# Hodgkin & Huxley (1952) model

### About this model

Original publication: | |
---|---|

Hodgkin & Huxley (1952): ‘A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve’, J. Physiol. 117: 500-544. | |

DOI: | https://doi.org/10.1113/jphysiol.1952.sp004764 |

### Model status

The current CellML model implementation runs in OpenCOR. The results have been validated against the data extracted from the figures in the published Hodgkin & Huxley (1952). The model structure, simulation results and limitation have been detailed in the following sections.

### Model overview

This workspace holds a CellML encoding of the Hodgkin & Huxley (1952) model. The Hodgkin & Huxley (1952) (HH) model is one of the foundational models of cellular electrophysiology. It defined the “standard” gating kinetics still used in many models today. The model includes potassium, sodium, and ‘leakage’ currents as well and the transmembrane electrical potential. The HH model was originally developed to investigate flow of electric charge in giant nerve axons in squid.

### Modular description

#### Components

CellML divides the mathematical model into distinct components, which are able to be re-used. The main CellML components are:

- Membrane potential component
- Membrane current component (the ionic current during a voltage clamp)
- Propagated action potential component
- Potassium current component
- Sodium current component
- Leakage current component
- Gating kinetics component – a single definition instantiated three times for the n, m, and h gates
- Gating rates components (open/close rates for n, m, and h gates respectively)
- Gate initialization components (steady state values of n, m, and h gates for specified membrane potentials)
- Temperature component
- Time component

Each of these blocks is itself a CellML model, which enables us to reuse the various components in future studies and models.

#### Experiments

Following best practices, this model separates the mathematics from the parameterisation of the model. The mathematical model is imported into a specific parameterised instance in order to perform numerical simulations. The parameterisation would include defining the stimulus protocol to be applied.

This workspace has three sets of experiments:

#### Simulation settings

Simulation settings are encoded in SED-ML documents for experiment execution. The python scripts to run simulation and reproduce the figures in the original paper are also included.

### Model history

The original model implementation is from VPH-MIP case study. The main modification is summarized as follows:

- Add the temperature component to enable the simulation at different temperatures.
- Add membrane current component, voltage clamp and voltage clamp experiment to simulate a membrane current during a voltage clamp.
- Add gate initialization components to enable the simulation of anode break excitation.
- Add propagated action potential model and action potential propagation experiment to simulate a propagated action potential (please see Known issues).
- Add the python scripts to run simulation and reproduce the figures in the original paper.

### Known issues

- The voltage clamp value cannot be -10 mV as the
*α*_{n}would be infinity. - The propagated action potential model does not work, which needs further investigation in future.
- The temperature unit is set to Kelvin in the CellML models. If you want to simulate the model behavior at temperature T with unit Celsius, you do not need to do conversion as the offset is cancelled in the mathematical expressions including temperature factor.
- You need to set appropriate parameters and initial values in the CellML files, if you want to run simulation using OpenCOR rather than the provided Python scripts.
- The
*V*in the model is defined relative to the resting potential, while the inward current is positive. This is different from the convention of modern physiological modelling.