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CHAPTER 4 Modulating Membrane Potentials 71
Refer to the nearby sidebar for an analogy. Figure4-2 is a model that represents
both continuous membrane resistance (due mostly to ion channels) and mem-
brane capacitance.
Integrating responses from synaptic signals
Neurons can receive thousands of synaptic inputs. All the synaptic electrical cur-
rents generated at the dendrites and cell soma integrate (summate) with all the
other synaptic currents. The net current moves passively along the axial cytoplas-
mic membrane throughout the neuron. Of particular importance is the integration
of all the incoming EPSPs and IPSPs at the cell soma and initial segment of its axon.
Consider these two types of integration:
»
Temporal: The integration of synaptic potentials from repetitive activation of
one synaptic input. When the action potential frequency is high enough in the
presynaptic axon, the synaptic responses combine with each other, leading to
a response that’s larger than the response to a single action potential.
»
Spatial: The integration of synaptic potentials from dierent nearby synaptic
inputs. Synaptic potentials produced within a short time window from nearby
synapses combine in the dendrites or soma and produce a larger response
than the response at a single synapse.
FIGURE4-2:
An electrical
model of the
distributed
membrane
resistance and
capacitance.
© John Wiley & Sons, Inc.
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72 PART 1 Getting Started with Neurobiology
Imagine a neuron at its resting potential of about –65 mV.Another neuron that’s
presynaptic to this one releases glutamate, which binds the neuron’s excitatory
glutamate receptors on multiple synapses. This activates the glutamate receptors,
which open cation channels and sodium ows in.
Say there are 40 synapses on a dendrite that are very close to each other and
simultaneously active; each produces a 1 mV response. The integrated responses
depolarizes the dendrite, changing the membrane potential from –65 mV to about
–35 mV. This dendritic depolarization spreads throughout the neuronal mem-
brane, but decays as it spreads. Other dendrites have EPSPs and IPSPs that also
spread toward the cell soma within some time window.
Most neurons have dendritic trees with lengths of less than a few hundred
micrometers. A major reason why interactions among inputs to a neuron can be so
complicated is because dendrites have cable properties for transmitting signals.
The way synaptic signals on dierent points on a dendrite interact depends on the
structure of the dendritic tree between the two points. Understanding how synap-
tic inputs are combined within branched dendritic trees is modeled using cable
theory, which is an important area of research in computation neuroscience. We
describe this further in Chapter5.
MEMBRANE CAPACITANCE: LIKE A
HYDRAULIC SYSTEM
To help you understand the eect of membrane capacitance, consider this analogy to a
hydraulic system. At one end is a piston in a cylinder, connected through a sti (but ex-
ible) pipe, to another piston in a cylinder. If you suddenly shove one piston in, then out,
that pressure pulse is communicated at the speed of sound in uid to the other piston,
which moves almost instantly in and out.
Instead consider cutting the sti but exible pipe in various places and putting in
expandable balloons as linkages. Now, when you shove one piston in, some of the uid
going through the rst section of pipe going directly to the second section goes instead
into inating the balloon between them, which takes some time. As this rst balloon
inates, it starts to send uid into the pipe going the second balloon, but it inates even
more slowly. After several such balloons, the last one barely even starts to inate before
the piston moves back.
Capacitance is like the capacity of the balloons in this analogy. The capacitance of typical
neural processes is such that no eective transient signal can be communicated from
one end to the other over more than a few hundred micrometers, even if there’s no
membrane leakage because of the capacitance and high axial conductance.
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CHAPTER 4 Modulating Membrane Potentials 73
An integrated postsynaptic signal received at the dendrite spreads and decreases
with time and distance. The combination of low membrane resistance and high
membrane capacitance means that synaptic input currents in one dendritic loca-
tion may be severely weakened, delayed, and smoothed when they arrive at some
other location.
In real neurons, even summated synaptic signals are so reduced over distances
larger than about 200 micrometers that they become ineective (low amplitude
and slow time course). This is the limit for passive signal propagation from the
most distal dendrites to the soma. Neurons need to overcome the problems of
weakened signals and signal smoothing if they’re to communicate over distances
larger than a few dendritic trees. For electrical signaling over larger distances,
neurons evolved active propagation, which we discuss in the next section.
