.
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Related Reading 
Beginning Perl for Bioinformatics |
Many biological data sources represent information in hierarchies. Remember the mnemonic "King Philip Came Over From Germany Speedily" you once learned in grade school biology class? It was supposed to help you remember the hierarchical taxonomy classifications: Kingdom Phylum Class Order Family Genus Species. Today, this information is a click away: the NCBI Taxonomy database contains the common and scientific names of every organism that is associated with a biological sequence in Entrez, in addition to the complete hierarchical taxonomic tree of species. At the NCBI Taxonomy Web site you can search for a given species, or browse up and down the taxonomic tree. One can learn, for instance, that the human species has the taxonomic definition "cellular organisms; Eukaryota; Fungi/Metazoa group; Metazoa; Eumetazoa; Bilateria; Coelomata; Deuterostomia; Chordata; Craniata; Vertebrata; Gnathostomata; Teleostomi; Euteleostome; Sarcopterygii; Tetrapoda; Amniota; Mammalia; Theria; Eutheria; Primates; Catarrhini; Hominidae; Homo/Pan/Gorilla Group; Homo; Homo sapiens."
The Structural Classification of Proteins, or SCOP, is another example of biological data organized in a hierarchy. SCOP manually clusters small families of related proteins into larger superfamilies that share common structure, and even larger clusters of classes that share more general fold topology. SCOP, and other databases like it, are commonly used as gold standards to compare the performances of homology-identifying sequence or structural-comparison algorithms such as SSEARCH, PSI-BLAST, HMMER, DALI, or VAST. Though not as deep a hierarchy as the NCBI Taxonomy tree, working with the SCOP dataset requires similar methods for hierarchical modeling.
Finally, the Gene Ontology consortium curates a controlled vocabulary dictionary of known biological processes, molecular functions, and cellular localizations. The GO database contains both general terms like enzyme or cell, and more specific terms like gluthione transferase and vacuole. These lists of terms and definitions are useful alone, but the real gold mine of information from the GO project is the carefully constructed ontology that relates more specific terms to their general counterparts.
While these projects have rich public Web sites for browsing and downloading
the data, none of them provide the means to compute on the data, to
relate your own data to theirs, or to query across the disparate
resources. Fortunately, all of these data sources can be freely obtained by
ftp or anonymous cvs for integration into a local,
custom-made relational database. But how does one represent hierarchical data in
a relational database? And, more importantly, how can one make efficient use of
such data?
seqdb_demo: A Simple Sequence DatabaseBefore we start looking at these issues, we'll briefly introduce a very simple
biosequence database schema, seqdb_demo, meant to store the
contents of the NCBI nonredundant
("nr") flatfile protein database. This database has approximately 1.2
million protein sequences, each of which has one or more descriptions (separated by ctrl-A characters):
>gi|10732787|gb|AAG22538.1| homocysteine S-methyltransferase-2 [Zea mays]
MVVTAAGSAEEAVRRWVDAAGGRLVLDGGLATELEANGADLNDPLWSAKCLLSSPHLIRK
VHMDYLEAGANIIITASYQATIQGFESKGFSKEQSENLLTKSVEIALEAREMFLKEHLEK
CKDGAVLIGGCCRTTPNTIRAIHRTLNKSPNKQQLPAVE
>gi|15241446|ref|NP_196966.1| putative protein; protein id: At5g14620.1
[Arabidopsis thaliana]^A
gi|11281152|pir||T48635 hypothetical protein T15N1.110 - Arabidopsis thaliana^A
gi|7573311|emb|CAB87629.1| putative protein [Arabidopsis thaliana]
MIVISGENVDIAELTDFLCAAQMAREFSEFYTEHEEQKPRHNIKKRRFESKGEPRSSVDD
EPIRLPNPMIGFGVPNEPGLITHRSLPELARGPPFFYYENVALTPKGVWETISRHLFEIP
KYGGFDLVIGGSPCNNLAGGNRVSRVGLEGDQSSLFFEYCRILEVVRARMRGS
The seqdb_demo database has a
seq table to hold each biosequence and an associated descriptions
table, descr that contains all descriptions of the sequence and
its various accession numbers from NCBI (the GI number) and/or its parent
database (SwissProt, EMBL, PDB, and so on):
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Here's an example query that shows the data from the nr flatfile snippet:
SELECT descr.*, SUBSTRING(seq, 1, 20) AS subseq
FROM seq
INNER JOIN descr USING (seq_id)
| descr_id | seq_id | gi | acc | db | descr | subseq |
|---|---|---|---|---|---|---|
| 1 | 1 | 10732787 | AAG22538.1 | gb | homocysteine S-methyltransferase-2 | MVVTAAGSAEEAVRRWVDAA |
| 2 | 2 | 15241446 | NP_196966.1 | ref | putative protein; protein id: At5g14620.1 | MIVISGENVDIAELTDFLCA |
| 3 | 2 | 11281152 | T48635 | pir | hypothetical protein T15N1.110 | MIVISGENVDIAELTDFLCA |
| 4 | 2 | 7573311 | CAB87629.1 | emb | putative protein | MIVISGENVDIAELTDFLCA |
We'll use and expand on this simple schema throughout this article. Our goal will be to see how to integrate other sources of hierarchical data into our simple sequence database, writing efficient SQL queries to make use of that data.
