Wednesday, January 04, 2006
New
discussion about signal pathways
and complex ontology
This is part of a discussion that will be moved to a Wiki page soon.
I am trying to get some notational structure to this issue of nested complexes, each level having emergence of function within the environment. The specific form and function of the emergence results from an ordering of events and how interactions occur. [1]
This is the very definition of natural complexity and stratification of organizational mechanisms.
***
First, I am conjecturing, as others have done also, that complexity comes from interactions, and that the notions of Rossler about endophysics and exophysics are proper. With these notions, the reactant has an internal "self" or autopoiesis (Maturana) that can vary responses based on state changes internal to the reactant. Work on Ising model, planar rotators, indicates that the internal dynamics of loosely coupled systems create emergent fields, field potentials, which then (the fields) interact with environment to produce a "selection" (Edelman might agree with this) of how and in what order participants express during the unseen part of the full expression of the complex.
Seeing the mechanisms involved in producing what is now the unseen part is of course the objective.
I follow Robert Rosen category theory on this question of interactions,
<quote: from Judith Rosen's recent discussion about her father's
work>
In my father's view, complexity has to do with relational
interaction. In natural systems, the
interaction between two entities can have effects that could not be predicted
based on any amount of knowledge about those two entities, in an of
themselves. This is complexity.
Furthermore, the way any
interaction takes place is as important as the interaction, itself. This comes
down to matters of relational context; to understand the effects of any given
interaction, the relational context would have to be known as well as the
interacting parties. "
<end quote>
So to the creation of some notation that maps to real OWL capabilities:
If we have a set of participants we might label this set with the letter A (for atoms).
As in physical chemistry, we find a set of elemental participants, molecules, which are then participants in proteins, and proteins in metabolic signal pathways.
But as was pointed out by Rosen, and Rashensky, the formalization of cell biology has these, so far not formalized, issues (that Geeta also addresses) related to how and when things occur.
The core issue to formalization might be the capture of situational details, and there might be a limit to the application of categorical abstractions (terms that logics can address) to modeling situational details. We just do not know.
But we might ignore individual differences (ie form categories) and "say" that a subset of the known atoms are aggregated together by some process of interaction. When we do this we humans make mental inductions of categories, and the resulting mental symbols are then perhaps encodable as "concepts" in ontological models. OWL organizes concepts into hierarchical classes. This imposes a useful "schema" but also imposes a metaphysics, ie that these sub-class codification is sufficient, that may or may not be proper in modeling the emergent aspects of signal pathways.
Other non mainstream, ontologies modeling does not focus on class, subclass schema. In these, the minimal information structure is a n-ary,
< (a(1) , a(2), . . . , a(n) >
where n is determined either situationally, or over time, as an aggregation of process like data mining or human construction. These types of ontological modeling have not become "standards" as yet. More than three groups are working in this area.
The non standard work generally holds to the principle that class-subclass schema, and first order logics should omitted during some type of formative measurement of observations and then added as details become available and class/concept categorization can be made. Without the class-subclass schema, the logic part of OWL has nothing to work with. I need to make a comment about the biopax-level1, because it is OWL in nature. This seems perfectly proper given the situation we have; very large and not well integrated data from the types of experimental apparatus that Geeta has referred to. This is why I have referred to this biopax-level1 as a "data ontology".
So some subset, B, of the set A is aggregated to produce a complex (whole) with "functional properties" { p(i) }. One is dealing with incomplete information, in that the set B is a conjecture due to measurement issues; the conformational aspects and other situational details are not always completely known, or even the science to understand might not yet be available. The functional properties of the resulting complex might be incomplete, or incorrect due to measurement and categorization issues.
This leads then into the Mills logic that the Soviets partially developed:
.
The feeling we have is that new formalization really only requires new language and the understanding of complexity as being "self entailed within the dynamics of the moment", however channeled by the functional needs of the larger system.
This new formalism requires one to step away from the hard formalism like OWL, since the formalism is composed of categorical abstractions over invariances that are observed (such as "functional properties" or "participants".) Too much of the casual elements are not observed and encoded as classes and subclasses.
However, and this is a big however, the "data ontology" is precisely what the bioinformatics community needs first. The development of an ontology reflecting the complexity issues can come second.
Paul Prueitt
[1] A system of nested complexes might be the model for a number of natural systems, including gene and cell expression. Business Ontology, based on class subclass hierarchy, has similar strengths and limitations as those seen in bioinformatics. An additional note on the metaphor between complex business interactions and complex biological reactant interactions is given in the next note à [118]