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Algebraic and combinatorial computational biology /
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 s...
| Clasificación: | Libro Electrónico |
|---|---|
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London ; San Diego, CA :
Academic Press is an imprint of Elsevier,
[2019]
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| Edición: | First edition. |
| Colección: | Mathematics in science and engineering.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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
- 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
- 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.