About the Book

Physical Models of Living Systems is a textbook intended for intermediate-level undergraduates in any science or engineering major. The only prerequisite for this course is first-year physics. Supplementary sections make the book also suitable as the basis of a graduate-level course.

Dozens of exercises are included at all levels of complexity, many involving computer work.

This low-cost edition expands the first one with four new chapters. I have also taken the opportunity to add many clarifications, update figures and references, and to add dozens of new exercises.

The e-book is available from Amazon for $9.99. Note that this fixed-format book works best on a big screen (free Kindle app for a laptop or desktop computer). The paperback book is available for suggested retail $49.99. This site conveniently looks up who is offering it and compares prices. For individuals, may I suggest ordering through a local bookshop in your community using its ISBN number: 978-1-7375402-4-3. University bookstores and libraries can get it from Ingram. Bookstores outside the US can open a free ipage account and then order through that ipage account.

The Prologue is freely available here. "To the Instructor" is freely available here.

Errata will be listed here.


With its integrated approach, Physical Models can be used as the basis for interdisciplinary courses in Physics, Biophysics, Bioengineering, or other Engineering departments. Throughout, the goal is for students to gain the fluency they need to derive every result for themselves. To that end, the text includes exercises at all levels of complexity, including many that guide students through computer-based solutions.

Readers will acquire several research skills that are often not addressed in traditional courses:

All of these basic skills, which are relevant to nearly any field of science or engineering, are presented in the context of case studies from living systems, including:

Intended Audience

Who takes this class?

At my institution, the students are undergraduates who have taken one year of university physics. No background in computer programming, and no Biology or Chemistry prerequisite courses are assumed. However, each chapter has a ”Track 2” appendix with more advanced material; with these sections and some assigned primary research articles, the book can also serve a graduate–level course.

Although the book is not about medicine per se, many students who take the course at Penn are premedical, in part because the course addresses many of the competencies that form the basis of the MCAT (see the MCAT guide).

The book has almost no overlap with my other books From Photon to Neuron and Biological Physics. Photon to Neuron focused on light in biology, including optical instruments as well as animal vision. Biological Physics focused on statistical physics, fluid flow, and neural impulses.

Instructor Resources

Please refer to the Instructor Resources Page.

Student Resources

Student resources, including videos, are available on the Student Resources Page.

Responses to the new edition:

“What I find special about this book is its elegance in transitioning from fundamental math to applications in biology and the analysis of real-world data. The book chapters integrate together beautifully and the problem sets are a rare asset.”

Prof. Amir Erez, Hebrew University

“An excellent book, well written and beautifully illustrated.... Lots of homework problems, comparisons to real data, and a winning combination of words, pictures, equations, and computer code... a masterpiece.”

Prof. Bradley Roth, Univ. of Oakland

“A wonderful textbook. It stretches life science students to not only see but also understand how randomness at the heart of living systems can lead to predictable outcomes. Students in my class, taught using PMLS, found the text to be intellectually challenging and, as a result, interesting and memorable.”

Prof. Douglas Martin, Lawrence University

“Each chapter introduces a mathematical concept of central importance to modeling biological systems. The book then immediately demonstrates how these mathematical ideas can be used to build and analyze models and, ultimately, to understand concrete biological phenomena. Most of these demonstrations include a computational component that illustrates the importance of simulations in the modeling process.”

Prof. Krešimir Josić, University of Houston in SIAM Review 2022

Responses to the first edition:

“There is growing interest in quantitative biology and biological physics, driven in part by the rising popularity of synthetic biology and systems biology. However, the development of educational materials has not kept pace with this emerging interest. Phil Nelson’s marvelous new book nicely fills this gap and will serve as a fantastic resource for the field.... The writing style is clear and accessible, and the examples and homework problems have been carefully designed and presented to enable students to become proficient in key concepts and principles at the interface of physics and molecular biology.... Students and professors alike will love this book.”

