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NATURAL TRANSFORMATION MODELS IN MOLECULAR BIOLOGY

Baianu, Professor Ion (1983) NATURAL TRANSFORMATION MODELS IN MOLECULAR BIOLOGY. [Conference Paper]

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Abstract

Molecular models in terms of Categories, Functors and Natural Transformations are introduced for unimolecular chemical transformations, multi-molecular chemical and biochemical transformations. Novel approaches to realization of Relational Biology Models of Complex System Biology are introduced in terms of Natural Transformations between Functors of Molecular Categories. Several applications of such natural transformations are then presented to protein biosynthesis, embryogenesis and nuclear transplant experiments. Other possible realizations in Molecular Biology and Relational Biology of Organisms are also suggested. Future developments will include: Fuzzy Relations in Biology; Categories of Lukasiewicz Logic Algebras and Intuitionistic Logic Algebras for Modeling of Complex Neural Network Processes; Stochastic, Genetic Networks in Lukn-Algebras, and Relational Biology Models of Complex Hormonal Controls.

Item Type:Conference Paper
Additional Information:New approaches to realization of Relational Biology Modeling of Complex System Biology in terms of Natural Transformations between Functors of Molecular Categories; Future developments will include: FUZZY RELATIONS ; Categories of Lukasiewicz Logic Algebras and Intuitionistic Logic Algebras for Modeling of Complex Neural Network Processes; STOCHASTIC, GENETIC NETWORKS in Lukn, L-ALGEBRAS; Relational Biology Models of Complex HORMONAL CONTROL and other METABOLIC PROCESSES. New approaches to realization of Relational Biology Modeling of Complex System Biology in terms of Natural Transformations between Functors of Molecular Categories; Future developments will include: FUZZY RELATIONS ; Categories of Lukasiewicz Logic Algebras and Intuitionistic Logic Algebras for Modeling of Complex Neural Network Processes; STOCHASTIC, GENETIC NETWORKS in Lukn, L-ALGEBRAS; Relational Biology Models of Complex HORMONAL CONTROL and other METABOLIC PROCESSES.
Keywords:Quantum Automata and Quantum Computation, Quantum Dynamics in terms of The Theory of Categories, Functors and Natural Transformations,Natural Transformations in Molecular Biology, Protein Biosynthesis Models, Embryogenesis models, Models of Nuclear Transplant Experiments in terms of Natural Transformations, Uni-molecular and multi-molecular transformations, Variable-Molecular-sets, molecular-set-variable (MSVs), Natural Transformations in Molecular Evolution
Subjects:Computer Science > Dynamical Systems
Computer Science > Complexity Theory
Computer Science > Artificial Intelligence
Biology > Theoretical Biology
ID Code:3675
Deposited By: Baianu, Professor I. C.
Deposited On:06 Jul 2004
Last Modified:11 Mar 2011 08:55

References in Article

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REFERENCES

Baianu, I. and Marinescu, M. 1968. Organismic Supercategories: I. Proposals for a General Unitary Theory of Systems. Bull. Math. Biophys., 30: 625-635.

Baianu, I. 1970. "Organismic Supercategories: II On Multistable Systems."Bull. Math.

Biophysics., 32: 539-561.

Baianu, I.1971 "Organismic Supercategories and Qualitative Dynamics of Systems."

Ibid, 33, 339-353.

Baianu, I. 1973. "Some Algebraic Properties of (M, R).Systems." Bull. Math. Biol., 35.

213-217.

Carnap. R. 1938. "'The Logical Syntax of Language" New York: Harcourt, Brace and Co.

Georgescu, G. and C. Vraciu 1970. "On the Characterization of Lukasiewicz Algebras." J Algebra, 16 4, 486-495.

Hilbert, D. and W. Ackerman. 1927. Grunduge.der Theoretischen Logik, Berlin: Springer.

McCulloch, W and W. Pitts. 1943. “A logical Calculus of Ideas Immanent in Nervous Activity” Ibid., 5, 115-133.

Pitts, W. 1943. “The Linear Theory of Neuron Networks” Bull. Math. Biophys., 5, 23-31.

