To understand life phenomena, we must consider form, structure, organization, motion, and the roles they play in “living” functions. This book explores such elements through mathematical methods. Beginning with an overview of dynamical systems and stochastic processes, the chapters that follow build on experimental advances in quantitative data in cellular processes to demonstrate the applications of these mathematical methods to characterize living organisms. The topics covered include not only cellular motions but also temporal changes in metabolic components, protein levels, membrane potentials, cell types, and multicellular patterns, which are linked to functions such as cellular responses, adaptation, and morphogenesis. This book is intended for undergraduates, graduates, and researchers interested in theory and modeling in biology, in particular cell, developmental, and systems biology, also those in the fields of mathematics and physics who are interested in these topics.

‘The explosion of quantitative biology creates novel pedagogical challenges. How to teach not only the foundational biological phenomena at an advanced level, but also the conceptual tools that are necessary for even a qualitative account of biological complexity? And how to attract physics and mathematics students to this emerging discipline? Takagi et al. have delivered an exciting textbook, covering, in only 300 pages, standard topics in dynamical systems theory such as feedback loops in cell systems, but also more advanced topics not usually represented at this level, such as pattern formation, number fluctuations of biomolecules, and even the origin of life and the role of information in biology. Building upon the authors’ important contributions to theoretical biology, this book is unique in its ability to inspire, as well as in its depth and clarity. I would enjoy teaching and learning from it and so will you!’

Nigel Goldenfeld - University of California San Diego