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.
Key Features
- Integrates a comprehensive selection of tools from computational biology into educational or research programs
- Emphasizes practical problem-solving through multiple exercises, projects and spinoff computational simulations
- Contains scalable material for use in undergraduate and graduate-level classes and research projects
- Introduces the reader to freely-available professional software
- Supported by illustrative datasets and adaptable computer code
1. Multi-scale graph-theoretic modeling of bimolecular structures
Greta Pangborn, Wiesner Emilie, John Richard R. Jungck, Manda Riehl, Debra Knisley and Jeff Randell Knisley
2. DNA nanostructures: Mathematical design and problem encoding
Jo Ellis-Monaghan, Nataša Jonoska and Greta Pangborn
3. Graphs associated with DNA rearrangements and their polynomials
Robert Brijder, Hendrik Jan Hoogeboom, Nataša Jonoska and Masahico Saito
4. Regulation of gene expression by operons: Boolean, logical, and local models
Matthew Macauley, Robin Lee Davies and Andy Jenkins
5. Modeling the stochastic nature of gene regulation: probabilistic Boolean networks
David Murrugarra and Boris Aguilar
6. Inferring interactions in molecular networks via primary decompositions of monomial ideals
Matthew Macauley and Brandilyn Stigler
7. Analysis of combinatorial neural codes: an algebraic approach
Nora Youngs, Carina Curto and Alan Veliz-Cuba
8. Predicting neural network dynamics: insights from graph theory
Katherine Morrison, Carina Curto
9. Multistationarity in biochemical networks: Results, analysis, and examples
Carsten Conradi and Casian Pantea
10. Optimization problems in phylogenetics: Polytopes, programming and interpretation
Gabriela Hamerlinck, Stefan Forcey and William Sands
11. Clustering via self-organizing maps on biology and medicine
Olcay Akman, Timothy D. Comar, Dan Hrozencik and Josselyn Gonzalez
12. Toward revealing protein function: Identifying biologically relevant clusters with graph spectral methods
Robin Lee Davies, Urmi Ghosh-Dastidar, Jeff Randell Knisley and Widodo Samyono
- Robeva, Algebraic and Discrete Mathematical Methods for Modern Biology, Mar 2015, 9780128012130, 382pp, $125.00
- Meerschaert, Mathematical Modeling 4e, Jan 2013, 9780123869128, 384pp, $109.95
- Doran, Bioprocess Engineering Principles, Apr 2012, 9780122208515, 926pp, $119.95
Upper division undergraduate and graduate students. Early career researchers in biology or mathematics, particularly those transitioning into the field of mathematical and computational biology. Some practitioners seeking a methods-based primer for the field
