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and relationships within a model. In terms of mathematical form, the descriptors of the
properties can be continuous, discrete or binary variables, even statements in human
language.
Similarity group (Cluster)
Neighborhood
Assembly
Pathway
Complex
Genome
Hierarchical Tree
Food network
Genetic network
Figure 2.
Molecular structures can be represented as entities and relationships [1,
13]. Implicit to a structure is the description of the underlying concepts (entities and
relationships as well as their properties), which can be summarized in an ontology
[14]. The same principle can be easily extended to genomic and “systems biology”
applications.
Entity/relationship models have been used in psychology as well. Erich Goldmeier's
“Similarity of visually perceived forms” defines similarity in terms of partial identities that
may include a varying proportion of entities and relationships [15, 16]. If we apply this
definition to molecular graphs such as shown in Figure 2, we arrive to a plausible
definition: Two molecular graphs are similar if they have a common sub-graph (Figure 3).
Figure 3.
Molecular similarity as sub-graph isomorphism. Similarity of structures
can be defined as a common sub-graph shared by two entity-relationship
descriptions.
Dedré Gentner [17] drew a map classifying the similarities of narrative descriptions
(Figure 4a), which can be extended without difficulties to the description of protein
structures (Figure 4b). For example, molecular descriptions are considered identical if they
consist of the same substructures and relationships. If two descriptions only share the
substructures but not the relationship, they are identical in terms of composition only. If the
relationships are identical, but not the substructures, we speak about equivalent topology.
Alpha-helices (and other protein secondary structure elements) are examples for this kind
