Living Matter: Algebra of Molecules

ISBN-13: 9781498741378 / Angielski / Twarda / 2015 / 160 str.

Leonid P. Buchatsky; Valery V. Stcherbic

Opis

This book provides a review of biochemistry as an algebra of molecules of living matter and utilizes Clifford algebras to discuss the basic biochemical processes of DNA replication, DNA transcription, RNA splicing and translation. Viral carcinogenesis is discussed in depth, specific attention is paid to the structural features of biomolecules that define a particular Clifford algebra, and useful examples of genetic information being transformed into Clifford algebras are provided.

Spis treści

PREFACE TO THE ENGLISH EDITION

PREFACE TO THE RUSSIAN EDITION

DNA STRUCTURE AND CLIFFORD ALGEBRA

DNA REPLICATION

CLIFFORD ALGEBRA

DNA REPLICATION AND CLIFFORD ALGEBRA

COMPLEMENTARY DNA PAIRS

CLIFFORD ALGEBRA OF DNA NUCLEOTIDES

KLEIN-GORDON EQUATION

Structural equations of 2-deoxyribose

Structural equations of phosphates

Structural equations of complementary pairs

Structural equations of nucleotide triplets

APPENDIX

MATHEMATICS OF CLIFFORD ALGEBRA

APPENDIX

HADAMARD MATRICES OF CLIFFORD ALGEBRAS

APPENDIX

CLIFFORD ALGEBRA Cl(4, 2)

APPENDIX

PRESENTATION OF CLIFFORD ALGEBRA

BY RNA MOLECULES

REFERENCES

　

tRNA MOLECULE IN AFFINE SPACE

CLIFFORD ALGEBRAS OF tRNA AND AMINOACYL-tRNA SYNTHETASES

CURVATURE TENSOR OF FOUR-DIMENSIONAL RIEMANN SPACE

CURVATURE TENSOR AND L-FUNCTION OF tRNA

HIDDEN SYMMETRY OF THE GENETIC CODE

Quadratic form of the genetic code

Graph of genetic code states

Interpretation of genetic code graph

DEGENERACY OF THE GENETIC CODE

REFERENCES

FINE-STRUCTURE CONSTANT IN PRESENTATION OF BIOMOLECULAS

FINE-STRUCTURE CONSTANT AND PROTEIN STRUCTURE

The structure of amino acids of the genetic code

Interpretation of reversed fine-structure constant

FINE-STRUCTURE CONSTANT AND ATP MOLECULE

Connection of ATP with fractional part of the constant 1/a

FINE-STRUCTURE CONSTANT AND DNA STRUCTURE

FINE-STRUCTURE CONSTANT AND CAP-STRUCTURE OF

mRNA

APPENDIX

CLIFFORD ALGEBRAS OF SIMPLE CHEMICAL COMPOUNDS

APPENDIX

ALGEBRAIC FORMULAE OF CONSTANT 1/a

Rosen formula

Wyler formula

COMMENTARY

COMMENTARY

REFERENCES

　

CANCER: VIRUSES, ATTRACTORS, FRACTALS

POLYOMAVIRUSES

Skew symmetry Т = 3 of polyomavirus protein capsid

STOCHASTIC HENON ATTRACTOR

Parameters of genome and proteins of polyomavirus capsid

Parameters of Henon map for polyomavirus proteins

Henon map parameters for antigens

Henon attractor

FRACTAL PROPERTIES OF T-ANTIGENS AND PROTEIN CAPSID OF POLYOMAVIRUSES

j -factor of large and small T-antigens

j -factor of polyomavirus protein capsid

MALIGNANT TUMOR IS A GIGANTIC COMPACTION OF THE FRACTAL STATE SPACE

Function of compaction of fractal states

Resonances of equivalence for benign tumour

Condensation of fractal states

CLIFFORD ALGEBRA OF TUMOR GROWTH

THE FUTURE OF ONCOLOGY

REFERENCES

TRANSFORMATION OF GENETIC INFORMATION TO CLIFFORD ALGEBRA

RNA SPLICING

Splicing phenomenon

Group of alternatives

Diagrams of introns

Alternative splicing

DISCRETE SYMMETRY OF GLOBULAR PROTEINS

Modular group SL(2, 5)

CLIFFORD ALGEBRA OF GLOBULAR PROTEINS

APPENDIX

CLIFFORD ALGEBRA OF SMALL T-ANTIGEN

OF SV40 VIRUS

APPENDIX

CLIFFORD ALGEBRAS OF GENETIC CODE AMINO ACIDS

REFERENCES

SUPPLEMENTARY MATERIALS

DNA coding of signature of Clifford algebra

DNA transcription and bundle of Clifford algebra

Butterfly Spin(p, q) – structure

Centrosome SpinY (p, p)- structure

Selected readings

INDEX

　

　

O autorze

Stcherbic, Valery V.; Buchatsky, Leonid P.