We'll start by storing and querying the NCBI Taxonomy database. From the NCBI FTP site, you can download the taxonomy-related data in tabular format and import the tables directly into your relational database. NCBI provides a separate table of the many possible names for each taxon, but we'll simplify the matter and store only the unique scientific name.
To represent the taxonomic hierarchy, NCBI has chosen a common
representation of tree structures. Using an endogenous foreign key
(parent_id), reference the primary key (taxon_id) of
the parental row:
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This representation, called an adjacency list, is easy to understand. Every
parent-child relationship is explicitly defined. Each taxon's
parent_id points to its parent taxon's taxon_id. To find the parent taxon of humans, we write:
SELECT *
FROM taxon AS parent
INNER JOIN taxon AS child
ON (child.parent_id = parent.taxon_id)
WHERE child.name = 'Homo sapiens'
We could manually repeat this query for each parent taxon we retrieve, up to the root of the tree. We can also find out how many unique species there are in the taxonomy tree by counting how many taxa are "terminal", in other words, they have no children:
SELECT COUNT(*)
FROM taxon AS terminal
LEFT JOIN taxon AS child
ON (child.parent_id = terminal.taxon_id)
WHERE child.parent_id IS NULL
This yields approximately 120,000 unique species. Estimates of the planet's true biodiversity are far greater than this value, so we know that the NCBI Taxonomy database is far from a complete representation of all organisms.
Finally, we can also download and capture the biosequence/species association information, adding a taxon_id foreign key to the descr table that references the taxon.taxon_id primary key. Now we can easily
write an SQL query that fetches all the human sequences present in GenBank:
SELECT descr.gi, descr.descr, seq.seq
FROM seq
INNER JOIN descr USING (seq_id)
INNER JOIN taxon USING (taxon_id)
WHERE taxon.name = "Homo sapiens"
But what if we want to retrieve all Primate sequences, including humans and other ape-like species? Or perhaps we'd like to retrieve all Bacterial sequences but only those that aren't also from the more specific Enterobacteria. With the adjacency list representation, we'd have to "walk" through the tree procedurally (usually recursively) to include or exclude the taxonomies of interest, collecting sequences as we walked along. While potentially prohibitively expensive in both time and memory requirements, Brian Jepson's DBIx::Tree Perl module, or database-native procedural TransactSQL-like languages, provides some facility for these activities, but are neither efficient nor a solution in a pure SQL environment.
