HUF1-1 RESTING MEMBRANE POTENTIAL

(2015-16)

Difference in ion concentrations between intracellular and extracellular fluid

Due to the difference in the concentrations of major ions present in extracellular (ECF) and intracellular fluid (ICF), and the cell membrane having different permeability towards these ions, ion movement across the cell membrane down the chemical/ concentration gradient creates the separation of minute quantities of charges that gives rise to the generation of membrane potential.

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Selective permeability of cell membrane and diffusion potential

Cells are bathed in extracellular fluid (ECF) containing high [Na+] and [Cl-], while intracellular fluid (ICF) has high [K+] balanced by protein anions [Pr-], PO4-, etc. to maintain electroneutrality.

Under the basal condition, the cell membrane is selectively more permeable to K+ than other ions (i.e. due to the presence of more K+ leak channels).

As a result, K+ diffuses out of the cells down its chemical/concentration gradient (i.e. chemical force). Since K+ movement is not accompanied by the impermeable protein anions inside the cell, this produces a charge separation - known as the diffusion potential, which gives rise to an opposing force (i.e. electrical force) against the chemical force.

It is referred to as the diffusion potential because the charge separation is driven by the diffusion of ions (e.g. K+) down its concentration gradient between ICF and ECF.

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Equilibrium potential (1)

Equilibrium potential of an ion (e.g. K+) is given by the diffusion potential/membrane voltage at which there is no net flux of ions across the cell membrane as the ion flux down the chemical gradient is exactly balanced by the ion flux moving in the opposite direction down the electrical gradient.

Equilibrium potential indicates the charge separation (i.e. cations and anions) across the membrane after reaching a steady state condition, and its magnitude is determined by the concentration gradient - as it provides the driving force to separate the charges.

According to convention, the equilibrium potential (also applicable to membrane potential) is taken as the net charge inside the cell relative to outside (which is assigned zero voltage).

The number of ions involved in setting up the equilibrium/membrane potential is infinitely small (e.g. change of intracellular [K+] by 1/40,000; 0.0025%) and in effect, has no impact on the overall ionic concentrations and balance of charges inside and outside of the cell.

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Equilibrium potential (2)

When each major ion is considered individually by assuming that the cell membrane is permeable only to that particular ion through the leak channels. In a mammalian neuron,

The values cited above for the equilibrium potentials of various ions cannot be generalized to all cell types in the human body.

the Cl- equilibrium potential (ECl) is around -75 mV.

the K+ equilibrium potential (EK) is around -90 mV.

the Na+ equilibrium potential (ENa) is around +60 mV.

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How to derive the Nernst equation

The chemical driving force (i.e. free energy, ΔG) for a substance (S) to move down its concentration gradient out of a cell (by convention) is given by:

where R is universal gas constant, T is the absolute temperature, z is the valency (charge) of the ion, E is the equilibrium potential, and F is Faraday’s constant.

If the substance is an ion [I] and the chemical force is balanced by the electrical force at equilibrium potential, then

Substituting in the constants (e.g. 310oK), and replacing natural log (ln) with log10 (log), then the calculated values of E for EK and ENa are given as:

Reference only

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Electrical potential given by the Nernst equation

The Nernst equation:

E = electrode potential or equilibrium potential (in volts; V).

[I] = ion concentration

R = universal gas constant (8.31 JK-1mol-1)

T = absolute temperature in Ko

F = Faraday’s constant 9.65 x 104 Cmol-1

Z = valency of the ion (+ for cations and – for anions)

ln = natural log (or 2.303 log)

E = RT

zF ln

[I]o

[I]i

E (in millivolt) = 61

z log

[I]o

[I]i

at 37oC (i.e. 310oK),

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Resting membrane potential (VM) given by the Goldman-Hodgkin-Katz equation

In real life, the cell membrane is permeable to multiple ion species. The resting membrane potential (VM) is represented by the weighted average of the equilibrium potential of each contributing ion (mainly K+, Na+ and Cl-), and the degree of weighting is determined by the relative permeability (Pion) (or conductance, g) of the membrane to each ion.