Rosen, R.1958.a.”A relational Theory of Biological Systems” Bull. Math. Biophys., 20, 245-260.

Rosen, R. 1958b. “The Representation of Biological Systems from the Standpoint of the Theory of Categories” Bull. Math. Biophys., 20, 317-341.

Russel, Bertrand and A.N. Whitehead, 1925. Principia Mathematica, Cambridge: Cambridge Univ. Press.

Applications of the Theory of Categories, Functors and

Natural Transformations, N-categories, Abelian or NonAbelian to:

Automata Theory/ Sequential Machines, Bioinformatics, Complex Biological Systems /Complex Systems Biology, Computer Simulations and Modeling, Dynamical Systems , Quantum Dynamics, Quantum Field Theory, Quantum Groups,Topological Quantum Field Theory (TQFT), Quantum Automata, Cognitive Systems, Graph Transformations, Logic, Mathematical Modeling, etc.

1. Rosen, R. 1958. The Representation of Biological Systems from the Standpoint of the Theory of Categories." (of sets). Bull. Math. Biophys. 20: 317-341.

2. Rosen, Robert. 1964. Abstract Biological Systems as Sequential Machines, Bull. Math. Biophys., 26: 103-111; 239-246; 27:11-14;28:141-148.

3. Arbib, M. 1966. Categories of (M,R)-Systems. Bull. Math. Biophys., 28: 511-517.

4. Cazanescu, D. 1967. On the Category of Abstract Sequential Machines. Ann. Univ. Buch., Maths & Mech. series, 16 (1):31-37.

5. Rosen, Robert. 1968. On Analogous Systems. Bull. Math. Biophys., 30: 481-492.

6. Baianu, I.C. and Marinescu, M. 1968. Organismic Supercategories:I. Proposals for a General Unitary Theory of Systems. Bull. Math. Biophys., 30: 625-635.

7. Comorosan,S. and Baianu, I.C. 1969. Abstract Representations of Biological Systems in Supercategories. Bull. Math. Biophys., 31: 59-71.

8. Baianu, I. 1970. Organismic Supercategories: III. On Multistable Systems. Bull. Math. Biophys., 32: 539-561.

9. Baianu, I. 1971. Organismic Supercategories and Qualitative Dynamics of Systems. Bull. Math. Biophys., 33: 339-354.

10. Baianu, I. 1971. Categories, Functors and Automata Theory. The 4th Intl. Congress LMPS, August-Sept. 1971.

11. Baianu, I. and Scripcariu, D. 1973. On Adjoint Dynamical Systems. Bull. Math. Biology., 35: 475-486.

12. Rosen, Robert. 1973. On the Dynamical realization of (M,R)-Systems. Bull. Math. Biology., 35:1-10.

13. Baianu, I. 1973. Some Algebraic Properties of (M,R)-Systems in Categories. Bull. Math. Biophys, 35: 213-218.

14. Baianu, I. and Marinescu, M. 1974. A Functorial Construction of (M,R)-Systems. Rev. Roum. Math. Pures et Appl., 19: 389-392.

15. Baianu, I.C. 1977. A Logical Model of Genetic Activities in Lukasiewicz Algebras: The Non-Linear Theory., Bull. Math. Biol.,39:249-258.

16. Baianu, I.C. 1980. Natural Transformations of Organismic Structures. Bull.Math. Biology, 42:431-446.

17. Warner, M. 1982. Representations of (M,R)-Systems by Categories of Automata., Bull. Math. Biol., 44:661-668.

18. Baianu, I.C.1983. Natural Transformations Models in Molecular Biology. SIAM Natl. Meeting, Denver, CO, USA.

19. Baianu, I.C. 1984. A Molecular-Set-Variable Model of Structural and Regulatory Activities in Metabolic and Genetic Systems., Fed. Proc. Amer. Soc. Experim. Biol. 43:917.

19. Baianu, I.C. 1987. Computer Models and Automata Theory in Biology and Medicine. In: "Mathematical models in Medicine.",vol.7., M. Witten, Ed., Pergamon Press: New York, pp.1513-1577.

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