Biomathematical model of the Translation of mRNA
&
Biomathematics of Cancer.
Table of contents
Purpose of the theory
Introduction
 Description of the mathematical model
 Parallel between the mathematics division and the translation of the mRNA .
 Why the Base 21
 Example using base 21
 The role of periodicals
 Division without any return and endless.
 Special property of the last figure of a Base.
 Periodical stopped by the repetition of a same figure to the dividend.
 Notion of complementary figures and sequences portraits.
 (Concepts developed for the needs of the mathematical model)
 List of Sequences Portraits and complementary figures at the base 10.
 List of possible quotients at the base 21.
 (For all figures of the base).
 List of sequences portraits at the base 21.
 (Those generating all the figures of the base, except the complementary figures))
 List of sequences portraits and complementary figures at the base 21.
 Protection of the integrity of the coded message.
 Basic programs
 IBPOLYA.ba
 IBGEN21.ba
 IBGEN20.ba
 IBADN21.ba
 IBADN20.ba
 IBSEQUEN.ba
 IBTABCO.ba
 IBQUOPO.ba
 Mathematical Model and Genetic Code
 (New approach concerning the understanding of genetic code and emergence of new features listed below)
 Correlation between the Mathematical Model and the Living.
 Codon: Instruction in 3 steps
 Nonspecificity CODON  AMINO ACID.
 ( Degeneracy of the code??? Questions to be asked )
 Quantitative numbering of the mRNA bases and angular quantification of Amino Acids.
 Numerical classification of Amino Acids versus the Threedimensional Shape of proteins.
 (Discussed with more details as provided under Chapter VI.).
Numerical classification of Amino Acids allows to update :
2 characteristics of classification
 The assignment of figures to Amino Acids: The first characteristic of classification, figures which
would represent the identification of amino acids.
 The value of the figure given to the amino acid: Characteristic outcomes of the first one, a value of
the figure which would be probably dependent on the role to play by the amino acid at the level of
angles in connection with the other amino acids.
 Division: its interpretation on the translation side of the mRNA.
 Example of the implementation of the division concept in the automation process.
 Example of a pathway towards a detailed step by step understanding
in the base 10.
 Schema of the path at the base 10
 Schema of the path at the base 21
 For a good automation of the division.
 Case of the complementary figures.
 "Rule for the comprehension in the use of a complementary figure.”
 Application of the rule of comprehension regarding the use of a complementary figure.
 Case going from sequence 4 to sequence 5.
 Case going from sequence 5 to sequence 4.
 To visualyse in detail 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).
 Example at the base 21 involving complementary figures.
 Another form of representation 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)
 Example of calculation of the complementary figures position.
 Positions of the complementary figures among the sequences portraits.
 "In summary", regarding the use of the complementary figure .
(Three sources contribute for a good automation of the division)
 The 3 sources contributing to the optimization of a good automation of the division when using sequences portraits.
( First source )
 The first source: dividing into 2 parts.
 The one coming from the properties of the mathematical model at the origin of the automation of the division.
 The one coming from implementation of certain criteria that support the automation of the division.
 First part: Properties of the mathematical model at the origin of the automation.
.
 The sequences portraits to remember (typical sequences portraits).
 The gap between the figures making up the sequences portraits (their role).
 The effect of inertia, emergent property which comes out from the results of divisions
performed from eligible combinations; results of inertia applied as a criterion
.
 Second part: The implementation of certain criteria supporting the automation of the division.
 The presence of the complementary figure at the requested sequence portrait level
during the processing of the manual or automated division
.
 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 .
 The increase of the inertia effect searched on the use of sequence portraits coming from
eligible combinations.
( second source)
 The second source: The one coming from the selection of an ideal combination among those eligible. Ideal combination that comes from the selected sequences portraits with which we will operate.
( third source)
 The third source: The one coming from the construction of the mRNA.
  Construction using the tables of RNA.
  Construction from data recorded by using the mRNA construction table on Excel file called "Construction of the mRNA Table". See 7.3.3.1d "Working page to be printed" .
  Construction using detailed construction table of an mRNA for a figure or a base at the time taking inertia into account. See table 7.3.1e ou 7.3.1j
( Thorough explanation of the 3 sources )
 Thorough explanation of the 3 sources.
 (contributing to an optimization of a good automationof the division during the use of sequences portraits) .
( Thorough explanation of the first source)
 The first source: dividing into 2 parts. (Such as stipulated in the point 7.2.1)
 Properties of the mathematical model at the origin of the automation of the division.
