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INTERNATIONAL SYMPOSIUM
ON NONLINEAR MECHANICS
6th ISNM NSA NIŠ '2003
Faculty of Mechanical Engineering
University of Niš
18000 - NIŠ, A. Medvedeva 14
Tel.: (+381 18) 524-915
Application of the Lagrange Equation to the Oscillation
of the Peptide Plane in Amino-Acids Chain
Tomic A.*, Ratkaj Z.**, Koruga Dj.**
*Peoples Observatory, Belgrade, SCG
**Faculty of Mechanical Engeneering, Belgrade, SCG
e-mail: "Aleksandar Tomic" <[email protected]>, [email protected]
We made an attempt to simulate oscillation of peptide planes – a planar
formation in amino-acid chains in tubulin subunits. Because of Curie simmetries in
living organisms we can use capability of classic Lagrange equations application.
New developed method gives possibility for calculation tree perpendicular proper
frequencies for each atom in peptide plane. The influences of four contacting and six
neibouring atoms can be settle up accounts. The effect of whole in chain oscillations
appears explicitly, with consequence that exist not two identical oscillating pictures
in chain of 450 amino-acids in tubulin subunits.
Introduction
Amino-acids are losing one molecule of water in process of connecting into aminoacid chain, so they can be presented as quasi 1-D object on figure 1. However,
peptide bond is planar, then the polypeptide chain has only two degrees of freedom
per residue. Skeleton atoms of nitrogen and carbon N-C-C are laterally connected
with atoms of oxygen and hydrogen, and
amino-acid tails (R).
R
H
122
N
o
5
45 111
0,1
25
13
0,
C
o
123,5
11 6
,5
20
0,10
C
H
o
24
0 ,1
120,5
o
O
0
Figure 1: Model of amino-acid in chain. Distances
between atoms are given in nanometers, while the
angles are in degrees. Skeleton of atoms which
make protein chain is given as a bold line.
o
Microtubules in living organisms are specially
interested from point of view of the
information physics theory. The information
physics encounters a synergetic theory of classical mechanics, quantum mechanics
and theory of information. Using this new scientific paradigm it is found that
microtubules with clathrins and water clusters in living cells are major biomolecular
devices which satisfy synergy principles of information phisics [1],[2]. Mass
numbers for amino acids and their numeric representation in alpha and beta tubuline
subunits are presented in Table 1. Basic skeleton of each amino-acid has the same
mass number (56 D), but mass of amino acids tail is from 1 to 130 D, where
1D  1,67  10 27 (kg) . The second important difference between tails appears in form
(Figure 2 - Table of amino-acids with their notation and structural formulas [12]). Three
main types of secondary structure of amino-acid are: helix, beta planes and random
chains [6] [7], [8], [9]. Each one of them has its specific function in proteins. 
tubuline monomer consists of 454 amino-acids while tubulin consists 450, with
total mass 50500 D and 50 230 D, respectively.
References
1. Dj. Koruga , Nanobiology, Vol.1, No 1, pp. 5-24. 1992. (Neuromolecular computing)
2. Dj. Koruga Dj, pp. 243-261 in Ed. D. Rakovic, Dj. Koruga. Consciousness
Scientific Challenge of the 21st Century, Eur. Cent. Peace Dev. U.N., Belgrade. 1996.
(Information physics: In search of a scientific basis of consciousness)
3. I. I. Oljhovski , Kurs teoreticheskoj mehaniki, Nauka, Moskva. (in Russian: Course of the
Theoretic Mechanic) , 1970.
4.V.V. Migulin , V. I. Medvedev , E. R. Mustelj .& V. N. Parigin , Osnovi teorij kolebanij,
Nauka, Moskva (in Russian: Bases of the Oscillation Theory) , 1979.
5. G. A. Jeffrey, An Introduction to Hydrogen Bonding, Oxford Univ. Pres, 1997.
6. T. L. Blundell & L. N. Johnson , Protein Crystalography, Academic Press. 1976.
7. P. S. Lomdahl, S. P. Layne .& I. J. Bigio, Los Alamos Science, Spring 1984, pp. 4-21.
(Solitons in Biology) 1984.
8.E. Nogales , M. Whittaker, R. A. Milligan & K. Downing , Cell, Vol 96, pp. 79-88. (HighResolution Model of the Microtubule), 1999.
9. J. Loewe, H. Li , K. H. Downing & E. Nogales, J. Mol. Biol., Vol. 313, pp. 1045-1057,.
(Refined Structure of  – Tubulin at 3.5 A Resolution), 2001.
10. A. Tomic, Flogiston, Vol. 4, No 7, pp. 151-168, (Planetary distances as golden section
-in Serbian) 1998.
11. A. Tomic A. & Dj. Koruga , Solar system determined by the Golden Mean,
XIII Nat. Conf. Of Yug. Astronomers, Belgrade 17-20.X 2002.(in print).
12. J. D. Watson, Molecular Biology of the Gene, 3rd ed., W.A.Benjamin, 1976.
13. Dj. Koruga, A. Tomic, Z. Ratkaj, Bioptron K3 Project ,(Calculation of changes of
energetic states and oscillatory processes in bio-molecules), Zepter International
Beograd, 2002.