Resting Membrane Potentials
The Lipid Bilayer is a Capacitor
• The electric signals of neurons arise from the
movement of charges – in the form of ions across the
plasma membrane.
• The membrane has 2 essential features:
1. The lipid bilayer is an impenetrable barrier to the
movement of ions across it. Ions can be stored within
the membrane within the “leaky” channels, thereby
actually occupying space among the phospholipid
tails. Thus, charge can be stored – like an electrical
capacitor!
That’s because the membrane is leaky to ions,
depending on the number and type of leaky channels,
and this must be constantly corrected at the expense
of ATP.
2. The lipid bilayer has high charge storage
capacity because it is very thin, enabling the
stored charge to get VERY close to the
corresponding, but opposite charge, lowering
their potential energy.
• This separation of charges generates an electric
field or potential difference across the
membrane, given by V = Q/C or
charge/capacitance.
• Your typical membrane has a capacitance of 1
μF/cm2, about 70% of which is due to the lipid
bilayer and the rest because of embedded
proteins.
At Rest, the Neuron Membrane is Permeable
to K+, Na+ and ClEvidence from radioactive tracer studies reveals
that all major ionic species can pass through
the resting neuronal membrane; i.e., there are
“leak channels” for these ions –
Outside
Inside
K+
K+
Na+
Na+
Cl-
Cl-
However, not all ionic species cross the
membrane at the same rate or to the same extent
1) Not all channels allow the same number of
ions to pass per unit time (i.e. carry the same
current), maybe due to structural differences
in the channels?
e.g1. The more narrow the channel the more difficult
it is for an ion to pass through the channel
(bumps into the wall, squeezes through, resulting
in decrease in the kinetic energy)
e.g2. There are different numbers of the different
channels in the membrane (i.e. there are more K+
leak channels than Na+ leak channels)
Permeability
A measure of how easy it is for an ion to cross the
membrane; takes into account ease to traverse a
channel or the number of channels, etc.
At rest, for giant squid axon –
Pk+ : PNa+ : PCl- = 1 : 0.04 : 0.45
Ratios differ for different species and different cell
types within a species.
Here, PK+ is 25 x higher than PNa+. In other
neuronal types, in rat, this difference can be as
high as 75 x greater.
The Basis of the Resting Membrane
Potential
[Marieb, E. Human Anatomy and Physiology, 5th ed.]
The Na+-K+ ATPase Coupled Pumps to
Counters the Resting Ionic Fluxes
• At rest, the low level influx of Na+ is balanced
by the low level efflux of K+.
• This leak must be countered over the long term
by the ATP-coupled pumps that maintain the
ionic concentration gradients across the
membrane.
The ATP-coupled Pump is Electrogenic
1) At rest, the passive ion fluxes (due to
concentration gradients and Vm) are countered by
the active ionic fluxes (due to the ATP-coupled
pumps).
2) Consequently, Vm is constant at -60 mV and the K+
and Na+ concentration gradients are also constant
through time.
3) Since the pump moves more Na+ out of the cell
than it moves K+ into the cell, it contributes to the
Vm, i.e. it contributes to the net negativity inside
the cell.
Membrane potentials (Vm) = a voltage difference
between the intracellular and extracellular
fluids.
• Vm is always negative inside relative to
outside.
• Vm ranges from -40 to -200 mV, depending
on the type of cell.
• Range of resting Vms for mammalian neurons
is -40 to -75 mV;
• Any electrical signaling involves deviating
from the resting value.
• This equilibrium point arises when the ratio of the
P(finding an ion on the high-energy side (outside))
P(finding an ion on the low-energy side (inside))
= e-ΔE/kT (i.e., Boltzmann Distribution).
The ΔE for the ion is given by Q x Vm and because
concentrations α probabilities, the result is the Nernst
Equation:
Vm = EK = (kT/ze)* ln{[K]o/[K]i}
Where e is the electronic charge and EK is the
equilibrium Nernst potential for K.
This can also be written as Ek = 58*log{[K]o/[K]i}
More on this later…
• Vm results from the asymmetric distribution of
charges on either side of the plasma membrane
(more negative inside than outside).
