Neurons and electrical signals

How a nerve cell makes a 100-millivolt spike, the equations that describe it, and why one neuron may be a deep network in disguise.

Introductory · about 14 min · updated 2026-10-02 · awaiting clinical review

Illustrative simulation excitatory inhibitory

Neurons signal with action potentials: brief, regenerating voltage pulses produced by sodium and potassium channels. This reading explains the resting potential, the Nernst and Goldman–Hodgkin–Katz equations, the Hodgkin–Huxley model and the integrate-and-fire neuron (with an interactive simulator), how myelin and the axon initial segment shape conduction, what goes wrong in multiple sclerosis and channelopathies, and new evidence that single human neurons compute like small deep networks.

Contents

A spark that thinks
What a neuron is
Why the brain signals with electricity
How the action potential works
When: milliseconds to decades
The equations behind the spike
When signalling fails
How we found out
Tools, models and the link to AI
Frontiers: one neuron, many layers
Check yourself

A spark that thinks

Every thought, movement and memory you have is carried by brief electrical pulses. A single pulse, the action potential, lasts only 1–2 milliseconds and swings the voltage across a nerve cell's membrane by about 100 millivolts, yet chains of these pulses steer everything from a blink to a surgeon's hand.^[1]

The machinery behind the pulse was worked out on the giant axon of the squid. Alan Hodgkin and Andrew Huxley turned their measurements into four coupled equations that still predict the shape and speed of the action potential, and shared the 1963 Nobel Prize in Physiology or Medicine with John Eccles for discoveries about the ionic mechanisms of nerve excitation and inhibition.^[2,3]

This reading follows the signal from the molecules that make it to the equations that describe it, then to what happens when it fails, and finally to the surprising discovery that a single human neuron can compute more than the textbook unit of an artificial neural network.^[4,5]

What a neuron is

A neuron has three working parts: dendrites, branching inputs that receive signals from other cells; the soma, the cell body that integrates them; and the axon, a single output cable that carries action potentials to synapses on other cells. Where one neuron meets the next, a synapse converts the electrical pulse into a chemical message and back into a voltage change in the receiving cell, the postsynaptic potential.^[1]

Neurons are not the only cells in the brain. Counting nuclei in dissolved brain tissue, Azevedo and colleagues found on average 86.1 ± 8.1 billion neurons and 84.6 ± 9.8 billion non-neuronal cells in the adult male human brain, overturning the often-quoted figures of 100 billion neurons and ten times as many glia. Only 19% of those neurons sit in the cerebral cortex, even though the cortex makes up 82% of the brain's mass.^[6]

Key numbers

Neurons in the adult male human brain: 86.1 ± 8.1 billion^[6]
Non-neuronal cells: 84.6 ± 9.8 billion^[6]
Share of neurons in the cerebral cortex: 19%^[6]
Resting membrane potential: about −65 mV^[1]
Action potential: about 100 mV for 1–2 ms^[1]
Signalling energy spent on action potentials (rodent grey matter estimate): 47%^[7]

Why the brain signals with electricity

Chemical signals diffuse slowly; electrical signals can cross a long axon in milliseconds. The action potential is regenerated as it travels, so it arrives at the far end of an axon with the same size it started with, rather than fading like a ripple.^[1,2]

Speed has a price. Attwell and Laughlin built an energy budget for excitatory signalling in rodent grey matter and estimated that action potentials consume about 47% of the signalling energy and the postsynaptic effects of glutamate about 34%, with the resting potential taking 13%. Because signalling is so costly, they argued, the brain should favour energy-efficient codes in which only a small fraction of neurons, 15% or fewer, are active at once.^[7]

How the action potential works

Ion pumps keep the inside of a mammalian neuron low in sodium (about 10 mM, against about 145 mM outside) and high in potassium (about 140 mM, against about 5 mM outside). Each gradient defines an equilibrium potential: about +67 mV for sodium and about −83 mV for potassium. The resting potential, about −65 mV, lies between the two and much nearer to the potassium value.^[1]

Hodgkin and Katz explained why: at rest the membrane is far more permeable to potassium than to sodium, so potassium dominates the voltage. Reducing the sodium outside the axon made the action potential smaller and slower, showing that the spike is driven by a brief, voltage-triggered rise in sodium permeability that swings the membrane towards the sodium equilibrium potential.^[8]

