Announcements:

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• Announcements

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• Last lecture
• Organization of the nervous system
• Introduction to the neuron
• Today electrical potential
• Generating membrane potential
• Nernst equation
• Goldman equation
• Maintaining ionic distributions

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Neural Signaling
A Simple Circuit
Between neurons
Within neurons
chemical electrical
electrical
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Bioelectric Potentials

• Neurons have an electrical potential (voltage)
  across the cell membrane
• The inside of the cell is more negative than the
  outside
• called the Resting Membrane Potential

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Measuring Membrane Potential
amplifier
microelectrode
Reference electrode
0 mV
cell
-80 mV
time
Bathing solution
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Electrophysiology techniques
Silver / Silver chloride wire electrode
Amplifier
output
Reference electrode
3M KCl solution
Glass micropipette
Very tiny hole (ltlt0.1?m)
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Resting Membrane Potential

• How is it generated?
• differential distribution of ions inside and
  outside the cell
• Selective Permeability of the membrane to some
  ions

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• How does unequal concentration of ions give rise
  to membrane potential ?

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Equal concentrations of ions
0 volts
Artificial ion selective membrane (only K, not
Cl-)
voltmeter
K
I
II
K
0.01 M KCL
0.01 M KCL
K
K
No net movement
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Unequal concentrations of ions
volts

-
Ion selective membrane (only K, not Cl-)
K
I
II
K
K
K
0.1 M KCL
0.01 M KCL
K
K
K
K concentration gradient
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Initial
New Equilibrium






CHEMICAL
CHEMICAL
ELECTRICAL
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Unequal concentrations of ions

• Initial diffusion of K down concentration
  gradient from I to II
• This causes charge to accumulate in II because
  and - charges are separated
• Remember that Cl- cant cross the membrane !
• Therefore II becomes positive relative to I

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Equilibrium Potential

• As II becomes , movement of K is repelled
• Every K near the membrane has two opposing
  forces acting on it
• Chemical gradient
• Electrical gradient
• These two forces exactly balance each other
• Called the electrochemical equilibrium

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• The electrical potential that develops is called
  the equilibrium potential for the ion.
• Electrical potential at which there is no net
  movement of the ion
• Note
• only a very small number of ions actually
  contribute to the electrical potential
• the overall concentrations of K and Cl in
  solution do not change.

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• To calculate the equilibrium potential of any ion
  (eg. K, Na, Ca,) at any concentration
• we use the Nernst Equation

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Nernst Equation
Ion Concentration I
Temp (?K)
Gas Constant
Equilibrium Potential of X ion (eg. K) in Volts
Ion Concentration II
Valence of ion (-1, 1, 2)
Faraday constant
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Nernst Equation

• At 18?C, for a monovalent ion, and converting to
  log10 ,the equation simplifies to

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• By convention electrical potential inside of
  cells is expressed relative to the outside of the
  cell

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Example K
-0.040 Volts - 40 mV
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• Therefore,
• initial movement of K down concentration
  gradient
• When electrical potential of -40 mV develops,
  there will be no net movement of K
• Thus K is in electrochemical equilibrium

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What if there is more than one permeable ion?
Permeable to K and Na, but not Cl-
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• To calculate the overall potential of multiple
  ions
• use the Goldman Equation
• Considers the permeability of ions and their
  concentrations

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Goldman equation
Voltage
Ion concentration
Permeability
Because Cl is negative
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Goldman equation

• Example, typical mammalian cell
• Assume permeability for Na is 1/100 of
  permeability for K, and permeability of Cl is 0
• Assume Kin 140, Kout5
• Nain 10, Naout120

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Goldman equation

• The resting membrane potential of most cells is
  predicted by the Goldman equation

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Summary Key Concepts

• Unequal distributions of an ion across a
  selective membrane
• causes an electrochemical potential called the
  equilibrium potential
• Two opposing forces act on ions at the membrane
• A chemical force down the concentration gradient
• An opposing electrical force

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Summary Key Concepts

• The equilibrium potential for an ion is described
  by the Nernst equation
• Cell membranes are permeable to more than one ion
  
• the membrane electrical potential is described by
  the Goldman equation

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So What???

• Everything the nervous system and muscles do
  depends on the resting membrane potential

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Sample question

• If two concentrations of KCl solution across a
  membrane give an equilibrium potential for K of
  -60 mV, what will the equilibrium potential be if
  the concentrations on each side are reversed
• -120 mV
• 0
• 60 mV
• -30 mV