Generating the Action Potential
Neurons evolved a specic boosting mechanism to transmit depolarizations over
long distances: the action potential. It overcomes the problem of the passive decay
of graded, electrotonic signals over distance. The action potential is an all-or-
nothing change of the membrane potential (voltage) that serves as the basic unit
of output electrical signaling in the majority of neurons.
The action potential is a large (change of approximately 80-100 mV) and rapid
(1 msec) depolarization, followed by a repolarization of the membrane potential
back to rest that takes about 3 to 5 msec. The key features of the action potential
are its size and regeneration. For a given neuron, the action potential has a char-
acteristic shape, time course and speed of propagation.
In the next sections we rst describe how the action potential is initiated at the
axon initial segment (in most neurons). Next we describe how the action potential
is propagated along an unmyelinated axon and a myelinated axon. When it reaches
the presynaptic terminus the action potential stimulates synaptic transmission,
which is the topic of Chapter5.
Reaching threshold for ring
The basis of the action potential is the opening of gated ion channels that include
voltage-gated sodium and voltage-gated potassium channels. Voltage-gated
channels rapidly open in response to a depolarization of the membrane potential.
They’re closed at the resting membrane potential and opened when the mem-
brane potential reaches about –55 mV, called threshold.
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74 PART 1 Getting Started with Neurobiology
A typical neuron has the potential to receive inputs from a thousand or more dif-
ferent neurons and send its outputs to a thousand or more neurons. The synaptic
inputs spread across the dendrites and soma. Because the amplitude of a single
synaptic input is typically less than 1 mV, multiple excitatory inputs must be inte-
grated to depolarize a neuron enough to reach threshold at the initial segment for
generating an action potential.
Integrating postsynaptic potentials
Integration of EPSPs and IPSPs occurs throughout the neuronal membrane all the
time. However, the place in the neuron where integration is important is at the
initial segment of the axon hillock because that’s where the action potential is
generated. It’s the rst place along the axon where voltage-gated sodium and
potassium channels are localized and concentrated.
If integration of all the incoming synaptic EPSPs and IPSPs reaches threshold
(–55 mV) in the neuron initial segment, the eect is to open voltage-gated sodium
channels. The sudden opening of many voltage-gated sodium channels produces
the rising phase of the action potential.
Activating voltage gated Na
+
channels
Threshold is determined by the voltage sensitivity of the voltage-gated sodium
channels and their localization and density at the initial segment of the axon hil-
lock. Threshold can be dierent for dierent types of neurons and ranges from
about –47 mV to –57 mV.
Opening voltage-gated sodium channels increases the conductance for sodium,
leading to the ow of sodium into the cell. This sodium current further depolar-
izes the initial segment and opens nearby voltage-gated sodium channels.
The situation is one of typical positive feedback in which the neuron is increasingly
being driven toward, but not quite to the sodium equilibrium potential (approxi-
mately +58 mV).
Inactivating Na+ channel and opening
voltage gated K
+
channels
This amplication causes the neuron to remain stuck in this depolarized condition
unless something happened to get it back to its resting potential. Two things work
to do this:
»
Sodium channels inactivate and they close themselves.
»
Voltage-gated potassium channels open.
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CHAPTER 4 Modulating Membrane Potentials 75
Following depolarization above threshold, the voltage-gated sodium channels
transition to the open state. But a rapid mechanism within the channel causes
them to transition to a closed, inactivated state, even though the membrane voltage
continues to be above threshold. To transition back to the closed but activatable
state (resting state), the neuron has to repolarize back to the resting potential.
Repolarization is aided by voltage gated potassium channel opening. Then the
cycle can begin again.
Repolarizing with voltage gated K
+
channels
Voltage-gated potassium channels are located near voltage-gated sodium chan-
nels. They’re also activated by threshold (–55 mV), but they open more slowly
than voltage-gated sodium channels. This delayed opening is important because
it ensures there will be a large initial depolarization. When voltage-gated potas-
sium channels open, potassium ows out of the neuron, which repolarizes the
membrane potential toward the resting membrane potential and potassium equi-
librium potential, around
75 mV
.
The voltage-dependent potassium channels also close after opening, but they
don’t inactivate. They close because their activity leads to repolarization of the
membrane potential back to the resting membrane potential. A lingering potas-
sium current produces the afterhyperpolarization or undershoot phase and the
relative refractory period (see the nearby sidebar). See how these events play out
in Figure4-3.