Example: PK > PCl > PNa, in the ratio of approximately 1 : 0.45 : 0.04

The resting membrane potential (VM) is given by an expanded version of the Nernst equation, the Goldman-Hodgkin-Katz (GHK) Equation (or simply abbreviated as the Goldman Equation):

VM = RT

zF ln

PK+ [K+]o + PNa+[Na+]o + PCl-[Cl-]i

PK+ [K+]i + PNa+[Na+]i + PCl-[Cl-]o

Note that the [Cl-]i / [Cl-]o is reversed as compared to [K+] and [Na+] because Cl- is an anion (i.e. z = -1), and its movement has the opposite effect on the membrane potential.

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Electrical equivalent circuit of ion fluxes across the cell membrane

The cell membrane can be viewed as a capacitor with electrical charges stored across its two surfaces. The membrane permeability to ions (different sizes with charges) can be better described as conductance (g) [or reciprocal of resistance (1/R)], which is related to electrical potential [voltage (V)] and ionic current (I) by: I = V / R I = V * g

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Resting membrane potential (VM) given by Hodgkin-Huxley equation

Calculation of VM based on the conductance of ions.

At the resting membrane potential, there is no net ionic current (or ion flow) crossing in or out of the cell,

INa + IK + ICl = 0

therefore,

gNa (VM – ENa) + gK (VM – EK) + gCl (VM – ECl) = 0

VM = (ENa* gNa)+ (EK * gK) + (ECl * gCl)

gNa + gK + gCl

The above gives a different representation of the resting membrane potential (VM) when compared with the Goldman-Hodgkin-Katz (GHK) Equation (calculated based on relative permeability):

VM = RT

zF ln

PK+ [K+]o + PNa+[Na+]o + PCl-[Cl-]i

PK+ [K+]i + PNa+[Na+]i + PCl-[Cl-]o

Electrochemical driving force for ion movement

Electrochemical driving force (or driving force) for the movement of a particular ion is given by the difference between the membrane potential and the ion’s equilibrium potential (VM – Eion).

It indicates the magnitude of electrochemical force and the direction of ion movement (i.e. sign relative to the charge of the ion).

0 mV

+60 mV

-70 mV

-90 mV

ENa

VM

EK

Driving force for Na+

Vm – ENa = -70 mV – (+60 mV) = -130 mV (Na+ is attracted by a net -130 mV to move into the cell.)

Driving force for K+

Vm – EK

= -70 mV – (-90 mV) = +20 mV (K+ movement out of the cell is favoured by a net +20 mV.)

Driving force for Na+ to move into the cell is greater than the driving force for K+ to leave the cell, however due to higher membrane conductance to K+ (gK) than Na+ (gNa), VM is closer to EK.

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Contribution of K+ and Na+ to resting membrane potential

0 mV

+60 mV ENa

-70 mV VM

-90 mV EK

Contribution by K+ and Na+ based on their driving force and relative conductance (gK >>> gNa) VM = -70 mV (which is closer to EK).

Driving force for Na+

VM – ENa = -130 mV

Driving force for K+

VM – EK = +20 mV

At rest, membrane potential will stabilize when Na+ influx is balanced by K+ outflux.

Based on the Ohm’s Law,

I = V/R

therefore,

IK = (VM - EK) * gK

INa = (VM - ENa) * gNa

and when IK = INa

(VM - EK) * gK = (VM - ENa) * gNa

(VM - EK)/(VM - ENa) = gNa / gK

The resting membrane potential is close to EK because the cell membrane has the highest K+ conductance, and therefore a small K+ electrochemical driving force would be sufficient to generate a K+ outflux that balances the Na+ influx.

Role of Na+-K+ pump in maintaining resting membrane potential

Since the resting membrane potential (VM =~70 mV) is away from the equilibrium potential of K+ and Na+, both ions are under electrochemical driving forces to move out of and into the cell, respectively. The leakage of these ions are recovered (K+) or removed (Na+) by the Na+/K+-ATPase/ pump, which has important contributions towards maintaining the intracellular ion concentration and membrane potential.

