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Biomathematical model of the Translation of mRNA and Biomathematics of Cancer.



Purpose of the theory

Introduction.

  1. Description of the mathematical model
    1. Parallel between the mathematics division and the translation of the mRNA .
    2. Why the Base 21
      1. Example using base 21
  2. The role of periodicals
    1. Division without any return and endless.
    2. Special property of the last figure of a Base
    3. Periodical stopped by the repetition of a same figure to the dividend
    4. Notion of complementary figures and sequences portraits
      • (Concepts developed for the needs of the mathematical model)
      1. List of Sequences Portraits and complementary figures at the base 10
      2. List of possible quotients at the base 21
        • (For all figures of the base).
      3. List of sequences portraits at the base 21
        • (Those generating all the figures of the base, except the complementary figures))
      4. List of sequences portraits and complementary figures at the base 21.
      5. Protection of the integrity of the coded message.
  3. Basic programs
    1. IBPOLY-A.ba
    2. IBGEN-21.ba
    3. IBGEN-20.ba
    4. IBADN-21.ba
    5. IBADN-20.ba
    6. IBSEQUEN.ba
    7. IBTAB-CO.ba
    8. IBQUO-PO.ba
  4. Mathematical Model and Genetic Code
    • (New approach for the code and emergence of new features)
    1. Correlation between the mathematical model and the phenomenon of life
    2. Codon: Instruction in 3 steps
    3. Non-specificity CODON - Amino Acid
      • (Degeneration of the code???)
    4. Quantification of the Bases and Amino Acids
    5. Classification of Amino Acids versus the Three-dimensional Shape of proteins.
      • (Discussed with more details as provided under Chapter VI.).
      1. The first characteristic of classification: Assignment of figures to Amino Acids.
      2. The second characteristic of classification: The value of the figure given to the amino acid.
    6. Division: its interpretation on the translation side of the mRNA
      1. Example of the implementation of the division concept in the automation process.
        1. Example of a pathway towards a detailed step by step understanding in the base 10.
        2. Schema of the path at the base 10
        3. Schema of the path at the base 21
    7. For a good automation of the division .
      1. Case of the complementary figures
        1. "Rule for the comprehension in the use of a complementary figure.”
        2. Application of the rule of comprehension regarding the use of a complementary figure.
        3. Case going from sequence 4 to sequence 5
        4. Case going from sequence 5 to sequence 4
        5. To see a more detailed image of what is happening at the level of the sequences portraits (See the table 7.1.5a " visualization of the rule of understanding in using the complementary figure)
        6. Example at the base 21 involving complementary figures.
        7. Representation under another form of the example 7.1.6 involving complementary figures and Fig. 7.1.7a - Application of the rule of the complementary figure at the base 21 ((example 7.1.6 reused)
        8. Example for calculation of positions for complementary figures .
        9. Table of positions for complementary figures
        10. "In summary", regarding the use of the complementary figure .
      2. The 3 sources contributing to the optimization of a good automation of the division when using sequences portraits.
        1. The first source: dividing into 2 parts.
          1. Properties of the mathematical model at the origin of the automation of the division.
          2. The implementation of certain criteria that support the automation of the division.
          1. First part: Properties of the mathematical model at the origin of the automation. .
            1. The sequences portraits to remember (typical sequences portraits).
            2. The gap between the figures making up the sequences portraits (their role).
            3. The effect of inertia, emergent property which come out from the results of divisions performed from eligible combinations; results of inertia applied as a criterion .
          2. Second part: The implementation of certain criteria supporting the automation of the division.
            1. The presence of the complementary figure at the requested sequence portrait level during the processing of the manual or automated division .
            2. The choice made on the figure(or amino acid) to reach or as a wanted choice, at all the 3 positions at the level of the quotient .
            3. The increase of the inertia effect searched on the use of sequence portraits coming from eligible combinations.
        2. The second source: The selection of an ideal combination among those eligible. Ideal combination related to the selected sequences portraits with which we will operate.
        3. The third source: The construction of the mRNA. Construction using the tables of RNA Construction data recorded by using the mRNA constructs table on Excel file called "Construction of the mRNA Table" .
      3. Thorough explanation of the 3 sources.
        • (contributing to an optimization of a good automated division during the use of sequencesportraits) .
        1. The first source: dividing into 2 parts.
          1. Properties of the mathematical model at the origin of the automation of the division.
          2. The implementation of certain criteria that support the automation of the division
          1. First part: Properties of the mathematical model at the origin of the automation of the division.
            1. Typical sequences portraits.
              • Table 7.3.1a - " Typical Sequences Portraits that are possible at the base 21".