The trace in Figure4-3 labeled “V” is the membrane potential, and the scale for
this trace is on the left. At the start of the plot, the membrane potential is at the
resting level, about –65 mV.As voltage-gated sodium channels open, the mem-
brane potential becomes depolarized to +30 or +40 mV, close to the sodium equi-
librium potential. The membrane potential then repolarizes to a level below the
resting potential, and then nally returns to the resting potential.
The other two traces in Figure4-3 show the sodium and potassium permeabilities
that control the membrane potential. The action potential is triggered by any
input that depolarizes the initial segment enough to reach threshold and open the
voltage-gated sodium channels. The permeability (conductance) of the voltage-
gated sodium channels is given by the g
Na
trace. The conductance is nearly zero at
the resting potential, rises to a maximum peak, and then returns to zero through
the transition from the open to the closed, inactivated state.
The opening and closing of the voltage-gated potassium channels, whose con-
ductance is g
K
, happens more slowly than the voltage-gated sodium channels.
They tend to drive the membrane potential toward the potassium-equilibrium
potential, around
75 mV
. The repolarizing phase of the action potential involves
both the inactivation of voltage-gated sodium channels and opening of voltage-
gated potassium channels.
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76 PART 1 Getting Started with Neurobiology
Moving to the refractory periods
The period immediately following an action potential when it’s impossible or
more dicult to elicit a second action potential is called the refractory period. It has
two phases:
»
Absolute refractory period: This is the time when the voltage-gated sodium
channels are inactivated. In this state no additional action potential can be
elicited, no matter how strong the depolarizing input at the initial segment
because the sodium channels won’t reopen. The absolute refractory period
sets the theoretical maximum frequency of action potential generation at
about 1,000 per second or 1,000Hz. The absolute refractory period also
ensures that the action potential travels in one direction toward the
presynaptic terminus and not back along the axon to the cell body.
»
Relative refractory period: The relative refractory period is when the
voltage-gated sodium channels have transitioned from inactivated back to
closed, activatable, but the voltage-gated potassium channels are still open.
Voltage-gated potassium channels determine the time course of the falling
phase and the relative refractory period. Because of the persistent potassium
current, during this period a greater depolarizing current at the initial segment
is required to reach threshold to generate an action potential.
FIGURE4-3:
Event sequence
underlying the
action potential.
© John Wiley & Sons, Inc.
https://t.me/med1917
CHAPTER 4 Modulating Membrane Potentials 77
The sodium-potassium pump runs all the time, causing the imbalance in ionic
concentrations between the inside and outside of the neuron. A single action
potential creates a temporary current through the membrane, which changes the
membrane potential, but it has little eect on the total ion concentrations within
the entire neuron. Even if all the sodium-potassium pumps shut down, up to mil-
lions of action potentials can occur before the cell starts to lose its concentration
dierence with respect to the cell exterior.
REFRACTORY PERIODS AND SPIKE
RATE CODING
Neurobiologists generally model synaptic inputs to neurons as currents injected into
the dendritic tree (refer to Chapter3) that are transformed into a train of spikes at the
cell soma or axon initial segment. If the ring rate were exactly proportional to total syn-
aptic current (above threshold), the relationship between synaptic current and spike
rate would be called linear. However, in reality, this relationship isn’t linear for two main
reasons:
•
Leakage currents through the membrane tend to shunt away synaptic current
more for low, slowly changing current levels than for rapidly changing ones.
•
At high spike rates, the refractory period requires disproportionally more synaptic
current to increase the spike rate. In fact, as the absolute refractory period is
approached, no amount of increased synaptic input current can increase the
spike rate.
One interesting result of this second factor is that the relationship between synaptic
input current and spike rate in most neurons is more like a logarithmic function than a
linear function. Psychophysical laws such as Weber’s and Fechner’s laws have long dem-
onstrated that the perception of magnitude in senses such as sight, sound, and touch
also follow a logarithmic relationship, where doubling the stimulus magnitude produces
less than a doubling of the sensory perceptual magnitude. Direct experimental compari-
sons between perception of magnitude and neural ring rates have shown that the
logarithmic spike compression underlies the logarithmic perception— that is, the per-
ceptual magnitude follows the neural ring rate, which itself is logarithmically related
to the magnitude of the stimulus.
