Bioelectric potentials, Ion pumps
Purves et al., Chapter 2 , also pp. 69-73, Figures from Chapter 4
I was first exposed to some of this material as a senior in 1969. Tom Ebrey
had a background in physics. He was young, and since he is still living,
but retired, I was happy to lunch with him in July, 2007 where he lives
(Seattle) since we go there now and then to see my son and his family. see:
R Crouch et al, A tribute to Thomas Ebrey, Photochem Photobiol, vol 82,
Excitable membrane has resting and action potentials
Ions are dissolved in water and are pumped using ATP -> ADP for energy
These ion gradients establish "batteries" as ions can flow through
Other than channels and pumps, membranes do not pass ions well
For resting potential, Potassium (K+) channels dominate
For action potential, Sodium (Na+) channels open (activate) then close (inactivate)
Toward the end, a different type of K+ channels open (activate) then close
(passively, they do not inactivate)
Action potentials are all-or-none big depolarizations
Synaptic (graded) and sensory (generator) potentials are smaller.
They can be of variable size and can be depolarizing or hyperpolarizing.
I use a Narishige PD-5 (Tokyo) horizontal puller
with controls for an early magnet, a heater, and a late (stronger magnet).
The heater glows red
while the first magnet pulls gently.
A microswitch with
a shim detects the melt and the early pull to kick in the harder pull.
After the second pull, two electrodes
Over the history of micropipettes, many tricks have been developed to get
the very narrow tip to fill. Currently, a capillary tube with an inner
filament has magic filling properties.
First you back fill the
butt end a little with a spinal tap needle.
The electrolyte (I use saturated NaCl for ERGs) is carried to the tip.
Then, you can finish back filling the elecrode with the syringe.
If equipment is dumping current into ground in various locations, then there
is a circuit with voltage differences despite the infinitesimal resistance
through ground. The result is ground loop noise. Thus it is wise to hook
all grounds to one central ground
tree. I hook this to water pipe ground with a big braided wire and bypass
all the equipment grounds, connecting to the tree instead.
In the set-up, a dissecting
microscope can be swung into position. The probe from the amplifier is in
the Faraday cage (painted flat black) near the fly. A micromanipulator allows
the electrode to be advanced toward the eye. The cage should not be cluttered
by electrically noisy stuff, but a microscope illuminator is necessary.
A hydraulic microdrive
(Kopf) [stepping motor driving water syringe on left and controller on rignt]
driving a slave syringe
helps to get the electrode into the eye.
An electrometer serves
as the differential preamplifier
In the old days, this could feed into a polygraph, a penwriter
that graphs voltage as a function of time, limited for speed by the momentum
of the pen
Also somewhat outdated is the oscilloscope
A permanent record can be made with a camera,
and the most famous is the Grass camera
Nowadays, the computer
is used for an oscilloscope. Here is a PowerBase 180 from Power Computing
(Mac work-alike) feeding into an Optiquest monitor using the PowerLab 410
from AD Instruments as the interface
Fig. 2.2 A p. 27
Insertion of stimulating and recording microelectrodes
Fig. 2.2 B p. 27
Voltage as a function of time ("graph") - resting and action potentials
Depending on direction of stimulation, passive potentials are depolarizing
Threshold to trigger action potential is shown
Square wave (stimulus) leads to exponential curve (recording) because of
Fig 2.1C p. 26
shows action potential again (unconfounded with other information) from
axon of spinal motor neuron
Fig 2.1 A&B p. 26
shows sensory stimulation (Pacinian corpuscle, touch receptor) and synaptic
potential in dendrite to show these are smaller (graded) potentials
1791 Luigi Galvani (Italy) (of Glvanometer fame) - nerve muscle electricity
1850 Herman von Helmholtz - speed of conduction (40 m/s)
Fig. 2.4 p. 29
Walther Hermann Nernst (Germany) (1864-1941) 1920 Nobel
Nernst equation says that ion gradient is equal and opposite to voltage
1902 (paper) Julius Bernstein apply Nernst equation, he thought that K+
permeability was lost during the action potential, while, in fact, the Na+permeability
increases (he should have noticed this in his data)
Fig. Box 2B p. 36 squid giant axons
1939 K. C. Cole and H. J. Curtis (US) introduced use of squid and showed
that membrane resistance decreases during passage of action potential
Invertebrates do not have myelin to speed the velocity of propagation of
the action potential.