Fortunately, an attractive alternative exists, called the nested-set
representation. SQL for Smarties author Joe Celko has long
endeavored to make people aware of this methodology, and I will carry on his
crusade here. The basic idea is this: instead of explicitly representing
relationships between immediate child-parent pairs with parent_id
foreign keys, we'll use two surrogate, calculated values--left_id
and right_id--appended to our taxon table. Without
showing yet how they're calculated, we'll simply require that the values in
these two fields have the following, useful property: for all parent-child
pairs, the child's left_id and right_id will be
between the parent's left_id and right_id
values. The same will be true of the child's children, and so on all the way
down the hierarchy:
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At first, these extra numbers may not seem very useful. Are they foreign
keys? What field do they reference? The answers are: No and they
don't. These two numbers represent the same hierarchical information as the
taxon_id, parent_id pairs, but implictly,
instead of explicitly. Fundamentally, the values in left_id and
right_id are just numbers, nothing else and could be changed to any
other set of numbers, as long as the between-ness property holds. But
it's exactly this property that provides the utility we need to select entire
subsets of taxonomies in one step. Now to select all Primate sequences we
can use this SQL:
SELECT descr.gi, descr.descr, seq.seq
FROM seq
INNER JOIN descr USING (seq_id)
INNER JOIN taxon USING (taxon_id)
INNER JOIN taxon AS include
ON (taxon.left_id BETWEEN include.left_id AND
include.right_id)
WHERE include.name = 'Primate'
Here, we've joined the taxon table onto itself in a
self-join governed by a BETWEEN clause that enforces the
implicit relationship between taxonomies encoded by the included parental
left_id and right_id values. The WHERE
clause specifies which taxonomy we wish to specifically include in the result
set. We can extend the same approach to select all Bacterial sequences
but now exclude any that are also Enterobacterial in origin:
SELECT descr.gi, descr.descr, seq.seq
FROM seq
INNER JOIN descr USING (seq_id)
INNER JOIN taxon USING (taxon_id)
INNER JOIN taxon AS include
ON (taxon.left_id BETWEEN include.left_id AND
include.right_id)
INNER JOIN taxon AS exclude
ON (taxon.left_id NOT BETWEEN exclude.left_id AND
exclude.right_id)
WHERE include.name = 'Bacteria'
AND exclude.name = 'Enterobacteria'
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left_id and right_idSo where do
these magic left_id and right_id values come from? To
generate these values, we must resort to a procedural language (in this case
Perl), in which we "walk" down the tree, visiting all of a taxon's children
before moving on to a taxon's sibling. (For example, we perform a depth-first
traversal of the tree). Whenever we first visit a taxon, we set its
left_id value before moving on to its children. When we're finished
with all of its children, we then set its right_id. We keep a
continuously increasing counter to use for the values. This process is
diagrammed in Figure 1, and shown in the Perl code in Example 1 below:
#!/usr/bin/perl -w
# depth-first tree traversal to generate left_id, right_id
use strict;
use DBI;
my $dbh = DBI->connect("dbi:mysql:seqdb_demo",
"seqdb_user",
"seqdb_pass")
or die $DBI::errstr;
my $children = $dbh->prepare("SELECT taxon_id
FROM taxon
WHERE parent_id = ?");
my $setleft = $dbh->prepare("UPDATE taxon
SET left_id = ?
WHERE taxon_id = ?");
my $setright = $dbh->prepare("UPDATE taxon
SET right_id = ?
WHERE taxon_id = ?");
my $ctr = 1;
my $rootid = 1;
walktree($rootid);
$dbh->disconnect;
sub walktree {
my $id = shift;
$setleft->execute($ctr++, $id);
$children->execute($id);
while(my ($id) = $children->fetchrow_array) {
walktree($id);
}
$setright->execute($ctr++, $id);
}
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| Figure 1 |
On a modest database server running MySQL, this process takes about 15 minutes to execute with the NCBI Taxonomy data. Since we only update our local database weekly (by reloading the entire NCBI Taxonomy datasets), we rebuild the entire nested-set representation after each database load. Methods to maintain the values in an incremental update/delete scenario are well known but will not be discussed here. For further information and an excellent treatment of adjacency list, and nested-set representations for tree-like data, Joe Celko's book, SQL For Smarties is highly recommended.
To build upon our simple biosequence database, we'll bring in additional information from the Gene Ontology project. Just as we previously asked for all sequences from any Primate, we now want to ask for all sequences that are either enzymes, or are found in mitochondria, or are enzymes found in mitochondria.
