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CHAPTER 4 Modulating Membrane Potentials 61
Chapter4
Modulating Membrane
Potentials
I
f we told you that your brain is full of batteries, you’d probably wonder if we
were insulting your intelligence or just plain crazy. But after you read this
chapter, you’ll see that neither is the case! Your brain’s neurons are cells that
specialize in rapid and precise electrical communication, integration, and pro-
cessing of information. In order for neurons to perform these wonderfully com-
plex tasks, they require a number of dierent components, such as membrane ion
transporters and ion channels. In this chapter, we explore how neurons establish
the resting membrane potential and how they change the membrane potential in
synaptic responses and the action potential.
Getting the Membrane Potential
A typical electrical circuit involves the movement of electrons in wires. However,
in cells, electrical signaling involves the separation and movement of ions in solu-
tion. Ions are atoms with positive or negative electrical charges. Neurobiologists
are interested in sodium, potassium, chloride, and calcium ions. Aqueous solutions
IN THIS CHAPTER
»
Going with the ow through ion
pumps and channels
»
Understanding neurons as batteries
»
Meeting Nernst and Goldman
»
Communicating at synapses
»
Exploring voltage gated channels
»
Generating and conducting action
potentials
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62 PART 1 Getting Started with Neurobiology
are less conductive than wires, but they’re good enough for the small distances
that ions need to move across and along the membrane.
The membrane potential refers to the dierence in electrical charge between the
inside and outside of the plasma membrane. For a cell to produce a membrane
potential it needs ion transporters and ion channels. Ion transporters create an
unequal distribution of ions across the membrane. Ion channels allow ion cur-
rents to ow across the membrane.
All cells have a resting membrane potential. However, only neurons and muscle
cells use changes in their membrane potential as a major mechanism for com-
munication or responses. Neurons employ several dierent types of electrical sig-
nals to encode and transfer information. In general they’re called either graded or
action potentials, which we discuss in the section “Changing the Membrane
Potential” later in this chapter. Here we examine the resting membrane potential.
Resting with the membrane potential
Neurons have a dierence in ionic concentrations between the inside cytoplasm
versus the extracellular uid outside the neuron. Ion transporters that use energy
in the form of ATP create this dierence in specic ion concentrations across the
membrane. Ion channels allow the ow of specic ions back across the mem-
brane. The most important ions that control the membrane potential are sodium
(Na
+
), potassium (K
+
), and chloride (Cl
-
).
When a neuron isn’t receiving synaptic inputs or generating outputs, it’s at rest.
At rest, current through constituently open (leak) ion channels generate a con-
stant voltage across the neuronal plasma membrane. Because the neuronal mem-
brane is an insulator separating two conductors (the inside ionic solution versus
the outside), it has capacitance. This capacitance is charged to the potential cre-
ated by the leak ionic currents. In the membrane, there are many more leak potas-
sium channels present than leak chloride or leak sodium channels. This results in
the inside of the membrane having a negative electrical charge compared to the
outside, between –60 mV to –70 mV at rest.
At rest, negative charges are concentrated inside the membrane and positive
charges are concentrated outside. The membrane potential exists only within a
few nanometers at the surface of the plasma membrane. These charge dierences
involve only a tiny fraction of the total charges in the solutions. Because they’re
localized at the surface of the membrane and because the membrane is thin, they
produce a signicant electrical potential across the membrane.
We discuss more about the membrane potential in the section “Establishing the
Membrane Potential with Leak Channels” later in this chapter. Here we describe
how neurons form the ion concentration gradients.
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CHAPTER 4 Modulating Membrane Potentials 63
Actively moving ions with transporters
Ion concentration gradients are established by membrane proteins called active
transporters, which actively move ions into or out of cells. Primary active trans-
porters use ATP hydrolysis to provide the energy to move ions against their con-
centration gradients. For the membrane potential, the sodium-potassium
transporter is essential. It’s also called a pump because it pumps sodium and
potassium up their concentration gradients, or an ATPase, because it hydrolyzes
ATP.From here, we call it the sodium-potassium pump.
The sodium-potassium pump transports three sodium ions out for every two
potassium ions transported in. With each cycle, the pump hydrolyzes one mole-
cule of ATP.The outside extracellular uid throughout the body resembles seawa-
ter, with high sodium and low potassium concentrations. Through the action of
this pump, the inside cytoplasm has the opposite: low sodium and high potassium
concentrations.
The sodium-potassium pump runs constantly, using ATP to create a disequilib-
rium or imbalance in the sodium and potassium concentrations across the mem-
brane, as you can see in Figure4-1.
FIGURE4-1:
The sodium-
potassium pump
creates a
disequilibrium
between sodium
and potassium
concentrations
inside versus
outside the cell.
© John Wiley & Sons, Inc.