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78 PART 1 Getting Started with Neurobiology
Encoding information: The neural code
After the membrane potential reaches the resting membrane potential, a subse-
quent action potential can be generated if the membrane potential (at the initial
segment) is depolarized above threshold. An action potential doesn’t typically
occur only once but occurs in what are called action potential trains, sets, or series.
The frequency and duration of the action potentials in the train depends on the
magnitude and duration of the summed graded potentials (inputs from synapses)
in the neuron. The net magnitude of excitatory currents in the neuron is thus
converted into a rate and pattern of action potential ring.
Conducting Action Potentials
Action potentials are conducted along the axon toward the axon terminal, presyn-
aptic to the next neuron. About half of all neurons in the central nervous system
(CNS) are unmyelinated and about half are myelinated. The majority of axons in
the peripheral nervous system (PNS) are myelinated.
In unmyelinated axons, voltage-dependent sodium and potassium channels are
located at every region along the axon and mediate continuous conduction. Depo-
larization activates voltage-gated sodium channels in the adjacent membrane
region, and sodium ows through the channel. This is the transmembrane current.
Once inside, the sodium moves along the membrane and diuses in the axoplasm.
This is the axial current. While the axial sodium current decays rapidly, the density
of the voltage gated sodium channels ensures that an action potential is initiated
in the next region of the membrane.
In continuous conduction, the transmembrane sodium current is followed by a
small axial sodium current. Voltage-gated potassium channels are also located all
along the axonal membrane where they repolarize the action potential at every
membrane along the axon. Thus, the action potential is generated and propagates
down the entire length of the unmyelinated axon membrane. It is regenerated
continuously along an unmyelinated axon, where the speed of action potential
conduction is between 1 to 10mm per msec.
Speeding action potentials
Two mechanisms can increase the rate of AP conduction: increasing the diameter
of an axon and myelination. The types of neurons that need increased speed of
action potential conduction are neurons with long axons. These include somatic
and autonomic lower motor neurons and sensory neurons in the PNS.Schwann
cells myelinate them (refer to Chapter1).
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CHAPTER 4 Modulating Membrane Potentials 79
In the CNS, projection/principal neurons are myelinated. They extend their axon
outside of one CNS region and make synapses with target neurons in another
region of the CNS.Oligodendrocytes myelinate them.
Conducting along myelinated axons
Myelinated axons have segments that are myelinated and that are interrupted by
small unmyelinated gaps called Nodes of Ranvier (hereafter referred to as Nodes).
Voltage-gated ion channels and transporters are localized at the Nodes. They’re
also the regions where sodium and potassium ions cross the membrane to estab-
lish the resting membrane potential and regenerate the action potential. In
myelinated axons, action potentials are conducted using saltatory conduction.
In saltatory conduction, the action potential is regenerated only at the Nodes
because those are the only regions of the axon where voltage-gated channels are
located. They’re also the only places where channels have access to the extracel-
lular uid. Depolarization at the Nodes leads to activation of voltage gated sodium
channels, allowing sodium ions to ow across the axonal membrane and into the
axoplasm, producing the transmembrane sodium current.
There are no channels or pumps in the myelinated segments. Myelination greatly
increases membrane resistance outside the Nodes. It reduces membrane capaci-
tance and decreases the time smearing of the signal. This enhances the axial
current.
Between the Nodes in the myelinated segments, the axial current ows passively
and reaches the next Node where it depolarizes the membrane potential above
threshold and activates voltage gated channels in the Node. Voltage-gated potas-
sium channels are also located only at the Nodes, so repolarization of the action
potential occurs at the Nodes as well. Therefore, the action potential is regener-
ated only at the Nodes. The axial current moves more rapidly than the time it
takes to produce the transmembrane current, thus saltatory conduction is faster
than continuous conduction.
The Nodes are spaced at the distance they’re so that they’re far enough for the
next jump to produce the next spike, but close enough so the membrane potential
doesn’t decay below threshold before it reaches the adjacent Node. Saltatory con-
duction travels at about ten times faster speed than in unmyelinated axons,
between 20 and 100 mm/msec.
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