            2. The gap between figures composing sequences portraits.
              • Table 7.3.1b - Gaps between the figures composing the sequences portraits
              • Table 7.3.1c – Schematic diagram of the ribosome, the holder of the division “First hypothesis” .
              • Table 7.3.1d - Schematic diagram of the ribosome, the holder of the division “second hypothesis ".
            3. The effect of inertia:Emergent property which come out from the results of the divisions performed from eligible combinations; results of inertia applied as a criterion.
              1. Mathematical visualization characterizing "the effect of inertia" Using the 7.3.1e table " Effect of inertia: Resistance against a malfunction of the division by the sequences portraits." .
              2. Setting up of the table of restD and flexibility .
                Table 7.3.1f - Table of the restD of the sequences portraits. (portrait format) .
                Table 7.3.1g - Table of restD of the sequences portrait. (landscape format).
              3. Quotient (normal division) and quotient (sequences portraits division) .
              4. Some 9 comments for a further explanation of the table 7.3.1e in order to understand better.
                1. In the top part of the table. Table 7.3.1h -This table indicates the origin of the restD on line B and C of the table 7.31e.
                2. For the bottom part of the table. Table 7.3.1i - Example of the annex table IIa showing the origin of the restD providing the de- velopment of the table of the sequences portraits restD at the level of the tables 7.3.1f or 7.3.1g
                3. For a same quotient obtained for a same position.
                4. If the gap between the two restD for a given position.
                5. The acceptable gap so that we may have a same quotient. Table 7.3.1j - Table of a detailed construction of a mRNA for a figure (or a base) one at a time, taking into account the inertia.
                6. That is this detailed flexibility.
                7. For negative differences between restD.
                8. The role of the sequences portraits restD table.
                9. Range or bracket of 20 (table of 20) .
          2. Second Part: The implementation of certain criteria supporting the automation of the division.
            1. The presence of the complementary figure at the requested sequence portrait level during the processing of the manual or automated division .
            2. The choice made on the figure ( or amino acid ) to reach or as a wanted choice, at all the 3 positions at the level of the quotient.
            3. The increase of the inertia effect searched on the use of the sequence portraits coming from eligible combinations.
        2. The second source: Coming from the selection of an ideal combination among those being eligible.
          1. The selection of an ideal combination
          2. Behavior of eligible combinations at the level of a certain number of performed divisions.
          3. Compiled results based on 2 classification criteria.
            1. First classification criterion: "Compilation of the number of different results".
            2. Second criterion of classification: "Compilation of the number of peaks for different figures".
        3. The third source: The one coming from the construction of mRNA using RNA table and the mRNA construction table.
          1. The role of the RNA table allows us to perform 2 tasks:.
            1. The first task: Role of combination eliminations.
            2. The second task: Role of construction of the mRNA.
            1. Illustration of a page forming a RNA table.
            2. Example of a graphic linked to a page of RNA table.
            3. Graphic linked at the bottom of a RNA table page .
            4. Construction table of the mRNA ( on Excel )
      4. Manual or automated division: Application at the base 21.
      5. Example of division at the base 21.
        1. Combination used 1 3 U O
        2. Combination used 3 9 Q O
        3. Combination used 1 3 7 O
        4. Combination used 1 Q E U
        5. Combination used 1 Q E O
        6. Combination used 1 Q E O
        7. Combination used 1 Q E O
    8. The problem of the ideal combination.
      1. Step 1: Selection by the typical sequences portraits.
        1. Typical séquences portraits table.
        2. Calculation of the number of possible combinations from the dividends of 8 typical sequences portraits.
        3. List of possible combinations from the dividends of 8 typical séquences portraits.
      2. Step 2: Selection based on the graphics from RNA tables.
        1. Example of a page from a mRNA table.
        2. Graphic example linked to a page of RNA table.
        3. Graphic linked at the bottom of each of the 20 pages constituting a RNA table .
        1. List of combinations with at most 6 missing figures.
      3. Step 3: Selection from the best behavior of the remaining combinations.
        1. List of the 10 divisions: (Step 3: Selection from the best behavior).
        2. Example of division made by computer from the IBgen21.BA basic program.
        1. The 2 classification criteria of possible combinations.
          1. Distribution of the results of differences: Manual division versus division made by a computer at the level of the 10 divisions for the 15 combinations.