 The implementation of certain criteria that support the automation of the division.
 First part: (as stipulated in the point 7.2.1.1).
Properties of the mathematical model at the origin of the automation of the division.
 The typical sequences portraits.
 Table 7.3.1a  " Typical Sequences Portraits that are possible at the base 21".
 The gap between figures making up the sequences portraits.
 Table 7.3.1b  Gaps between the figures making up 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 ".

 The effect of inertia: Emergent property which comes out from the results of the divisions performed from
eligible combinations; ( results of inertia applied as a criterion.)
 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." .
 Setting up of the table of restD and margin of manoeuvre .
Table 7.3.1f  Table of the restD of the sequences portraits. (portrait format) .
Table 7.3.1g  Table of restD of the sequences portraits. (landscape format).
 Quotient (normal division) , quotient (sequences portraits division and margin of manoeuvre .)
 Some 9 comments for a further explanation of the table 7.3.1e in order to understand better.
 In the top part of the table 7.3.1e , line α , B and C. Table 7.3.1h This table indicates the origin of the restD on line B and C of the table 7.31e.
 For the bottom part of the table 7.3.1e , line β (Quotient obtained by seq. portrait) line G or H. Table 7.3.1i Example of the annex table IIa showing the origin of the restD providing the development of the table of the sequences portraits restD at the level of the tables 7.3.1f or 7.3.1g
 Difference between restD ( RestD from the division by seq. portrait minus restD from the normal division) for a same quotient obtained for a same position.
 If the difference between the 2 restD line E (G  C) (RestD from the division by seq. portrait minus restD from the normal division) at the same position for a given position, makes us go out of the range of 20.
 The acceptable difference between 2 restD line F (HT  C (Difference that comes from the top of the range of 20 minus the value indicated by the restD of the normal division) so that we may have a same quotient for a same position to come at the level of 2 types of division , implies a negative value at theVé (E  F) line in order to respect the margin of manoeuvre
 It is margin of manoeuvre, detailed in Table 7.3.1e in line F , which allows the division by sequences portraits to return to the rails.
 For a negative difference between restD for the same position. ( Negative result : That comes from the restD of the division by seq. portraits minus the one from the normal division). Ensure negative value at the level of the Vé. line and the same quotient to come for both types of division.
 The role of the sequences portraits restD table. See table 7.3.1f.
 Bracket of 20 (table of 20) . Line A and I
 Second Part: The implementation of certain criteria supporting the automation of the division. ( As stipulated at the point 7.2.1.2 )
 The presence of the complementary figure at the level of the requested sequence portrait during the processing of the manual or automated division .
 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.
 The increase of the inertia effect searched on the use of the sequence portraits tested.
Table 7.3.1e and 7.3.1j – Detailed construction table of an mRNA for one figure ( or one base) at the time taking into account inertia, thus being able to help keep division by portrait sequence similar to normal division, and perhaps also thereby favoring the choice of a codon among those eligible for the same amino acid.
( Thorough explanation of the second source)
 The second source: ( As stipulated at the point 7.2.2 ) Coming from the selection of an ideal combination among those being eligible.
 The selection of an ideal combination.
 Behavior of eligible combinations at the level of a certain number of performed divisions.
 Compiled results based on 2 classification criteria.
 First classification criterion: "Compilation of the number of different
results".
 Second criterion of classification: "Compilation of the number of peaks for different figures".
( Thorough explanation of the third source)
 The third source: ( As stipulated at the point 7.2.3 ) The one coming from the construction of mRNA using RNA table and the mRNA
construction table.
 The role of the RNA table allows us to perform 2 tasks:.
 The first task: Role of combination eliminations.
 The second task: Role of construction of the mRNA.
 7.3.3.1a Illustration of a page forming a RNA table.
 7.3.3.1b Example of a graphic linked to a page of RNA table.
 7.3.3.1c Graphic linked at the bottom of a RNA table page .
 7.3.3.1d Construction table of the mRNA ( on Excel )
( end of thorough explanation of the third source )
 Manual or automated division: Application at the base 21.
 Example of division at the base 21.
 Combination used 1 3 U O
 Combination used 3 9 Q O
 Combination used 1 3 7 O
 Combination used 1 Q E U
 Combination used 1 Q E O
 Combination used 1 Q E O
 Combination used 1 Q E O
 The problem of the ideal combination.
 Step 1: Selection by the typical sequences portraits.
 Typical séquences portraits table.