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64 PART 1 Getting Started with Neurobiology
Storing Energy in Ion Gradients
In addition to the sodium-potassium pump, there are two additional primary
active transporters in neurons:
»
The calcium pump uses ATP hydrolysis to pump calcium from the inside to the
outside of the neuron.
»
A proton (H
+
) pump is also present at the plasma membrane to keep the pH
of the intracellular cytoplasm constant.
Many other negative and positive ions are present inside and outside neurons.
How are their gradients produced? Neurons express secondary active transport-
ers. They don’t hydrolyze ATP.Instead, they use another ion gradient to provide
the energy to move an ion up/against its concentration gradient. The sodium-
calcium exchanger allows sodium to move down its gradient into the neuron while
actively moving calcium out of the neuron. Chloride is transported by cation-
chloride co-transporters, like the potassium-chloride cotransporter.
Other ions and molecules, such as bicarbonate, phosphate, glucose, and amino
acids are transported into cells using secondary active transporters. Away from
the membrane, the total charges in the overall extracellular and intracellular
solutions are balanced. In addition, the overall total number of solutes (charged
and uncharged atoms and molecules) are the same inside and out so that the
osmotic pressure is balanced.
In addition to transporters that form the ion gradients, neurons also need use ion
channels to produce and change the membrane potential. Here we discuss the ion
channels.
Facilitating ion movement with channels
The ionic imbalances created by the transporter-pumps allow neurons to function
as batteries, capable of producing electrical currents, the movement of ions that
ow through ion channels in the membrane. The biophysical term for the ability
to conduct ion ow through the membrane is called its permeability, analogous to
the electrical unit conductance. The presence of ion pumps and ion channels in the
cell membrane make neurons electrical signaling devices.
Ion channels are membrane proteins that, when they’re open, allow the move-
ment of selective ions across the membrane. Ion channels don’t need energy or
ATP because selective ions are typically diusing down (along) their concentra-
tion and/or voltage gradient. The two main categories of ion channels are
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CHAPTER 4 Modulating Membrane Potentials 65
»
Leak channels: Also referred to as ungated, leak channels are constitutively
open, even at rest. Refer to the later section “Establishing the Resting
Membrane Potential with Leak Channels” for more information.
»
Gated channels: The majority of gated channels are closed at rest and
require a specic stimulus in order to be opened. We discuss this topic more
in the section “Changing the Membrane Potential” later in this chapter.
What happens when an ion gradient is present and ion channels are open? The
active transporters have produced a concentration gradient. If an ion channel is
open in the membrane, ions tend to diuse from the higher concentration side to
the lower concentration side. They also tend to move according to the voltage
gradient, with positive ions outside attracted to the negative voltage inside, for
example.
Thus, the two forces acting on an ion are the force of chemical diusion and force
of electrical charge. Together, these forces are known as the electrochemical
gradient or the driving force.
The reciprocal of the membrane permeability is its resistance. By ohms law,
V = I*R (voltage = current times resistance), each ionic current through the mem-
brane resistance produces a voltage. The net membrane voltage is the sum of the
contributions of all ionic currents.
Ions continue to ow through an opened ion channel down the chemical gradient
until the opposing electrical gradient caused by the membrane capacitance bal-
ances the chemical gradient force.
When the chemical and electrical gradients are equal in magnitude, the ion is said
to be in electrochemical equilibrium, and there will be no further ion movement. The
membrane potential that’s established at equilibrium is called the equilibrium
potential(E
x
) for that ion with a specic concentration gradient.
Calculating the equilibrium potential:
The Nernst equation
The equilibrium potential for an ion gradient can be calculated using the Nernst
equation— developed from basic thermodynamic principles by the 19th-century
German chemist Walter Nernst. The Nernst equation gives the Nernst-equilibrium
potential for an ion x (E
x
):
E
x
= 58 mV/z * log
10
([ion]
outside
/[ion]
inside
)
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66 PART 1 Getting Started with Neurobiology
The constant 58 mV comes from the evaluation of several other constants RT/F,
where R = universal gas constant, T= temperature in Kelvin (here room tempera-
ture), and F = Faraday constant. In the equation, * means multiplied by, / means
divided by, and log
10
means the base 10 log. The variables in the equation are z =
ion valance (charge of the ion), and [ion]
outside
and [ion]
inside
the ion concentrations
outside and inside the neuron.
In a typical mammalian neuron, the concentration of sodium (valence = +1) is ~
150 mM outside, 15 mM inside. The Nernst-equilibrium potential = 58 mV/+1 *
log
10
([150/15]) = + 58 mV.
In a typical mammalian neuron, the concentration of potassium (valence = +1)
is ~ 5 mM outside, 100 mM inside. The Nernst-equilibrium potential = 58 mV/+1 *
log
10
([5/100]) = –75 mV.Note the log of a fraction is negative; potassium has a
negative Nernst-equilibrium potential.