James J. Collins, Biological Engineering, MIT

“The strong thematic unity of the proposed book is a major strength. What students are most stunned and amazed by is how a handful of basic mathematical concepts (e.g., Poisson statistics, Bayes rules) can be used to understand myriad problems at many levels. Nelson’s book communicates these key concepts in a very engaging way. Choice of topic, strong thematic unity, and lucidness are its major strengths.”

Aravinthan Samuel, Dept of Physics & Center for Brain Science, Harvard University

"I love the combination of real data along with the simplified mathematical modeling. This is exactly the kind of thoughtful back-and-forth between the real world and the modeling world that I try to inculcate in my own students."

Ned Wingreen, Molecular Biology, Princeton University

"This text is beautifully written. It succeeds by presenting a clear and coherent point of view: It is essential to develop quantitative, testable models of biological phenomena and these models are based on the basic physical foundations of nature which are essential for understanding living systems and for developing the modern tools used to investigate their structure and dynamics."

Alex Levine, Chemistry, UCLA

“Excellent conversational tone that Nelson has perfected over time… Excellent mixtures of physical and biological examples, with enough technical content that students can appreciate and understand the biology, but without the jargon and details that often prevent abstract concepts from being easily understood — Illustrations and problems for students are great.”

Megan Valentine, Mechanical Engineering, University of California at Santa Barbara

“This is just the book that one needs to explain to students that mathematical modeling is useful in biology and that just a few mathematical concepts are behind the explosive growth of the biological understanding of the recent years. The interplay between models and experimental data throughout the book is great, and the emphasis on computational solutions with Matlab, with progressing difficulty, allow one to take a complete computer novice into the class.”

Ilya Nemenman, Physics, Emory University

“This book is a fantastic tool for students at the advanced undergraduate to graduate level. The section on randomness in biology is very clearly written with excellent problems and examples. The sections on the Luria-Delbruck experiment are particularly well-laid-out. Poisson Processes (Ch 7) was a favorite of my students and serves as the best example, in my opinion, of how to teach this material.... Overall, a wonderful book through and through.”

Stephanie Palmer, Biology, University of Chicago

Published reviews:

“Particularly compelling for its smooth integration of biological experiments, physical models, and computational exercises. Readers who complete the text will be well equipped with the computational and mathematical skills needed for a quantitative understanding of a range of biological systems.... Thanks to Nelson’s skillful writing and the excellent accompanying online resources, this book will appeal to a broad audience and teach even a beginner how to solve problems numerically.”

Eva-Maria Collins, Physics Today 2015 vol. 68 (12) pp. 56-58.

“[T]his excellent book will appeal to both students and professional scientists in the field of quantitative biology.... [T]he book feels personal in its selection of topics and the training journey on which it takes its readership. In our opinion, the combination of this uniqueness with technical accuracy makes the book a noteworthy and valuable addition to resources for advanced biophysics education... [T]he book conveys rich information, is clearly structured, and provides comprehensive data sets... Nelson shows how computational programming can be used effectively in modeling biological systems at the cellular and molecular levels.”

Dietlind L. Gerloff and Jonghoon Kang. Cell Biology Education (2016) vol. 15 (4) pp. fe11-fe11.

“Philip Nelson has done a terrific job.... There are numerous traits that make this text unique among the very many books of biological physics.... The presentation of materials is developed in an innovative fashion.... There is a nice balance between conceptual examples and end-of-the-chapter problems.... This book shows a nice intercalation of fundamental laws, brief descriptions of computational strategies for acquiring quantitative information, as well as their implications in biological physics and areas beyond that, including signaling processes, genetic switches, and cellular oscillators.... Physical Models of Living Systems... will benefit undergraduates as well as others with interests in genomics, proteomics, cellular signaling, bioengineering, regenerative medicine, and synthetic biology.”

Liviu Movileanu in American Journal of Physics 84 (6), June 2016.