Download Lecture notes 1 - University of Washington

Mathematics of Genome Analysis and Molecular
Modeling
Hong Qian, Department of Applied Mathematics, University of Washington, Seattle,
WA 98195, USA
E-mail: [email protected]
Abstract.
Contents
1 Introduction
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2 Introductory Molecular Biology
2.1 Nucleotides and Amino Acids . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Various sugars . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Nitrogenous bases: A, T, G, C . . . . . . . . . . . . . . . . . . . .
2.1.3 Nucleotide = nucleoside phosphate . . . . . . . . . . . . . . . . .
2.1.4 Amino acids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.5 Peptide bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Biopolymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Polynucleotides — deoxyribonucleic acid (DNA) and ribonucleic
acid (RNA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Polyamino acids, polypeptides, and proteins . . . . . . . . . . . .
2.2.3 Forces that shape the biopolymer structures . . . . . . . . . . . .
2.3 Central dogma of molecular biology . . . . . . . . . . . . . . . . . . . . .
2.3.1 Replications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Transcriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Translations and protein biosynthesis . . . . . . . . . . . . . . . .
2.3.4 Codons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.5 Differential equation models for gene expression dynamics . . . .
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3 Introduction to Probability Theory and Markov Chains
3.1 Review of discrete probability . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Discrete random variable and probability mass function . . . . . .
3.1.2 Expection, variance, and conditional probability . . . . . . . . . .
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CONTENTS
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2. Introductory Molecular Biology
2.1. Nucleotides and Amino Acids
2.1.1. Various sugars Sucrose, lactose, glucose, ribose and deoxyribos.
positions 3 and 5 .
2.1.2. Nitrogenous bases: A, T, G, C A and G are called purines, T and C are called
pyrimidines.
2.1.3. Nucleotide = nucleoside phosphate A nucleoside consists of a nitrogenous base
covalently attached to a sugar (ribose or deoxyribose) but without the phosphate group.
A nucleotide consists of a nitrogenous base, a sugar (ribose or deoxyribose) and one to
three phosphate groups.
nucleoside = sugar + base.
nucleotide = sugar + base + phosphate.
2.1.4. Amino acids
2.1.5. Peptide bond The carboxyle group of one amino acid reacts with the amino
group of another forms a peptide bond. Due to a double bond, the peptide has a planar
rigid structure. This uniquely defines the notion of (φ, ψ) angle.
2.2. Biopolymers
2.2.1. Polynucleotides — deoxyribonucleic acid (DNA) and ribonucleic acid (RNA)
Base paring: A—T and G—C; double helix structure.
2.2.2. Polyamino acids, polypeptides, and proteins primary sequence, secondary
structures: α-helix, β-sheets, Ramachandran plot.
2.2.3. Forces that shape the biopolymer structures Hydrogen bonds, responsible for
α-helix formation? Hydrophobic interactions, responsible for protein tertiary, globular
structure.
2.3. Central dogma of molecular biology
2.3.1. Replications
2.3.2. Transcriptions
2.3.3. Translations and protein biosynthesis
AMATH 532
Introductory Molecular Biology
• Nucleotides and amino acids
• Biopolymers: polynucleotides — deoxyribonucleic acid (DNA) and ribonucleic acid
• (RNA); poly‐amino acids, polypeptides, and proteins
• Central dogma of molecular biology; mathematical models for gene expressions
• Hydrogen bond, Ramachandran plot, and helix‐coil transition theory
• Advanced topics: Buckling and mechanical instability; supercoil, linking number and White’s formula
Various sugars
sucrose
lactose
glucose
ribose
deoxyribose
The forces that shape the protein structure
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hydrogen bonds,
helices,
hydrophobic interactions,
globular proteins
Central Dogma of Molecular Biology
Codons