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Part 1 Introduction

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Physiology at a Glance, Fourth Edition. Edited by Jeremy P.T. Ward and Roger W.A. Linden. © 2017 John Wiley & Sons, Ltd. Published 2017 by John Wiley & Sons, Ltd. Companion website: www.ataglanceseries.com/physiology

Electrical gradient

Concentration gradient

The Nernst equation

Electrical gradient Concentration gradient

––

––

– ––

–––

–Ve

Fixed charge

E = potentialz = valency (1 for K+)F = Faraday (charge per mole) (96 485 Coulombs per mole)

R = gas constant (8.314 Joules/mole/degree K)T = absolute temperature (Kelvin)

Driving force:EzF

[K+] = 4mM

[K+] = 120mM

K+ channel

Driving force:RT x Ln ( )

Na+

K+

K+

Extracellular Cytosol

Figure 5.1 Nernst equation and K+ equilibrium potential

4120

Rearrange:

RTzF

E = x Ln ( )

Solving for R, z and F, 37ºC, and log base 10:

Ek = 61 x Log ( ) = –90 mVDriving force:EzF

Driving force:RT x Ln ( )=

At equilibrium:

4120

4120 4

120

Repolarization

Depolarization

Threshold

1000100

0 0.5 1 1.5 2 2.5 3

Time (ms)

3.5 4 4.5 5 5.5 6

80

60

40

20

0

–20

–40

–60

–80

–100

100

Rel

ativ

e p

erm

eab

ility

10

1

0.1

PNa

PK

After hyperpolarization

Voltage-gated Na+

channels activate

Voltage-gated K+

channels activate

Voltage-gated K+

channels inactivated

Voltage-gated Na+ channels inactivate

Ligand-gatedNa+ channelsactivate

Stimuli notreaching threshold

Stimulus e.g.neurotransmitter

Figure 5.2 Voltage and permeability changes in an action potential of a nerve

Voltage

Mem

bra

ne p

oten

tial (

mV

)

Resting Em

Biological electricity5

Chapter 5 Biological electricity

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11Electrical events in biological tissues are caused by the movement of ions across the membrane. A potential dif-ference exists across the membranes of all cells (membrane

potential, Em), but only excitable tissues can generate action potentials (transient depolarization of a cell as a result of ion channel activity). Action potentials transmit information in nerve cells (Chapter 6) and trigger contractions in muscle cells (Chapter 15). Cell membranes are electrically polarized so that the inside is negative relative to the outside. In excitable tissues, resting Em is usually between –60 and –90 mV.

The resting membrane potentialThe resting membrane is more permeable to K+ and Cl– than to other ions (Chapter 4). The cell contains negatively charged molecules (e.g. proteins) which cannot cross the membrane. This fixed negative charge attracts K+, leading to accumulation of K+ within the cell (Chapter 2). However, the consequent increase in the K+ concentration gradient drives K+ back out of the cell. This means fewer K+ ions move into the cell than are required to achieve electrical neutrality with the fixed negative charges, and the inside of the cell therefore remains negatively charged compared to the outside, causing a potential difference across the membrane. Equilibrium is reached when the electrical forces exactly balance those due to concentration differences (Gibbs–Donnan equilibrium); the net force or electrochemical gradi-ent for K+ is then zero. If the membrane were only permeable to K+, the voltage at which this would occur (K+ equilibrium potential, EK) is defined purely by the K+ concentration gradient, and can be calculated from the Nernst equation (see Figure 5.1 for derivation). Thus, if intracellular [K+] were 120 mmol/L and extracellular [K+] 4 mmol/L, EK = ∼–90 mV. This applies to any ion, so if the membrane were only permeable to Na+ (only Na+ channels open) and intracellular and extracellular [Na+] were 10 and 140 mmol/L, respectively, the potential obtained at equilib-rium (ENa) would be +70 mV. To summarize, for any given intra-cellular and extracellular ionic concentrations, the equilibrium potential for that ion is the membrane potential required for the intracellular and extracellular concentrations to be in equilib-rium, i.e. for the electrochemical gradient to be zero. The differ-ence between the actual Em and the equilibrium potential for any ion is therefore a measure of that ion’s electrochemical gradient, the force driving it into or out of the cell.

Real cell membranes are permeable to other ions besides K+, but at rest their K+ permeability (PK) is much greater than that for other ions. In particular, the ratio of PK to Na+ permeability (PNa) ranges between 25:1 and 100:1 in nerve, skeletal and cardiac muscle cells. As a result Em in such cells at rest (resting membrane potential) is close to EK (–60 to –85 mV) and the electrochemical gradient for K+ is small. Em does not equal EK because there is permeability to other ions, notably Na+. As ENa is much more positive than Em, the Na+ electrochemical gradient is strongly inwards, forcing Na+ into the cell. However, as PNa is

relatively low, only a small amount of Na+ can leak in, though this is sufficient to slightly depolarize the membrane from EK. A consequence of the above is that if PNa were suddenly increased to more than PK, then Em would shift towards ENa. This is exactly what happens during an action potential, when Na+ channels open so that PNa becomes 10-fold greater than PK, and the membrane depolarizes.

The action potentialAction potentials are initiated in nerve and skeletal muscle by acti-vation of ligand-gated Na+ channels by neurotransmitters (Chap-ter 4 and 15). This increases PNa and causes Em to move towards ENa (i.e. become positive; Figure 5.2). This initial increase in PNa is however relatively modest, so the depolarization is similarly small. However, if the stimulus is sufficiently strong, Em depolar-izes enough to reach the threshold potential (∼−55 mV), at which point voltage-gated Na+ channels (Chapter 4) activate, causing further depolarization. This activates more voltage-gated Na+ channels so the process becomes explosively self-regenerating, leading to a large transient increase in PNa so it is 10-fold greater than PK. As a result, Em rapidly approaches ENa (∼+65 mV; see previously), causing the sharp positive ‘spike’ or depolarization of the action potential, which lasts about 1 ms in nerve and skel-etal muscle. The spike is transient because as Em becomes positive, the voltage-gated Na+ channels inactivate (Chapter 4) and PNa plummets, whereas a type of voltage-gated K+ channel (delayed rectifier) activates. Thus PK is again much larger than PNa and Em returns towards EK (repolarization); this takes about 1–2 ms. Delayed closure of the delayed rectifier K+ channels means that the PK:PNa ratio remains transiently greater than normal after repo-larization, causing a transient hyperpolarization (Figure 5.2).

Following depolarization the Na+ channels remain inactive for about 1 ms until the cell is largely repolarized and, during this period, they cannot be opened by any amount of depolarization. This is known as the absolute refractory period during which it is impossible to generate another action potential. For the following 2–3 ms, the transient hyperpolarization renders the cell more difficult to depolarize, an interval known as the relative refractory period, when an action potential can be generated only in response to a larger than normal stimulus. The refractory period limits the frequency at which action potentials can be generated to <1000/s and ensures that, once initiated, an action potential can travel only in one direction. Once triggered, an action potential will travel over the entire surface of an excitable cell (it is propagated) and will always have the same amplitude (it is all-or-nothing). The minute changes in ion concentrations that occur during an action potential are restored by the action of the Na+ pump; it is important to understand that the action potential is not due to changes in ionic concentrations, but to changes in ionic permeability. Note that action potentials in cardiac muscle differ somewhat from those in nerves and skeletal muscle (Chapter 22).