The difference between the Taxonomy data and the GO data is that specific GO terms may have multiple general parent terms. For instance, the focal adhesion kinase term has parental kinase, transferase, and signal tranducer terms. Fortunately, no term's parents can also be a child of the term. The hierarchy is one way, or directed. Generally, the GO term ontology is implemented as a specific graph structure called a directed acyclic graph or DAG.
Unlike the adjacency-list representation for trees, graphs cannot generally be stored in a single table. The GO terms (or other graph nodes) are stored in one table, and a second table is used to store a list of edges between nodes, with pairs of foreign keys referencing the node table:
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The go_edge table is another form of the adjacency list. To move
up and down the hierarchy requires a procedural language. Unfortunately, there
is no equivalent to the nested-set representation for these more general graph
structures. Instead, we'll build an entirely separate accessory table that
contains one row for every unique pair of nodes that can be connected
transitively; that is, if A is connected to B, and B is connected to C,
then A is transitively connected to C. Our transitive closure tables will
contain three rows corresponding to this relationship, one each for A & B, B
& C, and A & C; see the example below and Figure 2.
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| Figure 2 |
To fill the go_tc table, we will again require a procedural,
iterative approach. We begin by first copying all the rows from
go_edge into go_tc, setting length to one (for
completeness, we also add all the terms in go, setting length to
zero). We then iteratively add each new pair of terms that are two edges away
from each other, three edges away, four edges away, and so on until no new rows
have been inserted:
#!/usr/bin/perl -w
use strict;
use DBI;
my $dbh = DBI->connect("dbi:mysql:seqdb_demo",
"seqdb_user",
"seqdb_pass")
or die $DBI::errstr;
$dbh->do("INSERT INTO go_tc
SELECT go_acc AS child,
go_acc AS parent,
0 AS length
FROM go");
$dbh->do("INSERT INTO go_tc
SELECT child, parent, 1 AS length
FROM go_edge");
my $select = $dbh->prepare(q{
SELECT DISTINCT tc1.child,
tc2.parent,
tc1.length + 1
FROM go_tc AS tc1
INNER JOIN go_tc AS tc2
ON (tc1.parent = tc2.child)
WHERE tc2.length = 1
AND tc1.length = ?
});
my $insert = $dbh->prepare(q{
REPLACE INTO go_tc (child, parent, length)
VALUES ( ?, ?, ?)
});
my ($oldsize) =
$dbh->selectrow_array("SELECT COUNT(*) FROM go_tc");
my $newsize;
my $len = 1;
while (!$newsize || $oldsize < $newsize) {
$oldsize = $newsize || $oldsize;
$newsize = $oldsize;
$select->execute($len++);
while(my @data = $select->fetchrow_array) {
$insert->execute(@data);
$newsize++;
}
}
Building the go_tc table on our system takes just a few minutes.
As with the nested-set tree data, we won't bother to figure out how to make
incremental updates to go_tc when data changes in
go_edge. We'll simply run the transitive closure script immediately
following any changes to go or go_edge.
The last part of the GO data is the associations between some protein
sequences and GO terms; unlike an organism in the Taxonomy tree, a protein may
have multiple GO terms with which it's associated. Furthermore, the associations
are often made to SwissProt or TREMBL accessions, not NCBI GI numbers, so
instead of keying off of gi, we'll reference the acc
field of the descr table:
SELECT descr.gi, descr.descr, seq.seq
FROM seq
INNER JOIN descr USING (seq_id)
INNER JOIN go_assoc ON (descr.acc = go_assoc.seq_acc)
INNER JOIN go_tc ON (go_assoc.go_acc = go_tc.child)
INNER JOIN go_term ON (go_tc.parent = go_term.go_acc)
WHERE go_term.name = "enzyme"
AND descr.gi = ( SELECT MAX(gi)
FROM descr AS d
WHERE d.seq_id = descr.seq_id )
Unfortunately, because of MySQL's continued lack of support for SQL statements with sub-selects, we cannot use the previous solution directly. Instead, we break the previous statement into two parts: first we create a temporary table full of GI numbers from the sequence we want, and second, we use the temporary table to pull out the rest of the sequence-specific information:
CREATE TEMPORARY TABLE go_gi
SELECT MAX(descr.gi) AS gi
FROM descr
INNER JOIN go_assoc ON (descr.acc = go_assoc.seq_acc)
INNER JOIN go_tc ON (go_assoc.go_acc = go_tc.child)
INNER JOIN go_term ON (go_tc.parent = go_term.go_acc)
WHERE go_term.name = 'enzyme'
GROUP BY descr.seq_id
Then, to get at the corresponding sequence data:
SELECT descr.gi, descr.descr, seq.seq
FROM seq
INNER JOIN descr USING (seq_id)
INNER JOIN go_gi USING (gi)
The approach we've shown here can be extended to include any number of boolean conditions, such as "enzyme AND mitochondrion;" the trick will be to find sequences that have an accession (or accessions) associated with both terms.