• However, most of the intracellular and
extracellular “fluid” are homogenously distributed
(mixed, if you will) on either side of the
membrane, making the bulk of the fluid
electrically neutral.
• Charge separation is achieved in small pockets or
clouds (~ 2 μm) of charges spread over the
surface and attract each other on either side of the
membrane.
• For typical cellular values of [K]o & [K]I, EK+
~ -90 mV, which would be Vm, if the
membrane were permeable to only K+.
• IMPORTANT! Only a very small fraction –
only ~ 1ppm (10-6) have to leave the cell for
Vm to reach EK+ .
Electric Charges can arise within
Membranes in 2 ways:
1. Experimenters insert microelectrodes and
inject them.
2. Ion channels are open in the membrane.
e.g., K+ is the main ion that establishes the
resting membrane potential.
This channel is made up of 4 subunits
embedded within the membrane
How the Resting Membrane Potential
is Measured
Crystal Structure of the K+ Channel from above and
from the side
The K+ channel is structure such that a very narrow
tube through the inverted cone shape allows for only
50 H2O molecules and only 2 K+ in succession.
Because they strongly repel each other, when one enters,
one will be forced out.
Two things determine the Voltage
across the Membrane
1. Selective passage of ions through ion channels.
2. [Ion]s may differ on either side of the membrane.
The membrane potential Vm tends to oppose
(further) diffusion of K+ since a negative Vm
pulls K+ back into the cell.
There is a balance between the disordering effect of
concentration and the ordering effect of Vm.
What is this balance…?
There is also differential distributions of
different species of ions (biological charge
carriers) across the plasma membrane.
E.g., – giant squid axon (Loligo)
Ion [Cytoplasm] [Extracellular Fluid]
(mM)
(mM)
K+
400
20
Na+
50 440
Cl52 560
Organic385
0
Generalizations (although absolute values
differ across species and among cells from
the same organism)
[K+]I (inside) > [K+]o (outside)
[Na+]I < [Na+]o
[Cl-]I < [Cl-]o
[Organic-]I > [Organic-]o
Recall this slide?
Resting Membrane Potential, Vm
[Marieb, E. Human Anatomy and Physiology, 5th ed.]
Thus, the unique permeability characteristics of
the plasma membrane coupled with the
original K+ concentration gradient leads to the
establishment and maintenance of the Vm
without expenditure of energy.
Use of the Nernst Equation to Calculate Theoretical
Vm for a Membrane Permeable Only to K+
E = RT/zF ln [ion]o(outside)/[ion]I(inside)
E = membrane potential (Volts)
R = gas constant (8.3143 joules/deg-mole)
T = absolute temperature (273o + oC); usually 20oC for
giant squid axon
z = valence, including charge and number
F = Faraday’s constant (96,490 coulombs/mole)
Simplifying the Equation
1) RT/zF reduces to 0.025 Volts or 25 mVolts at
20oC and a valence of +1 (K+ and Na+)
2) Thus, E (mVolts) = 25 ln [ion]o/[ion]I
3) Converting to log10 :
E (mV) = 25 x 2.3 log [ion]o/[ion]I
E (mV) = 58 log [ion]o/[ion]I
If the Nernst Equation is a Good
Model of Membrane Potential
Development, What Should
Happen if We Change [K+]o?
Predict Vm when [K+]o = [K+]I
Semi log plot of Vm versus [K+]outside, i.e. changing [K+]o changes
the concentration gradient across the membrane and the Vm that
develops in response to that gradient
0
Normal Vm of
-75 mV
Vm
(mV)
-60
Normal [K+]o
-120
4
20
400
Log [K+]outside
• This is a common experimental technique used
when you want to stimulate (excite) (a)
neuron(s), say, in tissue culture or in brain
slices.
• The addition of KCl to the bath or medium
will result in a depolarization – (Why?).
• However, as we will see when we cover action
potentials, the preceding slide is applicable
only up to T0, given the all-or-none nature of
the AP.
What About Cl-?
1) Cl- permeability is relatively high
2) However, there is no active mechanism to
move Cl- across the membrane of most cells.
3) Consequently, Cl- passively distributes itself
across the membrane in relation to the Vm
established by Na+ and K+.