In their 1952 model, Hodgkin and Huxley described the membrane current as the sum of a sodium current, a potassium current and a small leak, each with a conductance that depends on voltage and time. Fast sodium activation makes the upstroke; slower sodium inactivation and potassium activation end it and briefly hold the membrane below rest, which is why a neuron cannot fire again immediately (refractoriness).^[2]

In many neurons the spike starts in the axon initial segment, a short stretch at the start of the axon where voltage-gated channels are packed at high density. Kole and Stuart describe it as a dynamic signal-processing unit that regulates how synaptic inputs are integrated, how excitable the neuron is and even how transmitter is released.^[9]

In myelinated nerve fibres the action potential jumps from one gap in the myelin to the next. Huxley and Stämpfli gave the experimental evidence for this saltatory conduction in 1949. How fast a myelinated fibre conducts depends on several things at once: in fibres of similar geometry speed is nearly proportional to diameter, and for a fixed axon diameter it increases with the thickness of the myelin.^[10,11]

From input to output in one neuron. The path of a signal through a neuron. Below threshold, inputs simply fade; above it, the axon initial segment fires an all-or-none action potential that is regenerated along the axon.^[1,9,10]

Text version of the diagram

Synaptic input: transmitter opens channels; a postsynaptic potential spreads. Leads to Dendrites.
Dendrites: inputs add up and fade with distance. Leads to Soma.
Soma: integrates the summed voltage. Leads to Axon initial segment (above threshold).
Axon initial segment: dense sodium channels; the spike usually starts here. Leads to Myelinated axon (action potential).
Myelinated axon: spike regenerates and jumps between gaps. Leads to Synaptic terminal.
Synaptic terminal: spike triggers transmitter release.

When: milliseconds to decades

Neural signalling runs on a millisecond clock: each action potential lasts 1–2 ms and is followed by a refractory period during which a second spike is harder or impossible to trigger. These two facts limit how fast a neuron can fire.^[1,2]

On the scale of a lifetime, the wiring keeps maturing. Comparing humans and chimpanzees, Miller and colleagues found that myelination of the neocortex is developmentally protracted in humans, with a delayed period of maturation that extends beyond late adolescence. Faster, insulated connections are therefore still being added in the late teenage years.^[12]

The equations behind the spike

Neuroscience has an unusually exact mathematical core. The equations below, from 19th-century thermodynamics to Hodgkin and Huxley's model, are still used in modern simulations.^[1,2]

Nernst equation (equilibrium potential of one ion)^[1]

E_X = \frac{RT}{zF}\,\ln\frac{[X]_{\text{out}}}{[X]_{\text{in}}}

The voltage at which the electrical pull on an ion exactly balances its tendency to diffuse down its concentration gradient. At body temperature (37 °C) $RT/F$ is about 26.7 mV, so for a monovalent ion every tenfold concentration ratio corresponds to about 61.5 mV.

Symbols in Nernst equation (equilibrium potential of one ion)
Symbol	Meaning	Unit
$E_X$	equilibrium (Nernst) potential of ion X	V
$R$	gas constant, 8.314 J mol⁻¹ K⁻¹	J mol⁻¹ K⁻¹
$T$	absolute temperature	K
$z$	charge number of the ion (+1 for Na⁺ and K⁺)	—
$F$	Faraday constant, 96,485 C mol⁻¹	C mol⁻¹
$[X]_{\text{out}},\ [X]_{\text{in}}$	concentrations outside and inside the cell	mol L⁻¹

Goldman–Hodgkin–Katz voltage equation^[8,13]

V_m = \frac{RT}{F}\,\ln\frac{P_K[K^+]_o + P_{Na}[Na^+]_o + P_{Cl}[Cl^-]_i}{P_K[K^+]_i + P_{Na}[Na^+]_i + P_{Cl}[Cl^-]_o}

With several ions crossing the membrane, the voltage is a permeability-weighted compromise between their Nernst potentials. At rest potassium permeability dominates, so $V_m$ sits near the potassium potential; during the spike the sodium permeability rises and $V_m$ swings towards the sodium potential. Chloride appears upside down because it carries negative charge.

