Math 3380: Mathematics in Molecular Biology
Fall 2005
Instructor: David Swigon
Office: Thackeray 519, 4126244689, swigon@pitt.edu
Lectures: TTh 2:30 – 3:45pm (NEW), Thack 524
Office Hours: By appointment.
Course Web Page: (check frequently for
changes and updates)
http://www.math.pitt.edu/~swigon/math3380.html
Course Description
The course will present an overview of mathematical models and techniques used in molecular biology, with the focus on DNA and protein sequence analysis, atomic level molecular modeling and genetic network modeling. It is recommended for graduate students in mathematical or computational biology, and also students in discrete and computational mathematics who want to learn about biological applications. No background in molecular biology or chemistry necessary.
Prerequisites
Undergraduate level probability theory and differential equations.
Textbook
There is no required textbook for the course. We will cover selected material from the following books:
[DEKM] Durbin, Eddy, Krogh, & Mitchison, Biological sequence analysis, Cambridge University Press 1999, ISBN: 0521629713
[EG] Ewens & Grant, Statistical Methods in Bioinformatics, Springer 2001, ISBN: 0387952292
[S] Schlick, Molecular modeling and simulation, Springer 2002, ISBN: 038795404X
Other relevant reading material and journal articles will be distributed during the course.
Grading Scheme
Homework Assignments: 1/3
Project & presentations: 1/3
Final Exam: 1/3
Schedule
The course will be divided into three segments: Biological sequence analysis, Molecular modeling, and Genetic network analysis. We will meet two times a week for 1.5 hours in the classroom and occasionally in a computer lab.
For the term project each student will be assigned a particular gene and his task will be to perform on that gene several analyses corresponding to the topics covered in the course, such as the sequence alignment with related genes from related organisms, evolutionary comparison, structural analysis of the corresponding protein, energy minimization of atomic level structure, molecular dynamics, genetic network analysis.
Student presentations on databases
Biological databases are essential sources of information to everyone doing modeling in molecular biology. To get an overview about various databases available, every week or so a pair of students will give ~10 min presentation about one of the following: NCBI, Genbank, Swissprot, KEGG, PDB & NDB, DNA microarrays, etc.
Note
This is a special topics course in applied mathematics which is intended to give you an introduction to mathematics and algorithms used in molecular biology. Emphasis will be placed on handson approach and problem solving. No formal theorems and proofs will be given.
Syllabus
Date 
Covers 
Topic 
Homework 
Notes 
Further material 
Aug 30 

Introduction 



Sep 1 
5.25.9 of [EG] 
Single sequence analysis 

[1] 

Sep 6 
2.12.9 of [DEKM] or 6.16.5 of [EG] 
Sequence alignment 

[2] 

Sep 8 
9.19.5 of [EG] 
Sequence alignment, BLAST 
[3],[4] 

Sep 13 
3.13.3 of [DEKM] or 11.111.2 of [EG] 
Hidden Markov Models 


Sep 15 
11.3 of [EG] 
Gene finding Alignment using HMM, 


[5] 
Sep 20 
6.16.5 of [DEKM] 
Multiple sequence alignments, CLUSTALW 



Sep 22 
7.17.4 of [DEKM] 14.114.6 of [EG] 
Phylogenetics – building of trees 


Sep 27 
8.18.6 of [DEKM] 
Probabilistic evolutionary models 


Sep 29 

Review of sequence analysis 
Bring Lecture notes 5, 7 


Oct 4 
3.13.4 of [S] 
Biological macromolecules, proteins and DNA 



Oct 6 
5.15.3 of [S] 
Nucleic acid structure 



Oct 11 
4.14.10 of [S] 
Protein structure, PDB 



Oct 13 
7.38.8 of [S] 
Molecular forces 

NEW 

Oct 18 
9.19.5 of [S] 
Algorithms in molecular mechanics 

Bring Lecture10 
[6], [7] 
Oct 20 
10 of [S] 
Problems of Molecular mechanics Energy minimization algorithms 

[8] 

Oct 27 
11 of [S] 


[9] 

Nov 1 
12 of [S] 
Molecular dynamics algorithms 
[10], [11],[12] 

Nov 3 

DNA topology 

[13][16] 

Nov 10 

DNA mechanics and statistical mechanics 

[17][20] 

Nov 15 

Metabolic networks 

[21][24] 

Nov 17 

Metabolic networks 



Nov 22 

Systems biology of cells, Genetic networks 

[25][26] 

Nov 29 

Bayesian models 

[27][30] 

