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BME 502 / 1997 / handout #3
BME 502: Handout on Active Membrane Properties
regenerative characteristics of the action potential
first noted in experiments using a variety of preparations, but clearest demonstration of
regenerative property from use of preparations such as the giant squid axon, because two
recording electrodes can be placed at different spatial locations along its length
in such experiments, clear that there was a delay between the appearence of an axon
potential at one recording site vs the other, yet amplitude-time course remained
also clear that there was a specific threshold of depolarization that must be reached for the
regenerative event to be initiated
BME 502 / 1997 / handout #3
using voltage-clamp, observe the following in response to voltage steps from resting membrane
potential to - 9 mV
three major currents observed
capacitive current
transient inward current
delayed, sustained outward current
ion substitution and channel blockade experiments (see figure below) allow separation and
BME 502 / 1997 / handout #3
identification of each current
TTX, eliminates inward current
command voltage past +60 mV, ENa
ion substitution: e.g., replace Na+ with choline
TEA, eliminates most of outward current
command voltage past -85 mV, EK
leakage current (K+ and Cl-)
so if in the presence of TTX and TEA apply depolarizing command
voltage, see capacitive current and sustained outward current
BME 502 / 1997 / handout #3
resolves into a transient inward current, a delayed outward current, and a sustained leakage
BME 502 / 1997 / handout #3
transient inward current and delayed outward current reflect two different channel species:
BME 502 / 1997 / handout #3
voltage-clamp analyses performed
by stepping membrane potential
from rest to various test potentials,
and plotting peak transient Na+
current and steady-state K+
current reveals voltagedependence of currents in
curvature of I-V relation
BME 502 / 1997 / handout #3
on the basis of these and other data, an equivalent circuit model of the conductances underlying
the resting membrane potential and action potential:
previously have seen that an equivalent circuit can be specified for a channel (population)
g, conductance for the ion passing through the membrane
E, equilibrium potential for that ion
using a modified form of Ohm's Law,
ionic conductance for a given ion, e.g., K+
I K+ = g K+ ( V m - E K+ )
g K+ =
I K+
( V m - E K+ )
concept of equivalent circuit for a channel can be extended to entire membrane
equivalent circuit for a patch of membrane considering individual conductances for each ion
species conductances for total current flow through all channels of same species
variable conductances for voltage-sensitive conductances
BME 502 / 1997 / handout #3
** for the equivalent circuit model to be justified, it is necessary to demonstrate that the relation
between ionic current and membrane potential is linear for a condition of constant
permeability, i.e., satisfies Ohm's law -- requires a determination of "instantaneous currentvoltage relation" -- stepping the voltage to a first holding potential (V1 in figures below) long
enough to increase permeability and then stepping to a second holding potential (V2 in figures
below) and measuring the current with 10-30 μsec before additional changes in permeability
can occur **
for Na+ current:
for K+ current:
BME 502 / 1997 / handout #3
given a linear relation between current and voltage (see above),
changes in conductances gNa and gK during a voltage-clamp can now readily calculated by
applying the equations below to the separated currents
g K+ =
I K+
( V m - E K+ )
g Na+ =
I Na+
( V m - E Na+ )
characteristics of inward Na+ current
rapidly activating (compared rates of rise below for Na+ and K+)
rate of activation depends on magnitude of membrane depolarization (left panel)
BME 502 / 1997 / handout #3
Na+ conductance rapidly inactivates
inactivation process is both both voltage-dependent
(p.43, fig. 14, Hille)
and time-dependent
(p.45, fig. 15, Hille)
once inactivated, membrane must be hyperpolarized to remove inactivation
experimental analysis of inactivation process:
small depolarizing step; followed by large depolarizing step
initial small step activates voltage-dependent Na, but channels inactivate
quickly so when large step etc
can determine the percentage of channels that are inactivated at different Vm
thus, if include hyperpolarizing pre-step, find that current generated by
command voltage step is greater than if pre-step is resting membrane
BME 502 / 1997 / handout #3
potential  some channels are inactivated even at rest
time course of inactivation process
paired pulse experiment
compare magnitudes of currents in response to identical command steps