0 mV

+60 mV

-70 mV

-90 mV

ENa

VM

EK

Driving force for Na+ to move into cell = VM – ENa

= -70 – (60) mV = - 130 mV

Driving force for K+ to move out of cell = VM – EK

= -70 – (-90) mV = + 20 mV

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The pump activity is balanced by a higher Na+ influx than K+ outflux. (V’M-ENa) * gNa > (V’M-EK) * gK

I’Na > I’K

As Na+/K+-ATPase pumps 3Na+ out for every 2K+ into the cell, it creates unequal charge distribution and a small electrical potential across cell membrane. Thus, Na+/K+-ATPase is referred to as an electrogenic pump.

Contribution of the electrogenic Na+/K+ pump to resting membrane potential

Na+/K+-ATPase is also responsible for pumping Na+ out of the cell and K+ back into the cell following the generation of an action potential.

0 mV

+60 mV ENa

-70 mV V M

-90 mV EK

The unequal transport of 3Na+/2K+ ions makes the inside of the cell more negative than what it should be based on 1:1 (Na+:K+) transport.

V’M (Na/K ATPase)

In most cell types, contribution of the electrogenic Na+/K+-ATPase to the resting membrane potential is quite small (~ 3-5 mV).

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Contribution of Cl- to resting membrane potential

0 mV

+60 mV ENa

-70 mV V’M at rest

-90 mV EK

-75 mV ECl

The contribution of Cl- to the attainment of resting membrane potential is small:

The membrane conductance to Cl- is less when compared with that of K+ (gCl << gK).

VM is close to ECl, thus the net driving force (VM -ECl) to move Cl- into (or out) of the cell is small.

ECl is close to VM because in most cells (with no Cl- pumps or carriers), Cl- passively distributes across cell membrane until ECl approximates VM with little or no net driving force for further movement.

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Factors determining resting membrane potential

Intracellular and extracellular [K+] and [Na+] in determining their equilibrium potential.

Difference in membrane conductance/ permeability to K+ and Na+.

Presence of impermeable intracellular protein anion (Pr-).

Activity of Na+/K+ pump.

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Summary - resting membrane potential (RMP)

RMP represents the electrical potential inside the cell relative to outside (assigned zero voltage) in the absence of excitation (or inhibition).

RMP is contributed by the weighted sum of the equilibrium potentials of K+ (-90 mV), Na+ (+60 mV) and Cl- (-75 mV), based on their concentration gradient and relative permeability/conductance across the cell membrane. Since these parameters differ in different cell types, their RMP are not the same.

As the cell membrane has higher conductance to K+ than Na+, RMP (-70 mV) is closer to the equilibrium potential of K+ (EK) than that of Na+ (ENa) .

RMP forms the basis for some cells to become excitable (i.e. through the operation of voltage-gated ion channels and/or generation of action potential). The membrane potential changes can be further linked to the release of signaling molecules from cells (e.g. release of neurotransmitter) or the generation of intracellular messengers.

Na+ electrochemical gradient across cell membrane is also used for driving the secondary active transport of other molecules (glucose, amino acids) and/or ions.

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Neurons are excitable cells capable of generating action potential which serves as nerve impulses propagating down the axons at high speed. This permits rapid, long distance communication between different parts of the nervous system.

Generation of action potential for cell signaling

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Alteration of cell function linked to membrane potential change and operation of voltage-gated ion channel

A generalized scheme illustrating different intracellular signalling events originating from membrane depolarization that produces a rise in cytosolic [Ca2+]. Membrane depolarization either triggers the opening of voltage-gated Ca2+ channels on cell surface for the influx of extracellular Ca2+ or the Ca2+ release from intracellular store. Rise in cytosolic Ca2+ in turn functions as an intracellular messenger to produce various cellular changes (e.g. enzyme activity, cell motility, contraction in muscle cells, exocytosis of secretory vesicles - hormones, neurotransmitters, etc.)

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Cell signalling linked to membrane depolarization

Glucose-induced insulin release. The entry of glucose into pancreatic b cells results in increased generation of ATP. The binding of ATP to ATP-sensitive K+ channels causes these channels to close, thus reducing the efflux of K+ from the cell. The resulting small membrane depolarization triggers the opening of voltage-sensitive Ca2+ channels. The influx of Ca2+ raises intracellular Ca2+ concentration, triggering the exocytosis of insulin-containing secretory vesicles.

