Transcript The Ontology of the Gene Ontology

Species and Classification in
Biology
Barry Smith
http://ifomis.org
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10-9 m
DNA
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Organism
Organ
10-1 m
Tissue
Cell
10-5 m
Organelle
Protein
DNA
10-9 m
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New golden age of classification*
~ 30 million species
30,000 genes in human
200,000 proteins
100s of cell types
100,000s of disease types
1,000,000s of biochemical pathways
(including disease pathways)
*… legacy of Human Genome Project
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Organism
Organ
10-1 m
Tissue
Cell
10-5 m
Organelle
Protein
DNA
10-9 m
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FUNCTIONAL GENOMICS
proteomics,
reactomics,
metabonomics,
phenomics,
behaviouromics,
toxicopharmacogenomics
…
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The incompatibilities between different
scientific cultures and terminologies
immunology
genetics
cell biology
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have resurrected the problem of the unity
of science in a new guise:
The logical positivist solution to
this problem addressed a world in
which sciences are associated
with printed texts.
What happens when sciences are
associated with databases?
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… when each (chemical, pathological,
immunological, toxicological) information
system uses its own classifications
how can we overcome the
incompatibilities which become apparent
when data from distinct sources are
combined?
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Answer:
“Ontology”
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= building software artefacts
standardized classification systems/
controlled vocabularies
so that data from one source should be
expressed in a language which
makes it compatible with data from
every other source
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Google hits (in millions) 25.4.06
ontology
52.4
ontology + philosophy
2.7
ontology + information science 6.0
ontology + database
7.8
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A Linnaean Species Hierarchy
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(Small) Disease Hierarchy
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Combining hierarchies
Organisms
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Diseases
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via Dependence Relations
Organisms
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Diseases
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A Window on Reality
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A Window on Reality
Diseases
Organisms
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A Window on Reality
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How to understand species (aka
types, universals, kinds)
Species are something like invariants in
reality which can be studied by science
Species have instances: this mouse, this cell,
this cell membrane ...
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Entity =def
anything which exists, including things and
processes, functions and qualities, beliefs
and actions, documents and software
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Domain =def
a portion of reality that forms the subjectmatter of a single science or technology or
mode of study;
proteomics
radiology
viral infections in mouse
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Representation =def
an image, idea, map, picture, name or
description ... of some entity or entities.
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Analogue representations
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Representational units =def
terms, icons, photographs, identifiers ...
which refer, or are intended to refer, to
entities
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Composite representation =def
representation
(1) built out of representational units
which
(2) form a structure that mirrors, or is intended
to mirror, the entities in some domain
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The Periodic Table
Periodic Table
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Ontologies are here
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Ontologies are representational
artifacts
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What do ontologies represent?
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A
B
C
515287
521683
521682
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DC3300 Dust Collector Fan
Gilmer Belt
Motor Drive Belt
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instances
A
B
C
515287
521683
521682
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DC3300 Dust Collector Fan
Gilmer Belt
Motor Drive Belt
types
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Two kinds of composite
representational artifacts
Databases, inventories: represent what is
particular in reality = instances
Ontologies, terminologies, catalogs:
represent what is general in reality =
types
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What do ontologies represent?
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Ontologies do not represent
concepts in people’s heads
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Ontology is a tool of science
Scientists do not describe the concepts in
scientists’ heads
They describe the types in reality, as a step
towards finding ways to reason about (and
treat) instances of these types
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The biologist has a cognitive representation
which involves theoretical knowledge
derived from textbooks
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An ontology is like a scientific text;
it is a representation of types in reality
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Two kinds of composite
representational artifacts
Databases represent instances
Ontologies represent types
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Instances stand in similarity relations
Frank and Bill are similar as humans,
mammals, animals, etc.
