Mathematical Concepts and Methods in Modern Biology: Using Modern Discrete Models

Mathematical Concepts and Methods in Modern Biology offers a quantitative framework for analyzing, predicting, and modulating the behavior of complex biological systems. The book presents important mathematical concepts, methods and tools in the context of essential questions raised in modern biology.

Designed around the principles of project-based learning and problem-solving, the book considers biological topics such as neuronal networks, plant population growth, metabolic pathways, and phylogenetic tree reconstruction. The mathematical modeling tools brought to bear on these topics include Boolean and ordinary differential equations, projection matrices, agent-based modeling and several algebraic approaches. Heavy computation in some of the examples is eased by the use of freely available open-source software.

Features self-contained chapters with real biological research examples using freely available computational toolsSpans several mathematical techniques at basic to advanced levels Offers broad perspective on the uses of algebraic geometry/polynomial algebra in molecular systems biology

Preface by Raina Robeva and Terrell Hodge Chapter 1. Mechanisms for Gene Regulation: A Boolean Network Model of the Lac Operon Chapter 2. Epigenetic Features of the Lac Operon: Comparing Boolean and Ordinary Differential Equations Models Chapter 3. Inferring the Topology of Gene Regulatory Networks: An Algebraic Approach to Reverse Engineering Chapter 4. Global Dynamics Emerging from Local Interactions: Agent-based Modeling for the Life Sciences Chapter 5. Agent-based Models and Optimal Control in Biology: An Algebraic Approach Chapter 6. Neuronal Networks: A Discrete Model Chapter 7. Predicting Plant Population Growth: Modeling with Projection Matrices Chapter 8. Metabolic Pathways Analysis: A Linear Algebraic Approach Chapter 9. Identifying CpG Islands: Sliding Windows and Hidden Markov Models Chapter 10. Codon Usage: From Elementary Probability to Algebraic Geometry Chapter 11. Phylogenetic Tree Reconstruction: Geometric Approaches