CREATE TEMPORARY TABLE go_gi
SELECT MAX(descr.gi) AS gi,
COUNT(DISTINCT go_term.name) AS count
FROM descr
INNER JOIN go_assoc ON (descr.acc = go_assoc.seq_acc)
INNER JOIN go_tc ON (go_assoc.go_acc = go_tc.child)
INNER JOIN go_term ON (go_tc.parent = go_term.go_acc)
WHERE ( go_term.name = "enzyme"
OR go_term.name = "mitochondrion"
)
GROUP BY descr.seq_id
HAVING count = 2
We've done a few things differently here. For each unique sequence,
we're collecting the count of how many different requested GO terms it
satisfies. To enforce the boolean logic for "enzyme AND mitochondrion," we use
an accessory value, count, and require (via the HAVING count
= 2 clause) that the rows returned have the correct number of GO terms
associated with them. To get "enzyme OR mitochondrion," simply remove the
HAVING clause, and the associated count field.
To implement exclusions, such as "enzyme AND mitochondrion NOT mitochondrial
matrix," the usual mechanism is to extend the WHERE clause with a NOT
EXISTS sub-select:
WHERE ( go_term.name = "enzyme"
OR go_term.name = "mitochondrion"
) AND NOT EXISTS (
SELECT seq_id
FROM descr AS d
INNER JOIN go_assoc ON (d.acc = go_assoc.seq_acc)
INNER JOIN go_tc ON (go_assoc.go_acc = go_tc.child)
INNER JOIN go_term ON (go_tc.parent = go_term.go_acc)
WHERE go_term.name = "mitochondrial matrix"
AND descr.seq_id = d.seq_id
)
But again, since MySQL doesn't support subselect statements, we
have to resort to placing the results of the subselect statement into a
temporary table, go_gi_exclude, and altering our normal
SELECT statement to implement a LEFT JOIN:
CREATE TEMPORARY TABLE go_gi
SELECT MAX(descr.gi) AS gi,
COUNT(DISTINCT go_term.name) AS count
FROM descr
INNER JOIN go_assoc ON (descr.acc = go_assoc.seq_acc)
INNER JOIN go_tc ON (go_assoc.go_acc = go_tc.child)
INNER JOIN go_term ON (go_tc.parent = go_term.go_acc)
LEFT JOIN go_gi_exclude
ON (descr.seq_id = go_gi_exclude.seq_id)
WHERE ( go_term.name = "enzyme"
OR go_term.name = "mitochondrion"
) AND go_gi_exclude.seq_id IS NULL
GROUP BY descr.seq_id
HAVING count = 2
Between the inclusionary HAVING count = n mechanism
and the exclusionary NOT EXISTS (or LEFT JOIN
alternative) mechanism, all manners of boolean queries can be constructed.
The lesson here is that often the obvious way to model data (such as adjacency lists of tree or graph edges) is not the most efficient data model with which to query or compute. Alternatives such as the nested-set implicit representation of a tree-like hierarchy, or the transitive closure of a graph structure costs very little to create, and provides one-step mechanisms to extract informative subsets of the data. Commercial relational database products that advertise native support for hierarchical data are often simply transparently building and managing these same representations. Now you know how to it yourself.
In the next installment, we'll look at some alternatives to modeling temporal or historical biological data.
Aaron Mackey is involved with the BioPerl and GMOD software projects, and distributes his own simple biosequence relational database tool package, seqdb, for educational purposes.
Copyright © 2009 O'Reilly Media, Inc.