Human, mammal and animal are types at
different levels of granularity
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types
substance
organism
animal
mammal
cat
siamese
frog
instances
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science needs to find uniform ways
of representing types
ontology =def a representational artifact whose
representational units (which may be drawn from
a natural or from some formalized language) are
intended to represent
1. types in reality
2. those relations between these types which
obtain universally (= for all instances)
lung is_a anatomical structure
lobe of lung part_of lung
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is_a
A is_a B =def
For all x, if x instance_of A then x
instance_of B
cell division is_a biological process
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Entities
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Entities
universals (species, types, taxa, …)
particulars (individuals, tokens, instances)
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Canonical instances within the
realm of individuals
= those individuals which
1. instantiate universals (entering into
biological laws)
2. are prototypical
 Canonical Anatomy: no Siamese twins,
no six-fingered giants, no amputation
stumps, …
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Entities
universals
junk
junk
instances
junk
example of junk particulars: desk-mountain
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Entities
human
inst
Jane
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Ontologies are More than Just
Taxonomies
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The Gene Ontology
7 million google hits
a cross-species controlled
vocabulary for annotations of
genes and gene products
deeper than Darwinianism
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When a gene is identified
three important types of questions need to
be addressed:
1. Where is it located in the cell?
2. What functions does it have on the
molecular level?
3. To what biological processes do these
functions contribute?
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GO has three ontologies
biological
processes
molecular
functions
cellular
components
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GO astonishingly influential
used by all major species genome projects
used by all major pharmacological research
groups
used by all major bioinformatics research
groups
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GO part of the Open Biological
Ontologies consortium
Fungal Ontology
Plant Ontology
Yeast Ontology
Disease Ontology
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Mouse Anatomy
Ontology
Cell Ontology
Sequence Ontology
Relations Ontology
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Each of GO’s ontologies
is organized in a graph-theoretical
structure involving two sorts of links or
edges:
is-a (= is a subtype of )
(copulation is-a biological process)
part-of
(cell wall part-of cell)
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The Gene Ontology
a ‘controlled vocabulary’
designed to standardize annotation of
genes and gene products
used by over 20 genome database and
many other groups in academia and
industry
and methodology much imitated
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The Methodology of Annotations
Scientific curators use experimental observations
reported in the biomedical literature to link gene
products with GO terms in annotations.
The gene annotations taken together yield a slowly
growing computer-interpretable map of
biological reality,
The process of annotating literature also leads to
improvements and extensions of the ontology,
which institutes a virtuous cycle of improvement
in the quality and reach of future annotations
and of the ontology itself.
The Gene Ontology as Cartoon
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cellular components
molecular functions
biological processes
1372 component terms
7271 function terms
8069 process terms
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The Cellular Component
Ontology (counterpart of anatomy)
membrane
nucleus
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The Molecular Function Ontology
protein stabilization
The Molecular Function ontology is
(roughly) an ontology of actions on the
molecular level of granularity
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Biological Process Ontology
death
An ontology of occurrents on the level of
granularity of cells, organs and whole
organisms
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GO here an example
a. of the sorts of problems confronting life
science data integration
b. of the degree to which formal methods
are relevant to the solution of these
problems
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Each of GO’s ontologies
is organized in a graph-theoretical data
structure involving two sorts of links or
edges:
is-a (= is a subtype of )
(copulation is-a biological process)
part-of
(cell wall part-of cell)
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Linnaeus
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Entities
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Entities
universals (kinds, types, taxa, …)
particulars (individuals, tokens, instances …)
Axiom: Nothing is both a universal and a particular
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Entities
universals*
*natural, biological, kinds
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Entities
universals
instances
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universals are natural kinds
Instances are natural exemplars of
natural kinds
(problem of non-standard instances)
Not all individuals are instances of
universals
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Entities
universals
instances
instances
penumbra of borderline cases
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Entities
universals
junk
junk
instances
junk
example of junk: beachball-desk
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Primitive relations:
inst and part
inst(Jane, human being)
part(Jane’s heart, Jane’s body)
A universal is anything that is instantiated
An instance as anything (any individual) that
instantiates some universal
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Entities
human
inst
Jane
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A is_a B
genus(B)
species(A)
instances
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is-a
D3* e is a f =def universal(e)  universal(f)
 x (inst(x, e)  inst(x, f)).
