Combinatorial Computational Biology of RNA

Pseudoknots and Neutral Networks

By: Christian Reidys

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Hardcover | 1 November 2010

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268 Pages

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24.77 x 16.51 x 1.91

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In this monograph, new combinatorial and computational approaches in the study of RNA structures are presented which enhance both mathematics and computational biology. It begins with an introductory chapter, which motivates and sets the background of this research. In the following chapter, all the concepts are systematically developed. The reader will find * integration of more than forty research papers covering topics like, RSK-algorithm, reflection principle, singularity analysis and random graph theory * systematic presentation of the theory of pseudo-knotted RNA structures including their generating function, uniform generation as well as central and discrete limit theorems * computational biology of pseudo-knotted RNA structures, including dynamic programming paradigms and a new folding algorithm * analysis of neutral networks of pseudo knotted RNA structures and their random graph theory, including neutral paths, giant components and connectivity All algorithms presented are freely available through springer.com and implemented in C. A proofs section at the end contains the necessary technicalities. This book will serve graduate students and researchers in the fields of discrete mathematics, mathematical and computational biology. It is suitable as a textbook for a graduate course in mathematical and computational biology.

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"This book is devoted to the study of the structure of combinatorial models of the ribonucleic acid (RNA). ... This book can serve as an introduction to the study of combinatorial computational biology as well as a reference of known results and state of the art in this topic." (Ludovit Niepel, Zentralblatt MATH, Vol. 1207, 2011)

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You Can Find This Book In

Non-Fiction Science Biology, Life Sciences Biochemistry Life Sciences in General Genetics excluding Medical Mathematics Applied Mathematics Computing & I.T.Databases Data Capture & Analysis Science in General

Maths for Scientists Combinatorics & Graph Theory Evolution

Introduction	p. 1
RNA secondary structures	p. 3
RNA pseudoknot structures	p. 8
Sequence to structure maps	p. 10
Folding	p. 15
RNA tertiary interactions: a combinatorial perspective	p. 19
Basic concepts	p. 23
k-Noncrossing partial matchings	p. 23
Young tableaux, RSK algorithm, and Weyl chambers	p. 24
The Weyl group	p. 26
From tableaux to paths and back	p. 28
The generating function via the reflection principle	p. 34
D-finiteness	p. 41
Symbolic enumeration	p. 45
Singularity analysis	p. 47
Transfer theorems	p. 47
The supercritical paradigm	p. 49
The generating function F_k(z)	p. 50
Some ODEs	p. 50
The singular expansion of F_k(z)	p. 52
n-Cubes	p. 56
Some basic facts	p. 58
Random subgraphs of the n-cube	p. 60
Vertex boundaries	p. 61
Branching processes and Janson's inequality	p. 62
Exercises	p. 64
Tangled diagrams	p. 67
Tangled diagrams and vacillating tableaux	p. 67
The bijection	p. 70
Enumeration	p. 78
Combinatorial analysis	p. 85
Cores and Shapes	p. 88
Cores	p. 88
Shapes	p. 91
Generating functions	p. 98
The GF of cores	p. 99
The GF of k-noncrossing, -canonical structures	p. 103
Asymptotics	p. 109
k-Noncrossing structures	p. 109
Canonical structures	p. 114
Modular k-noncrossing structures	p. 120
Colored shapes	p. 123
The main theorem	p. 128
Exercises	p. 136
Probabilistic Analysis	p. 143
Uniform generation	p. 143
Partial matchings	p. 145
k-Noncrossing structures	p. 147
Central limit theorems	p. 154
The central limit theorem	p. 155
Arcs and stacks	p. 159
Hairpin loops, interior loops, and bulges	p. 168
Discrete limit laws	p. 175
Irreducible substructures	p. 178
The limit distribution of nontrivial returns	p. 183
Exercises	p. 186
Folding	p. 187
DP folding based on loop energies	p. 191
Secondary structures	p. 191
Pseudoknot structures	p. 194
Combinatorial folding	p. 198
Some basic facts	p. 199
Motifs	p. 201
Skeleta	p. 204
Saturation	p. 208
Neutral networks	p. 213
Neutral networks as random graphs	p. 213
The giant	p. 216
Cells	p. 218
The number of vertices contained in cells	p. 223
The largest component	p. 229
Neutral paths	p. 234
Connectivity	p. 237
Exercises	p. 241
References	p. 245
Index	p. 253
Table of Contents provided by Ingram. All Rights Reserved.

Combinatorial Computational Biology of RNA

Pseudoknots and Neutral Networks

At a Glance

Hardcover

Industry Reviews

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How to return your order

Defective items

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