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of partial identity, since in this case the identity of amino acid residues (i.e. the entities) is
immaterial. All identities and similarities are true only at the given level of description (e.g.
backbone conformation, amino acid composition, etc.).
A
B
Analogy
Literal
Similarity
Identical
Shape
Identical
Structures
Abstraction
Similar
Str uctures
Common
Topol ogy
Metaphor
Dissimilar
Str uctures
Common
Substructures
Identical
Composition
Mere
Appearance
Anomaly
Attributes shared
Substructures shared
Figure 4
. Identity, different kinds of similarity and non/identity can be pictured as
regions in a plot of shared entities vs. shared relationships. This representation was
developed by Dedré Gentner for narrative descriptions [17] (A), but can be extended
to molecular descriptions as well (B).
Figures 4 implies that similarity of two molecules can be captured if we can define
equivalencies between their constituents, i.e. if we match the similar parts of the two
descriptions to each other. Finding common substructures relies on matching, and some
numerical parameter of matching is used in most cases as a measure of similarity. For
example, two 3D structures are obviously similar if more than 90% of their alpha carbons
can be superposed. We mention that matching is used not only for establishing similarity,
but also for finding complementarity, such as surface-complementarity used in molecular
docking, or strand-complementarity used in the analysis of anti-sense RNA.
Based on the above concept we can define two further concepts, similarity groups
and functional units. The similarity group is such a group of molecules that are connected
by structural similarity. This similarity can be local or global (see 2.3) or it can be general
or specific (section 3.3). Biologically important similarity groups, such as those of protein
domains belong to the latter class, as all group members are characterised by a common
sequence-description or a common fold-description.
Functional units denote a group of molecule that jointly fulfil a biological function.
Enzymes, regulators and substrates of a metabolic pathway are examples of functional unit.
Members of a functional unit are similar in their common function, but they do not need to
be structurally similar. This is thus a contextual similarity, as opposed to the structural
similarity.
1.3 Elements of molecular descriptions
1.3.1 Focusing of descriptions
The entity-relationship framework and the underlying category definitions can be used to
construct a very large number of description that can focus on various aspects of a
molecular model [13]. One of the practical ways of generating simplified descriptions is to
concentrate on parts of a molecule that are important for the actual goal of the analysis.
Starting from a generalized theoretical model containing detailed descriptions of all entities
and relationships in various forms, one can derive simplified descriptions by omitting some
of the descriptors. For example, a hydrophobicity plot is a description of protein structure
wherein the entities are amino acid residues described in terms of only two parameters, the
sequence position and the residue hydrophobicity index. On the other hand fold