genus(A)=def universal(A)  B (B is a A 
B  A)
species(A)=def universal(A)  B (A is a B 
B  A)
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solve problem of false positives
insist that
A is_a B
holds always as a matter of scientific law
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nearest species
nearestspecies(A, B)=def A is_a B &
C ((A is_a C & C is_a B)  (C = A or C = B)
B
A
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Definitions
highest genus
lowest species
instances
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Lowest Species and Highest Genus
lowestspecies(A)=def
species(A) & not-genus(A)
highestgenus(A)=def
genus(A) & not-species(A)
Theorem:
universal(A)  (genus(A) or
lowestspecies(A))
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Axioms
Every universal has at least one instance
Distinct lowest species never share
instances
SINGLE INHERITANCE:
Every species is the nearest species to
exactly one genus
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Axioms governing inst
genus(A) & inst(x, A) 
B nearestspecies(B, A) & inst(x, B)
EVERY GENUS HAS AN INSTANTIATED
SPECIES
nearestspecies(A, B)  A’s instances are
properly included in B’s instances
EACH SPECIES HAS A SMALLER CLASS
OF INSTANCES THAN ITS GENUS
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Axioms
nearestspecies(B, A)
 C (nearestspecies(C, A) & B  C)
EVERY GENUS HAS AT LEAST TWO
CHILDREN
nearestspecies(B, A) & nearestspecies(C, A) &
B  C)  not-x (inst(x, B) & inst(x, C))
SPECIES OF A COMMON GENUS NEVER
SHARE INSTANCES
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Theorems
(genus(A) & inst(x, A))  B (lowestspecies(B) & B
is_a A & inst(x, B))
EVERY INSTANCE IS ALSO AN INSTANCE OF
SOME LOWEST SPECIES
(genus(A) & lowestspecies(B) & x(inst(x, A) &
inst(x, B))  B is_a A)
IF AN INSTANCE OF A LOWEST SPECIES IS AN
INSTANCE OF A GENUS THEN THE LOWEST
SPECIES IS A CHILD OF THE GENUS
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Theorems
universal(A) & universal(B)  (A = B or A
is_a B or B is_a A or not-x(inst(x, A) &
inst(x, B)))
DISTINCT UNIVERSALS EITHER STAND
IN A PARENT-CHILD RELATIONSHIP
OR THEY HAVE NO INSTANCES IN
COMMON
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Theorems
A is_a B & A is_a C
 (B = C or B is_a C or C is_a B)
UNIVERSALS WHICH SHARE A CHILD
IN COMMON ARE EITHER IDENTICAL
OR ONE IS SUBORDINATED TO THE
OTHER
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Theorems
(genus(A) & genus(B) & x(inst(x, A) &
inst(x, B)))  C(C is_a A & C is_a B)
IF TWO GENERA HAVE A COMMON
INSTANCE THEN THEY HAVE A
COMMON CHILD
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Expanding the theory
Sexually reproducing organisms
Organisms in general
To take account of development (child,
adult; larva, butterfly)
Biological processes
Biological functions
-- at different levels of granularity
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How to understand species (aka
types, universals, kinds)
Species are something like invariants in
reality which can be studied by science
Species have instances: this mouse, this cell,
this cell membrane ...
http:// ifomis.org
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Universal, Classes, Sets
A class is the extension of universal
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Class =def
a maximal collection of particulars
determined by a general term (‘cell’,
‘mouse’, ‘Saarländer’)
the class A
= the collection of all particulars x for
which ‘x is A’ is true
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Universals and Classes vs. Sums
The former are marked by granularity:
they divide up the domain into whole units,
whose interior parts are traced over.
The universal human being is instantiated
only by human beings as single, whole
units.
A mereological sum is not granular in this
sense (molecules are parts of the
mereological sum of human beings)
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A bad solution
Identify both universals and classes with sets in
the mathematical sense
Problem of false positives
adult  child
lion in Leipzig  lion
animal owned by the Emporer  mammal
mammal weighing less than 200 Kg  animal
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Sets in the mathematical sense
are marked by granularity
Granularity = each class or set is laid across
reality like a grid consisting
(1) of a number of slots or pigeonholes
each (2) occupied by some member.
Each set is (1) associated with a specific number
of slots, each of which (2) must be occupied
by some specific member.
A class survives the turnover in its instances:
both (1) the number of slots and (2) the
individuals occupying these slots may vary
with time
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But sets are timeless
A set is an abstract structure, existing
outside time and space. The set of human
beings existing at t is (timelessly) a
different entity from the set of human
beings existing at t because of births and
deaths.
Biological classes exist in time
Darwin: because the universals of which
they are extensions exist in time
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