A color-coded graphical guide to the Hodgkin and Huxley papers

Abstract

The five papers published by Hodgkin and Huxley in 1952 are seminal works in the field of physiology, earning their authors the Nobel Prize in 1963, and ushering in the era of membrane biophysics. The papers present a considerable challenge to the novice student, but this has been partly allayed by recent publications that have updated the reporting of current and voltage to reflect the modern convention, and two books that describe the contents of the papers in detail. A disadvantage is that these guides comprise hundreds of pages, requiring considerable time and energy on behalf of the reader. We present a concise guide to the Hodgkin and Huxley papers that includes only essential content, with the data presented in a linear and logical manner. We have color-coded figures for ease of understanding and included boxes that summarise key information for easy reference. It is our expectation that this Illuminations article will act an accessible introduction for students to the work of Hodgkin and Huxley, and hopefully foster an appreciation for a fascinating story that repays in depth study.

Hysteresis in memristors produces conduction inductance and conduction capacitance effects

“…22 The central paradigm of the chemical inductor, and historically the original formulation, is given by the Hodgkin–Huxley equations that describe the temporal dynamics of action potentials in neurons. 23–26…”

Iontronic Nanopore Model for Artificial Neurons: The Requisites of Spiking

“…Based on the recent analysis of minimal spiking devices, we argue that effective spiking is obtained in a single nanopore by the limit cycle sustained oscillations occurring in a Hopf bifurcation. , We construct a physically plausible channel model that contains the main ingredients of a single oscillating memristor, indicated in Figure b. These oscillations in a “smooth” system described by only two nonlinear differential equations suffice to represent an excitable neuron for nanofluidic neuromorphic networks, rather than going all the way down to the more structurally complex HH approach and its advanced transient properties . To establish the criteria for sustained voltage oscillations in nanopore systems, based on impedance spectroscopy measurements, we analyze the dynamical properties of the system using the method of characteristic frequencies that determines the stability conditions. ,, …”

“…Then the neuron “fires” and it becomes updated to a base level, forming the integrate-and-fire (IF) type of models. On the other hand biophysical models are based on the original HH formulation and its many developments. − Their electrical response is smooth and is well represented by a family of highly nonlinear differential equations that describe in detail the temporal evolution of action potentials in biological cells. For example, once the excitation is elicited, natural neurons respond with a repetitive action potential of fixed size, irrespective of the magnitude of the stimulus .…”

“…While HH neuron , contains three state variables (one for the potassium channel and two for the sodium channel) with a total of 4 differential equations, here we take advantage to the fact that HH can be simplified to a “minimal” single state variable as in eqs and , while holding the main properties of the action potential …”

“…These oscillations in a "smooth" system described by only two nonlinear differential equations suffice to represent an excitable neuron for nanofluidic neuromorphic networks, rather than going all the way down to the more structurally complex HH approach and its advanced transient properties. 10 To establish the criteria for sustained voltage oscillations in nanopore systems, based on impedance spectroscopy measurements, we analyze the dynamical properties of the system using the method of characteristic frequencies that determines the stability conditions. 5, 28,29 As a preliminary step, we describe briefly the general structure of a "minimal" spiking neuron model.…”