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Intracellular [Na+] is low and it is maintained by the active extrusion of Na+ by the Na+/K+ ATPase. The Na+ concentration gradient thus created can be used to drive the transport of other substances against their concentration gradients into or out of the cell through secondary active transport. The above illustrates a few examples.

Secondary active transport driven by Na+ gradient

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Extracellular [K+] has a major impact on the excitability of neurons and other excitable cells as it will render the resting membrane potential (RMP) less negative (hyperkalemia – depolarize) or more negative (hypokalemia – hyperpolarize), shifting it closer or further away from the threshold for excitation.

EK = 61 log[K+]o

[K+]i

EK = 61 log[K+]o

[K+]i

[K+]o

[K+]i

Effect of extracellular [K+] on membrane potential and excitability

When [H+] in ECF increases (i.e. fall in pH, acidaemia), H+ moves into cells to be buffered by intracellular proteins. H+ influx displaces intracellular K+, causing K+ efflux. In alkalaemia, H+ shifts from ICF to ECF causing K+ to move in reverse direction from ECF to ICF.

Insulin, b-adrenergic agonists (e.g. epinephrine) and thyroid hormone shift K+ into cells by stimulating Na+/K+-ATPase.

Cell lysis results in the leakage or discharge of intracellular K+ to ECF.

In cell dehydration (hyperosmolarity), increase in intracellular [K+] steepens the concentration gradient for K+ efflux through leak channels. Efflux of water also draws K+ with it.

K+ leaves the cell during the repolarization phase of an action potential. In exercise, repeated AP in skeletal muscle cells leads to a small rise in extracellular [K+].

Factors affecting extracellular [K+]

Effect of exercise on plasma [K+]

In exercise, plasma [K+] increases with time and the level of intensity. This could be explained by [K+] leaving the muscle cells during the repolarization phase of repeated action potential.

Inhibition of Na+/K+-ATPase

Na+/K+-ATPase is inhibited by

ouabain (an inhibitor of Na+/K+-ATPase)

depletion or inadequate supply of ATP [i.e. lack of oxygen or energy supply (hypoxia, ischaemia); presence of metabolic inhibitor (cyanide)].

Role of Na+/K+-ATPase in maintaining cell volume

Changes that occur following the inhibition of Na+/K+-ATPase

Cell swelling (net water influx as more ions/particles enter the cell)

Membrane depolarization [due to greater influx of Na+, fall in [K+]i, opening of voltage-sensitive Na+ and/or Ca2+ channels]

Cell death from hypoxia, depletion of energy supply or metabolic poisoning

Na+/K+-ATPase activity is stimulated by rise in intracellular Na+ or extracellular K+

Glossary on membrane potential

Qu. Estimate which of the following ions gives the highest absolute value of equilibrium potential?

Ion Approximate [ion]o/ [ion]I

Na+

K+

Cl-

Ca2+

Qu. Calculate the equilibrium potential for each of the ions.

E = 61

z log

[ I ]o

[ I ]i

Based on the Nernst Equation, at 37oC (i.e. 310oK),

Qu. Which of the following ions would give the highest electrochemical driving force?

Driving force = VM – Eion

(assuming a VM of -70 mV)

Ion Eion (in mV) VM - Eion

Na+

K+

Cl-

Ca2+

Qu. What is the impact of 5 mM increase in extracellular [K+]o or [Na+]o on the equilibrium potential?

Ion Original

[ion]o/ [ion]I

Revised [ion]o/ [ion]I

Na+

K+

Ion Original

Eion

Revised Eion

Na+

K+

Questions

How K+ contribute to the development of an electrical potential across the cell membrane?

How membrane depolarization occurs following the closure of K+ channels (e.g. ATP-sensitive K+ channels)?

Why extracellular [K+] has a major impact on the resting membrane potential?

Explain how hypokalaemia produces membrane hyperpolarization and hyperkalaemia produces membrane depolarization.