| Description |
1 online resource (xvi, 418 pages) : color illustrations |
| Series |
Mathematics in science and engineering |
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Mathematics in science and engineering.
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| Contents |
Chapter 1: Multiscale Graph-Theoretic Modeling of Biomolecular Structures; 1.1 Introduction; 1.1.1 The Molecules of Life; 1.2 Graph Theory Fundamentals; 1.3 Modeling RNA Structure; 1.3.1 RNA Secondary Structure Features; 1.3.2 Tree and Dual Graph Models of RNA Secondary Structure; 1.3.2.1 RNA Tree Graphs; 1.3.2.2 Using Graph Statistics to Understand RNA Secondary Structure; 1.3.2.3 RNA Dual Graphs; 1.3.2.4 Online RNA Resources; 1.3.3 Homework Problems and Projects5058 1.4 RNA Structure and Matchings1.4.1 L & P Matchings; 1.4.2 The C & C Family; 1.4.3 Homework Problems and Projects; 1.5 Hierarchical Protein Models; 1.5.1 Weighted Graph Invariants; 1.5.2 Homework Problems and Projects; References; Further Reading; Chapter 2: Tile-Based DNA Nanostructures; 2.1 Introduction; 2.2 Laboratory Process; 2.3 Graph Theoretical Formalism and Tools; 2.3.1 Flexible Tiles; 2.3.2 Flexible Tiles, Unconstrained Case; 2.3.3 Flexible Tiles, Constrained Case; 2.3.4 The Matrix of a Pot; 2.4 Rigid Tiles; 2.5 Computation by Self-Assembly; 2.6 Conclusion |
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2.7 Resource MaterialsAcknowledgments; References; Further Reading; Chapter 3: DNA rearrangements and graph polynomials; 3.1 Introduction; 3.2 Gene Assembly in Ciliates; 3.2.1 Biological Background; 3.2.2 Motivational Example; 3.3 Mathematical Preliminaries; 3.4 Mathematical Models for Gene Rearrangement; 3.4.1 Graphs Obtained From Double Occurrence Words; 3.4.2 Double Occurrence Words Corresponding to Graphs; 3.5 Graph Polynomials; 3.5.1 Transition Polynomial; 3.5.2 Assembly Polynomial; 3.5.3 Reduction Rules for the Assembly Polynomial; 3.5.4 Rearrangement Polynomial 5058 3.6 GeneralizationsAcknowledgments; References; Chapter 4: The Regulation of Gene Expression by Operons; 4.1 Basic Biology Introduction; 4.1.1 The Central Dogma and Gene Regulation; 4.1.2 Types of Operons; 4.1.3 Two Well-Known Operons in E. coli; 4.1.3.1 The Lactose Operon; 4.1.3.2 The Arabinose Operon; 4.2 Continuous and Discrete Models of Biological Networks; 4.2.1 Differential Equation Models; 4.2.2 Bistability in Biological Systems; 4.2.3 Discrete Models of Biological Networks; 4.3 Local Models; 4.3.1 Polynomial Rings and Ideals for the Nonexpert; 4.3.2 Finite Fields |
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4.3.3 Functions Over Finite Fields4.3.4 Boolean Networks and Local Models; 4.3.5 Asynchronous Boolean Networks and Local Models; 4.3.6 Phase Space Structure; 4.4 Local Models of Operons; 4.4.1 A Boolean Model of the lac Operon; 4.4.2 A Boolean Model of the ara Operon; 4.5 Analyzing Local Models With Computational Algebra; 4.5.1 Computing the Fixed Points; 4.5.2 Longer Limit Cycles; 4.6 Software for Local Models; 4.6.1 GINsim; 4.6.2 TURING: Algorithms for Computation With FDSs; 4.7 Concluding Remarks; References 500 Chapter 5: Modeling the Stochastic Nature of Gene Regulation With Boolean Networks |
| Summary |
Algebraic and Combinatorial Computational Biology introduces students and researchers to a panorama of powerful and current methods for mathematical problem-solving in modern computational biology. Presented in a modular format, each topic introduces the biological foundations of the field, covers specialized mathematical theory, and concludes by highlighting connections with ongoing research, particularly open questions. The work addresses problems from gene regulation, neuroscience, phylogenetics, molecular networks, assembly and folding of biomolecular structures, and the use of clustering methods in biology. A number of these chapters are surveys of new topics that have not been previously compiled into one unified source. These topics were selected because they highlight the use of technique from algebra and combinatorics that are becoming mainstream in the life sciences |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (EBSCO, viewed October 19, 2018) |
| Subject |
Computational biology.
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Bioinformatics.
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Computational Biology
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NATURE -- Reference.
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SCIENCE -- Life Sciences -- Biology.
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SCIENCE -- Life Sciences -- General.
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Bioinformatics
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Computational biology
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| Form |
Electronic book
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| ISBN |
9780128140697 |
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0128140690 |
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