Symbols in Goldman–Hodgkin–Katz voltage equation
Symbol	Meaning	Unit
$V_m$	membrane potential	V
$P_K, P_{Na}, P_{Cl}$	membrane permeabilities to each ion	m s⁻¹
$[\cdot]_o, [\cdot]_i$	concentrations outside and inside	mol L⁻¹

Hodgkin–Huxley membrane equation^[2]

C_m\frac{dV}{dt} = -\bar g_{Na}\,m^3h\,(V-E_{Na}) - \bar g_K\,n^4\,(V-E_K) - g_L\,(V-E_L) + I_{\text{ext}}

Current through the membrane capacitance equals the sum of three ionic currents and any injected current. The sodium conductance is switched on by the activation variable $m$ (cubed) and off by the inactivation variable $h$ ; the potassium conductance is switched on by $n$ (to the fourth power). Hodgkin and Huxley's fitted maximal conductances for the squid axon were 120 (sodium), 36 (potassium) and 0.3 (leak) mS cm⁻², with a membrane capacitance of 1 µF cm⁻².

Symbols in Hodgkin–Huxley membrane equation
Symbol	Meaning	Unit
$C_m$	membrane capacitance per unit area	µF cm⁻²
$V$	membrane potential	mV
$\bar g_{Na}, \bar g_K, g_L$	maximal sodium and potassium conductances and leak conductance	mS cm⁻²
$m, h, n$	gating variables between 0 and 1	—
$E_{Na}, E_K, E_L$	reversal potentials of each current	mV
$I_{\text{ext}}$	externally applied current per unit area	µA cm⁻²

Gating kinetics^[1,2]

\frac{dx}{dt} = \alpha_x(V)\,(1-x) - \beta_x(V)\,x, \qquad x \in \{m, h, n\}

Each gate opens at a voltage-dependent rate $\alpha_x$ and closes at a rate $\beta_x$ . Because $m$ is fast and $h$ and $n$ are slow, the sodium current rises first and is then cut off while the potassium current grows, which shapes the spike and the refractory period.

Symbols in Gating kinetics
Symbol	Meaning	Unit
$x$	a gating variable (fraction of gates open)	—
$\alpha_x(V), \beta_x(V)$	opening and closing rate constants, functions of voltage	ms⁻¹

Cable length constant^[1]

\lambda = \sqrt{\frac{r_T}{r_L}}

Along a passive dendrite or axon, a steady voltage decays with distance over the characteristic length $\lambda$ . A leakier membrane (smaller $r_T$ ) or a thinner, more resistive core (larger $r_L$ ) makes $\lambda$ shorter, so distant synaptic inputs have less effect at the soma.

Symbols in Cable length constant
Symbol	Meaning	Unit
$\lambda$	electrotonic length constant	mm
$r_T$	transversal (membrane) resistance times unit length	Ω cm
$r_L$	longitudinal (core) resistance per unit length	Ω cm⁻¹

Leaky integrate-and-fire neuron^[1,14]

\tau_m \frac{du}{dt} = -\left[u(t) - u_{\text{rest}}\right] + R\,I(t), \qquad u \geq \vartheta \;\Rightarrow\; \text{spike, then } u \to u_{\text{reset}}

The simplest useful neuron model: the membrane is a leaky capacitor that integrates input current, and every time the voltage reaches a threshold the model emits a spike and resets. The idea goes back to Louis Lapicque's 1907 work on frog nerve. It keeps integration, threshold and reset but leaves out the spike's shape and, in this basic form, adaptation.

Symbols in Leaky integrate-and-fire neuron
Symbol	Meaning	Unit
$\tau_m = RC$	membrane time constant	ms
$u(t)$	membrane potential	mV
$u_{\text{rest}}$	resting potential	mV
$R$	membrane resistance	MΩ
$I(t)$	input current	nA
$\vartheta$	firing threshold	mV

Firing period for a constant current^[1]

T = t_{\text{ref}} + \tau_m \ln\frac{R I_0}{R I_0 - (\vartheta - u_{\text{rest}})}, \qquad R I_0 > \vartheta - u_{\text{rest}}

Solving the integrate-and-fire equation for a constant current $I_0$ , with reset to rest, gives the time between spikes. Below the threshold current no spikes occur; above it the rate $1/T$ rises steeply and then saturates near $1/t_{\text{ref}}$ . The interactive model below plots exactly this.

