Mathematical Concepts in Gene Regulatory Networks

This book provides a vital bridge between molecular biology and mathematics. From the Central Dogma to the chemical master equation, the book guides readers through the mathematical mechanisms underlying toggle switches, oscillations, and stochasticity. By focusing on minimal models, it emphasizes the geometric intuition behind dynamic phenomena, unveiling how biological systems navigate these underlying structures. Key Features: Geometric Intuition over Pure Algebra: Emphasizes visual rate plots, phase planes, and nullclines to map equilibria, stability, bifurcations, oscillations, making deep dynamic concepts accessible to quantitative biologists. Active "Explorations": Replaces passive reading with dedicated, hands-on computational sections that challenge the reader to break, build, and interact with the toy models presented in the text. Computational Integration: Pairs directly with a companion GitHub repository, providing custom MATLAB and XPPAUT scripts to simulate deterministic differential equations and stochastic Gillespie algorithms. Progressive Rigor: Seamlessly transitions from elementary derivatives and basic Hill kinetics to advanced topics like delay differential equations and stochastic processes. Conceptually rich and conversational in its prose, this book is designed for biology graduate students and advanced undergraduates stepping into mathematical biology, as well as applied mathematicians seeking to ground their dynamic models in biological reality. It serves as an essential manual for any researcher aiming to build, simulate, and physically understand the mathematical architectures underlying living systems.