Theoretically, this velocity increases with the radius, and so invertebrates
use giant axons when fast action potentials are needed.
Squid uses quick mantle contraction and jet propulsion through siphon in
(from R. D. Keynes, The nerve impulse and the squid, Scientific American,
Fig. 2.7 A&B p. 35
1950's Sir Alan L. Hodgkin & Sir Andrew F. Huxley (Great Britain)
Prize in Physiology and Medicine for "ionic mechanisms...excitation
inhibition...nerve cell membrane"
In general, They showed what was stated above:
For action potential, Na+ channels open then close, K+ channels open (then
Fig. Chapter 4 Box A p. 59
Erwin Neher & Bert Sackmann (Germany) for patch clamp
Prize in 1991 "incredibly small electric currents that pass through
an ion channel "
This electrode technique records from single channels which are distinct
Fig. 4.4A p. 64
Membranes (shows ion channel in membrane)
Fluid mosaic, two layers of lipids such as polar phospholipids with proteins
some points not emphasized in text but recalled from cell biology:
-imbalance of lipids, inositol lipids on inside, signalling
-glycolipids on outside (like gangliosides)
proteins span membrane - based on hydrophobic alpha helix
Voltage gated Na+ channel for action potential
Here is a pdf
Circuits (equivalent circuits)
Battery, anode:+, anions:-, Cathode:-, cations:+
Current = i (Amps), defined as + to - (Benjamin Franklin)
Potential (potential difference): V or E (Volts)
(1) Battery (source of electromotive force, EMF)
(2) Current flow through a resistor
battery and resistor in circuit
E = IR (Ohm's law), R in units of Ohms, W
G is conductance, 1/R, "mho" = Siemens (S)
I = gV
Fig. 2.2 B (again) p. 27
note delay in depolarizing or hyperpolarizing membrane
Membrane capacitance (not emphasized in book)
see pdf again
Thus, this is a low (frequency) pass (high cut-off) filter
Typically, capacitance adds delays
There are also high pass filters
Sodium - potassium "pump"
Fig. 2.4 (again) p. 29
shows elementary properties of pump
Fig. 4.9A p. 72
Uses 1/3 (2/3 if high electrical activity) of cell
Fig. 4.10B p. 73
"Electrogenic" - imbalance of 3 Na+ - 2 K+ cause current to flow,
contribute a few mV
Calculation to show only a few mV
Here's a pdf
of the calculations
Fig. 4.11AB p. 74
10 membrane spans
homologies with Ca++ pump in sarcoplasmic reticulum
homologies with bacterial K+-ATPase
Ouabain binds to pump and blocks it
From the plant digitalis purpurea (purple finger) [foxglove], we get digitalis,
another cardiac glycoside.
They look like a steroid bound to a few sugar groups with glycoside bonds.
In myocardial cells (heart muscle cells), blocking the Na+ pump slows a
Ca2+/Na+ exchanger, increasing intracellular Ca2+ for stronger heart contractility
in some sisorders.