Symbols in Firing period for a constant current
Symbol	Meaning	Unit
$T$	interval between spikes	ms
$t_{\text{ref}}$	absolute refractory period added after each spike	ms
$I_0$	constant input current	nA

Try it

Input current I2.0 nA

Membrane time constant τ10 ms

In 200 ms: 12 spikes (60 Hz); the formula, for the mean current without noise, gives 63 Hz. Spiking needs R·I above V_th − E_L = 15 mV, that is I above 1.5 nA.

Illustrative parameters: E_L = −65 mV, V_th = −50 mV, reset −65 mV, R = 10 MΩ, refractory period 2 ms; Euler integration with a 0.05 ms step. Spikes are drawn as vertical lines; the model has no spike shape.

Raise the input current until the neuron starts to fire, then shorten or lengthen the membrane time constant. Below about 1.5 nA nothing happens (the drive never reaches threshold); above it the firing rate climbs, and the simulated rate closely matches the formula above.^[1]

When signalling fails

Losing the insulation. Multiple sclerosis is primarily an inflammatory disorder of the brain and spinal cord in which focal lymphocytic infiltration damages myelin and axons. Early on, inflammation is transient and remyelination occurs but is not durable, so episodes of neurological dysfunction usually recover. Over time widespread microglial activation and chronic neurodegeneration take over, and disability accumulates. Evoked potentials reveal the interference with conduction in previously myelinated pathways.^[15]

Faulty channels. Because the action potential depends on precisely tuned ion channels, a single faulty channel gene can cause disease. Claes and colleagues screened seven unrelated patients with severe myoclonic epilepsy of infancy (Dravet syndrome) and found a de novo mutation in the neuronal sodium-channel gene SCN1A in every one of them.^[16]

Where the spike begins. Kole and Stuart's review of the axon initial segment points to a critical role for this small region in disease, which makes sense: it sets the threshold at which a neuron turns its inputs into output.^[9]

How we found out

Milestones

1907Louis Lapicque models nerve excitation as a capacitor that charges until a threshold, the origin of the integrate-and-fire neuron.^[14]
1943David Goldman derives a constant-field theory of membrane potential; McCulloch and Pitts publish the threshold logic neuron that later inspires artificial neural networks.^[13,17]
1949Hodgkin and Katz show the action potential depends on external sodium; Huxley and Stämpfli give evidence for saltatory conduction.^[8,10]
1952Hodgkin and Huxley publish their quantitative model of membrane current.^[2]
1963Nobel Prize to Eccles, Hodgkin and Huxley for the ionic mechanisms of excitation and inhibition.^[3]
1976Neher and Sakmann record the current through single ion channels.^[18]
1991Nobel Prize to Neher and Sakmann for the function of single ion channels in cells.^[19]
1998The first atomic structure of a potassium channel explains how it lets potassium through but not smaller sodium ions.^[20]
2003Nobel Prize in Chemistry to Roderick MacKinnon for structural and mechanistic studies of ion channels.^[21]
2020Dendrites of human cortical neurons are found to fire a new kind of calcium-mediated action potential.^[4]

Tools, models and the link to AI

Two technologies turned the ion channel from a hypothesis into a molecule. The patch clamp let Neher and Sakmann record the tiny current through a single channel in 1976, and X-ray crystallography revealed the structure of a bacterial potassium channel in 1998: four identical subunits form a pore whose narrow selectivity filter, only 12 ångströms long, holds potassium ions but not the smaller sodium ions.^[18,20]

Models range from detailed to drastically simplified. Hodgkin–Huxley-type models track every conductance; integrate-and-fire models keep only integration, threshold and reset, which makes it possible to simulate large networks. The artificial neuron of modern AI goes further still: McCulloch and Pitts reduced a neuron to a logical threshold unit in 1943, and today's deep networks use smooth versions of the same idea, a weighted sum passed through a nonlinearity, with no spikes and no time.^[1,17]

Three levels of neuron model^[1,2,17]
Model	What it keeps	What it leaves out
Hodgkin–Huxley	sodium, potassium and leak currents; spike shape; refractoriness	dendritic structure (in its single-compartment form)
Leaky integrate-and-fire	integration of input, threshold, reset	spike shape; adaptation (in the basic form)
Artificial unit (deep learning)	weighted sum of inputs and a nonlinearity	spikes, timing, ion channels, dendrites