Flipped because
of negative
valence on Cl-
Vresting = 58 log [Cl-]I/[Cl-]o
Set by Na+ and K+
Cl- passively distributes itself across the membrane such
that the concentration gradient balances the Vm.
Net -
Net +
Concentration gradient
Cl-
ClElectrical gradient = Vm
A Modification of the Nernst Equation is
the Goldman-Hodgkin Equation can be
used to Predict Vm when the Membrane is
Permeable to Multiple Ions
PK  [K  ]o  PNa  [Na ]o  PCl  [Cl ]i
RT
Vm 
 ln
F
PK  [K  ]i  PNa  [Na ]i  PCl  [Cl ]o
Vm theoretical = - 60 mV ~ the empirically
measured value in a resting neuron
What happens to the Vm when leak
channels for Na+ and Cl- are introduced
into the membrane?
Exercise #1 = Draw equilibrium in a resting
neuron. Start with a liver cell in equilibrium
and add Na+ leak channels to the membrane.
(Hint #1: See Time0+1 when Na+ is just starting
to enter the cell - the second image to follow
this slide). (Hint #2 : at equilibrium Vm = -60
mV and [K+]I>[K+]O and [Na+]I<[Na+]O
Explanation
1) Na+ enters the cell and depolarizes the membrane.
The rate of entry is low and is set by the # and
structure of the Na+ leak channels and the Na+
concentration gradient.
2) The Vm no longer balances the K+ concentration
gradient.
3) A small amount of K+ is now able to leave the cell.
4) At equilibrium, the rate of entry of Na+ is equal to
the rate of exit of K+ and the Vm is constant at a
new value of -60 mV; i.e. more + than for “liver
cell” equilibrium. At equilibrium there is no net
movement of charge.
Explanation (cont’d)
5) The Vresting is much closer to EK+ than ENa+
because the permeability of the membrane to
K+ is much greater than the permeability of
the membrane to Na+.
A Simple Neural Network to Demonstrate
Signaling within the Nervous System
Synapse = site of cell to cell communication in the
Presynaptic neuron = carries
nervous system; electrical signal gets converted to a
information as an electrical signal
chemical signal (neurotransmitter) then back into an
(action potential) toward the synapse
electrical signal
Postsynaptic
neuron = carries
information as an
electrical signal
away from the
synapse
Membrane Potentials - to recap:
A. All living cells have membrane potentials
(Vm) = a voltage difference between the
intracellular and extracellular fluids; they are
always negative inside relative to outside
(convention in neurophysiology); Vm ranges
from -40 to -200 mV(olts) depending on the
type of cell; mammalian neurons have a range
of resting Vms from -40 to -75 mV and
electrical signaling involves a change away
from the resting value
1) Recording a Vm – begin with both
electrodes in the extracellular fluid
Recording apparatus =
ohmmeter, amplifier,
oscilloscope or computer
Intracellular electrode = glass
pipette drawn out to a small tip
diameter (~0.5 um); filled with
highly conductive KCl solution
KCl
Liver cell =
non-excitable
cell
AgCl
electrodes
(wires)
KCl
Extracelluar
electrode =
larger glass
pipette also filled
with KCl solution
+75
Vm
1
(mVolts)0
2
-75
Time (sec)
Liver cell =
non-excitable
cell
KCl
KCl
2) Recording a Vm – impale cell with
intracellular electrode
B. Membrane Potentials Result from Differential Distributions of Electrical Charges
Across the Plasma Membrane; but the bulk of the intracellular and extracellular
fluids are electrically neutral; charge separation exists in a small cloud of ~2 um
spread over the intracellular and extracellular surfaces of the plasma membrane
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Remember this slide from earlier? There is a
differential distributions of different species of
ions (biological charge carriers) across the plasma
membrane.
E.g., – giant squid axon (Loligo)
Ion [Cytoplasm] [Extracellular Fluid]
(mM) (mM)
K+
400
20
Na+
50 440
Cl52 560
Organic- 385
0
And this? Generalizations (although absolute
values differ across species and among cells
from the same organism)
[K+]I (inside) > [K+]o (outside)
[Na+]I < [Na+]o
[Cl-]I < [Cl-]o
[Organic-]I > [Organic-]o
Building a Model of Membrane Function that Explains
Empirical Measures of Vm and Ionic Concentration
Differences
Exercise #1 = draw equilibrium for a membrane
freely permeable to all cations, i.e. the laws of
simple diffusion explain the observations. (See
following slide.)
