The Resting Potential

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The Resting Potential
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Figure 11-22. The ionic basis of a membrane
potential. A small flow of ions carries
sufficient charge to cause a large change in the
membrane potential. The ions that give rise to
the membrane potential lie in a thin (lt 1 nm)
surface layer close to the membrane, held there
by their electrical attraction to their
oppositely charged counterparts (counterions) on
the other side of the membrane. For a typical
cell, 1 microcoulomb of charge (6
1012monovalent ions) per square centimeter of
membrane, transferred from one side of the
membrane to the other, changes the membrane
potential by roughly 1 V. This means, for
example, that in a spherical cell of diameter 10
µm, the number of K ions that have to flow out
to alter the membrane potential by 100 mV is only
about 1/100,000 of the total number of K ions in
the cytosol
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V - 70 mV
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The Na/K pump explains non-equilibrium
distributions of Na and K

• If an ions concentration gradient is not in
  agreement with what the Nernst Planck equation
  predicts, work is being done to keep the system
  out of equilibrium.
• Na and K distributions across the plasma
  membrane are kept away from diffusional
  equilibrium by the Na/K pump. The energy is
  provided by hydrolysis of ATP.

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3. It is a major part of the energy budget of
excitable cells, especially small ones. 4. It is
inhibited by specific drugs ouabain, digitalis
and other cardiac glycosides derived from plants
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Recall that EK -90 mV Ena 60 mV Ecl -70 mV
So, for this typical cell with a membrane
potential of about -70 mV, Cl- is in equilibrium
whereas both K and Na are out of
electrochemical equilibrium. That could only
happen if some energy were being spent to keep
them that way.
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This diagram shows the sizes of the driving
forces that act on Na and K when the
concentration ratios across the membrane are 1/10
for Na and 1/30 for K and the resting potential
is -70 mV.
60 ENa
0
Driving force on Na 130 mV
mV
Resting potential
-70
Driving force on K 20 mV
-90 EK
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The magnitude and polarity of the resting
potential are determined by two factors

• 1. The magnitude of the concentration gradients
  for Naand K between cytoplasm and extracellular
  fluid.
• 2. The relative permeabilities of the plasma
  membrane to Na and K.

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Since the Na and K concentration gradients are
opposite, you could think of the membrane
potential as the outcome of a tug-of-war between
the two gradients. The winner (defined as the
ion that can bring the membrane potential the
closest to its own equilibrium potential) is
determined by the relative magnitudes of the K
and Na gradients and the relative permeability
of the membrane to the two ions.
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K is the winner on both counts its gradient is
about 30/1 as compared to Nas 10/1, and the
membranes of most cells are 50-75 times more
permeable to K than Na.
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The Goldman Equation describes the membrane
potential in terms of gradients and permeabilities
In words, the Goldman equation says The
membrane potential is determined by the relative
magnitudes of the concentration gradients, each
weighted by its relative permeability.
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What ions have to appear in the Goldman equation?

• To be accurate, the Goldman equation must include
  a term for each ion that is
• a. not at equilibrium, and
• b. for which there is significant permeability
• So, for those cells which actively transport Cl-,
  a Cl- term must be added. To do so, Cl-in and
  Cl-out have to be inverted relative to the
  cation terms, because of the charge difference.

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Action Potentials
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What are they?

• Rapid, brief, depolarizations of the membrane
  potentials of excitable cells (neurons, muscle
  cells, some gland cells), initiated by an
  appropriate stimulus to a sensory receptor
  (chemical, physical or electromagnetic), or
  chemical signals released by neurons and received
  by other neurons, muscle cells or gland cells.

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Characteristics of Action Potentials

• Show threshold for initiation
• Are all-or-nothing - their magnitude is not
  graded to stimulus intensity.
• Spread throughout the plasma membrane by a
  non-decremental process- the magnitude of the AP
  does not diminish with distance.
• Followed by a refractory period during which it
  is difficult or impossible to initiate another
  action potential.

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Physiological Function

• Action potentials are the means of rapid
  (milliseconds), long-distance (up to
  meters)communication in the body
• As opposed to
• chemical messages - which can be long-distance,
  but slow (seconds to minutes)
• decremental electric currents - which are rapid,
  but can only operate over short distances (a few
  tens of microns)

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We will examine the change in the voltage of a
small piece of excitable membrane as we drive a
current across it.
Volts

_ _ _ _
_ _ _ _

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Notice that the same current strength causes a
smaller voltage change for hyperpolarizing pulses
than depolarizing pulses - its easier to
depolarize the membrane than to hyperpolarize it.

