Resting Membrane Potential
• Membrane potential at which neuron
membrane is at rest, ie does not fire action
potential
• Written as Vr
Ionic Equilibrium Potential
• Membrane Potential (potential difference
across the plasma membrane) at which the
net flow of an ion type = zero
• The number of ions moving into the cell =
the number of ions moving out of the cell
for a particular species of ion
Nernst Equation Variables
• Assumes that membrane is permeable to
that ion
• As temperature increases the diffusion
increases
• As charge on the molecule increases, it
decreases the potential differences needed
to balance diffusion forces.
Simplified Eion (at 37°C)
•Eion = 2.303 RT/zF log [ion]o/[ion]in
• Ena = 61.54mV log [Na]o/[Na]I = 62 mV
• EK = 61.54mV log [K]o/[K]I = -80 mV
• ECa = 30.77mV log [Ca]o/[Ca]I = 123 mV
• CCl = -61.54mV log [Cl]o/[Cl]I = - 65 mV
Goldman Equation
• Vr= RT/F ln Pk[K]o+Pna[Na]o+PCl[Cl]i
Pk[K]I+Pna[Na]I+PCl[Cl]o
Also known as the constant field equation
because it assumes that electrical field of
the membrane potential is equal across the
span of the membrane
Membrane Permeability
• Membrane is 50 more permeable to K than
to Na
• Pk/Pna = 50
• PCl/Pk = 0
• The membrane is so impermeable to
Chloride that you drop it from the equation
Goldman Equation
•Vr= RT/F ln Pk[K]o+ Pna[Na]o+ PCl[Cl]i
Pk[K]I+ Pna[Na]I+ PCl[Cl]o
• Eion = 2.303 RT/zF log Pk[K]o+Pna[Na]o
Pk[K]I+Pna[Na]I
• Vr= 61.54 mV log 50[5]o +1[150]o
50[100]i+1[15]I
• = - 65mV
Not to study
• Donnans equilibrium
• Osmolarity considerations
Action Potential
Changes in Ion Permeability allows inward Na
flux and triggers an increased outward K flux
through voltage gated ion channels
Causes transient change in Membrane Potential
The change in ion permeability is triggered by
transient depolarization of the membrane
Conductance = g
• How many charges (ions) enters or leaves
cell (inverse of resistance)
• due to:
– number of channels/membrane area
• Highest density at axon hillock
– number of open channels
– ion concentration on either side of membrane
– Measured in Siemens (S), in cells pS (pico; -12)
Historical Figures
• Hodgkin and Huxley
won Nobel Prize for
Voltage clamp in 1961
• Sakman and Nehr won
Nobel Prize for Patch
Clamp in 1991
• used to identify the ion
species that flowed
during action potential
• Clamped Vm at 0mv to
remove electric driving
force than varied
external ion
concentration and
observed ion efflux
during a voltage step
• measured
ion
flow
through
individual
channels
• shows
that
each
channel is either in
open
or
closed
configuration with no
intermediate. The sum
of many recordings
gives you the shape of
sodium conductance.
Information Coding
• Is NOT in shape of action potential
• Is in the action potential frequency of firing
—how many are triggered
• In the action potentials pattern or timing of
propagation
Conductance = g
• How many charges (ions) enters or
leaves cell (inverse of resistance)
• due to:
– number of channels/membrane area
• Highest density at axon hillock
– number of open channels
– ion concentration on either side of
membrane
– Measured in Siemens (S), in cells pS (pico; -12)
Generation of Resting Membrane
Potential (-70mV)
• Plasma membrane
• Selective permeability, permeable to K, not
Na
• Unequal distribution of ions across
membrane
– Due to open potassium channels and closed
sodium and chloride channels
• Action of ion pumps 3Na/2K ATPase
Ion
Inside
Outside Cross PM
K+
125
5
yes
NA+
12
120
no
Cl-
5
125
yes
H2O
55,000
55,000
yes
Anion-
108
0
no
Ionic Equilibrium Potential
• The membrane potential that balances the
ions concentration gradient so that there is
no net current for that ion.
• No permeability factor.
Equilibrium Potential of An Ion
• The membrane potential at which the net
driving force propelling the ion in = the net
driving force propelling the ion out.
• Written Eion; ENa, ECl, EK
Nernst Equation
• Eion = 2.303 RT/zF log [ion]o/[ion]in
•
•
•
•
•
Eion = ionic equilibrium potential
Z= charge of ion
F= Faraday’s constant
T= absolute temperature (0Kelvin/-273°C)
R= gas constant
Action Potential: a
transient and rapid
sequence of changes in
the membrane potential
Action Potentials
Can travel up to
100 meters/second
Usually 10-20 m/s
0.1sec delay
between muscle and
sensory neuron
action potential
Membrane Permeability
• Membrane is 50 more permeable to K than
to Na
• Pk/Pna = 50
• PCl/Pk = 0
• The membrane is so impermeable to
Chloride that you drop it from the equation
Goldman Equation
•Vr= RT/F ln Pk[K]o+ Pna[Na]o+ PCl[Cl]i
Pk[K]I+ Pna[Na]I+ PCl[Cl]o
• Eion = 2.303 RT/zF log Pk[K]o+Pna[Na]o
Pk[K]I+Pna[Na]I
• Vr= 61.54 mV log 50[5]o +1[150]o
50[100]i+1[15]I
• = - 65mV
Ion Permeability
• Changes during action potential
• The plasma membrane becomes permeable
to sodium ions
– Permeability increases from 0.02 to 20=1000
fold increase
• Causes Em aka Vr to approach Ena at positive
voltages = +20mV
overshoot
Falling
rising
undershoot
6 Characteristics of an Action
Potential
• #1 Triggered by depolarization
• a less negative membrane potential that
occurs transiently
• Understand depolarization, repolarization
and hyperpolarization
#2 Threshold
• Threshold depolarization needed to trigger
the action potential
• 10-20 mV depolarization must occur to
trigger action potential
#3 All or None
• Are all-or- none event
• Amplitude of AP is the same regardless of
whether the depolarizing event was weak
(+20mV) or strong (+40mV).
