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Resting potential
The relatively static membrane potential of quiescent cells is called the
resting membrane potential (or resting voltage), as opposed to the specific
dynamic electrochemical phenomena called action potential and graded membrane
potential.
Apart from the latter two, which occur in excitable cells (neurons, muscles, and
some secretory cells in glands), membrane voltage in the majority of non-excitable
cells can also undergo changes in response to environmental or intracellular
stimuli[citation needed]. In principle, there is no difference between resting
membrane potential and dynamic voltage changes like action potential from
biophysical point of view: all these phenomena are caused by specific changes in
membrane permeabilities for potassium, sodium, calcium, and chloride ions, which
in turn result from concerted changes in functional activity of various ion
channels, ion transporters, and exchangers. Conventionally, resting membrane
potential can be defined as a relatively stable, ground value of transmembrane
voltage in animal and plant cells.
Any voltage is a difference in electric potential between two points - for
example, the separation of positive and negative electric charges on opposite
sides of a resistive barrier. The typical resting membrane potential of a cell
arises from the separation of potassium ions from intracellular, relatively
immobile anions across the membrane of the cell. Because the membrane
permeability for potassium is much higher than that for other ions (disregarding
voltage-gated channels at this stage), and because of the strong chemical
gradient for potassium, potassium ions flow from the cytosol into the
extracellular space carrying out positive charge, until their movement is
balanced by build-up of negative charge on the inner surface of the membrane.
Again, because of the high relative permeability for potassium, the resulting
membrane potential is almost always close to the potassium reversal potential.
But in order for this process to occur, a concentration gradient of potassium
ions must first be set up. This work is done by the ion pumps/transporters and/or
exchangers and generally is powered by ATP.
In the case of the resting membrane potential across an animal cell's plasma
membrane, potassium (and sodium) gradients are established by the Na+/K+-ATPase
(sodium-potassium pump) which transports 2 potassium ions inside and 3 sodium
ions outside at the cost of 1 ATP molecule. In other cases, for example, a
membrane potential may be established by acidification of the inside of a
membranous compartment (such as the proton pump that generates membrane
potential across synaptic vesicle membranes).[citation needed]
Contents
In most quantitative treatments of membrane potential, such as the derivation of
Goldman equation, electroneutrality is assumed; that is, that there is no
measurable charge excess in any side of the membrane. So, although there is an
electric potential across the membrane due to charge separation, there is no
actual measurable difference in the global concentration of positive and
negative ions across the membrane (as it is estimated below), that is, there is
no actual measurable charge excess in either side. That occurs because the
effect of charge on electrochemical potential is hugely greater than the effect
of concentration so an undetectable change in concentration creates a great
change on electric potential.
Generation of the resting potential
Cell membranes are typically permeable to only a subset of ions. These usually
include potassium ions, chloride ions, bicarbonate ions, and others. To simplify
the description of the ionic basis of the resting membrane potential, it is most
useful to consider only one ionic species at first, and consider the others
later. Since trans-plasma-membrane potentials are almost always determined
primarily by potassium permeability, that is where to start.
Panel 1 of the diagram shows a digramatic representation of a simple cell where
a concentration gradient has already been established. This panel is drawn as if
the membrane has no permeability to any ion. There is no membrane potential,
because despite there being a concentration gradient for potassium, there is no
net charge imbalance across the membrane. If the membrane were to become
permeable to a type of ion that is more concentrated on one side of the membrane,
then that ion would contribute to membrane voltage because the permeant ions
would move across the membrane with net movement of that ion type down the
concentration gradient. There would be net movement from the side of the
membrane with a higher concentration of the ion to the side with lower
concentration. Such a movement of one ion across the membrane would result in a
net imbalance of charge across the membrane and a membrane potential. This is a
common mechanism by which many cells establish a membrane potential.
