Neurons

Fox Chapter 6 and 7. Note that web material is especially important for this lecture

Figure
TRANSPARENCY (from intro book)

Figure 7.1a
typical neuron
Connections, from other neurons, created graded electrical potentials at synapses, on dendrites and cell bodies.
Cell body integrates the synaptic excitatory and inhibitory voltages.
If there is net excitation, axon propagates the all-or-none, non -decemental action potential quickly over long distances.

Overview

Excitable membrane has resting and action potentials
Ions are dissolved in water and are pumped using ATP -> ADP for energy, Na+-K+-ATPase.
This "sodium pump" uses 1/3 (2/3 if high electrical activity) of cell
These ion gradients establish "batteries" as ions can flow through channels.
Other than channels and pumps, membranes do not pass ions well (covered before).
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.

History

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

Walther Hermann Nernst (Germany) (1864-1941) 1920 Nobel in Chemistry.
Nernst equation says that ion gradient is equal and opposite to voltage difference.
(often misunderstood)
1902 (paper) Julius Bernstein apply Nernst, K+ permeability lost in action potential.
(insightful but short of the full story)

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

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)

Electrical concepts

Fig. 6.26
Sodium is high outside.
Potassium is high intracellularly.

Figure
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

delay in depolarizing or hyperpolarizing membrane
Membrane capacitance
Thus, this is a low (frequency) pass (high cut-off) filter
Typically, capacitance adds delays
There are also high pass filters

Derivation of Nernst potential

Fig. 6.26 (again)
Because of the potassium gradient there is a resting potential of about -65-70 mV

Figure
pdf
Assume two compartments in communication
(ions like K+ or Na+ dissolved in each)
Free energy (of each system) = RT ln Ci + ziFF
chemical electrical
F is absolute potential, C is concentration, i is given ion, e.g. K+ or Na+
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

K+ in 140, K+ out 5
Na+ in 5-15, Na+ out 145

Fig. 6.27
Because of the potassium gradient there is a resting potential of about -65-70 mV
(like before but with voltmeter drawn in

Goldman equation

Figure
pdf

There is an equation that looks like the Nernst equation except that is has sodium (Na+), potassium (K+) and chloride (Cl-) and their relative permeabilities. Permeabilities change as a function of time.

David Goldman, 1943
assume constant field, this derivation is "beyond the scope of this course" (way too dificult)

Vm = 58 log PK[K+]out + PNa[Na+]out + PCl[Cl-]in
PK[K+]in + PNa[Na+]in + PCl[Cl-]out

(see pdf for equation drawn more neatly)

Note that in and out are reversed for Cl- since it is an anion while Na+ and K+ are cations.

There is a membrane model with 3 batteries (note that the sodium and potassium batteries are reversed because the gradients of these two cations are opposite).

The relative permeabilities are modelled by variable resistors (potentiometers) [where variable conductances, the inverse of resistances, are more analogous to variable permeabilities]

Wheatstone bridge

Figure
see bottom of this pdf
How to determine an unknown resistor
Use two knowns as voltage divider
use a variable and the unknown as another voltage divider
Use a galvanometer as a null detector between the two nodes

Cole and Curtis used an AC bridge to show that resistance decreased during the action potential

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].

Reference

R. D. Keynes, The nerve impulse and the squid, Scientific American, December, 1958

Exam questions from 2004 - 2011 relating to this outline

Graded potentials can be added to each other. What is the expression used to describe an action potential that relates to the statement that "you cannot add one action potential onto the top of another?"

all-or-none

Why is it more useful to use conductance rather than resistance in discussing membranes or membrane channels?

electrical conductance more intuitively relates to ion permeability

Reminder: The Goldman equation looks like the Nernst equation except that it includes concentrations (in and out) plus permeabilities for all three ions - Na+, K+ and Cl-. Only one of these 9 values changes at the beginning of the action potential. Which?

permeability for Na+

What would a hyperpolarizing graded potential do to the probability that a spike would be fired at the axon hillock?

decrease probability

"Potential is equal and opposite to chemical gradient." Answer either (1) What was assumed? or (2) Who won the Nobel Prize in Chemistry for doing this derivation?

1 energies of two compartments are equal 2 Nernst

Voltage is shown to change as an exponential function of time because of what particular component in an equivalent circuit model?

capacitance

"Invertebrate axons propagate faster with increasing size with diminishing returns." Answer either (1) What specifically relates to radius (Don't just repeat velocity of propagation)? or (2) Why diminishing returns?

