=Paper=
{{Paper
|id=None
|storemode=property
|title=Substance concentrations as conditions for
the realization of dispositions
|pdfUrl=https://ceur-ws.org/Vol-754/hastings_krmed2010.pdf
|volume=Vol-754
}}
==Substance concentrations as conditions for
the realization of dispositions==
https://ceur-ws.org/Vol-754/hastings_krmed2010.pdf
Substance concentrations as conditions for
the realization of dispositions
Janna Hastings1*, Christoph Steinbeck1, Ludger Jansen2 and Stefan Schulz3
1
European Bioinformatics Institute, Hinxton, UK
2
Department of Philosophy, University of Rostock, Germany
3
Institute for Medical Informatics, Statistics and Documentation, Medical University
of Graz, Austria
Abstract. Ontologies aim to represent what is general, by means of
universal statements. In contrast, dispositional predications capture
knowledge about what is likely to happen if a certain set of circumstances
obtain, which is crucial in investigative research such as in drug
discovery and systems biology, where entities which are constitutionally
dissimilar can nevertheless have similar behavior in a biological context.
While such dispositional properties are increasingly included in
biomedical ontologies, the circumstances under which the dispositions
are realized are seldom explicitly modeled, and doing so is problematic
due to the necessary restriction to binary relations in OWL ontologies. In
this paper we address this shortcoming, focusing on the bioactivity of
small molecules at varying levels of concentration within a living organ-
ism as our problem domain, although our approach is generalizable to
other problems. We discuss the ontological nature and representation of
dispositions and their realization; consider the nature of concentrations
and their representation; and finally we detail an approach to linking
dispositions to the conditions for their realization which regards
conditions as triggers for the process in which the disposition is realized.
1. Introduction
A fundamental tenet of ontologies in general and biomedical ontologies in particular is
to make statements that are universally true. These statements are often considered to
be statements about universals that, in turn, imply universally quantified statements
about the instances of the universals involved (Smith, 2006) that is, they describe
categorical properties. On the other hand, dispositional or functional properties are
often contrasted with categorical properties because they specify what will occur if the
correct circumstances obtain, which is a hypothetical property (Arp, 2008).
Dispositional or functional views on biomedical information are crucial in investigative
research such as in drug discovery and systems biology, where entities which are
constitutionally dissimilar can nevertheless have surprisingly converging behavior in a
biological context; and vice versa. Thus we seem to face a dilemma: On the one hand,
dispositional statements seem to be hypothetical rather than categorical, but on the
other hand they are essential to a proper description of the biomedical domain, thus are
increasingly being included in biomedical ontologies, examples of which are the
ChEBI ‘roles’ (de Matos, 2010) and the Gene Ontology molecular functions (GO
Consortium, 2000).
This dilemma is dissolved, we will argue, by recognizing that what is hypothetical in a
disposition ascription is not the ascription of the disposition itself, but the expectation
of its realization, which is conditional. The hard problem that remains is how to
represent the realization conditions of a biomedical disposition, which are seldom
explicitly included in biomedical ontologies. One reason for this may be the technical
difficulty in adequately capturing the required nuances within a formalism allowing for
only binary relations, such as OWL (Schulz, 2009).
In this paper we address this shortcoming, focusing on the bioactivity of small
molecules at varying levels of concentration within a living organism as our problem
domain, although our approach is generalizable to other problems. First, we discuss the
ontological nature and representation of dispositions and their realization; then we
consider the nature of concentrations and their representation. Finally, we explicitly
link dispositions to the conditions for their realization.
2. Background
We will shortly present the biochemical and ontological background needed for our
discussion.
2.1. Biochemical background
Small molecule bioactivity: Small molecules such as drugs or metabolites are essential
ingredients in all the processes of life. The presence or absence of varying quantities of
specific kinds of molecules can mean the difference between life and death. The
biochemical mechanisms underlying the bioactivity are extremely varied and complex,
although the basic mechanism is the binding (usually involving several non-covalent
chemical interactions) of the small molecule to some organic macromolecular target.