Frontiers: one neuron, many layers

Recordings from human cortex removed during epilepsy surgery revealed something new. Gidon and colleagues found that the dendrites of layer 2/3 pyramidal neurons fire calcium-mediated dendritic action potentials whose amplitude is largest for threshold-level input and smaller for stronger input. These graded spikes let a single human neuron classify linearly non-separable inputs, a computation (like exclusive-or) conventionally thought to need a multilayer network.^[4]

How much computation is inside one neuron? Beniaguev, Segev and London trained deep networks to reproduce, millisecond by millisecond, the input–output behaviour of a detailed model of a layer 5 cortical pyramidal cell. They needed a temporally convolutional network with five to eight layers; when NMDA receptors were removed from the model, a network with a single hidden layer was enough.^[5]

Neurons also come in many kinds. Characterising the gene expression and electrical behaviour of over 4,200 GABAergic interneurons from mouse visual cortex, and the shapes of 517 of them, Gouwens and colleagues defined 28 types with consistent morphological, electrophysiological and transcriptomic properties.^[22]

Check yourself

Roughly how many neurons does the adult human brain contain, and what share of them is in the cerebral cortex?
Show answer
About 86 billion (86.1 ± 8.1 billion), with only about 19% in the cerebral cortex.
Which ion's entry drives the upstroke of the action potential, and how was this shown?
Show answer
Sodium. Hodgkin and Katz showed that reducing external sodium made the action potential smaller and slower.
In the Hodgkin–Huxley equation, what do the variables m, h and n represent?
Show answer
Gating variables: m activates and h inactivates the sodium conductance; n activates the potassium conductance.
Why does myelin speed up conduction?
Show answer
The action potential jumps between the gaps in the myelin (saltatory conduction) instead of travelling continuously along the axon.
What does the cable length constant λ tell you about a dendrite?
Show answer
The distance over which a steady voltage decays along it; a longer λ means distant inputs have more effect at the soma.
In the integrate-and-fire model, why is there no firing below a certain current?
Show answer
If R·I is smaller than the gap between threshold and rest, the voltage settles below threshold and never triggers a spike.
What did Beniaguev and colleagues find about single neurons and deep networks?
Show answer
Reproducing a detailed layer 5 pyramidal neuron model needed a five-to-eight-layer temporal convolutional network; without NMDA receptors one hidden layer sufficed.

Glossary^[1,9,10]

Action potential: A brief, all-or-none voltage pulse (about 100 mV, 1–2 ms) that carries a neuron's output along its axon.
Resting potential: The voltage across the membrane of a neuron at rest, about −65 mV inside relative to outside.
Nernst potential: The voltage at which an ion's electrical and diffusional forces balance, so there is no net flow.
Gating variable: A number between 0 and 1 giving the fraction of ion-channel gates of one kind that are open.
Refractory period: The interval after a spike during which another spike is harder or impossible to trigger.
Axon initial segment: The first part of the axon, rich in voltage-gated channels, where action potentials usually begin.
Myelin: An insulating wrapping around axons that allows saltatory, faster conduction.
Saltatory conduction: Propagation in which the action potential jumps between gaps in the myelin.
Length constant: The distance over which a steady voltage decays along a passive cable such as a dendrite.
Integrate-and-fire model: A simplified neuron that sums its input until a threshold, then emits a spike and resets.