as a function of inter-pulse interval
equivalent to examination of a feedback system, or a feedforward system in the
case of the pre-step or inactivation at rest
characteristics of outward K+ current
slowly activating
rate of activation depends on magnitude of membrane depolarization
no inactivation
BME 502 / 1997 / handout #3
explanation for transmembrane changes accompanying action potential
change in permeability initially due to ligand-gated channel opening
PNa+ increases
large driving force, Na+ enters
causes change in Vm
change in Vm leads to opening of voltage-dependent Na+ channels
also leads to opening of voltage-dependent K+ channels
driving force greater for Na+ so depolarization predominates
as Vm  ENa, driving force for Na+ 
and driving force for K+ 
Na+ channels inactivate
membrane current carried increasingly by K+
because of EK, K+ current leads to repolarization and hyperpolarization (undershoot)
BME 502 / 1997 / handout #3
Functional Consequences of Na+ and K+ Channel Kinetics
given the characteristics of the Na+ and K+ currents underlying the action potential, there are
multiple functional consequences for the functional, dynamic properties of neurons:
consequences w/re to threshold
when INa exceeds IK
thus, no constraint on part of soma that initiates action potential
except density of Na+ channels relative to other channels
consequences w/re to shape of action potential
sharp rise-fall
consequences w/re to input required for triggering action potential
slow depolarization not sufficient
release of hyperpolarizing current can lead to action potential w/o epsp
consequences w/re to propagation of action potential
directionality of action potential propagation when initiated at soma (initial segment)
bi-directionality of propagation when initiated at center of axon
Interactions Between Active and Passive Membrane Properties
other functional consequences emerge when the properties of these active conductances are
considered in terms of their interaction with passive membrane properties:
consequences w/re to rate of propagation
axon (cell) diameter:
larger cell diameter and rm , ri , and λ (already discussed)
large axon diameter also increases velocity of axon potential propagation:
BME 502 / 1997 / handout #3
ri 
so with larger diameter axons, lateral spread is greater, i.e., passive membrane properties
determine speed of conduction of action potential
BME 502 / 1997 / handout #3
myelination consists of wrapping of glial cell processes around axon
leads to saltatory conduction: action potential propagation at Nodes of Ranvier only
myelination leads to an apparent increase in thickness of the membrane by increasing rm
increasing rm increases the ratio of rm to ri , just as would occur if diameter increased, so
current flows farther in the axial direction (shown in figure below)
 conduction velocity increases with higher specific membrane resistance and/or
myelination of the axon
BME 502 / 1997 / handout #3
degree of axonal branching: branch point failure
from small diameter to larger diameters
from myelinated portion of axon to non-myelinated portion
en passage axons and terminal fields
BME 502 / 1997 / handout #3
Active Conductances In Addition to Na+ and K+ Currents Underlying Action Potential
conductances introduced to date:
IK(l) leakage K+ conductance; linear, voltage-independent current
resting Vm largely determined by this conductance
blocked by cesium, injected intracellularly
blocked by TEA extracellularly
fast, voltage-dependent Na+ conductance
characteristics:strongly voltage-dependent
rapidly activating
rapidly inactivating
pharmacology: TTX or QX-314
distributon: greatest density within axon and particularly axon hillock
this species of Na+ conductance is the basis for the action potential, so clearly present in
axons; but also found in soma and dendrites
BME 502 / 1997 / handout #3
voltage-dependent K+ conductance
also called the "delayed rectifier" because conductance increases only with depolarizing
slow kinetics; slow activation (5 msec) and no inactivation
partially responsible for repolarization and initial hyperpolarization of membrane
blocked by TEA
thus, three major conductances:
leak conductance, carried primarily by K+, which contributes substantially to resting
membrane potential
voltage-dependent Na+ conductance that is highly voltage-dependent, and is primarily
responsible for reaching threshold and the rising phase of the action potential
(iii) voltage-dependent K+ conductance that is primarily responsible for the repolarization of the
membrane following the action potential
 can account for the resting membrane potential, and the rising and falling phases
of the action potential
what is right with this picture?