            1. Table listing the discrepancy.
          2. Application of 2 classification criteria.
            1. Table of classification according to 2 selection criteria . .....
            2. Three dimensional graphic ranking of the first 8 from the 15 remaining combinations.
            3. Three dimensional graphic ranking of the last 7 from the 15 remaining combinations.
      4. The choice of the combination.
        1. Possible ways for the classification.
  5. Description and Use of the Theoretical Mathematical Model(Use and Application of the model to the gene.)
    1. Its use (via the description of tools necessary to its use) )
      1. Regarding computer programs.
        1. Schema of organization.
      2. Division operation at the base 21 through the conversion table 10 / 21 .
      3. Conversion table base 10 / 21.
      4. Construction tables of mRNA.
      5. Construction card of mRNA.
    2. Its application : (raising the problem of the construction of a gene).
      1. Explanation of the Table of RNA.
      2. Example about a table of RNA.
      3. Dummy example of the construction of a mRNA using the tables of RNA from the values assigned to the bases A, G, C, U and to a predetermined choice of amino acids to which have been also assigned values through the base 21.
      4. Conclusion.
        1. Pattern of distribution found in bacteria.
        2. Pattern of distribution found in animal cells.
        3. List of amino acids.
  6. Amino acids and three-dimensional shape versus theoretical model.
    1. Structure and purpose of the chapter.
    2. The "Why or the mathematical reason"
    3. Amino acids and three-dimensional shape.
      1. Existence of parameters allowing the development of the three-dimensional shape.
      2. The protein folding "matter of chance? "
    4. The dynamic features of an amino acid .
      1. Mechanical aspect of the internal movement of an amino acid.
        1. Internal movement of an amino acid.
          • -Schema: Showing the mechanical aspect of the internal movement of an amino acid.
        2. Amino acid, seen from a different perspective.
          • -Schema: View of the infrastructure of an amino acid from another perspective .
      2. Description and characterization of the peptide link between two amino acids.
        • - Schema: Formation of the peptide link by elimination of a water molecule.
        • - Schema: Internal mechanical aspect of the internal movement of several amino acids and partial character of a double bond of the peptide link.
        • - Schema: Mechanical aspect of the internal movement of amino acids.
      3. Classification of amino acids.
        • - List of 20 amino acids used in the composition of a protein (first part).
        • - Continuation of the list of amino acids (second part).
    5. Relationship between amino acids "Possible Classification" .
      1. Mathematical modal versus relationship between amino acids.
        • - Table: Couples / Angles of direction (first part).
        • - Table: Couples / Angles of direction (second part).
      2. Hypothesis on how to determine the angle of a pair of amino acids.
        1. Three-dimensional direction possibilities determined by the axes of an amino acid.
          • -Schema: Representing the possibilities of three-dimensional directions determined by the 2 axes of rotation of an amino acid.
        2. Hypothesis of visualization of directions of an angle coming from a couple of amino acids.
        3. Neutralization of the angle of direction of the first amino acid and determination of the tridimensional angle by the second amino acid.
          • Scheme: Hypothesis of visualization of direction of the angle coming from a couple of amino acids.
    6. Tridimensional shape versus the mathematical model (What does the mathematical model allow us to consider).
    7. What the current genetic code cannot even consider.
  7. The case of the addition of Poly - A (animal cell) to mRNA versus the theoretical model.
    1. Role of the poly – A : We no longer know!
    2. Figure VI a : Maturation of a mRNA.
    3. Meaning of Poly – A : in the context of the theory presented in this book.
      1. End of the sentence signal.
      2. Security measure.
    4. Figure VI b : Hypothesis on the Poly - A ensuring the achievement of a completion of the end of the sentence signal.
  8. Assessment of the number of adenine required in order to achieve the zero state
    • (The evaluation is being done in 3 steps)