1 space (length) constant 2 it increases with the square root of the radius

"The AC Wheatstone bridge Cole and Curtis used went out of balance indicating that the 'unknown' resistor changed." Answer either (1) What was this resistor? or (2) When did it go out of balance?

1 the axon membrane's resistance 2 when there was an action potential

E=IR. Answer one of these. (1) What are the units for E? (2) What are the units for I? (3) What are the units for R? (4) What is this relationship called?
 
(1) Volts (2) Amps (3) Ohms (4) Ohm's law
 
9. After the equilibrium assumption in the derivation of the Nernst equation, the chemical gradient is shown to be equal and opposite to (what)?
 
Voltage (electrical gradient)

In a simple circuit with a battery connected to the resistor, what is the slope of the line if amperes are plotted on the ordinate (Y-axis) and volts are plotted on the abscissa (X-axis)?

conductance (Siemens)

An exponential change in membrane voltage as a function of time is caused by what electrical property of the membrane?

capacitance

Voltage arises from either a battery (a source of electromotive force) or (what)?

current flowing through an impedance (such as a resistor)

What is assumed about the total energy (chemical AND electrical) on one side of the membrane vs. on the other side of the membrane to allow Nernst equation to be derived?

the two energies are assumed to be the same

Suppose, with a given set of permeabilities and the standard concentrations, the Goldman equation approximated the resting potential. What would you need to change to calculate the peak of the action potential from the Goldman equation?

increase sodium permeability

Write an equation obeying Ohm's law relating voltage and current but using conductance rather than resistance.

if E=IR (Ohm's law), then E=(1/g)I, so I=GE

What is assumed in the derivation of the Nernst equation?

energy of two compartments is the same which is tantamount to saying that electrical and chemical gradients are equal but opposite

What two components are used in the circuits of high- and low-pass filters to give them the property of having a time constant?

R & C

Permeability to what ion increases at the beginning of the action potential?

sodium

Write an equation expressing conductance as a function of resistance.

G=1/R

Faraday's constant (9.65 x 104 Coulombs/mole) is important in expressing electrical component of energy of a thermodynamic system. What do you need to multiply the charge of an individual ion (1.6 x 10-19 Coulombs/ion) by to get Faraday's constant?

Avagadro's number (the number of ions per mole)

What is the name and polarity of the electrode to which cations would migrate in solution?

cathode is negative

After the nerve cell integrates the excitatory and inhibitory post-synaptic potentials, which part of the cell propagates the action potential (if threshold is reached)?

axon

If I graphed Ohm's law with Voltage on the Y axis and current on the X axis, I would get a line. What is the slope?

R

Invertebrates do not have myelin. What adaptation allows for fast action potentials in invertebrates?

giant axons

What type of impedance makes it so that Voltage would change as a function of time?

capicitance

What is the expression commonly used to describe an action potential and to differentiate it from a graded synaptic potential?

all-or-none

What is the term for the inverse of resistance, an electrical term analogous to relative permeability?

conductance, g

There are two components of energy in a thermodynamic system. Which component is RT times the log of the concentration?

chemical energy

Both resistance and capacitance are membrane impedances. In what way is capacitance distinguished from resistance?

Voltage across capacitor changes as a function of time

The squid does not have myelin. How does the squid have fast action potentials?

Giant axons

Around 1900, Bernstein explained the action potential by a loss of the selective K+ permeability during the action potential. Although insightful, this was two bricks shy of a load. What, in fact, changes and in what direction.

Na+ permeability goes up (depending on how you read "what direction," inward flow)

Voltage can arise from a battery and (what else)?

current flowing through a resistor

How does the capacitance of the axon compare with that of the axon membrane plus the myelin?

many membrane layers, each with capacitance, add reciprocally, hence the answer is "lower with myelin"

People do not have giant axons while squids do. How do we achieve, in our axons, what squids do with that adaptation (giant axons)?

myelin

What happened to axon resistance when Cole and Curtis used the AC Wheatstone bridge as the action potential was passing?

went down

When batteries and resistances for sodium and potassium are drawn to model the Goldman equation, what special properties do the resistors have to account for the resting and action potentials?

must be variable (potentiometers)

How do Schwann cells vs oligodendrocytes differ with respect to investing axons with myelin?

Schwann, one axon, oligo a few

During propagation of the action potential, what depolarized the axon to threshold at any given location?

the action potential at one place triggers

A deliberate slight of hand had me graphing Ohm's law with the X and Y axes reversed. Thus, we talked about "conductance" which relates to what way of describing how well ions traverse a membrane channel?

permeability

Why might a middle-aged person who had recovered partially from "infantile paralysis" (polio) experience a relapse?