In panel 2 of the diagram, the cell membrane has been made permeable to
potassium ions, but not the anions (An-) inside the cell. These anions are
mostly contributed by protein. There is energy stored in the potassium ion
concentration gradient that can be converted into an electrical gradient when
potassium (K) ions move out of the cell. Note that K ions can move across the
membrane in both directions but by the purely statistical process that arises
from the higher concentration of K inside the cell, there will be more K ions
moving out of the cell. Because there is a higher concentration of K ions inside
the cells, their random molecular motion is more likely to encounter the
permeability pore (ion channel) than is the case for the K ions that are outside
and at a lower concentration. An internal K+ is simply "more likely" to leave
the cell than an extracellular K+ is to enter it. It is a matter of simple
diffusion doing work by dissipating the concentration gradient. As potassium
leaves the cell, it is leaving behind the anions. Therefore a charge separation
is developing as K+ leaves the cell. This charge separation creates a
transmembrane voltage. This transmembrane voltage is the membrane potential. As
potassium continues to leave the cell, separating more charges, the membrane
potential will continue to grow. The length of the arrows (green indicating
concentration gradient, red indicating voltage), represents the magnitude of
potassium ion movement due to each form of energy. The direction of the arrow
indicates the direction in which that particular force is applied. Thus, the
building membrane voltage is an increasing force that acts counter to the
tendency for net movement of K ions down the potassium concentration gradient.
In Panel 3, the membrane voltage has grown to the extent that its "strength" now
matches the concentration gradient's. Since these forces (which are applied to K+
ions) are now the same strength and oriented in opposite directions, the system
is now in equilibrium. Put another way, the tendency of potassium to leave the
cell by running down its concentration gradient is now matched by the tendency
of the membrane voltage to pull potassium ions back into the cell. K+ continues
to move across the membrane, but the rate at which it enters and leaves the cell
are the same, thus, there is no net potassium current. Because the K+ is at
equilibrium, membrane potential is stable, or "resting".
The resting voltage is the result of several ion-translocating enzymes (uniporters,
cotransporters, and pumps) in the plasma membrane, steadily operating in
parallel, whereby each ion-translocator has its characteristic electromotive
force (= reversal potential = 'equilibrium voltage'), depending on the
particular substrate concentrations inside and outside (internal ATP included in
case of some pumps). H+ exporting ATPase render the membrane voltage in plants
and fungi much more negative than in the more extensively investigated animal
cells, where the resting voltage is mainly determined by selective ion channels.
In most neurons the resting potential has a value of approximately -70 mV. The
resting potential is mostly determined by the concentrations of the ions in the
fluids on both sides of the cell membrane and the ion transport proteins that
are in the cell membrane. How the concentrations of ions and the membrane
transport proteins influence the value of the resting potential is outlined
below.
The resting potential of a cell can be most thoroughly understood by thinking of
it in terms of equilibrium potentials. In the example diagram here, the model
cell was given only one permeant ion (potassium). In this case, the resting
potential of this cell would be the same as the equilibrium potential for
potassium.
However, a real cell is more complicated, having permeabilities to many ions,
each of which contributes to the resting potential. To understand better,
consider a cell with only two permeant ions, potassium and sodium. Consider a
case where these two ions have equal concentration gradients directed in
opposite directions, and that the membrane permeabilities to both ions are equal.
K+ leaving the cell will tend to drag the membrane potential toward EK. Na+
entering the cell will tend to drag the membrane potential toward the reversal
potential for sodium ENa. Since the permeabilities to both ions were set to be
equal, the membrane potential will, at the end of the Na+/K+ tug-of-war, end up
halfway between ENa and EK. As ENa and EK were equal but of opposite signs,
halfway in between is zero, meaning that the membrane will rest at 0 mV.
Note that even though the membrane potential at 0 mV is stable, it is not an
equilibrium condition because neither of the contributing ions are in
equilibrium. Ions diffuse down their electrochemical gradients through ion
channels, but the membrane potential is upheld by continual K+ influx and Na+
efflux via ion transporters. Such situation with similar permeabilities for
counter-acting ions, like potassium and sodium in animal cells, can be extremely
costly for the cell if these permeabilities are relatively large, as it takes a
lot of ATP energy to pump the ions back. Because no real cell can afford such
equal and large ionic permeabilities at rest, resting potential of animal cells
is determined by predominant high permeability to potassium and adjusted to the
required value by modulating sodium and chloride permeabilities and gradients.