These mechanisms are regulated by the surrounding environmental conditions. For
example, the transport of oxygen in the human bloodstream from the lungs to the cells
where it is consumed is allosterically regulated, displaying sigmoidal behavior as a
function of the concentration of the substrate (oxygen) (Berg 2002). The partial
pressure of oxygen in the lungs is 100 torr, while that in the tissues is 20 torr. The
change in oxygen pressure results in a change in the binding affinity of the oxygen,
which results in a release of around 66% of the carried oxygen. The key is the change
in binding affinity which depends on the concentration of the substrate.
2.2. Ontological background
Dispositions: In the aftermath of the verificationism of the logical positivist movement,
dispositions have long been regarded as dubious or superfluous. Meanwhile, however,
their importance for science has been rediscovered (Cartwright, 1989) and dispositions
are again being discussed in Ontology (Mumford, 1998; Molnar, 2003). We will here
follow the Basic Formal Ontology (BFO) (IFOMIS, 2010) and treat dispositions as
dependent continuants. Continuants are entities that have no temporal parts, but exist as
a whole at every moment of their existence. They are dependent because they need a
bearer in order to exist (as all properties and relations do) (Arp, 2008; Jansen 2008).
Dispositions are special realizables, that is, they are related to processes which are their
realizations: dissolving in water is the realization of water solubility, and conducting
electricity the realization of conductibility.
Concentrations: Concentrations are system properties, i.e. they are properties of a
complex bearer, a mixture, and a concentration ascription describes how much of one
ingredient (or fraction) is contained in the mixture. Like dispositions, concentrations
cannot exist without a bearer; they, too, are dependent continuants. Concentrations are
relational properties: a concentration is always a concentration of something in
something, e.g., of alcohol in an alcohol-water mixture. Often, as in this case, the
mixture in question is a solution, and the concentration in question is the concentration
of the solute in the solvent. Concentrations relate two amounts of matter. In this aspect
the ontological notion of concentration is stricter than the common sense concept of
concentration where we say "100% alcohol" but refer to a pure substance and not a
mixture, or where we characterize a non-alcoholic beverage by "0% alcohol
concentration" but mean the complete absence of alcohol in the mixture.
3. Models
3.1. Dispositions
Dispositional properties can be viewed in two ways. On the one hand, dispositions
point to their realization in the future, which is only hypothetical. For example,
considering the disposition of aspirin to treat pain, we find that there are many
molecules of aspirin which never treat any pain and many instances of pain which are
never treated by aspirin. On the other hand, dispositions are part of the present state of
the things they are ascribed to. And in so far as they are present properties of their
bearers they are neither hypothetical nor a matter of probability only. It is not the
disposition, but its realization which is hypothetical. We can formalize this
dispositional property of aspirin in terms of its realization along the following lines:
PortionOfAspirin ⊑ ∃ bearerOf.(Disposition ⊓
∀ hasRealization.(Treating ⊓ ∃ hasParticipant.Pain))
Using this pattern we express that for each particular portion of aspirin there is a
particular disposition of a certain kind. This disposition is then described by
constraining the kind of process by which it can be realized. But, a portion of a dozen
aspirin molecules is not sufficient to treat pain in any organism. Furthermore, a
hundred 300mg tablets ingested at the same time may cause complications such as
severe bleeding and intoxication before ever treating pain. Yet in the formula above,
these conditions are not described. We will address this point later, as we now turn to a
model of concentrations.
3.2. Concentrations
Let us take a simple example referring to instances of substance portions, e.g. a
particular mixture of 10g of water with 10g of glucose. In discussing this example, we
will use lower case letters for particulars and initial capitals for universals. We have
three entities of interest:
(i) the water/glucose mixture wgmix, (ii) the water fraction wcoll, i.e. the collection of all
water molecules, and (iii) the glucose fraction gcoll, i.e. the collection of all glucose
molecules. Following Schulz (2006), we distinguish between molecule collections
(homogeneous pluralities of molecules of the same kind) and compounds (entities that
are defined as sums of non-overlapping sortally distinct parts). Mixtures are a special
case of compounds, and the fractions are their non-overlapping but maximally mixed
components.
wcoll and gcoll are components of wgmix; wgmix is the mereological sum of wcoll and gcoll.
