The Resting Potential

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The Resting Potential
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Cells are electrical batteries

• Virtually all cells have a steady transmembrane
  voltage, the resting potential, across their
  plasma membranes.
• The negative pole of the battery is the interior
  of the cell the positive the exterior.
• All voltage values are measured relative to some
  baseline in this case, we usually take the
  solution surrounding the cell as the ground or
  baseline, and so resting potential values are
  expressed as negative numbers.
• We can measure the resting potential by inserting
  a metal or glass electrode across the plasma
  membrane, placing a second (ground) electrode
  near the cell surface, and connecting a voltmeter
  to the electrodes.

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The set-up for recording membrane potentials
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What are the sources of this electrical potential
energy?

• Direct contributions from pumps that move charge
  this would include both the Na/K pump (almost
  all cells) and the V-type H ATPase (restricted
  to a few cell types).
• Diffusion potentials arising from ionic gradients

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Diffusion potentials and the concept of
electrochemical equilibrium

• Imagine two solutions of differing ionic
  composition, separated by a barrier. For
  example, lets let the solute be KCl and the
  gradient be 101.
• Depending on the permeability properties of the
  barrier, there are 4 possible outcomes (but two
  of them are boring)

KCl
KCl
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The non-boring outcomes

• 1. barrier permeable to K but not to Cl- K
  will attempt to diffuse from left to right but
  very soon the pull of the left-behind Cl- will
  become equal to the push of the concentration
  gradient, and the system will come into
  electrochemical equilibrium with a net negative
  charge on the left side of the barrier and a net
  positive charge on the right side.
• 2. barrier permeable to Cl- but not to K
  exactly the opposite will happen, resulting in a
  net negative charge on the right side and an
  opposing positive one on the left side.
• These are equilibria, so they will persist
  without any energy expenditure as long as the
  system is not disturbed.

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The boring outcomes

• 1. barrier permeable to both ions a temporary
  diffusion potential will exist because the
  diffusion coefficient of K and Cl- differ, but
  ultimately concentrations will be equal on both
  sides and there will be no voltage at equilibrium
  boring!
• 2. barrier permeable to neither ion no change at
  all very boring!

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The Nernst Equation relates chemical and
electrical driving forces
R and T have their usual meanings, Z is the ionic
charge (1 for K), and F is Faradays Number, a
fudge factor that converts from coulombs (a
measure of static charge) to molar units. For
ease of calculation, it helps to know that if we
fill in constants and convert to 10-base logs,
the equation yields 55 mV of potential for every
additional decade of ionic gradient at room
temperature or about 60 mV at mammalian body
temperature.
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60 ENa
This diagram shows the Nernstian equilibrium
potential values for Na and K when the
concentration ratios across the membrane barrier
are 1/10 for Na and 1/30 for K - these are
typical values for real cells
0
mV
-90 EK
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Possible misconceptions typical illustrations
grossly under-represent the numbers of ions, so
that it seems that the cell below has more than
twice as many negatively charged ions inside it
as positively charged ions
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The real situation

• The charge on the membrane is generated by an
  extremely small charge imbalance and represents
  very few ions. The oppositely-charged ions
  clustered on the inside and outside of the
  membrane are such a small portion of the total
  number of each category of ion, that for a large
  neuron, if one K diffuses out of the cell for
  every 10 million K inside the cell, the effect
  is to produce a membrane potential of 100mV
  inside-negative!

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60 ENa
Where is the resting potential in this?
0
mV
-70
-90 EK
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Implications of the previous slide

• The resting potential cannot be explained as a
  pure K or pure Na diffusion potential
• Neither K nor Na is in electrochemical
  equilibrium K is close, but Na is way off.

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The Na/K pump explains the non-equilibrium
distributions of Na and K

• If an ions concentration gradient is not in
  agreement with what the Nernst 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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Now, how do we explain the resting potential?
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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 Na and 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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Leak Channels

• Despite the overall high resistance of the
  membrane, some leak channels are open in the
  resting membrane. A few of the leak channels
  allow Cl- through, a few allow Na through, but
  most of the leak channels allow K to pass
  through.
• Given that there are leak channels, which way
  will each ion move through the leak channels, on
  average?

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We can quantify the effects of the Na and K
gradients

• We just have to know the relative magnitudes of
  the concentration gradients and the relative
  permeabilities

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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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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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How do things look to Na?
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Na is not conflicted!

• Both the concentration gradient and the
  internally-negative membrane potential favor
  entry into the cell.

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The way things look to K

• The forces on K are outward, down its
  concentration gradient, and inward, responding to
  the attraction of the negative interior

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The way things look to Cl-
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Chloride is often passively distributed..

• Cl- is driven out, repulsed by the negative
  charge inside, but it is driven in by its
  concentration gradient. The result can be that
  Cl- is contented at the resting membrane
  potential, with its two forces balanced.

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A little review of electrical terms
Ohms Law ( I V/R ) is the relationship between
electrical force and flow. The driving force (V
or E units of volts) this is potential
energy. Resistance is R (units ohms)
conductance (G) is the inverse of resistance
(units mohs or siemens) Current (I) is in units
of amps One amp is the current that flows when
the driving force is 1 volt and the resistance is
one ohm (or the conductance is 1 Siemen).
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Relevant membrane properties resistance and
capacitance

• The lipid bilayer has a high electrical
  resistance (i.e., charged particles do not move
  easily across it) and it separates two very
  conductive (salty) solutions.
• The lipid bilayer is thin (about 50 Angstroms).
  The thinness of the membrane allows it to store a
  relatively large amount of charge, i.e., have a
  high capacitance very small differences in the
  electrical balance of charges inside the cell
  easily attract opposite charges to the outside of
  the cell.

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Net current flow across the membrane is zero at
rest.(or at any time when the potential is stable)
An important corollary of Ohms law is that when
the membrane potential is stable, net current
flow across it is zero. If net current flow is
not zero, Vmembrane has to be changing.
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Current Flow causes the membrane potential to
change
In physiology (unlike physics), current is
defined as the flow of positive charge. A net
inward current is thus equivalent to flow of
cation into the cell (or anion out of the cell),
either of which would cause depolarization -
change toward a less inside-negative membrane
potential. The opposite change is
hyperpolarization.
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Membrane response to injected current
After the injected current is turned off, the
membrane potential moves pretty quickly back to
the resting level What is going on?.
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Some factors that cause depolarization

• K extracellular
• Na extracellular
• Na permeability
• K permeability