In a typical mammalian neuron, the concentration of chloride (valence = –1)
is ~150 mM outside and 13 mM inside. The Nernst-equilibrium potential =
58 mV/–1 * log
10
([150/13]) = –65 mV. Note the valence of chloride is –1 and
chloride has a negative Nernst-equilibrium potential, close to the resting mem-
brane potential.
Establishing the Resting Membrane
Potential with Leak Channels
In addition to ion concentration gradients produced by ion transporters, at rest
the membrane contains leak channels that are constitutively open. Leak channels
allow ions to move from regions of higher to lower concentration by diusion.
Leak potassium, sodium, and chloride channels are open at rest.
Why is the resting membrane potential negative on the inside of the membrane?
The simple reason is because at rest, there are many more leak potassium and
chloride channels in the plasma membrane than others, such a sodium. This dif-
ference in the number of leak channels at rest is produced by gene expression.
There are about 20 to 40 times more leak potassium channels expressed than leak
sodium channels, whereas there are two to four times more potassium leak chan-
nels than leak chloride channels.
Why is the resting membrane potential between −60 mV to −70 mV? The potas-
sium leak current predominates at rest, driving the membrane potential to the
–75 mV potassium Nernst-equilibrium potential. The resting membrane potential
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CHAPTER 4 Modulating Membrane Potentials 67
is close to, but not quite as negative as the potassium Nernst-equilibrium poten-
tial because of leakage chloride channels. They tend to clamp the membrane at
their Nernst-reversal potential, typically near –65 mV.
The sodium-potassium pump contributes a small amount to the resting mem-
brane potential. It transports two potassium ions into the cell for every three
sodium ions that are pumped out. It’s electrogenic, which could cause a net increase
in one positively charged sodium ion outside the cell for each round of pumping.
However, many of the extra sodium ions are used immediately by secondary active
transporters. In addition, pumps act much more slowly than ion channels, so the
current produced by the pump is quite small. The sodium-potassium pump con-
tributes between –5 to –10 mV to the resting potential.
If there’s a dierence between the membrane potential and the Nernst-
equilibrium potential, and if an ion channel is open, then ions ow through that
channel. To determine how much current will ow and in which direction, the
driving force is what you need to know.
Finding the driving force on an ion
The driving force on an ion indicates what the combined forces are on an ion. It’s
the dierence between the electrical force of the membrane potential (V
m
) and the
electrochemical force from the concentration gradient (E
x
from the Nernst equa-
tion) DF = V
m
– E
x
.
At rest, the driving force for sodium is –65 mV– 58 mV = –123 mV.At rest, the
driving force for potassium is –65 mV– (–77 mV) = + 12 mV.At rest, the driving
force for chloride is –65 mV– (–65 mV) = 0 mV.The sign on the driving force
indicates, if channels are opened, whether the movement of ions will be into or
out of the neuron. For a positive ion, a negative driving force indicates ow into
the neuron and a positive driving force indicates a ow out of the neuron.
Calculating using the Goldman-Hodgkin-
Katz equation
The Nernst equation tells you what the Nernst-equilibrium potential would be for
a single ion gradient. But multiple ionic concentration dierences exist across the
neuronal membrane. Because ion channels can open, the conductance (permea-
bility) to ions can change. Given the concentration dierences of these dierent
ions, what is the actual membrane potential if ion permeabilities change?
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68 PART 1 Getting Started with Neurobiology
The Goldman-Hodgkin-Katz (GHK) equation calculates the membrane potential
(voltage) that results from all the ionic currents across the membrane through
various channels. It expands on the Nernst equation by considering multiple ions
and their individual permeabilities. The GHK equation is as follows:
RT
zF
ln
PK PNaPCl
PK PNaPCl
m
KN
aCli
Ki Na iCl
00
0
P is the relative permeability to each ion and is determined by which ion channels
are open. The chloride terms are reversed in the numerator and denominator of
the GHK equation. This is because the valence (z) for chloride is
1
, while it’s
1
for sodium and potassium. If you set the permeabilities of two of the ions to zero,
the GHK equation reduces to the Nernst equation for the remaining ion.
Neurons express both leak and gated ion channels. Open channels determine the
permeability to the ions they conduct. Gated ion channels are opened by specic
signals, such as binding of a neurotransmitter, depolarization of the membrane
potential, or presence of a sensory stimulus. Using the GHK equation you can esti-
mate the membrane potential at rest and during every point in a neuron’s poten-
tial change as channels open and close.
Changing the Membrane Potential
Neurons use changes in the membrane potential, known as electrical signaling, as
the basis of communication. To change the membrane potential, neurons open (or
close) gated ion channels. Opening or closing gated channels changes the perme-
ability for specic ions, and therefore, their ow across the membrane, which in
turn changes the membrane potential.
