Fibonacci Application to the DNA B-form double helix structure analyses

Goncharenko V.V., Mikulionok I.O., Tkachenko A.O., Gerasimov G.V.

National technical university of Ukraine “Kyiv polytechnic institute”, Kyiv, Ukraine

 

Golden ratio of Fibonacci was shown to be in accord with the general principles of an orderly spiral evolution of forms from primitive to advanced types. In every repeated evolution cycles living systems have progressed to the point which are more than previous by a factor of 1.534 [1]. From the “golden ratio” of Fibonacci standpoint the DNA B-form double helix structure analyses are of interest to the bionic engineering model researchers. This form of DNA has a two groove in its spirals, with a ratio of phi in the proportion of the major groove to the minor groove. [2].

This model is characterized by the standard parameters: the external diameter of a rod-like DNA B-form double helix equals 2.0 nm; the helical repeat (the number of base pair per turn): ; the helical rise per base pair:  nm [3]; helical twist per base pair

                                                     .                                                                (1)

This model is characterized also by the alternative parameters: the wining angle of B-DNA:  [4]; the helical backbone arc length per base pair:  nm; the effective diameter of backbone:  nm; the hydration water occupies 50 percent of the intermolecular volume of the DNA B-form double helix [5,6].

When employing these “golden ratio” of Fibonacci as the helical twist per base pair () the helical repeat  has been adjusted by the application of equation (1). When employing the helical repeat  the winding angle  (Fibonacci number) of the application of equation (2)

                                                                                                        (2)

and accurate definitions of the helical backbone arc length ( nm).

It is common knowledge that an effective diameter dw of the hydrated water molecule equals 0.3 nm [7].

The external bimolecular layer volume of hydrated water  nm3 on the DNA B-form double helix can be calculated from the external open backbone surface

                                                                .                                                                    (3)

The intermolecular hydrated water volume , where intermolecular volume of the DNA B-form double helix per base pair can be determined as

                                              nm3.                                            (4)

The hydrated water concentration in the DNA B-form double helix  (near the Fibonacci number) can be determined as

                                             .                                           (5)

Adult human organisms contain from 60 percent (near the Fibonacci number) to 80 percent of water [8,9].

From the results obtained it may be concluded that:

– the Fibonacci “golden ratio” provides a useful tooling of the serious scientific basis;

– the detections of the universal parameters like the Fibonacci “golden ratio” in the DNA B-form double helix structure ranked among the convincing arguments for a conception of the intellect design [10] which have found scientific use.

 

References

1. Fisher, R. Fibonacci Applications and strategies for traders. – New York, John Wiley and Sons. Inc., 1993.

2. Goncharenko, V.V.; Loboda, P.I.; Goncharenko, M.V.; Verba, A.Yu.; Gaydar, V.S. Integration of DNA and Bionical Engineering. International Journal of Applied Mechanics and Engineering. 2011, Vol.16, N 2. pp. 359–369.

3. Goncharenko, V.V.; Goncharenko, M.V.; Rudometov, S.V.; Fedoseeva, A.E. Mathematical basis of Helical Rise of the DNA B-form double helix. Mediterranean–East–Europe meeting multifunctional nanomaterial’s: “Nano-Euro-Med 2011”: International scientific conference. Uzhgorod (Ukraine), 2011, p. 205.

4. Goncharenko, V.V.; Loboda, P.I.; Goncharenko, M.V.; Tkachenko, A.O.; Heilmaier, M. What is the veritable winding angle value of the DNA B-form double helix? Fullerenes and Nanostructures in condensate medium: Collection of scientific papers. Minsk, Publishing Center of BGU, 2011, pp. 396–401.

5. Goncharenko, V.V.; Loboda, P.I.; Goncharenko, M.V.; Mozyrskaya, M.V.; Heilmaier, M. Bionical model: computational analysis of Hydration of the major and minor grooves separately for stretched and compressed DNA. “Physical and chemical principles of formation and modification of micro- and nanostructures”: Proceedings of the Fourth International Scientific Conference, 6–8 October 2010, Kharkiv (Ukraine), 2010, pp. 219–223.

6. Goncharenko, V.V.; Loboda, P.I.; Goncharenko, M.V. Hydration degree of the stretched and compressed molecules of DNA: bionical model. “Molecular biology: Advanced and Perspectives”: The 4-th International / MBG Conference for Young scientists. Kyiv, Bioinformatics. – 2011. – P. 212.

7. Saenger, W. Principles Nucleic Acid Structures. New York, Springer–Verlag, 1987.

8. Kutimskaya, M.A.; Burzunova, M.Yu. The function of the water in major structures in alive systems. Progress of the modern natural history, 2010, Vol. 10, pp. 43–45. (in Russian)

9. Brill, G.E.; Petrosyan, V.I.; Sinitzyn, N.I.; Yolkin, V.A. Maintenance of structure water matrix – mayor mechanism gomeostatic tuning in alive systems. Biomedical radioelectronics, 2000, N 2, pp. 18–23. (in Russian)

10. Meyer, S.C. The Explanatory Power of Design: DNA and the Origin of Information. Mere Creation: Science, Faith and Intelligent Design; Edited by Dembski, William A. (Intervarsity Press: Downers Grove, Illinois), 1998, pp. 114–147.