exactly the set of mechanisms that is optimal for low-failure transmission over cables,
i.e., for communication between neurons -- and is what is found in axons
what is wrong with this picture?
will result in a system that is not very information rich, particularly if a frequency code is
the basis for information transmission in the nervous system
will be difficult for a relatively small depolarization to lead to an action potential
(because of leakage current -- the driving force for which will increase as the
membrane depolarizes), because of the rapid inactivation of Na+ conductances, and
because of the voltage-dependent K+ conductances
for any input that is sufficiently strong to initiate an action potential, will be very difficult
to modulate the interspike interval given the removal of Na+ channel inactivation that
results from repolarization by the K+ channels and the steep voltage-dependence of
the Na+ channels
BME 502 / 1997 / handout #3
must introduce more mechanisms that allow greater variation of interspike interval as a
function of variation in the subthreshold membrane potential
slow, voltage-dependent Na+ conductance
activated near rest, and non-inactivating near rest
blocked by TTX but not by QX-314
can be separated from fast Na+ conductance by using ramp depolarizations: ramp
BME 502 / 1997 / handout #3
stimulation effective because slow depolarizations result in rapid inactivation of fast Na+
BME 502 / 1997 / handout #3
the less rapid the rate of
depolarization, the more linear is the
I-V curve because of the greater
inactivation of fast Na+
conductances relative to their
inactivation, and thus, the more
predominant is the slow, voltagedependent Na+ conductance
the more rapid the rate of
depolarization, the greater activation
of fast Na+ conductances relative to
their inactivation, and thus, the
greater the magnitude of the
negative slope conductance
reflecting the fast Na+
functional significance
of slow Na+ current is
an amplification of
small synaptic
potentials: responses
with and without INa(s)
upper panel: responses
at rest; EPSP leads to
action potential
discharge with INa(s)
lower panel: responses
relative to rest; EPSP
is enhanced with INa(s)
BME 502 / 1997 / handout #3
IK(C) K+ conductance; also called IC or fast AHP
activated by an increase in intracellular free Ca2+ (and because of voltage-dependence of
Ca2+ channels, also exhibits a voltage-dependence indirectly)
rapid kinetics; activated with 1-2 msec; total duration of 20-50 msec
responsible for repolarization and hyperpolarization of membrane
highly sensitive to TEA
determines inter-spike interval and # spikes in a burst
shortened action potential duration means that inactivation of Na+ channels removed
sooner that if repolarization determined only by delayed rectifier, so increases the dynamic
range of neuron by increasing upper limit of firing frequency
calcium-activated K+
conductance; also called
slow AHP
very slow kinetics; duration
can extend to beyond 1000
insensitive to TEA; relative
voltage insensitive
contribution easily seen in
phenomenon called
if apply a depolarizing,
long duration pulse
initial response of several
action potentials
inter-spike interval
gradually lengthens; cell
eventually stops firing
determines inter-burst interval and to a certain extent, # spikes in a burst
BME 502 / 1997 / handout #3
triggered by increase in intracellular Ca2+; but current also regulated by a second
messenger events, because manipulations that increase intracellular cAMP also decrease
so can block current with blockade of Ca2+, or with activation of cAMP; e.g., membrane
permeable cAMP analog, 8-bromo cAMP, decreases AHP but with no change in Ca2+
sensitive to NE, ACh
Ca2+ conductances; voltage-dependent
typically examined in the presence of TTX and TEA, with cesium in electrode
typical waveform: long-duration depolarization; plateau potential
first Ca2+ conductance discovered was a high threshold, non-inactivating channel; now
termed the L-type
BME 502 / 1997 / handout #3
L-type channels
activation requires relatively large depolarizations because of high threshold
holding potential: -50 to -20; command voltage: half-maximal at -15 mV