When the membrane becomes more negative (less positive) than the negative
resting potential, it’s hyperpolarized. When it’s more positive (less negative) than
the negative resting potential, it’s depolarized. The term “depolarized” is some-
what of a misnomer because open sodium channels can drive the membrane
potential toward the sodium Nernst potential (+58 mV), which is technically pos-
itively polarized.
Neurons change their membrane potential in two types of electrical signaling. One
is synaptic transmission which involves graded potentials that we introduce in the
following sections. The other type is the action potential that we discuss in the
section “Generating the Action Potential” later in this chapter.
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CHAPTER 4 Modulating Membrane Potentials 69
Communicating at synapses
Although neurons dier extensively in their morphologies, most neurons have
branched processes called dendrites, as well as the cell soma, that receive synaptic
input from other neurons. The incoming synaptic signaling leads to changes in
the membrane potential through the opening of gated ion channels at the synapse.
Most neurons also have a single output, the axon that produces and conducts the
outowing electrical signal called the action potential. Neurons use the opening of
gated ion channels to produce and conduct the action potential. Action potentials
are then used to initiate synaptic transmission at the synapse where the signal is
transmitted to other neurons or cells.
Synapses are typically contacts between an axon terminal of a presynaptic neuron
and the dendrite or cell soma of a postsynaptic neuron. The two types of synapses
are electrical and chemical. In vertebrates with large, complex nervous systems,
the vast majority of synapses are chemical, whereas a small minority are electri-
cal. Both types of synapses involve ion channels. We discuss electrical and chemi-
cal synapses in Chapter5 and briey describe chemical synapses in the following
sections.
Looking at neurotransmitter
gated channels
A chemical synapse is formed when the axon terminal of the presynaptic neuron
releases a chemical called a neurotransmitter (NT) that binds to a receptor on the
postsynaptic membrane, usually on the dendrite or cell soma. NT binding to
receptors on the postsynaptic membrane can open or close ion channels or have
other eects. A presynaptic neuron can release an NT that’s either excitatory,
inhibitory, or modulatory (refer to Chapters5 and6).
Synaptic receptors called ionotropic receptors directly open channels that allow the
ow of ions through the membrane when they bind NTs. Other NT receptors called
metabotropic receptors have the receptor and channel functions located in separate
protein complexes in the membrane.
NT receptors that conduct sodium cause depolarization of the membrane poten-
tial, called an excitatory postsynaptic potential (EPSP). An example is the ionotropic
glutamate receptor. NT receptors that conduct chloride ions cause a hyperpolar-
ization of the membrane potential and produce an inhibitory postsynaptic poten-
tial (IPSP). An example is the GABA
A
receptor.
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70 PART 1 Getting Started with Neurobiology
Focusing on graded potentials: Passive
changes in membrane potentials
A neuronal plasma membrane can be modeled electrically as an insulating mem-
brane that separates an inner conductive core from the outer, extracellular uid,
which is also conductive. Because of their dimensions, dendrites and axons have
what are called cable properties. The dendritic and axonal plasma membranes have
resistance, which is normally very high except where open ion channels and
transporters are present. The plasma membranes also function as capacitors that
can be charged and store charge.
Eyeing features of graded potentials
Excitatory and inhibitory postsynaptic potentials (EPSPs and IPSPs) are graded
potentials because the magnitude and duration of the response is graded. That is,
the size of the response depends on the amount of neurotransmitter released, the
number of receptors, and the distance from the synapse. Typical EPSPs and IPSPs
are small, about 1 mV or less in size for a duration of about 1 msec.
The other feature of graded potentials is that they’re passive signals, also called
electrotonic signals. They decrease rapidly from where they’re produced. Current
conduction along the dendrite or soma membrane and in the cytoplasm involves
passive current ow.
EPSPs and IPSPs decrease exponentially with increasing distance from the syn-
apse and increasing time after it was produced. Typically, the potential falls to a
small fraction of its initial value at a distance of a few of millimeters away from
the synapse and within a few milliseconds of the end of synaptic transmission.
The progressive decrease in the amplitude of the induced potential change along
a neuronal process such as a dendrite or axon occurs because the current leaks out
through ion channels and is reduced by axial or dendritic length resistance.
Diminishing synaptic signals
These factors lead to a decrease in the graded potential along a neuronal process,
whether an axon or dendrite:
»
The cytoplasm along the neural process has axial resistance, decreasing the
voltage from the start of that process toward the end.
»
The nite, though large, membrane resistance allows some leakage of current
across the membrane rather than owing down it toward the end.
»
The membrane has capacitance, the ability to store charge. This is the most
important factor.
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