0.1 Natural Transformations of Organismic Structures
Biological systems, or living organisms are characterized by relational structures and
their dynamic transformations which can be represented as natural transformations of
heterofunctors in organismic supercategories(OS). Such OS-structures can be specified
mathematically either by using the Yoneda-Grothendieck Lemma and construction, or they can
be directly derived by a mathematical interpretation of the first ten axioms of ETAS,
plus two additional axioms defining both ‘self-repair’ of metabolic components and
complete reproduction in terms of genetic coding, translational genomics and epigenetic
meta-processes.
Natural transformations of organismic structures allow for the extension of both Rashevsky’s
organismic set theory and Robert Rosen’s Metabolic-Replication Systems Set-Categorical
approach to relational biology based on the concepts of molecular set variables and variable
categories; the latter concepts are generalizations of Anthony Bartholomay’s definition of
molecular sets, and the consideration of variable categories with structure instead of
only the discrete topology of sets. Further details concerning mathematical, logical and
complex modeling are provided in the following list of publications and related web (html)
links.
References
[1] I.C. Baianu: 1977, A Logical Model of Genetic Activities in Łukasiewicz Algebras:
The Non-linear Theory. Bulletin of Mathematical Biophysics, 39: 249-258.
[2] I.C. Baianu: 1980, Natural Transformations of Organismic Structures. Bulletin of
Mathematical Biophysics 42: 431-446.
[3] I.C. Baianu: 1983, Natural Transformation Models in Molecular Biology., in
Proceedings of the SIAM Natl. Meet., Denver, CO.; An Eprint is here available .
[4] I.C. Baianu: 1984, A Molecular-Set-Variable Model of Structural and Regulatory
Activities in Metabolic and Genetic Networks., FASEB Proceedings 43, 917.
[5] I.C. Baianu: 1987a, Computer Models and Automata Theory in Biology and
Medicine., in M. Witten (ed.), Mathematical Models in Medicine, vol. 7., Pergamon Press,
New York, 1513-1577; CERN Preprint No. EXT-2004-072:.
[6] I.C. Baianu: 1987b, Molecular Models of Genetic and
Organismic Structures, in Proceed. Relational Biology Symp. Argentina; CERN Preprint
No.EXT-2004-067:MolecularModelsICB3.doc.
[7] I.C. Baianu, Glazebrook, J. F. and G. Georgescu: 2004, Categories of Quantum
Automata and N-Valued Łukasiewicz Algebras in Relation to Dynamic Bionetworks,
(M,R)–Systems and Their Higher Dimensional Algebra, Abstract of Report is here
available as a PDF and html document
[8] R. Brown R, P.J. Higgins, and R. Sivera.: “Non–Abelian Algebraic Topology”,(in
preparation). available here as PDF.
[9] R. Brown, J. F. Glazebrook and I. C. Baianu: A categorical and higher dimensional
algebra framework for complex systems and spacetime structures, Axiomathes
17:409-493. (2007).
[10] L. Löfgren: 1968. On Axiomatic Explanation of Complete Self–Reproduction. Bull.
Math. Biophysics, 30: 317-348.
[11] Contributed Review. 2009. GNUL download. “DNA Molecular Models and
Dynamics.”
