Bioelectric potentials, Ion pumps

Purves et al., Chapter 2 , also pp. 69-73, Figures from Chapter 4

Personal Reflection

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, 2006.

Overview

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 channels
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.

Electrophysiology

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 are made.

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 or hyperpolarizing
Threshold to trigger action potential is shown
Square wave (stimulus) leads to exponential curve (recording) because of capacitance

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

History

1791 Luigi Galvani (Italy) (of Glvanometer fame) - nerve muscle electricity in frog
1850 Herman von Helmholtz - speed of conduction (40 m/s)

Fig. 2.4 p. 29
Walther Hermann Nernst (Germany) (1864-1941) 1920 Nobel in Chemistry
Nernst equation says that ion gradient is equal and opposite to voltage difference
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 escape response.

TRANSPARENCY
(from R. D. Keynes, The nerve impulse and the squid, Scientific American, December, 1958).

Fig. 2.7 A&B p. 35
1950's Sir Alan L. Hodgkin & Sir Andrew F. Huxley (Great Britain)
1963 Nobel 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 close)

Fig. Chapter 4 Box A p. 59
Erwin Neher & Bert Sackmann (Germany) for patch clamp
Nobel Prize in 1991 "incredibly small electric currents that pass through an ion channel "
This electrode technique records from single channels which are distinct molecular entities.

Membranes

Fig. 4.4A p. 64
Membranes (shows ion channel in membrane)
Fluid mosaic, two layers of lipids such as polar phospholipids with proteins embedded
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

Electrical concepts

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
RC circuits
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
Na+-K+-ATPase
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
(molecular structure)
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
Measure efflux
note that K+ (out) is needed for it to work
DNP (dinitrophenol) blocks ATP synthesis - pump slows

Derivation of Nernst potential

See pdf

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

See pdf

Goldman equation
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

Kirchoff's laws

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?

capacitance

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.

individual channels

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 transport

"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 potential?

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 action potential?).

myelin

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?).

capacitance

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 out)

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?

conductance increased

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?

conductance (g)

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?

voltage, time

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.)

generator-sensory, graded-synaptic

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?

inactivation

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?

electrical component

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)?

inactivate

"Other than channels and pumps, membranes do not pass ions well." Why not?

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?

chemical gradient

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 of current?

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 sodium pump

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.
 
capacitance
 
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?).
 
conductance
 
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 channel
 
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