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 specialized mathematical theory, and concludes by highlighting connections with ongoing research, particularly open questions. The work addresses problems from signaling, gene regulation, genomics, RNA folding, infectious disease dynamics, drug resistance modeling, phylogenetics, neuroscience, and ecological networks. Supporting online supplements are provided to aid instruction and provide practical experience with the material.

Integrates a comprehensive selection of tools from computational biology into education or research programsEmphasizes practical problem-solving through multiple exercises, projects and spinoff computational simulationsContains scalable material for graduate classes and project useSupported by illustrative datasets and adaptable MATLAB computer code

1. Multi-scale graph-theoretic modeling of bimolecular structures 2. DNA nanostructures: Mathematical design and problem encoding 3. Graphs associated with DNA rearrangements and their polynomials 4. Regulation of gene expression by operons: Boolean, logical, and local models 5. Modeling the stochastic nature of gene regulation: probabilistic Boolean networks 6. Inferring interactions in molecular networks via primary decompositions of monomial ideals 7. Analysis of combinatorial neural codes: an algebraic approach 8. Predicting neural network dynamics: insights from graph theory 9. Multistationarity in biochemical networks: Results, analysis, and examples 10. Optimization problems in phylogenetics: Polytopes, programming and interpretation 11. Clustering via self-organizing maps on biology and medicine 12. Toward revealing protein function: Identifying biologically relevant clusters with graph spectral methods