Dec 1 

Nonlinear ODE models 



Dec 6 

Monotone systems 


[31][33] 
Dec 8 

Boolean and logic network models 

[34][37] 

Dec 13 

Stochastic effects in gene expression 

[38][40] 

Dec 15 

Stochastic simulation 
[41][43] 
Related Papers
[1] Stormo, DNA binding sites: representation and discovery. Bioinformatics 16 (2000)
[3] Altschul et al., Basic local alignment search tool. JMB 215 (1990)
[5] Burge & Karlin, Prediction of complete gene structures in human genomic DNA, JMB 268 (1997)
[6] Karplus & McCammon, Molecular dynamics simulation of macromolecules, Nature Struct. Bio. (2002)
[8] Nocedal, Theory of Algorithms for Unconstrained Optimization, Acta Numerica (1992)
[9] Metropolis et al., Equation of state calculation by fast computing machines, JCP (1953)
[10] Skeel, Zhang, & Schlick, A family of symplectic integrators, SIAM J. Sci. Comput. (1997)
[11] Schlick et al, Algorithmic challenges in computational molecular biophysics, JCP (1999)
[12] Schlick et al., Biomolecular dynamics at long timesteps, Ann. Rev. Biophys. Biomol. Struct. (1997)
[13] Fuller, The writhing number of a space curve, PNAS (1971)
[14] Vologodskii, Topology and physics of circular DNA (1992)
[15] Pohl, DNA and differential geometry, Math. Intelligencer (1980)
[16] White, Introduction to the geometry and topology of DNA structure, Mathematical methods for DNA sequences, CRC (1989)
[18] Bustamante et al., Single molecule studies of DNA mechanics, Cur. Opin. Struct. Bio. (2000)
[19] Charvin et al., Twisting DNA: Single molecule studies, Contemporary Physics (2004)
[21] Feinberg, The existence and uniqueness of steady states for a class of chemical reaction networks, Arch. Rational Mech. Anal. (1995)
[22] Hofmeyr, Metabolic control analysis in a nutshell (2001)
[23] Vo et al.
, Reconstruction and Functional Characterization of the Human Mitochondrial Metabolic Network Based on Proteomic and Biochemical Data, JBC (2004)
[24] Gunawardena, Notes on Metabolic Control Analysis, (2002)
[27] Friedman et al. Using Bayesian networks to analyze expression data, JCB (2000)
[30] Huang, Gene expression profiling, genetic networks, and cellular states, JMM (1999).
[31] Sontag, Molecular Systems Biology and Control, (2005)
[32] Enciso & Sontag, On the stability of testosterone
dynamics, JMB (2004)
[34]
Edwards,
Analysis of continuoustime switching networks, Physica D (2000).
[35]
Mestl
et al., Chaos in highdimensional neural and gene networks, Physica D (1996).
[37]
Thomas,
Multistationarity, the basis of cell differentiation and memory II., Chaos
(2001).
[38]
Thattai & van
Oudenaarden, Intrinsic noise in gene regulatory networks, PNAS (2001)
[39] Kepler & Elston, Stochasticity in transcription regulation, Biophys.J., (2001)
[40]
Rao
et al., Control, exploitation and tolerance of intracellular noise, Nature
(2002)
[41]
Gillespie, Exact
stochastic simulation of coupled chemical reactions, JPC (1977)
[43]
Vilar et al.,
Mechanisms of noiseresistance in genetic oscillators, PNAS (2001)
Rudimentary
introduction to DNA and molecular biology:
Molecular Biology and Genetics Primer for Mathematicians
Ron Shamir’s Course notes on sequence
analysis, pattern searching, and hidden Markov models
For
a standard introduction to molecular biology I recommend the following
undergraduate textbook:
Free
textbook on molecular dynamics (Google account required):
Rapaport
& Rapaport, Art of Molecular Dynamics Simulation
NCBI (National Center for Biotechnology
Information) includes GenBank and many other databases
KEGG (Kyoto Encyclopedia of Genes and
Genomes)
RegulonDB (Transcription regulation in E. coli)
SBML (Systems Biology Markup Language)
BCM multiple sequence alignments
Biosequence analysis– complements Durbin et al. book, JAVA & applet codes
Hidden
Markov Models for sequence analysis
Construction of phylogenetic trees
Molecular
Visualization and Modeling
RasMol  basic tool used by majority, small code, fast
PyMol  Python based, excellent graphics and visualization options
BioNetS (Biochemical Network Stochastic Simulator)
XPPAUT (General purpose ODE solver)
DESS (Ordinary differential equations solver  Applet)