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July 1, 2008, A Summary of 2,000 pages recently copyrighted by the Author

Abstract:

Organismic supercategories have flexible, algebraic and topological structures that transform naturally under heteromorphisms or heterofunctors. Different approaches to Relational Biology and Biodynamics, developed by Nicolas Rashevsky, Robert Rosen and by the author, were previously compared with the classical approach to qualitative dynamics of systems. Natural transformations of heterofunctors in organismic supercategories lead to specific modular models of a wide range of life processes involving quantum dynamics in genetic systems, ontogenetic development, fertilization, regeneration, neoplasia and oncogenesis. Axiomatic definitions of categories and supercategories of Complex Biological Systems allow for dynamic computations of cell transformations that may lead to neoplasia, and in certain intriguing cases to malignancy. The concepts of quantum automata and quantum computation are applied in the context of quantum genetics and genetic networks to study their nonlinear dynamics. In a previous publication (Baianu,1971a) the formal concept of quantum automaton was introduced and its possible implications for genetic and metabolic activities in living cells and organisms were considered. This was followed by a report on quantum and abstract, symbolic computation based on the theory of categories, functors and natural transformations (Baianu,1971b). The notions of topological semigroup, quantum automaton,or quantum computer, were then suggested with a view to their potential applications to the analogous simulation of biological systems, and especially genetic activities and nonlinear dynamics in genetic networks. Further, detailed studies of nonlinear dynamics in genetic networks were carried out in categories of n-valued, Lukasiewicz Logic Algebras that showed significant dissimilarities (Baianu, 1977; Baianu et al., 2006-2008) from the oversimplified Boolean models of human neural networks.A categorical and Topos framework for Lukasiewicz Algebraic Logic models of nonlinear dynamics in complex functional genomes and cell interactomes is proposed. Lukasiewicz Algebraic Logic models of genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable 'next-state functions' is extended to a Lukasiewicz Topos endowed with a n-valued Lukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis. Novel results and specific applications concerning cell interactomics, dynamics of genetic-proteomic networks and signaling pathways, development, regeneration, the control mechanisms of cell dynamic programming in cells, neoplastic transformations and oncogenesis are then derived on the basis of complex system modeling and biomolecular network representations in categories of Lukasiewicz Logic Algebras and Lukasiewicz-Topos. Molecular models in terms of categories, functors and natural transformations were then formulated for unimolecular chemical transformations, as well as multi-molecular chemical and biochemical transformations. Previous applications of computer modeling, classical automata theory, and relational biology to molecular biology, oncogenesis and medicine were extensively reviewed Novel approaches to solving the realization problems of Relational Biology models in Complex System Biology are introduced in terms of natural transformations between functors of such biomolecular supercategories. Natural transformations of organismic superstructure were developed for modelling protein biosynthesis, embryogenesis and nuclear transplant experiments. Other possible realizations in Molecular Biology and Relational Biology of Organisms are here suggested as a novel approach to Bioinformatics to Interactomics and Relational Quantum Genetics. http://www.kli.ac.at/theorylab/Keyword/R/RelationalBio.html http://cogprints.org/3674/ http://www.informatics.bangor.ac.uk/public/mathematics/research/preprints/07/cathom07.html

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