Download Lecture 3 - GATech Math

Math 8803/4803, Spring 2008:
Discrete Mathematical Biology
Prof. Christine Heitsch
School of Mathematics
Georgia Institute of Technology
Lecture 3 – January 10, 2008
Overview
• Feedback is important
• Today: (an incomplete) biology primer
– Disease inheritance (translation: nature is arbitrarily more
complex than we think)
– Challenge: sequence, structure, function
• Next week: combinatorics on biological words and the
thermodynamics of nucleotide sequences
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Mendelian inheritance
Single locus, recessive disease inheritance such as cystic fibrosis.
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Complication 1
Single locus, dominant disease inheritance such as Huntington’s
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Complication 2
Single locus, X-linked disease inheritance such as hemophilia
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Complication 3
Complex multilocus inheritance such as hereditary breast cancer
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Complication 4
Gene splicing, editing, and regulation
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Complication 5
Crossing-over and recombination during meiosis
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Complication 6
22 pairs of autosomal chromosomes, 1 pair of sex chromosomes
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Biotech moment: FISH
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Complication
7
Mutation
Mutation
Types of mutation
Types of mutation
Deletion
Duplication
Inversion
Deletion
Duplication
Inversion
Insertion
Chromosomal mutations
Chromosome 20
Chromosome 20
Chromosome 4
Chromosome
4
Translocation
Insertion
Insertion
Derivative
Chromosome 20
Chromosome 20
Chromosome 20
Chromosome 20
Chromosome 20
Derivative
Chromosome 4
Chromosome 4
Chromosome 20
Chromosome 4
Chromosome
Chromosome
Chromosome 4
4
Translocation
Chromosome 20
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Derivative
Chromosome
20
National
Institutes
of Health
4
Translocation
Chromosome 20
Derivative
Chromosome 20
National Human Genome Research Institute
10
Division of Intramural Research
But there’s hope. . .
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From chromosomes to proteins
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A question of scales
Chromosome
Chromosome
Chromatid Chromatid
Nucleus
Telomere
Centromere
Telomere
Cell
Histones
Base Pairs
DNA(double helix)
G
T
C
C
A
A
G
G
A
T
C
T
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National
Institutes
of Health
13
National Human Genome Research Institute
Division of Intramural Research
Open problem: chromatin packing
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The fundamental challenge
How are structure and function encoded in biological sequences?
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Biological sequences: DNA, RNA, proteins
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Open problem: protein folding
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Nucleotide sequences: DNA and RNA
AU
AT
C
C
G
G
's
's
Ribonucleic acid(RNA)
C
Cytosine
C
Cytosine
NH2
H
H
NH2
C
C
H
N
C
C
H
O
H
N
C
C
N
C
C
H
N
H
G
Guanine
G
Guanine
O
N
O
C
H
C
N
N
H H
C
C
C
H
N
H H
C
N
C
C
H
N
H
N
H
A
N
C
C
H
N
N
C
C
N
H C
N
H
C
C
H
N
H
H
Uracil
U
T
Thymine
O
O
C
H
C
H
H
NH2
Sugar
phosphate
backbone
H
N
H
Base pair
C
C
H
N
Adenine
C
H C
N
C
H
A
NH2
N
N
Nitrogenous
Bases
H
Adenine
H
H3 C
O
H
N
C
C
H
N
Nitrogenous
Bases
National
Institutes
of Health
C
C
H
N
C
C
H
N
O
H
H
replaces Thymine in RNA
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O
H
RNA
DNA
Ribonucleic acid
Deoxyribonucleic acid
Nitrogenous
Bases
National Human Genome Research Institute
Division of Intramural Research
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Base pair
“Discrete” Watson-Crick base pairs
Deoxyribonucleic Acid (DNA)
Sugarphosphate
backbone
Nitrogenous Bases
Sugarphosphate
backbone
Base pairs
G
C
Guanine
Cytosine
O
A
P
T
G
P
S
Hydrogen
bonds
S
N
N
C
T
C
C
H
N
A
S
N
N
P
G
P
G
Nucleotide
C
C
HN
H
H
T
Thymine
O
C
C
C
H
N
N
C
C
H
N
H
O
C
H3C
H
N
H
H
Uracil O
C
H
N
O
P
C
C
H
C
S
S
O
U
S
S
P
H
H C
T
Base pair
C
hydrogen bonds
P
C
H
NH2
S
P
N
Adenine
S
P
C
N
H
A
A
H
N
H
P
S
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C
S
P
C
C
C
H
P
S
NH2
hydrogen bonds
H
C
C
C
H
N
H
H
replaces Thymine in RNA
19
Combinatorics + Molecular Biology =
Discrete Mathematical Biology
Plane trees and RNA
secondary structures
0
F
W1
F
C 1 W2
00
1
0
C1
0
10
W4
01
1
W3
1
0
DNA code words and
de Bruijn sequences
11
1
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Acknowledgements
• Access Excellence Graphics Gallery
http://www.accessexcellence.org/RC/VL/GG/
• Talking Glossary of Genetic Terms
http://www.genome.gov/glossary.cfm
• Basic Genomics Image Gallery
http://genomics.energy.gov/gallery/basic genomics/
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