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As the strength of depolarizing current is
increased, there is a sudden transition to an
action potential - a threshold has been crossed.

• A threshold stimulus - defined in terms of
  current intensity and duration - is one that is
  able to initiate an action potential 50 of the
  time.

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The next slide shows a complete action potential
as it would be recorded in squid giant axon.
(Not all cell types show a hyperpolarizing
afterpotential as obvious as is seen here.)
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In this set of experiments the axonal membrane is
voltage-stepped to -40mV, 0 mV or 40 mV, and the
resulting conductance changes for Na and K are
plotted over time. Note that the Na conductance
is self-terminating the K conductance is not
(at least within the timeframe shown here).
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The next slide shows that the conductance change
of the stimulated (and unclamped) cell explains
the voltage change of an action potential. The
conductance change is the sum of the two separate
conductance (g) changes for Na and K that were
recorded under clamp conditions. Conductance
permeability x driving force, so the conductance
changes are essentially permeability changes.
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The Refractory Period
Following an action potential, there is a brief
period during which an excitable cell cannot
initiate a second action potential. This is the
absolute refractory period.
Following the absolute refractory period is a
longer period during which it is more difficult
to bring the membrane to threshold for a second
action potential - this is the relative
refractory period.
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In the experiment shown on the next slide, a
cell is given a pair of stimulus pulses with a
variable time interval . As the interval is made
shorter, the threshold rises, because the second
stimulus starts to fall in the cells relative
refractory period. The threshold becomes
essentially infinite in the millisecond or so
just after the first AP (I.e. the second stimulus
comes during the absolute refractory period.
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Questions

• How does depolarization cause an AP and what is
  responsible for threshold?
• What factors determine the duration of an AP?
• Why is the membrane refractory to a second
  stimulus for a time after an AP?
• Why is it easier to depolarize the membrane than
  it is to hyperpolarize it?

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These questions can now be answered in terms of
the behavior of voltage-gated channels for Na
and K
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Na channels can exist in three distinct states,
which form a cycle

• Most channels are closed, but available, at rest
  potential - depolarization increases open
  probability. At threshold the channels enter a
  positive feedback cycle in which .

depolarization
activation
This positive feed back explains the rapid rise
or upsweep of the spike when threshold is reached.
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The open state or activated state of Na
channels is followed by inactivation - a closed
state in which the channel cannot be reopened by
depolarization. This explains the downturn of
the spike before it has time to reach
Ena. Inactivation is removed by some combination
of repolarization and time, returning the channel
to the available state.
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The Na channel has two gates - an activation
gate in the interior of the channel and an
inactivation gate suspended from the
intracellular domain.
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Na channel behavior is revealed by patch clamping
The experiment on the next slide shows the
single-channel currents recorded from 7
individual Na channels in response to a
depolarizing voltage step. Notice how random the
behavior is - the different channels open at
different times, stay open for different times,
and may flicker closed a time or two before each
finally inactivates. The summed current from the
channels is shown in the bottom trace. The
Nacurrent that flows across a patch of membrane
during an action potential is the sum of its many
single-channel currents.
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In this slide inward currents are shown as
downward deflections
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K channels differ from Na channels in that they

• Open more slowly in response to depolarization
• Close (slowly) in response to repolarization
• Do not show time-dependent inactivation.

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Note that the trace of the summed current rises
more slowly than for the Na channel, and that
the channels continue to be active as long as the
depolarization is maintained
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Threshold can now be redefined

• as the stimulus intensity/duration that has a 50
  probability of opening enough Na channels to
  cause the inward Na current to exceed the
  outward K current.
• When the inward Na current exceeds the outward
  K current, the system enters the positive
  feedback cycle that leads to an AP

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Three factors make threshold hard to reach

• Depolarization increases the driving force for K
  and decreases it for Na
• Depolarization opens K channels as well as Na
  channels.
• Open Na channels do not stay open - they
  inactivate.

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The refractory period is determined by two
separate factors Na channel recovery from
inactivation and K channel closing.

• Early in the refractory period, most Na channels
  are still in the inactivated state, and so not
  available.
• In the middle of the refractory period, some Na
  channels have become available, but the number of
  open K channels is still greater than at rest.
• The refractory period wanes as the last
  voltage-sensitive K channels close.