Neuron Simulator: Action Potential, Nerve Conduction and Synapses
A free neuron simulator: the Hodgkin-Huxley action potential with sodium and potassium gates, threshold and refractory periods, TTX, TEA, lidocaine, hyperkalaemia and temperature; saltatory conduction along myelinated and unmyelinated axons with multiple sclerosis demyelination and block; EPSP and IPSP summation; the neuromuscular junction with myasthenia gravis and train-of-four; and a Nernst and Goldman equation calculator.
For learning only. These are teaching models (the classic Hodgkin-Huxley squid axon and simplified synapses), not patient models. Do not use them for clinical decisions or drug doses.
The full Hodgkin-Huxley model of a nerve membrane (squid giant axon, 1952), solved step by step. Give the membrane a pulse of current and watch the voltage, the sodium gates (m opens fast, h closes slower), the potassium gate (n) and the currents that make the spike. The moving line replays it in slow motion; move the pointer over the graphs to read any moment.
The amplifier holds the voltage still and measures the current it has to inject; the current flowing through the channels is the opposite. Inward (Na⁺ entering) is drawn below zero, outward (K⁺ leaving) above. The panel on the left plots the peak sodium and late potassium current for every step voltage (the I-V curve).
Drugs, potassium and temperature
A whole axon: one stretch of membrane after another, each running the Hodgkin-Huxley equations and passing current to its neighbours along the inside of the fibre (the cable equation). Stimulate the left end and watch the impulse travel. Myelin wraps the gaps between the nodes of Ranvier, so the impulse jumps from node to node (saltatory conduction). Damage the myelin in the middle stretch to see slowing and block, as in multiple sclerosis or Guillain-Barré.
Nerve conduction study, done on the model
A clinical nerve conduction study stimulates a nerve and records it at two places. Speed = distance between the two places ÷ difference in arrival time; the size of the response tells how many fibres got through. A drop in size between the two places (more than about half) is conduction block; slowing with a normal size points to demyelination, a small response at both places to axon loss.
Fibre types (Erlanger-Gasser classes)
A neuron collects inputs on its dendrites. Each excitatory synapse (green) gives a small bump up, an EPSP; each inhibitory synapse (red) a small dip or a clamp near rest, an IPSP. One EPSP is far too small; the neuron fires only when enough of them add up at the axon hillock to reach threshold (about −55 mV): many at once (spatial summation) or quickly one after another (temporal summation). Click a synapse, or press 1 to 5.
At the neuromuscular junction each nerve impulse releases a few hundred packets (quanta) of acetylcholine (ACh). ACh opens receptors on the muscle endplate and makes an endplate potential (EPP) that is normally 2-4 times bigger than needed to fire the muscle fibre: the safety factor. Acetylcholinesterase (AChE) breaks ACh down within a millisecond. With repeated stimulation each impulse releases a little less, which only matters when the safety factor is small: the fade seen with myasthenia gravis and with blocking drugs.
Each ion is pulled two ways: down its concentration gradient and by the voltage. The Nernst equation gives the voltage where the two balance for one ion (its equilibrium potential). The cell's real resting voltage is a weighted mix decided by how permeable the membrane is to each ion: the Goldman-Hodgkin-Katz equation. Type concentrations or pick a case.
How the neuron simulator works
Everything on this page runs in your browser from published equations; nothing is uploaded. It is a teaching tool for students of physiology, medicine, nursing, pharmacy and physiotherapy, and for anyone who wants to see why a nerve fires.
The action potential
The model is the one Alan Hodgkin and Andrew Huxley fitted to their voltage-clamp recordings of the squid giant axon (J. Physiol. 117:500-544, 1952; Nobel Prize 1963), written in the modern convention with the resting voltage at −65 mV: maximal conductances 120 (Na⁺), 36 (K⁺) and 0.3 (leak) mS/cm², reversal potentials +50, −77 and −54.4 mV, capacitance 1 µF/cm². It is solved with a 4th-order Runge-Kutta method in 0.01 ms steps. Checks the page passes: rest −65 mV, a 1 ms threshold of about 7 µA/cm², a spike peak near +40 mV, an undershoot towards EK, an absolute refractory period of several milliseconds followed by a relative one, and a conduction speed of 18.6 m/s in the cable at 18.5 °C (Hodgkin and Huxley calculated 18.8 m/s and measured 21.2 m/s).