Post polio syndrome has sprouts of motor neurons going away (motor unit goes back to before recovery of function)

In terms of understanding resting, graded and action potentials, what does the Goldman equation (and its equivalent circuit) convey that the Nernst equation does not?

it takes into account several ions and their relative permeabilities

Applying the equilibrium assumption in deriving the Nernst equqtion (both thermodynamic systems have the same energy) we show that the electrical potential difference (across the membrane) is equal and opposite to (what?)?

chemical gradient

A current is injected into a membrane to change the membrane's voltage. How does the membrane capacitance change the membrane voltage?

it causes delay (as the membrane capacitance charges)

A deliberate slight of hand had me graphing Ohm's law with the X and Y axes reversed. In this "I-V curve" what is the slope of this line?

conductance (g)

Why do squids have giant axons? Your answer can be behavioral, it can pertain to the properties of giant axons, or it can be comparative (comparing squid with "higher" nervous systems).

so they can contract their mantle for the escape response synchronously, giant axons conduct faster, invertebrates do not have myelin

Why is salutatory conduction so much faster than conduction without myelin?

all that insulation forces the action potential to jump way ahead to the next node of Ranvier

Why is the prefix "oligo" applicable to olidodendrocytes?

they myelinate several axons in the CNS

"Capacitors in series add reciprocally." What does this say about the capacitance of myelin?

less current would leak out of the axon through the membrane capacitance where there is myelin

Why do squids have giant axons? Your answer can be behavioral, it can pertain to the properties of giant axons, or it can be comparative (comparing squid with "higher" nervous systems).

so they can contract their mantle for the escape response synchronously, giant axons conduct faster, invertebrates do not have myelin

Why is salutatory conduction so much faster than conduction without myelin?

all that insulation forces the action potential to jump way ahead to the next node of Ranvier

Why is the prefix "oligo" applicable to olidodendrocytes?

they myelinate several axons in the CNS

"Capacitors in series add reciprocally." What does this say about the capacitance of myelin?

less current would leak out of the axon through the membrane capacitance where there is myelin

By passive spread, a spike at one place depolarizes the axon ahead of it (and behind it) to threshold. Why is conduction unidirectional?

because the sodium channels behind it are inactivated, causing the absolute refractory period

Why might a middle-aged person who had recovered partially from "infantile paralysis" (polio) experience a relapse?

Post polio syndrome has sprouts of motor neurons going away (motor unit goes back to before recovery of function)

An oscilloscope presents the action potential like a graph. What are on the X and Y axes?

X time, Y voltage

Why was Golgi's technique, so exquisitely used by Ramon y Cajal, a contribution worthy of the Nobel Prize?

Among a zillion cells, one cell could be seen in its entirety

The Voltage across the membrane is ­p;RT/F times a number. R is in units of Joules/(mole x degreeKelvin) and F is in units of Coulombs/mole. Of course, we could use the term "Volts" for membrane Voltage. Alternatively use the information provided above to state what other units could be used for membrane Voltage.
 
Joules per Coulomb
 
From the 1930s to the 1950s, why did Cole and Curtis, also Hodgkin and Huxley, choose the squid instead of the frog to characterize action potential conductances?
 
The axon is big
 
I stimulate an axon with a >square wave< (an immediate step upward of voltage). Does the axon act as a high-pass filter or a low-pass filter? Justify.
 
Slow upsweep implies low pass (high cutoff)
 
"The sum of potentials, batteries and current flowing through resistors, around a loop of a circuit is zero. Also the sum of currents flowing into the junction in a circuit is zero." Whose laws are these?
 
Kirchoff's
 
In an equivalent circuit of the Goldman equation, there are batteries and resistors. What particular feature do these (in the Goldman model) resistors have?
 
They are variable resistors (potentiometers)
 
What was concluded about the properties of the axon during an action potential on the basis of Cole and Curtiss AC Wheatstone bridge experiment?
 
Resistance goes down
 
"Exponential" is the term describing Voltage as a function of time for charging or discharging a capacitor in an RC circuit. Draw this graph (for charging or discharging or both) where V is the battery's Voltage.

charging - goes up quickly then slowly, leveling off to V; discharging - goes down quickly from V then leveling


Return to Syllabus

Return to Stark home page

This page was last updated on June 8, 2015