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.
- 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. DNA nanostructures: Mathematical design and problem encoding 2. Understanding DNA rearrangements: Graphs and polynomials 3. Multi-scale graph-theoretic modeling of bimolecular structures 4. Toward revealing protein function: Identifying biologically relevant clusters with graph spectral methods 5. Multistationarity in biochemical networks: Results, analysis, and examples 6. Regulation of gene expression by operons: Boolean, logical, and local models 7. Modeling the stochastic nature of gene regulation: probabilistic Boolean networks 8. Inferring interactions in molecular networks via primary decompositions of monomial ideals 9. Analysis of combinatorial neural codes: an algebraic approach 10. Predicting neural network dynamics: insights from graph theory 11. Clustering via self-organizing maps on biology and medicine 12. Optimization problems in phylogenetics: Polytopes, programming and interpretation 13. The relative accuracy of SVDquartets on simulated data with varying model conditions: connecting algebraic statistics to data analysis
Raina Robeva was born in Sofia, Bulgaria. She has a PhD in Mathematics from the University of Virginia and has led multiple NSF-funded curriculum development projects at the interface of mathematics and biology. She is the lead author of the textbook An Invitation to Biomathematics (2008) and the lead editor of the volume Mathematical Concepts and Methods in Modern Biology: Using Modern Discrete Models (2013), both published by Academic Press. Robeva is the founding Chief Editor of the research journal Frontiers in Systems Biology. She is a professor of Mathematical Sciences at Sweet Briar College and lives in Charlottesville, Virginia.
Matthew Macauley is an Associate Professor at Clemson University in South Carolina. Since finishing his PhD in mathematics from the University of California, Santa Barbara, he has been a research visitor at the Biocomplexity Institute of Virginia Tech, the Institute for Systems Biology in Seattle, and the University of South Denmark. He has also taught internationally in both South Africa and Taiwan. Macauley has supervised two PhD and four MS students, as well as a number of undergraduate research students. With Raina Robeva, he has co-organized three faculty development workshops on teaching discrete and algebraic methods in mathematical biology to undergraduates.