Fig. 4.10A p. 73
classic experiment by Hodgkin and Keynes (1955)
Fire off a zillion action potentials in radioactivce sodium to preload
note that K+ (out) is needed for it to work
DNP (dinitrophenol) blocks ATP synthesis - pump slows
Derivation of Nernst potential
Assume two compartments in communication
(ions like K+ or Na+ dissolved in each)
Free energy (of each system) = RT ln Ci + ziF(Potential)
RT ln Ci is chemical energy
ziF(Potential) is electrical energy
F is absolute potential, C is concentration, i is given ion, e.g. K+ or
Na+, z is valence, ln is natural (to be base e) logarythm
T is tempreature in degrees Kelvin
R = 8.31 Joules/moleoK
F = 9.65 x 104 Coulombs/mole
[ = 6.02 x 1023 ions/mole x 1.6 x 10-19 Coulombs/ion ]
Assume equilibrium which means
(1) no flux
(2) electrical and chemical gradients equal and opposite
(3) energies of two compartments the same
Simple algebra and the fact that log10 = 2.3 x ln gives:
EK+ = 58 log [K+]out / [K+]in
Table 2:1 p. 35
ion gradients for mammalian neuron:
K+ in 140, K+ out 5
Na+ in 5-15, Na+ out 145
Fig. 2.5 C p. 32
shows dependence on external K+
Fig. 2.8 AB p. 37
also shows this
David Goldman, 1943
assume constant field
Vm = 58 log PK[K+]out + PNa[Na+]out + PCl[Cl-]in
PK[K+]in + PNa[Na+]in + PCl[Cl-]out
Cole and Curtis use AC bridge to show resistance of membrane decreases as
action potential goes by
Such a membrane model seems to suggest a confusing circuitry, simplified
by several simple concepts.
Kirchoff's first law: at any junction, sum of currents is zero.
Kirchoff's second law: sum of changes in potential around loop is zero.
There is a pdf
to illustrate a problem and its solution using Kirchoff's laws.
The solution involves 3 equations with 3 unknowns (high school algebra)
[or determinants, slightly more advanced high school algebra].
Exam questions from 2005 - 2012 that apply to this outline
An action potential is (1) all-or-none, (2) non-decremental, and (3) in
the direction of making the inside of the cell more positive. Pick one of
those three attributes and say how a synaptic potential differs if it differs.
potentials can add to each other, they get smaller with distance, they may
also be hyperpolarizing
"Cole and Curtis's bridge went out of balance." What did we learn
from their 1939 work on the squid giant axon with the Wheatstone bridge?
conductance goes up as the action potential passes
"A square wave of current injection led to a hyperpolarization that
was low pass filtered." That different shape was because of what property
of the membrane?
In the Goldman equation, concentrations (in and out) of sodium, potassium
and chloride, and permeabilities for all three ions, are shown. There is
an equivalent circuit (with electrical components) for the Goldman equation.
What is used in the circuit model for the sodium permeability? Be thorough
enough in your answer to address what happens to sodium permeability during
the action potential.
a variable resistor (potentiometer) that lets sodium permeability go up
Current flows through (what?) in the patch clamp technique that earned Neher
and Sackman the 1991 Nobel Prize.
Ouabain is applied to the cell. Answer either (1) Why does the membrane
potential change by a few mV? or (2) Why doesn't the membrane potential
go away right away?
3 sodiums to 2 potassiums make the pump electrogenic, otherwise potentials
are based on huge reservoirs of ion gradients that would run down very slowly
if the pump were blocked
In Hodgkin and Keyne's1955 experiment, what happened to the efflux of radioactive
sodium mediated by the "sodium pump" when extracellular potassium,
already low, was really lowered?
it decreased sharply because sodium transport relies on exchange with potassium
"Inside a Ca2+-sequestering cistern inside a cell is sort of like outside
the cell." For these two compartments (inside, say, sarcoplasmic reticulum
and extracellular fluid), how does the Ca2+ concentration relate to the
cytoplasmic calcium ion concentration?
calcium outside the cell is higher than in cytoplasm
In an experimental validation of the theory, it was shown that the slope
equals 58 mV per 10-fold change in K+ gradient. After the researchers had
an electrode measuring the resting potential, what did they do?
change the extracellular potassium ion concentration
Variable resistors are in an equivalent circuit model of the Goldman equation.
Which resistor is changed, and in what direction, at the start of the action
the sodium resistance is decreased
When an invertebrate needs a fast action potential, it has a giant axon
because it lacks (what specialization that vertebrates posess to speed the
A micropipette is touched to the membrane but not inserted into the cell.
Answer either (1) What is this technique called? Or (2) What would it allow
you to do?
(1) patch clamp (2) record current from individual channels
When a square wave of current is injected into the cell, the Voltage change
is gradual because of (what property of the membrane?).