In a healthy animal cell Na+ permeability is about 5% of the K permeability or
even less, whereas the respective reversal potentials are +60 mV for sodium (ENa)and
-80 mV for potassium (EK). Thus the membrane potential will not be right at EK,
but rather depolarized from EK by an amount of approximately 5% of the 140 mV
difference between EK and ENa. Thus, the cell's resting potential will be about
−73 mV.
In a more formal notation, the membrane potential is the weighted average of
each contributing ion's equilibrium potential (Goldman equation). The size of
each weight is the relative permeability of each ion. In the normal case, where
three ions contribute to the membrane potential:
Em is the membrane potential, measured in volts
EX is the equilibrium potential for ion X, also in volts
PX is the relative permeability of ion X in arbitrary units (e.g. siemens for
electrical conductance)
Ptot is the total permeability of all permeant ions, in this case PK+ + PNa+ + PCl-
Membrane transport proteins
For determination of membrane potentials, the two most important types of
membrane ion transport proteins are ion channels and ion transporters. Ion
channel proteins create paths across cell membranes through which ions can
passively diffuse without direct expenditure of metabolic energy. They have
selectivity for certain ions, thus, there are potassium-, chloride-, and sodium-selective
ion channels. Different cells and even different parts of one cell (dendrites,
cell bodies, nodes of Ranvier) will have different amounts of various ion
transport proteins. Typically, the amount of certain potassium channels is most
important for control of the resting potential (see below). Some ion pumps such
as the Na+/K+-ATPase are electrogenic, that is, they produce charge imbalance
across the cell membrane and can also contribute directly to the membrane
potential. Most pumps use metabolic energy (ATP) to function.
Equilibrium potentials
For most animal cells potassium ions (K+) are the most important for the resting
potential. Due to the active transport of potassium ions, the concentration
of potassium is higher inside cells than outside. Most cells have potassium-selective
ion channel proteins that remain open all the time. There will be net movement
of positively charged potassium ions through these potassium channels with a
resulting accumulation of excess negative charge inside of the cell. The outward
movement of positively charged potassium ions is due to random molecular motion
(diffusion) and continues until enough excess negative charge accumulates inside
the cell to form a membrane potential which can balance the difference in
concentration of potassium between inside and outside the cell. "Balance" means
that the electrical force (potential) that results from the build-up of ionic
charge, and which impedes outward diffusion, increases until it is equal in
magnitude but opposite in direction to the tendency for outward diffusive
movement of potassium. This balance point is an equilibrium potential as the net
transmembrane flux (or current) of K+ is zero. The equilibrium potential for a
given ion depends only upon the concentrations on either side of the membrane
and the temperature. It can be calculated using the Nernst equation:
Eeq,K+ is the equilibrium potential for potassium, measured in volts
R is the universal gas constant, equal to 8.314 joules·K−1·mol−1
T is the absolute temperature, measured in kelvins (= K = degrees Celsius + 273.15)
z is the number of elementary charges of the ion in question involved in the
reaction
F is the Faraday constant, equal to 96,485 coulombs·mol−1 or J·V−1·mol−1
[K+]o is the extracellular concentration of potassium, measured in mol·m−3 or
mmol·l−1
[K+]i is likewise the intracellular concentration of potassium
Potassium equilibrium potentials of around -80 millivolts (inside negative) are
common. Differences are observed in different species, different tissues within
the same animal, and the same tissues under different environmental conditions.
Applying the Nernst Equation above, one may account for these differences by
changes in relative K+ concentration or differences in temperature.