References

Gerstner W, Kistler WM, Naud R, Paninski L. Neuronal Dynamics. Cambridge University Press 2014. doi:10.1017/CBO9781107447615
Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology 1952;117(4):500-544. doi:10.1113/jphysiol.1952.sp004764
Nobel Prize Outreach. The Nobel Prize in Physiology or Medicine 1963. NobelPrize.org 1963. https://www.nobelprize.org/prizes/medicine/1963/summary/
Gidon A, Zolnik TA, Fidzinski P, Bolduan F, Papoutsi A, Poirazi P, Holtkamp M, Vida I, Larkum ME. Dendritic action potentials and computation in human layer 2/3 cortical neurons. Science 2020;367(6473):83-87. doi:10.1126/science.aax6239
Beniaguev D, Segev I, London M. Single cortical neurons as deep artificial neural networks. Neuron 2021;109(17):2727-2739.e3. doi:10.1016/j.neuron.2021.07.002
Azevedo FAC, Carvalho LRB, Grinberg LT, Farfel JM, Ferretti REL, Leite REP, Jacob Filho W, Lent R, Herculano-Houzel S. Equal numbers of neuronal and nonneuronal cells make the human brain an isometrically scaled-up primate brain. Journal of Comparative Neurology 2009;513(5):532-541. doi:10.1002/cne.21974
Attwell D, Laughlin SB. An energy budget for signaling in the grey matter of the brain. Journal of Cerebral Blood Flow and Metabolism 2001;21(10):1133-1145. doi:10.1097/00004647-200110000-00001
Hodgkin AL, Katz B. The effect of sodium ions on the electrical activity of the giant axon of the squid. The Journal of Physiology 1949;108(1):37-77. doi:10.1113/jphysiol.1949.sp004310
Kole MHP, Stuart GJ. Signal processing in the axon initial segment. Neuron 2012;73(2):235-247. doi:10.1016/j.neuron.2012.01.007
Huxley AF, Stämpfli R. Evidence for saltatory conduction in peripheral myelinated nerve fibres. The Journal of Physiology 1949;108(3):315-339. doi:10.1113/jphysiol.1949.sp004335
Waxman SG. Determinants of conduction velocity in myelinated nerve fibers. Muscle and Nerve 1980;3(2):141-150. doi:10.1002/mus.880030207
Miller DJ, Duka T, Stimpson CD, Schapiro SJ, Baze WB, McArthur MJ, Fobbs AJ, Sousa AMM, Sestan N, Wildman DE, Lipovich L, Kuzawa CW, Hof PR, Sherwood CC. Prolonged myelination in human neocortical evolution. Proceedings of the National Academy of Sciences of the USA 2012;109(41):16480-16485. doi:10.1073/pnas.1117943109
Goldman DE. Potential, impedance, and rectification in membranes. Journal of General Physiology 1943;27(1):37-60. doi:10.1085/jgp.27.1.37
Brunel N, van Rossum MCW. Lapicque's 1907 paper: from frogs to integrate-and-fire. Biological Cybernetics 2007;97(5-6):337-339. doi:10.1007/s00422-007-0190-0
Compston A, Coles A. Multiple sclerosis. The Lancet 2008;372(9648):1502-1517. doi:10.1016/S0140-6736(08)61620-7
Claes L, Del-Favero J, Ceulemans B, Lagae L, Van Broeckhoven C, De Jonghe P. De novo mutations in the sodium-channel gene SCN1A cause severe myoclonic epilepsy of infancy. American Journal of Human Genetics 2001;68(6):1327-1332. doi:10.1086/320609
McCulloch WS, Pitts W. A logical calculus of the ideas immanent in nervous activity. The Bulletin of Mathematical Biophysics 1943;5(4):115-133. doi:10.1007/BF02478259
Neher E, Sakmann B. Single-channel currents recorded from membrane of denervated frog muscle fibres. Nature 1976;260(5554):799-802. doi:10.1038/260799a0
Nobel Prize Outreach. The Nobel Prize in Physiology or Medicine 1991. NobelPrize.org 1991. https://www.nobelprize.org/prizes/medicine/1991/summary/
Doyle DA, Cabral JM, Pfuetzner RA, Kuo A, Gulbis JM, Cohen SL, Chait BT, MacKinnon R. The structure of the potassium channel: molecular basis of K+ conduction and selectivity. Science 1998;280(5360):69-77. doi:10.1126/science.280.5360.69
Nobel Prize Outreach. The Nobel Prize in Chemistry 2003. NobelPrize.org 2003. https://www.nobelprize.org/prizes/chemistry/2003/summary/
Gouwens NW, Sorensen SA, Baftizadeh F, Budzillo A, Lee BR, Jarsky T, et al.. Integrated morphoelectric and transcriptomic classification of cortical GABAergic cells. Cell 2020;183(4):935-953.e19. doi:10.1016/j.cell.2020.09.057

A spark that thinks

What a neuron is

Key numbers

Why the brain signals with electricity

How the action potential works

When: milliseconds to decades

The equations behind the spike

When signalling fails

How we found out

Milestones

Tools, models and the link to AI

Frontiers: one neuron, many layers

Check yourself

Check yourself

Glossary[1,9,10]

References

Related readings

Glossary^[1,9,10]