These three particulars bear the following qualities:
They have a mass (wgmix 20g; wcoll and gcoll 10g each);
They have a defined number of molecules (cardinality);
Only wgmix has a defined volume, as wcoll and gcoll are scattered objects.
We turn to the question: what are the concentrations and which entities are the bearers?
Note that there are different kinds of concentration, the most important in biology and
medicine being:
mass percentage: mass of gcoll /mass of wgmix
mole fraction: number of molecules in gcoll / number of molecules in wgmix
mass/volume percentage: mass of gcoll /volume of wgmix
In all cases we have
a portion of a mixture of a kind (here wgmix ), which bears qualities like mass,
volume, temperature;
fractions which are component of this mixture (here gcoll and wcoll ), but which are
not mixture themselves, and which bear qualities like mass (but not volume);
concentration of fractions in mixtures, e.g. gcoll in wgmix.
To formalize this ontologically, we observe that all particular collections of glucose
molecules instantiate the class Gcoll, and have granular (repeated multitudinously) parts
which instantiate G:
G ⊑ EntireMolecule
Gcoll ⊑ HomogeneousCollection
Gcoll ≣ ∃ hasGranularPart.G ⊓ ∀ hasGranularPart.G
For a mixture with several components, its "fractions":
WGmix ⊑ Mixture
WGmix ⊑ = 1 hasComponent.Gcoll ⊓ =1 hasComponent.Wcoll
where each component is a distinct fraction of the mixture. A concentration can be
ascribed to a particular homogeneous collection iff this collection is a component of a
mixture, as expressed by the axiom:
∃ bearerOf.Concentration ≡ Homogeneous collection ⊓ ∃ componentOf.Mixture
with
Concentration ⊑ ∃ inheresIn.(HomogeneousCollection ⊓ ∃ componentOf.Mixture)
The class Concentration can then further be specified in terms of the kind of
concentration as explained above, e.g.
VolumeConcentration ⊑ Concentration
MassConcentration ⊑ Concentration
as well as in terms of the participating substance portions:
BloodGlucoseVolumeConcentration ≡ VolumeConcentration ⊓
∃inheresIn.(PortionOfGlucose ⊓ ∃ componentOf.PortionOfBlood)
This states that wherever there is a blood glucose volume concentration there must be a
portion of glucose and a portion of blood. In contradistinction to the glucose/water
example we here have blood as an overly complex mixture with probably tens of
thousands of fractions. The example demonstrates, however, that the exact composition
of the mixture does not need to be specified. Quantitative measures of concentrations,
as referred to in common discourse, are attributes of instances of Concentration.
3.3. Conditional realization of dispositions
We now have a formalism for defining dispositions, in terms of the process in which
they are realized; and concentrations, in terms of the substances from which they are
composed. We here attempt to relate the latter as a precondition for the realization of
the former. We need to create a relationship between a disposition, a condition
(concentration), and a realization in a biological process. This cannot be
straightforwardly represented in OWL as the required relationship is ternary rather than
binary. Indeed, if the probability of the realization of the disposition is also made
explicit, the resulting relationship is quaternary: see the
Has_realization_under_conditions_with_probability relation introduced in Schulz &
Jansen (2009). The challenge at this point is to do justice to the ontology of
dispositions, within the restrictions of OWL. In section 3.1, we suggested the following
example of a disposition ascription:
PortionOfAspirin ⊑ ∃ bearerOf.(Disposition ⊓
∀ hasRealization.(Treating ⊓ ∃ hasParticipant.Pain))
In section 3.2, we were able to define the volume concentration of aspirin in the blood
along the following line:
BloodAspirinVolumeConcentration ≡ VolumeConcentration ⊓ ∃inheresIn.
