Mathematics of Genome Analysis

by Jerome K. Percus

• ISBN13: 9780521585262
• ISBN10: 0521585260
• Format: Paperback
• Copyright: 2001-12-03
• Publisher: Cambridge University Press

Summary

The massive research effort known as the Human Genome Project is an attempt to record the sequence of the three trillion nucleotides that make up the human genome and to identify individual genes within this sequence. The description and classification of sequences is heavily dependent on mathematical and statistical models. This short textbook presents a brief description of several ways in which mathematics and statistics are being used in genome analysis and sequencing.

Author Biography

Jerome K. Percus is Professor of Physics and Mathematics at the Courant Institute of Mathematical Sciences and Department of Physics at New York University

Table of Contents

Preface	ix
Decomposing DNA	1	(12)
DNA Sequences	1	(5)
Restriction Fragments	6	(3)
Clone Libraries	9	(1)
Assignment 1	9	(4)
Recomposing DNA	13	(29)
Fingerprint Assembly	13	(5)
Anchoring	18	(5)
Restriction-Fragment-Length Polymorphism (RFLP) Analysis	23	(4)
Assignment 2	27	(1)
Pooling	28	(7)
Assignment 3	35	(1)
Reprise	36	(6)
Sequence Statistics	42	(39)
Local Properties of DNA	42	(7)
Long-Range Properties of DNA	49	(4)
Longest Repeat	50	(3)
Assignment 4	53	(20)
Displaced Correlations	53	(1)
Nucleotide-Level Criteria	54	(7)
Batch-Level Criteria	61	(4)
Statistical Models	65	(8)
Assignment 5	73	(1)
Other Measures of Significance	73	(8)
Spectral Analysis	73	(5)
Entropic Criteria	78	(3)
Sequence Comparison	81	(37)
Basic Matching	81	(15)
Mutual-Exclusion Model	82	(3)
Independence Model	85	(2)
Direct Asymptotic Evaluation	87	(2)
Extreme-Value Technique	89	(7)
Assignment 6	96
Matching with Imperfections	92	(11)
Score Distribution	92	(5)
Penalty-Free Limit	97	(2)
Effect of Indel Penalty	99	(1)
Score Acquisition	100	(3)
Multisequence Comparison	103	(4)
Locating a Common Pattern	103	(2)
Assessing Significance	105	(2)
Assignment 7	107	(11)
Category Analysis	108	(3)
Adaptive Techniques	111	(7)
Spatial Structure and Dynamics of DNA	118	(11)
Thermal Behavior	118	(5)
Dynamics	123	(4)
Effect of Heterogeneity	127	(1)
Assignment 8	127	(2)
Bibliography	129	(8)
Index	137