    1. First and third steps: Table showing the developed strands and the achieved results.
      1. Graphics : number of adenine used after the cut versus the addition for figures from 1 to 20.
    2. Second step: Input of calculation parameters in the computer with the Program - Poly-A.
      1. Testing frequency.
      2. Beginning of the verification.
      3. Labeling of amino acids.
    3. For the assessment of the number of adenine required in order to achieve the zero state.
      1. A frequency of verification at every 3 quotients was retained.
      2. Beginning of the verification in position 1 has been retained.
      3. A start of labeling in position 1 has been retained.
    4. Another occurrence about the input of the parameters.
    5. Results of the calculations with the computer: (see annex XV)
    6. Conclusion :
      1. Roles developed and assigned to the poly - A.
      2. Poly - U and a tryptophan operon.
        1. Case of the poly-U located at the end of mRNA coding for the tryptophan operon.
        2. Case of the poly - U located at the end of the tryptophan operon LEADER.
          1. Low concentration in tryptophan.
          2. High concentration in tryptophan.
      3. Epilogue.
        1. About the poly-A (poly-U) versus the current theory of the genetic code


  9. ---FIN De ce que j'ai de traduit.-----

  10. Cancer , types de dommage, réparation et non réparation
    • ( Introduction et généralité )
    1. Le problème du cancer. ( Point de vue des connaissances actuelles )
      1. Définition du cancer.
      2. Type de cancer.
        1. Carcinome.
        2. Sarcome.
        3. Leucémie.
          1. Leucémie Aigue.
          2. Leucémie chronique.
          • Définition : Leucémie chronique Myéloide (Myélome)
          • Définition : Leucémie chronique Lymphoide (lymphome)
      3. Cancer : La théorie la plus acceptée actuellement.
      4. Agents cancérigènes responsables de dommages causés à l’ ADN .
        1. Agents physiques.
        2. Composés inorganiques.
        3. Composés organiques.
        4. Agents parasiteurs.
      5. Altération de l ’ ADN et Types de dommages.
        1. Altération de l’ ADN ( Type de mécanismes responsables)
        2. Type de dommages:
          1. Une base incorrecte sur un brin.
          2. Bases manquantes.
          3. Modification de bases.
          4. Le bris de un des 2 brins composant l’ ADN .
          5. Le bris des deux brins de l’ ADN.
          6. Cross – linking.
      6. Schématisation des dommages et réparations.
        1. Base incorrecte sur un brin ne pouvant former de liens hydrogène avec la base correspondante sur l’autre brin.
          1. Dommage dû à une erreur de réplication.
          2. Dommage dû à une désamination.
          3. Exemple de désamination :
            • ( transition cytosine -> uracile )
        2. Bases manquantes ( dépurination )
        3. Modification des bases ( dimère de thymines )
          • Types de réparation
          1. Excision.
          2. Photoréactivation.
          3. Postréplication recombinaison.
          4. SOS Repair.
          5. Résumé du point 1.6.3 ; Modification des bases.
        4. Le bris de un des deux brins composant l’ ADN.
        5. Le bris des deux brins de l’ ADN.
        6. Le cross-linking.
          1. Type d’adducteur causant les cross-linking.
            1. Cross-linking Interstrand ( avec adducteur moléculaire ).
            2. Cross-linking Intrastrand ( avec adducteur moléculaire ).
            3. Cross-linking ( avec adducteur protéinique ).
          2. Cross-linking et réparation.
      7. Segmentation de l’ ADN et formation d’ ARNm incomplet.
        1. Dimère de thymines et fragmentation de l’ ADN.
          1. Rencontre de la polymérase III avec un dimère de thymines et hypothèse de formation d` ARNm incomplets ou de type brisé.
          2. Segmentation possible de l’ ADN contenant des dimères de thymines.
            1. Le premier type de segmentation
              • ( Impliqué dans la recombinaison postréplicative)
              • Schéma : Hypothèse de formation d’ARNm incomplets ou de type brisé.
            2. Le deuxième type de segmentation
              • Schéma : Hypothèse de formation d’ARNm incomplets ou de type brisé.
            3. Hypothèse de formation d’ARNm incomplets ou de type brisé.
              1. Conditions nécessaires à la formation d’ARNm incomplets ou de type brisé.
        2. Autres types de dommages et fragmentation de l’ADN
          1. Le bris de un des 2 brins ==> segmentations possibles
          2. Le bris des 2 brins ==> segmentations possibles
          3. Le cross-linking ==> segmentations possibles
          4. Cas de l’anémie de Fanconi
        3. L’ expérience de strasbourg ou la preuve indirecte possible de l’existence dans le cytoplasme de la cellule, d’ ARNm incomplets traduits en protéines par les ribosomes.
          1. Syndrome de Cockayne.
          2. Xeroderma pigmentosum.
        4. Conclusion
  11. Cancer et Biomathématique
    1. Nouvelle approche théorique du cancer.
      1. Le problème du cancer : un non lieu.
      2. Le potentiel de la biomathématique et de la bioinformatique comme outil de travail.
    2. Approche biomathématique du cancer.
      • - Figure 10 .A : Exemple d’ une division déclencheur de périodique.
      1. Hypothèse sur la boucle de procédure déduit à partir du modèle mathématique.
        1. Visualisation à partir du concept de la division.
          • - Figure 10.b : Visualisation à partir du concept de la division.
        2. Visualisation au moyen du concept de la transposition de la division en procédé d’automatisation par le biais des séquences portraits.
          • - Figure 10.c : Visualisation au moyen du procédé d’automatisation.
        3. Comment d’un point de vue hypothétique, le mécanisme d’un périodique peut-être expliqué ou compris au niveau d’une division effectuée au moyen des séquences portraits.
          • - Figure 10.d : Visualisation de la boucle au niveau des séquences portraits.



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