Cole and Curtis showed that a bridge went out of balance in the squid giant
axon as the action potential went on by. What fundamental conclusion did
they draw from this?
resistance went down (conductance up)
"Theoretically, sodium should not flow in when the sodium channels
open." Answer either (1) Whose theory? Or (2) Why not?
(1) Nernst (2) chemical and electrical gradients equal and opposite
"If I could wave a magic wand and instantly abolish the sodium potassium
pump while I had an electrode in the cell," Answer either (1) Why would
the membrane potential NOT change a lot (immediately)? Or (2) Why WOULD
the membrane potential change immediately by just a few mV?
(1) gradients were established and would not run down quickly (2) the electrogenic
sodium pump is based on the imbalance (3 sodium ions in to 3 potassium ions
Hodgkin and Keynes found that removing extracellular K+ decreased the Na+
efflux from the "sodium pump." Why would this be the case?
even though extracellular potassiun is low, the Na+-K+ATP needs to pump
K+ to pump Na+
Paving the way for the Nobel Prize winning Hodgkin and Huxley work, what
could you conclude from the Cole and Curtis finding that the AC bridge went
out of balance as the
action potential goes by?
The time constant (=RC) describes the properties of what kind of filter
placed before the input of a differential amplifier?
low (or high) pass (or cut-off)
Faraday's constant is the charge of a mole of ions, 9.65 x 104 coulombs/mole
= Avagadro's number x the elementary charge (charge of a single ion). What
would be the units of
the elementary charge?
coulombs per ion
An appropriately low dose of the cardiac glycoside digitalis would improve
myocardial contractility by blocking what?
sodium pump directly, sodium calcium exchange indirectly
The equilibrium assumption in the derivation of the Nernst equation means
that what two gradients are equal and opposite?
electrical and chemical
Why is the "sodium pump" electrogenic?
because of the imbalance (2K+/3Na+)
If I were on the ordinate (Y axis) and V were on tha abscissa (X axis),
what electrical term is used to describe the slope of the line?
How do you use the patch clamp method to determine the properties of a channel
gated by intracellular ligands like cAMP or cGMP?
get the channel, break off that hunk of membrane, then you can dip the inside
of the channel
In the numerator of the Goldman equation, we find intracellular potassium
and sodium but extracellular chloride. Why the difference?
Cl is -, others are +
On an oscilloscope (polygraph or computer), an action potential is a graph
of what as a function of what?
In the circuit diagram model for the Goldman equation, potentiometers are
used instead of resistors. Why?
resistance is variable
Why does a glass micropipette have high resistance?
it is so small, a narrow path of electrolyte
In contrast with "all-or-none" give the general term for those
smaller potentials of variable size that can be either depolarizing or hyperpolarizing.
(One is for sensory receptor potentials the other for synaptic potentials.)
Describe the technique developed by the Nobel Prize winners Neher and Sackmann
that allowed the measurement of currents through single channels.
patch clamp puts the tip of an electrode up against a channel
The action potential is all-or-none in part because you cannot trigger one
spike on top of another. In other words, there is a refractory period. What
property of the sodium channel is responsible?
What molecule has an ouabain binding site?
the Na+-K+-ATPase (sodium pump)
I said, "capacitance adds delays." Draw the graphs for a square
wave of current injection and the corresponding hyperpolarization to show
the low pass filtering of membrane capacitance.
look on p 61
What imbalance makes ATPase electrogenic?
3 Na+/ 2 K+
Faraday's constant, the charge of a mole of ions in Coulombs per mole, is
used to solve for which specific component of energy in the derivation of
the Nernst equation?
Why didn't the efflux of radioactive Na+ go to zero immediately when Hodgkin
and Keynes blocked ATP synthesis with DNP (dinitrophenol)?
the pump keeps working until the ATP runs out
What factors are applied to the concentrations of Na+ and K+ to allow the
Goldman equation to account for both resting and action potentials?
relative permeabilities (conductances)
After being open, sodium channels have something, and the word "close"
does not fully convey the meaning of (what is the correct word)?
"Other than channels and pumps, membranes do not pass ions well."
The center of the membrane is hydrophobic
In contrast with the term "all-or-none," what does the term "graded"
signify in describing membrane potentials?