- Threshold is not a fixed voltage: it is where the inward sodium current outruns the outward potassium and leak currents, so a short strong pulse and a long weak one both work (strength-duration). The page marks the voltage where the rise first exceeds 20 mV/ms.
- Refractory periods. Right after a spike most sodium channels are inactivated (h is low) and potassium channels are still open, so no stimulus can fire another spike (absolute refractory period, defined here as "not even at 20 times the normal threshold"), then only a stronger one can (relative refractory period).
- Potassium. The outside potassium moves EK by exactly what the Nernst equation predicts (26.7 mV × ln(K/4) at 37 °C). High potassium (hyperkalaemia) depolarises the resting membrane, which inactivates sodium channels: spikes get smaller and slower and can fail, the reason severe hyperkalaemia is dangerous for the heart. Low potassium hyperpolarises it.
- Drugs. TTX and TEA are modelled as a simple fraction of channels blocked. Lidocaine is a simplified "modulated receptor" sketch (after Hondeghem and Katzung, 1977): it binds sodium channels mainly while they are open or inactivated and lets go over about 300 ms, so the block grows with firing rate. The rates are chosen to show the idea, not fitted to a real dose.
- Temperature. Gate speeds scale with Q10 = 3 from 6.3 °C. The squid model stops firing above about 30 °C (heat block); a real mammalian nerve works at 37 °C with different channel kinetics, so times here are slower than in a human nerve.
Conduction
The axon is a chain of short compartments (the cable equation, solved implicitly) with the squid axon's radius (238 µm) and axoplasm resistance (35.4 Ω·cm). In the myelinated version, short nodes with five times the channel density alternate with 1 cm internodes whose myelin divides the capacitance and leak by 200; damage lowers that factor towards bare membrane. The model gives the physics (how myelin speeds conduction, how damage slows and then blocks it, why warming a damaged fibre can block it), but it is a squid-sized fibre. The "human fibre" speed is therefore an estimate: Hursh's rule of about 6 m/s per µm of diameter for myelinated fibres (1939), and about 1.5 m/s × √(diameter in µm) for unmyelinated C fibres, multiplied by the slowing the model shows through the damaged stretch.
Synapses
The summation neuron is a conductance-based integrate-and-fire cell (membrane time constant 20 ms, rest −70 mV, threshold −55 mV, excitatory reversal 0 mV, inhibitory reversal −75 mV like a chloride synapse), with each synapse's effect at the soma reduced by e−distance/300 µm for a passive dendrite. A real neuron has active dendrites and thousands of synapses. The neuromuscular junction model releases a fraction of a vesicle pool per impulse (the pool refills over about 1.5 s, faster during high-frequency trains), with an endplate potential that saturates and a population of fibres with thresholds of 10-20 mV. The six conditions are illustrative settings chosen to reproduce the textbook patterns (normal train-of-four ratio 1, fade in myasthenia gravis and with non-depolarising blockers, improvement with an AChE inhibitor, increment at high rates in Lambert-Eaton syndrome), not fitted to patients.
Sources
- Hodgkin AL, Huxley AF (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500-544.
- Hursh JB (1939). Conduction velocity and diameter of nerve fibers. Am J Physiol 127:131-139. Rushton WAH (1951). A theory of the effects of fibre size in medullated nerve. J Physiol 115:101-122.
- Goldman DE (1943). Potential, impedance and rectification in membranes. J Gen Physiol 27:37-60. Hodgkin AL, Katz B (1949). J Physiol 108:37-77.
- Hondeghem LM, Katzung BG (1977). Time- and voltage-dependent interactions of antiarrhythmic drugs with cardiac sodium channels. Biochim Biophys Acta 472:373-398.
- Hille B. Ion Channels of Excitable Membranes, 3rd ed. Kandel ER et al. Principles of Neural Science, 6th ed. Wood SJ, Slater CR (2001). Safety factor at the neuromuscular junction. Prog Neurobiol 64:393-429.
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