I am writing a book on the theory of action potentials. I will post chapters on this website as I write them. Note however that this is essentially preparatory work for the book, and I am probably going to rewrite and reorganize it quite extensively. So do not expect a very well organized and didactical text at this stage; only the essential content should remain. I would be happy to read your comments, in particular if you find errors or omissions: please let me know and I will reward you with your name in the acknowledgments!
The plan is to start with standard biophysics of excitability, and then I will expose more advanced topics, such as: how spikes initiate in real life (as opposed to when you stimulate an axon), how excitability changes on different time scales, and how a cell learns to spike. The book adopts a systemic viewpoint; that is, the goal is to understand how the coordination of channels creates and maintains functional action potentials. I would also like to give an epistemological flavor to it that I find is missing in most textbooks: what is a model, how is it built and tested, what is its empirical value, etc.
Why this book and who is it for? With this book, I am hoping to bring theoreticians to the field of neural excitability, and to give them the necessary material that is currently scattered over many references. Currently, the field is largely dominated by experimental biologists. Yet, as I will try to convey, this is a field where one can ask many key neuroscientific questions in a context where the link between structure and function is much less speculative than in neural network research, including questions of learning and adaptation, and where one can actually develop quantitative, testable theories. As a bonus, I would also be happy if I could manage to convey some elements of theory to biologists.
Prerequisites. In principle you do not need to know much about biology to read this book, as I will try to introduce the necessary information. I am expecting some mathematical skills, mostly calculus and basics of differential equations, but nothing very advanced. Regarding physics, electrophysiology is obviously a lot about electricity. In the current version, I am assuming the reader has some basic knowledge of electricity (what current and charges are, Ohm's law). But I am planning to add a primer on electricity.
I am also compiling a general bibliography on action potential theory (books and reviews only).
Here is a tentative outline (available chapters are in bold):
- Action potentials. An overview of action potentials, their scientific history and their function. Brian notebooks for chapter 1. Last update: 9.6.2016
- The membrane potential. The biophysical basis of membrane polarization. Brian notebooks for chapter 2. Last update: 9.6.2016
- Action potential of an isopotential membrane. Basic biophysics of the squid giant axon and Paramecium, and the Hodgkin-Huxley model. Brian notebooks for chapter 3. Last update: 19.7.2016
- Excitability of an isopotential membrane. Theoretical analysis of excitability in isopotential models [Some content to be added on excitability types]. Last update: 14.3.2017.
- Propagation of action potentials (technical draft). The cable equation; active propagation in unmyelinated and myelinated axons. Last update: 13.4.2017.
- Spike initiation in the axonal initial segment (incomplete draft). Excitation through the soma and AIS, as opposed to excitation of the middle of a squid axon. Last update: 5.4.2018.
- Dynamics of excitability. How excitability (spike threshold) changes at different time scales (adaptation and plasticity).
- Energy consumption.
- Learning to spike. How a cell builds and maintains a functional spiking system.