 Calculation of the possible number combinations from the dividends of 8 typical sequences
portraits.
 List of possible combinations from the dividends of 8 typical séquences portraits.
 Step 2: Selection based on the graphics from RNA tables.
 Example of a page from a mRNA table.
 Graphic example linked to a page of RNA table.
 Graphic linked at the bottom of each of the 20 pages constituting an RNA table .
 List of combinations with at most 6 missing figures.
 Step 3: Selection from the best behavior of the remaining combinations.
 List of the 10 divisions: (Step 3: Selection from the best behavior).
 Example of division made by computer from the IBgen21.BA basic program.
 The 2 classification criteria of possible combinations.
 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.
 Picture of disparities.
 Application of 2 classification criteria.
 Table of classification according to 2 selection criteria.
 Three dimensional graph of the classification of the first 8 from the 15 remaining combinations.
 Three dimensional graph of the classification of the last 7 from the 15 remaining combinations.
 The choice of the combination.
 Possible ways for the classification.
 Description and Use of the Theoretical Mathematical Model
( Use and Application of the model to mRNA. )
 Its use (via the description of tools necessary to its use. )
 The programs computing.
 Schema of organization.
 Regarding computer programs .
 The choice of the special characters for the base 21.
 Purpose of the programs : Construction of mRNA for the end of analysis by the mathematical model.
 Copyright.
 Division operation at the base 21 through the conversion table 10 / 21.
 Conversion table base 10 / 21.
 Construction tables of mRNA.
 Construction Board of mRNA on Excel.
 Its application (raising the problem of the construction of an mRNA).
 Explanation of the Table of RNA.
 Example about a table of RNA.
 Dummy example of the construction of a mRNA using the tables of RNA from a combination of which the values were assigned to the bases A, G, C, U and to a predetermined choice of amino acids to which were also assigned in a random way values by drawing among the figures of the base 21.
 Conclusion.
 Pattern of distribution found in bacteria.
 Pattern of distribution found in animal cells.
 List of amino acids.
 Appendices of the frequencies and RNA's table connected with the artificial example of the point 2.3 ( includes 12 pages ).
 Amino acids and threedimensional shape versus theoretical model.
 Structure and purpose of the chapter.
 The "Why or the mathematical reason"
 Amino acids and threedimensional shape.
 Existence of parameters allowing the development of the threedimensional shape.
 The protein folding "matter of chance? " .
 The 4 dynamic characteristics of an amino acid.
 The 2 axes of rotation of an amino acid.
( First characteristic of an amino acid see pge 105 point 4 )
 Mechanical aspect of the Internal movement of an amino acid, similar to a german equatorial mount of a telescope
 Diagram : 4.1.1a Showing the mechanical aspect of the internal movement of an amino acid.
 Amino acid, seen from a different perspective.
 Diagram : 4.1.2a View of the infrastructure of an amino acid from another perspective .
 Description and characterization of the peptide bond between two amino acids.
( Second characteristic of an amino acid see pge 105 point 4 )
 Diagram : 4.2a Formation of the peptide bond by elimination of a water molecule.
 Diagram : 4.2c Internal mechanical aspect of the internal movement of several amino acids and partial character of a double bond of the peptide bond.
 Diagram : 4.2d Mechanical aspect of the internal movement of amino acids.
 Classification of amino acids.( Third characteristic of an amino acid see pge 105 point 4 )
 4.3.1 List of 20 amino acids used in the composition of a protein (first part).
 4.3.2  Continuation of the list of amino acids (second part).
  Angle between two amino acids " possible Classification ".
( Fourth characteristic of an amino acid see pge 105 point 4 )
 Mathematical modal versus relationship between amino acids.

 5.1 Hypothesis on how to determine the angle of an amino acid pair.
 5.1.1 Possibilities of threedimensional directions determined by the 2 axes of an amino acid.
 5.1.1a  Diagram representing the possibilities of threedimensional directions determined by the two axes of rotation of an amino acid..
 5.1.1b  Diagram : Same diagram as 5.1.1a , but closeup.
 5.1.2  Hypothesis of angle direction visualization from a couple of amino acids.
 5.1.3  Neutralization of the direction angle of the first amino acid according to a visualization
plane and determination of the threedimensional angle caused by the second amino acid.
 5.1.3a  Diagram : Hypothesis of visualization of angle direction from a couple of amino acids.
 5.1.3b  Diagram : Same diagram as 5.1.3a , but closeup.
 – Threedimensional form versus the mathematical model.
