A MATHEMATICAL REPRESENTATION
OF THE CENTRAL DOGMA IN
MOLECULAR BIOLOGY
1
Juanyi Yu
AGENDA
  Introduction
  The
Central Dogma of Molecular Biology
  Problem Definition
  Propositions
  Future Work
2
INTRODUCTION
  Previous



work
Cellular level control systems approach
Hidden Markov Model (HMM): statistical model
Base-by-base structural model
  Motivation

To develop an intra-cellular structural model which
can fully describe the information flow under the
Central Dogma of Molecular Biology and can
facilitate the application of control theory into
biological systems
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AGENDA
  Introduction
  The
Central Dogma of Molecular Biology
  Problem Definition
  Propositions
  Future Work
4
THE CENTRAL DOGMA
  Gene

Segments of DNA that encodes instructions that
allow a cell to produce specific products, usually
proteins
  Protein


synthesis
General, special and unknown transfers
Replication, transcription and translation
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6
http://www.geocities.com/avinash_abhyankar/molecular/central_dogma.htm
  Standard
genetic codes
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AGENDA
  Introduction
  The
Central Dogma of Molecular Biology
  Problem Definition
  Propositions
  Future Work
8
GENERAL FORMULA
  Double-stranded
DNA are separated into two
single strands, template sequence and
complementary sequence
  Transfer matrix for template sequence
  Transfer
matrix for complementary sequence
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DNA HYBRIDIZATION
  General
  An
formula
imperfect hybridization
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RNA SELF-HYBRIDIZATION
  Structure
analysis of RNA self-hybridization
sequences
  General
formula
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  Two
  An
common subsequences of folded RNA
example of RNA self-hybridization
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PROTEIN SECONDARY STRUCTURE
  Basic

units
  Example
(c)
α helix, β sheets and
loops
  General
formula
  Five
types of protein
secondary structure
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AGENDA
  Introduction
  The
Central Dogma of Molecular Biology
  Problem Definition
  Propositions
  Future Work
15
PROPOSITIONS
  Similar

DNA sequences
Two equal-length DNA sequences that have less than
a certain percentage (10% in practice) of noncomplementary base-pairs are called similar DNA
sequences.
  Division
rule for RNA self-hybridization
sequences

According to different orientations, RNA sequences
are divided into different branches, branches can be
further divided into basic units, dangling strands,
stem regions and loops.
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  Division
rule for RNA self-hybridization
sequences (continued)



The number of bases in two subsequences of the same
branch need to be equal. If not, make them equal by
adding zero row vector at appropriate row(s).
The first unit in the first branch must be a dangling
strand or a stem region.
A branching loop is usually considered as a single
branch.
  Recovering
character-based RNA from transfer
matrix
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  Classification






of amino acids
Non-polar: Ala, Gly, Ile, Leu, Met, Phe, Pro, Trp and
Val
Polar: Asp, Glu, Arg, His, Lys, Asn, Cys, Gln, Ser,
Thr and Tyr
Acidic: Asp and Glu
Basic: Arg, His and Lys
Neutral
Augmented transfer matrix
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
Polar if

Acidic if

Basic if
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AGENDA
  Introduction
  The
Central Dogma of Molecular Biology
  Problem Definition
  Propositions
  Future Work
20
GENE MUTATION
  Causes


Natural process
Induced by mutagens: α, β, γ and x-rays,
ultraviolet light, chemical mutagens
  Types





of mutations
of mutations
Silent mutation
Neutral mutation
Missense mutation
Nonsense mutation
Frameshift mutation
  General
formula
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  An
example
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DRAFTED SYSTEM EQUATION
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