#4 No Change in Size
• Propagates without
decrement along
axon
The shape (amplitude &
time) of the action
potential does not change
as it travels along the axon
#5 Reverses Polarity
• At peak of action potential the membrane
potential reverses polarity
• Becomes positive inside as predicted by the
Ena Called OVERSHOOT
• Return to membrane potential to a more
negative potential than at rest
• Called UNDERSHOOT
#6 Refractory Period
• Absolute refractory period follows an action
potential. Lasts 1 msec
• During this time another action potential
CANNOT be fired even if there is a
transient depolarization.
• Limits firing rate to 1000AP/sec
Stimulating electrode:
Introduces current that can
depolarize or
hyper-polarize
Recording electrode:
Records change in
Potential of the membrane
At a distance away
At Threshold Na influx equals K efflux
Voltage (mVolts) along Y axis
Time (msec)
Voltage Sensitive Ion Channels
• Sodium
• Potassium
Ionic Equilibrium Potential
• Membrane Potential (potential difference
across the plasma membrane) at which the
net flow of an ion type = zero
• The number of ions moving into the cell =
the number of ions moving out of the cell
for a particular species of ion
Regenerative Process:
Once one Na channel
Opens, Na enters,
Depolarizes membrane,
More and more Na
Channels open leading to
More sodium influx &
causes upward &
depolarizing (more +)
phase of the AP
What does a sodium
Channel look like?
It is one large protein
With 4 domains that
Each loop through the
Plasma membrane 7
Times.
Property of Voltage Dependent
Sodium Channel
• Sodium channel opens for 1-2 millisecond
following threshold depolarization
• then inactivates and does not open even if
Vm is depolarized.
• This is called sodium channel inactivation
and contributes to the repolarization of Vm
Na Channel Gates
•M gate= activation gate
on Na channel; opens
quickly when membrane
is depolarized
•H gate- inactivation gate
on Na channel; Closes
slowly after membrane is
depolarized
•causes the absolute
refractory period for AP
propagation
Potassium Channel Property
• K channels open with a delay and stay open
for length of depolarization
• Repolarize the Vm to Ek= -75mV which is
why you have hyperpolarization.
• Also called a delayed rectifier channel
Gate on the Delayed Rectifier
Potassium Channel
•K channels have a
single gate (n) that stays
open as long as Vm is
depolarized.
• n gate on K channels
opens very slowly this
allows the Vm to
depolarize due to Na
influx; Na and K
currents do not offset
each other right away
Refractory Period
• Refractory period due to Na channel
inactivation and the high gk
• Subsequent Action potential cannot be
generated
2 ways to increase AP
propagation speed
• Increase internal diameter of axon which
decreases the internal resistance to ion flow
• Increase the resistance of the plasma
membrane to charge flow by insulating it
with myelin.
See and understand
what happens to the form
Of the action potential
When you add a voltage
Sensitive calcium channel
And a calcium gated
Potassium channel
Test question : think about
This and the next 2 slides
Channel Density
• Density is how many channels are in a unit
area of plasma membrane, ie how closely
they are packed together.
• Determines the length of the membrane that
will be depolarized at a given time
Understand
•
•
•
•
Regenerative nature of action potential
Orthodromic and antidromic
Voltage gates in sodium channel
Threshold potential sodium and potassium fluxes
are balanced
• Initial segment of axon = axon hillock
• Two mechanisms for increasing speed of action
potential propagation
• Saltatory conduction
Understand
• Action potential occurs because sodium
and potassium fluxes change the charge
on the cell membrane not because the
fluxes change ion concentrations.
Definition
V=IR
V=voltage, I=current, R=resistance
• g=1/R
g=conductance
• Vm=membrane voltage
• Vr=voltage of membrane at rest
Permeability and Conductance
• gna is low at Vr because sodium
channels are closed
• gk is higher than gna at Vr because some
potassium channels are open.
• V=I/R Ohms Law
• G=conductance=1/R
Definitions
• Current=net flow of
ions per unit time
• 1 ampere of current
represents movement
of 1 coulomb of
charge per second
• Resistance- frictional
forces that resists
movement of ions or
charges
• Measured in ohm
• Current (A)= V/R
Definitions
• Conductance is the
reciprocal of
resistance and
measures the ease with
which current flows in
an object.
• Measured in siemens
(S)
• Capacitance refers to the
ability of plasma
membrane to store or
separate charges of
opposite signs.
• Myelin has high
capacitance so stores
charges and ions do not
move across the
membrane
• Measured in Farads