! ! ! " ! # # " $ $ ! $ % " & " "'$()!($(*!+$(,!!-$.!/$0 1 2324 & 5 6 & 7! 5 % 1 8 9 : & 3 !"#$!"#$ ! !"#$% & #" ' ! ( ' ) *+" ' # # +*,-." /" %0 1 / 2-*3 & # " ' ! ( ' ) # # 2-*3 Miloje M. Rako64 G E N E T I C C O D E The Cipher and the Key LAMBERT Academic Publishing Contents Chapter 1 The Cipher and the Key 1. INTRODUCTION ............................................................................................................. 1 2. A POSSIBLE SCENARIO OF SELECTION OF CONSTITUENTS .......................... 3 O P ................................................................ 3 2.2. The starting molecules and derivatives ..................................................................... 11 2.2.1. Derivative of derivative ..................................................................................... 11 2.2.2. Diversity enriching and economicity ................................................................. 13 2.3. The branching structures ........................................................................................... 14 2.3.1. The "mapping" from the head to the body ......................................................... 15 2.3.2. The pure hydrocarbon AAs ................................................................................ 15 3. NUCLEOTIDE TABLES AND THEIR FACES .......................................................... 16 3.1. The 24 permutations of four Py-Pu bases .................................................................. 16 3.2. The nucleon number balances ................................................................................... 16 3.3. The atom number balances ........................................................................................ 23 3.4. The sense of the modification of R ...................................................... 25 4. A SPECIFIC CHEMICAL COMPLEMENTARITY AS THE CIPHER ............. 27 4.1. Three types of distinct chemical complementarity .................................................... 28 4.2. Nuancing and balancing of chemical structures and properties ................................ 29 4.3. The chemical complementarity as a neighborhood logic .......................................... 30 4.3.1. The best possible permutation arrangement ....................................................... 30 4.3.2. Dissimilarity in similarity .................................................................................. 32 4.4. The cipher in relation to particles balance ................................................................. 33 5. THE POLARITY IN RELATION TO THE CIPHER KEY ...................................... 34 5.1. The final result ........................................................................................................... 34 5.2. The final result in relation to some previous ones ..................................................... 39 6. CONCLUDING REMARKS .......................................................................................... 40 Chapter 2 Analogies of Genetic and Chemical Code.................................................................................. 45 1. Preliminaries .................................................................................................................... 45 1.1. Analogies with quantum physics ............................................................................... 45 1.2. Agreement-disagreement principle ........................................................................... 47 1.3. Some other mathematical formalisms ....................................................................... 48 2. New insights ..................................................................................................................... 49 2.1. The problem of lanthanides arrangement in the PSE ............................................... 49 2.2. Specific arithmetical patterns .................................................................................... 50 2.3. Quantum like relationships within nucleotides arrangements ................................... 58 2.4. Specific algebraic patterns ......................................................................................... 63 2.5. Key relationhips between GC and PSE ..................................................................... 63 2.6. Some additional observations on Genetic code ......................................................... 65 3. Discussion ......................................................................................................................... 68 3.1. Another understanding of the periodic system .......................................................... 69 3.2. Another similarities ................................................................................................... 70 3.3. Some additional observations .................................................................................... 70 4. Conclusion ........................................................................................................................ 71 III Chapter 3 Chemical Distinctions of Protein Amino Acids within Genetic code ...................................... 83 REFERENCES ...................................................................................................................... 97 Chapter 4 The Enigma of Darwin's Diagram ........................................................................................... 101 1.Introduction .................................................................................................................... 102 2. Methodology .................................................................................................................. 103 4. Results and discussion ................................................................................................... 106 4.1. Primary and secondary branches of species "A" and "I" ......................................... 106 4.2. The riddle of the genetic code ................................................................................. 108 4.3. Darwin's solution to the riddle of the genetic code ................................................. 108 4.4. Nodes and branchings ............................................................................................. 110 4.5. BinaryMcodeM "#R " .................................................................. 111 4.6. The balances of the number of branches for two species ("A" and "I") .................. 111 4.7. The "Prime Quantum 037" ...................................................................................... 113 4.8. Primary and secondary branches for "other nine species" ...................................... 113 4.9. Primary and secondary branches for all 11 species ................................................. 114 4.10. Improbable and unexpected result ......................................................................... 115 4.11. More than improbable result ................................................................................. 116 5. Concluding remarks ...................................................................................................... 116 REFERENCES ............................................................................................................... 196 Supplement 1 Genetic Code as a Coherent System ........................................................................................ 201 1. Preliminaries .................................................................................................................. 201 2. Four stereochemical types of AAs ................................................................................ 205 3. Four diversity types of AAs .......................................................................................... 209 3.1. The uniqueness of the number 26 ............................................................................ 210 3.2. The unity of two realities M chemical and mathematical ......................................... 212 3.3. The uniqueness of the number 48 ............................................................................ 216 4. Harmonic structures ..................................................................................................... 219 4.1. Determination by Golden mean ................................................................................ 219 4.2. Golden mean M enzyme determination .................................................................... 222 4.3. The Li $ R ..................................................................................... 224 4.4. A specific harmonic structure .................................................................................. 228 5. Concluding remark ....................................................................................................... 230 Appendix: Some source harmonic structures ................................................................. 231 Supplement 2 Golden and Harmonic Mean in the Genetic Code .................................................................