Hint = Vm is 0 mV at time0 and timeeq
Time0
Vm = 0 mV
K+
K+
“chemical force”
magnitude and direction
of net diffusion
Na+
Na+
Hypothetical
membrane
freely
permeable to
all cations
inside
outside
Timeeq
Vm = 0 mV
K+
K+
“chemical force”
magnitude and direction
of net diffusion
Explain:
1) Equal sizes of
ions
Na+
2) Doubleheaded
arrows
Na+
Hypothetical
membrane
freely
permeable to
all cations
3) No Vm
inside
outside
Answers:
1) Diffusion continues until both cations are equally
distributed across the membrane (law of diffusion).
2) The membrane is freely permeable to both cations so
they continue to move across the membrane once
equilibrium is achieved, but there is no NET exchange of
the ions across the membrane.
3) The original cation concentration gradients were the
same approximate magnitude, so when ionic
concentrations equilibrate across the membrane the
same number of positive charges have left the cell as have
moved into the cell. Therefore no charge separation, i.e.
Vm, has been created.
What do we do with this model of
membrane function?
Reject it because it does not agree with
empirical measures of Vm and ionic
concentration gradients
Building a Model of Membrane Function that Explains
Empirical Measures of Vm and Ionic Concentration
Differences
Exercise #2 = draw Time0+3xK+ exit for a
membrane permeable only to K+. (See following
slide.)
Hint = Vm is 0 mV at time0
= Membrane
Time0
Vm = 0 mV
K+
is
impermeable
to ion
K+
“chemical force”
magnitude and direction
of net diffusion
Na+
Na+
Cl-
Cl-
Organic-
Organic-
inside
Hypothetical
membrane
freely
permeable to
only K+
outside
Time0+3xK+ exit
= Membrane
Vm = developing
K+
K+
-
“electrical
force” (and
direction of
movement)
developing
+
-
+
-
+
Na+
“chemical force”
magnitude and direction
of net diffusion
Na+
Cl-
Cl-
Organic-
Organic-
inside
is
impermeable
to ion
Hypothetical
membrane
freely
permeable to
only K+
outside
Answers:
1) Diffusion of K+ out of the cell begins at Time0 and at
Time0+3xK+ exit 3 + charges (in the form of potassium) have
left the cell, leaving net negativity behind inside the cell.
2) The + charges outside the cell repel other + charges (or
the – charges inside the cell attract + charges) causing
some K+ to move back into the cell. This charge separation
is nothing more than a Vm developing across the plasma
membrane.
3) At this point, the “chemical force” is still greater than
the “electrical force” and there is net movement of K+ out
of the cell.
Building a Model of Membrane Function that Explains
Empirical Measures of Vm and Ionic Concentration
Differences
Exercise #2 = draw Timeeq for a
membrane permeable only to K+.
Hint = at Timeeq there is no NET exchange of K+
across the membrane and
[K+]I > [K+]o
Timeeq
= Membrane
Vm = -75 mV
K+
K+
---
“electrical
force” =
- “chemical
force”
“chemical force”
magnitude and direction
of net diffusion
+++
---
+++
---
+++
Na+
Na+
Cl-
Cl-
Organic-
Organic-
inside
is
impermeable
to ion
Hypothetical
membrane
freely
permeable to
only K+
outside
Answers:
1) So much K+ has left the cell in response to its
concentration gradient that an “electrical force” that is
equal in magnitude but opposite in direction to the
“chemical force” has developed across the plasma
membrane.
2) For every K+ that leaves the cell in response to the
concentration gradient another K+ enters the cell in
response to the “electrical force” and there is no NET
exchange of K+ across the cell.
3) The “electrical force” is nothing more than the Vm that
develops across the membrane to balance the
concentration gradient.
What do we do with this model of
membrane function?
Accept it because it agrees with empirical
measures of Vm and ionic concentration
gradients.
Thus, the unique permeability characteristics of
the plasma membrane coupled with the
original K+ concentration gradient leads to the
establishment and maintenance of the Vm
without expenditure of energy.