For common usage the Nernst equation is often given in a simplified form by
assuming typical human body temperature (37 C), reducing the constants and
switching to Log base 10. (The units used for concentration are unimportant as
they will cancel out into a ratio). For Potassium at normal body temperature one
may calculate the equilibrium potential in millivolts as:
Likewise the equilibrium potential for sodium (Na+) at normal human body
temperature is calculated using the same simplified constant. You can calculate
E assuming an outside concentration, [K+]o, of 10mM and an inside concentration,
[K+]i, of 100mM. For chloride ions (Cl-) the sign of the constant must be
reversed (-61.54 mV). If calculating the equilibrium potential for calcium (Ca2+)
the 2+ charge halves the simplified constant to 30.77 mV. If working at room
temperature, about 21 C, the calculated constants are approximately 58 mV for K+
and Na+, - 58 mV for Cl- and 29 mV for Ca2+. At physiological temperature, about
29.5 C, and physiological concentrations (which vary for each ion), the
calculated potentials are approximately 67 mV for Na+, -90mV for K+, -86 mV for
Cl- and 123 mV for Ca2+.
Resting potentials
The resting membrane potential is not an equilibrium potential as it relies on
the constant expenditure of energy (for ionic pumps as mentioned above) for its
maintenance. It is a dynamic diffusion potential that takes this mechanism into
account—wholly unlike the equilibrium potential, which is true no matter the
nature of the system under consideration. The resting membrane potential is
dominated by the ionic species in the system that has the greatest conductance
across the membrane. For most cells this is potassium. As potassium is also the
ion with the most negative equilibrium potential, usually the resting potential
can be no more negative than the potassium equilibrium potential. The resting
potential can be calculated with the Goldman-Hodgkin-Katz voltage equation using
the concentrations of ions as for the equilibrium potential while also including
the relative permeabilities, or conductances, of each ionic species. Under
normal conditions, it is safe to assume that only potassium, sodium (Na+) and
chloride (Cl-) ions play large roles for the resting potential:
This equation resembles the Nernst equation, but has a term for each permeant
ion. Also, z has been inserted into the equation, causing the intracellular and
extracellular concentrations of Cl- to be reversed relative to K+ and Na+, as
chloride's negative charge is handled by inverting the fraction inside the
logarithmic term. *Em is the membrane potential, measured in volts *R, T, and F
are as above *PX is the relative permeability of ion X in arbitrary units (e.g.
siemens for electrical conductance) *[X]Y is the concentration of ion X in
compartment Y as above. Another way to view the membrane potential is using the
Millman equation:
or reformulated
where Ptot is the combined permeability of all ionic species, again in arbitrary
units. The latter equation portrays the resting membrane potential as a weighted
average of the reversal potentials of the system, where the weights are the
relative permeabilites across the membranes (PX/Ptot). During the action
potential, these weights change. If the permeabilities of Na+ and Cl- are zero,
the membrane potential reduces to the Nernst potential for K+ (as PK+ = Ptot).
Normally, under resting conditions PNa+ and PCl- are not zero, but they are much
smaller than PK+, which renders Em close to Eeq,K+. Medical conditions such as
hyperkalemia in which blood serum potassium (which governs [K+]o) is changed are
very dangerous since they offset Eeq,K+, thus affecting Em. This may cause
arrhythmias and cardiac arrest. The use of a bolus injection of potassium
chloride in executions by lethal injection stops the heart by shifting the
resting potential to a more positive value, which depolarizes and contracts the
cardiac cells permanently, not allowing the heart to repolarize and thus enter
diastole to be refilled with blood.
Measuring resting potentials
In some cells, the membrane potential is always changing (such as cardiac
pacemaker cells). For such cells there is never any “rest” and the “resting
potential” is a theoretical concept. Other cells with little in the way of
membrane transport functions that change with time have a resting membrane
potential that can be measured by inserting an electrode into the cell.
Transmembrane potentials can also be measured optically with dyes that change
their optical properties according to the membrane potential.
Summary of resting potential values in different types of cells
The resting membrane potential in different cell types are approximately:
Skeletal muscle cells: −95 mV
Smooth muscle cells: –60mV
Astroglia: –80 to –90mV
Neurons: –60 to –70mV