(PortionOfAspirin ⊓ ∃ componentOf.PortionOfBlood)
We know that a certain concentration of aspirin in the blood is necessary in order to
have the pain relieving disposition of aspirin realized. We can revise our suggestion
from section 3.1 in order to incorporate this fact by using our new way to express
concentrations plus a new relation hasTrigger. While a full discussion of this relation
would require more space than we have available here, for the purpose of this study it
is sufficient to interpret a trigger rather simplistically as a circumstance without which
a process cannot occur. Combining these tools, we get:
PortionOfAspirin ⊑ ∃ bearerOf.(Disposition ⊓ ∀ hasRealization.(Treating ⊓
∃ hasParticipant.Pain ⊓ ∃ hasTrigger. SufficientConcentration))
where, of course, SufficientConcentration ⊑ BloodAspirinVolumeConcentration.
4. Discussion
The problem of the ontology of dispositional properties is not a new one, although its
relevance to biomedical informatics is recent. Many representatives of the formal
ontology community defend the perspective that representations of non-categorical
properties lie at the borderline or outside the realm of ontology (Rector, 2008; Schulz,
2009) and emphasize that the current representational formalisms such as OWL are not
well suited to express modal or probabilistic knowledge and lead to unintended models
if used to represent, say, the knowledge that a disease X may have the symptom Y, or
that a molecule A tends to interact with a molecule B (Schulz, 2010). Others advocate
the inclusion of dispositions and tendencies in their ontologies (Schulz & Jansen, 2009;
Jansen, 2007), and our approach aligns with the latter. Key to our approach is the
analysis of dispositional properties as being necessarily realized if the correct
circumstances obtain, thus allowing us to reformulate the circumstances as a trigger for
the process of realization.
Dispositional properties are closely related to probabilistic knowledge representation.
The expression of such probabilistic knowledge within OWL ontologies has been
discussed by Rector et al. (2008), who propose several workarounds including in
particular the introduction of an explicit construct for ‘may’ into the language syntax
and semantics to accommodate relations of possibility, although it is still not clear how
the magnitude of a probability should be captured in their proposed formalism.
Probabilistic logics such as those described in Lucasiewicz (2008) provide a much
more expressive formalism for this type of knowledge, but at the expense of additional
complexity which may not be acceptable to the ordinary domain scientists who create
and/or make use of biomedical ontologies.
Our analysis has been in the context of molecular bioactivity and concentrations, but
could easily be extended to dispositional properties and conditions in general. More
challenging will be the extension to a general treatment of conditions for ontological
assertions, as the truths of most domain descriptions in biomedical science can be
regarded as contextual truths which apply under certain circumstances. Such contextual
truths include the composition and arrangement of bodily organs in organisms (the
circumstances here are "normality" or "canonicity", and additionally "health" (Schulz
& Hahn, 2007)), and the shape of molecular entities (where the circumstances include
temperature, pressure, and environment).
5. Conclusion
Much recent work in biomedical ontology has focused on clarifying the top-level
distinctions between kinds of entities in ontologies. Our work focuses on one
particularly problematic kind of entity, viz. dispositional properties, which require a
particular set of circumstances to obtain in order to be realized, regarding the relevant
circumstances as a necessary trigger for realization. We provide an ontological analysis
of concentrations as one kind of circumstance.
We see this work as a contribution to the analysis of dispositions and in particular to
the explicit formalization of the conditions under which dispositions are realized.
Future work will explore the representation of conditional properties of biomedical
objects beyond dispositional properties, and extend our strategies to other triggering
circumstances, like temperature, (blood) pressure or infections.
Acknowledgements
This work was supported by (i) the BBSRC, grant agreement number BB/G022747/1
within the "Bioinformatics and biological resources" fund; and (ii) by the DFG, grant
agreement number JA 1904/2-1, SCHU 2515/1-1 GoodOD (Good Ontology Design).
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