(What does the mathematical model allow us to consider).
  What the current genetic code in its understanding and empirically established, cannot envisage.
 – Hypothesis suggested by the mathematical model. ( couples/Angles of direction).

 8a  Couples / angles of direction ( first part, page 1 for number 1 to 10 )
 8b  Couples / angles of direction ( second part, page 2 for number 11 to 20 )
 The case of the addition of Poly  A (animal cell) to mRNA versus the theoretical model.
 Role of the poly – A

 Figure VI a : Maturation of a mRNA.
 End of the sentence signal.

 Figure VI b : Hypothesis on the Poly  A ensuring or providing a final sentence signal.
 Assessment of the number of adenine required in order to achieve the zero state
 (The evaluation is being done in 3 steps)
 First and third steps: Table showing the developed strands and the achieved results.
  Table of the number of adenines needed after break strand to reach the zero state for each of the base 21 figures.
 – Graphic : Table of the number of adenines needed to reach the zero state for each of the base 21 figures.
 Second step: Input of calculation parameters in the computer with the PolyA  program.
 – Verification frequency.
 – Beginning of the verification.
 – Marking of amino acids.
 For the evaluation of the number of adenines required in order to reach the zero state at the level of this example.
A frequency of verification at every 3 quotients was retained.
Beginning of the verification in position 1 has been retained.
A start of labeling in position 1 has been retained.
  Other situation regarding parameters input.
  Computer calculation results : (see annex XV)
  One of the roles assigned to the poly  A according to the theory.
 Poly  U and tryptophan operon. ( What interresting here, is the presence of PolyU.)
7.1  Case of the polyU located at the end of mRNA coding for the tryptophan operon.
7.2  Case of the poly  U located at the end of the tryptophan operon LEADER. ( L region )
7.2.1  Low concentration in tryptophan.
7.2.2  High concentration in tryptophan.
  Repair mechanism for polyA tails by adding uridine ( PolyU )
  Conclusion.
 The Cancer Problem
  Definition of Cancer.
  Type of cancer.
 Carcinoma: Epithelial structure constituting the majority of all tumors.
 Sarcoma: Origin of connective tissue of muscles, cartilage, fat and bone cells
 Leukemia: Divided into 2 types
  Acute Leukemia
  Chronic Leukemia
  Acute Leukemia: Associated with anemic and hemorrhagic infectious syndrome.
  Chronic Leukemia : Divided into 2 types.
  Chronic Leukemia Myeloid ( Myeloma)
  Chronic Leukemia Lymphoid (Lymphoma)
  Carcinogenic agents responsible for DNA damage.
 3.1  Physical agents.
 3.2  Inorganic compounds.
 3.3  Organic compounds.
 3.4  Parasitic agents.
 Cancer: The most accepted theory currently in science.
  DNA damage and Types of damage.
 5.1  DNA alteration. ( Types of mechanisms responsible )
 5.2  Types of damages.
 5.2.1  An incorrect base on one strand.
 5.2.2  Missing Bases.
 5.2.3  Modification of bases.
 5.2.4  Breaking one of the two strands of DNA.
 5.2.5  The two strands of DNA are broken.
 5.2.6  Cross – linking.
 Cancer and Biomathematic Model
 New theoretical approach to cancer.
  The cancer problem: no place.
  The potential of biomathematics and bioinformatics as working tools.
  Biomathematical approach to cancer.
  Hypothesis on the procedure loop derived from the biomathematic model.
 2.1.1  Visualization from the concept of division
 2.1.2  Visualization by means of the concept of the conversion of the division into the automation process through the portrait sequences.
 2.1.3  How, from a hypothetical point of view, the mechanism of a periodical can be explained or understood at the level of a division performed by the portrait sequences.
 2.1.4 Cancer et PolyA
 2.1.5 – Is it a case of defense reaction to maintain the integrity of the information ?
 – The three requirements established by the biomathematic model for the possibility of intrigger the cancer process eukaryotic cells.
 1 – Presence of broken or incomplete mRNA from an unrepaired damaged DNA.
 2 – A lack of polyA addition at the end of the incomplete mRAN sequence.
See Fig. 10e : Transcript showing the 2 required sequences determining the site of mRNA cleavage and polyadenilation.
 3 – A translation at the level of the cytoplasme of the incomplete or broken mRNA, by the ribosome which implies the crossing of the nuclear membrane to cytoplasme without addition of polyA.
* * * * * * * * * * * *

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