They can be of varying size
n a 1902 paper, Bernstein, applying the principles learned from Nernst,
proposed that K+ permeability was lost during the action potential. In what
way was this wrong? In what way was it insightful?
Wrong, K+ permeability was not lost, right - relative K+ permeability less
because that of Na+ is more
After assuming that the energies of two compartments are equal, algebra
boils the Nernst equation down to saying that the membrane voltage is equal
and opposite to what?
I told a story about how capacitors hold a charge (that can shock a person
when they discharge). How did that story relate to the passive voltage response
of the membrane at the end of stimulation of the membrane by a square wave
After stimulation ends abruptly, membrane voltage returns to baseline gradually
Right when ATP converts to ADP to power the sodium pump, what becomes of
the inorganic phosphate?
Before it is free, it is bound to pump molecule
Pick either word, "cardiac" or "glycoside" and tell
me why the expression applies to digitalis.
In heart muscle cells, blocks Na+ pump slows Ca2+/Na+ exchanger, increasing
intracellular Ca2+ for stronger contractility, glycoside bonds.
In Hodgkin and Keynes' classic experiment on the sodium pump, how did they
obtain numbers for the Y-axis (ordinate) that relate to sodium efflux?
measured radioactivity aftyer loading axon with radioactive sodium
Why is there a direct (electrogenic), though small, contribution of the
Na+-K+-ATPase to the membrane potential?
because 3 Na+'s are pumped per 2 K+'s
"Slope = 58 mV per tenfold change in K+ gradient." Answer either
of the following: How did they do this experiment? OR Why would it be expected
to be this way?
Change extracellular potassium, cause voltage = -58 times the log (to the
base 10) of the ion gradient
What does the Goldman equation tell us beyond the Nernst equation?
takes into account pooled voltage based on sodium, potassium and chloride
(ion gradients and relative permeabilities)
When the AC (fast) Wheatstome bridge of Cole and Curtis swung out of balance,
what did that tell us about the membrane events at that moment?
resistance changed (decreased) during action potential
"The cause of the resting potential is potassium ions flowing through
the potassium channel." Why is this not the whole truth?
in the equilibrium assumption, no ions need to flow for voltage
Why would an inside out patch be useful in studying channels gated by ligands
generated by the intracellular signal transduction cascade?
can "dip" it into solutions with such ligands (like cAMP and cGMP
Address 1, 2, or 3. Ouabain is a (1) cardiac (2) glycoside that binds (3)
a very important molecule.
can strengthen a weak heart beat, that describes the chemical bond, the
Hodgkin and Keynes were studying the properties of (what?) when they measured
the efflux of radioactive sodium from the squid giant axon.
the sodium pump
Why might a glass micropipette distort the shape of an action potential
without the proper amplifier?
has high resistance and capacitance, hence makes a low pass filther that
clips a fast signal
Membranes (and glass micropipettes) have resistance. But they also have
(what else?) that causes the voltage change to be delayed.
Permeability of a particular ion, say sodium, across the membrane is inversely
related to the resistance across the membrane for that ion and directly
related to (what electrical property?).
Explain why the electrical potential calculated with the Nernst equation
is called the equilibrium potential.
The assumption is tantamount to equilibrium (electrical and chemical potentials
equal and opposite
Answer one of these about Cole and Curtis's AC Wheatstone bridge (1) What
is meant by "voltage divider?" or (2) What did they conclude on
the basis of their bridge going out of balance?
Two resistors in a row where the voltage acroee each is IR, resistance decreases
(during the action potential
Describe or draw how Nobel prize winners Neher and Sackmann measured current
through individual channels.
The patch clamp electrode nudges against the membrane where there is one
Why did the efflux of radioactive sodium from the squid giant axon eventually
decrease when DNP inactivated the mitochondria in Hodgkin and Keynes classic
experiment in the 1950s?
without ATP, the sodium pump stops
You are recording the membrane potential (resting potential). What happens
to this potential if you replace the extracellular fluid with potassium
chloride at the same concentration as the intracellular concentration?
It goes to zero (from, say, -70)
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This page was last updated on October 15, 2012