comparison of inactivation properties of high-threshold
(right) and low-threshold (left) calcium currents
sustained inward current; does not exhibit strong
inactivation, so longer duration currents
however, shows inactivation that depends on [Ca+]i but
not voltage (see right)
much larger conductance than other Ca2+ channels
blocked by many divalent cations, but especially by
agonist, dihydropyridines such as Bay K8644
antagonist, nimodipine or nifedipine
can substitute Ba2+ for Ca2+ for L-type channel
BME 502 / 1997 / handout #3
later became clear that there was a low threshold Ca2+ conductance vs. high threshold
BME 502 / 1997 / handout #3
in above figure, Ca2+ currents are emphasized by using a high Ba2+ concentration
extracellularly and including Cs+ in the recording electrode
two holding (EH) potentials are used, -30 mV and -80 mV
several command voltages used, but results to two are shown, -20 mV and +10 mV
because of high threshold of L-type channel and fast inactivation of T-type channel,
stepping from -30 mV will reveal L-type Ca2+ current only
stepping from -80 mV will reveal both L-type and T-type currents (shown in left panels)
subtracting results for -30 mV from results for -80 mV (shown in right panels) gives data
for T-type
BME 502 / 1997 / handout #3
T-type channels
"low-threshold" calcium current
activated and inactivated over a range similar to that for Na+ channels
holding potential: -65 to -85
command voltage: half maximal at -40 mV
transient inward current; 100-200 ms duration
conductance not that large
insensitive to dihydropiridines; but blocked by Ni2+
T-type vs L-type Ca2+ channel kinetics:
BME 502 / 1997 / handout #3
N-type channels
depolarization, and inactivates slowly
holding potential: -65 to -85; command
voltage: -25 mV (half-maximal)
transient inward current; 500 ms duration
blocked by ώ-conotoxin
T-type vs N-type vs L-type Ca2+
channel I-V curves
BME 502 / 1997 / handout #3
voltage-dependent K+, called the A-current (can only detect in presence of TTX and Mn2+
to block Ca2+)
conductance=0 at rest but quickly activated when depolarized: within 5-10 msec;
relatively rapid inactivation: within 20-30 msec
blocked by 4-aminopiridine; relatively insensitive to TEA; can be separated from IK(DR)
by substraction (see below)
voltage-dependent K+
much like the IK(A) current except that activation and inactivation occurs within a
voltage range that is 15-20 mV more depolarized than for the A-current
so introduces a hyperpolarizing effect to slow larger magnitude depolarizations
inactivates very slowly: over the course of seconds
BME 502 / 1997 / handout #3
function: has a stabilizing
effect on membrane
potential; activated during
initial phases of a
depolarization and acts to
shunt what otherwise would
be a rapid initiation of
action potentials
voltage-gated inward K+ current, or inward rectifier
activated by hyperpolarization, with no inactivation; characteristics are the basis of
hyperpolarization leading to a decrease in input resistance, and thus, a rectification of
the I-V relationship
passes K+ ions inward more efficiently than in the outward direction
voltage range for activation shifts as a function of [K+]o; voltage-dependency of
activation due to channel block by Mg2+ (from intracellular fluid; thus, differs from
NMDA), which is removed by hyperpolarization
function of IK(IR) is to contribute
to stabilization of membrane
potential by preventing severe
hyperpolarization of neuron to
membrane potentials at which
the membrane would become
figure: dashed lines show
instantaneous I-V relation;
solid lines show steady-state
BME 502 / 1997 / handout #3
q-current, or, "queer" current
inward rectifying, non-selective cation channel
top panel: when recording
membrane potential (not
voltage clamp, injecting
hyperpolarizing current
activates IQ, decreasing
membrane resistance,
which leads to the "sag" in
the membrane potential
bottom panel: under
voltage clamp conditions, a
hyperpolarizing command
step activates IQ ; slowly
increasing current
illustrates slow activation
BME 502 / 1997 / handout #3
BME 502 / 1997 / handout #3
BME 502 / 1997 / handout #3