(Chapter 9-8 of KS)
The action potential and cellular excitability
1.- The cellular action potential
2.- Voltage clamp, current clamp
3.- Ion channels and the AP. HH theory.
4.- AP propagation and cable properties of nerve and muscle
Readings: 1.- HODGKIN AL, HUXLEY AF. A quantitative description of
membrane current and its application to conduction
and excitation in nerve. J Physiol. 1952 Aug;117(4):500-44.
2.- Fenwick EM, Marty A, Neher E. A patch-clamp study of bovine
chromaffin cells and of their sensitivity to acetylcholine.
J Physiol. 1982 Oct;331:577-97.
3.- Jiang Y, Ruta V, Chen J, Lee A, MacKinnon R. The principle of
gating charge movement in a voltage-dependent K+ channel.
Nature. 2003 May 1;423(6935):42-8.
Keywords:
Action potential
All-or-none response
Threshold, peak, refractory period
Overshoot
Voltage clamp, current clamp
TTX, TEA, Saxitoxin
Activation, inactivation, gating currents
Ensemble average
HH model
Space constant, conduction velocity
Propagated action potential
Problems:
1.- Describe concisely the driving forces of ion flux in excitable cells.
What factors determine the direction of ion flux?
2.- Describe the ionic events that underlie the action potential.
3.- Suppose that you have a chromaffin cell under voltage and space clamp
conditions. Draw the instantaneous I-V relationship for the K+ conductance.
Draw the I-V relationship that you predict results from changing the
ionic conditions so that now [K]o= 145 mM and [K]i=5 mM?
The three principal cell types to study excitability
were the squid giant axon, the node of Ranvier
and isolated muscle fibers.
Basic properties of action potentials.
A, The upper panels show four
graded hyperpolarizing stimuli and
the Vm responses. The lower
panels show four graded
depolarizing stimuli and the Vm
responses. Note that the two largest
stimuli evoke identical action
potentials. B, A stimulating electrode
injects current at the extreme left of
the cell. Four recording electrodes
monitor Vm at equidistant sites to
the right. If the stimulus is
hyperpolarizing, the graded Vm
responses decay with distance from
the stimulus site. If the stimulus is
depolarizing and large enough to
evoke an action potential, a full
action potential appears at each of
the recording sites. However, the
action potential arrives at the most
distant sites with increasing delay.
Nerve and muscle excitability. The curve in A represents the combination of the
minimum stimulus intensity and duration that is required to reach threshold and evoke
an action potential.
Changes in ionic conductance that underlies the action potential. (Data from Hodgkin
AL, Huxley AF: A quantitative description of membrane current and its application to
conduction and excitation in nerve. J Physiol (Lond) 117:500-544, 1952.) I strongly
suggest that you read this paper! It’s a classic and led to their Nobel prize in physiology
and medicine.
Basic properties of action potentials. A, The upper panels show four graded hyperpolarizing stimuli and the Vm responses. The
lower panels show four graded depolarizing stimuli and the Vm responses. Note that the two largest stimuli evoke identical action
potentials. B, A stimulating electrode injects current at the extreme left of the cell. Four recording electrodes monitor Vm at
equidistant sites to the right. If the stimulus is hyperpolarizing, the graded Vm responses decay with distance from the stimulus
site. If the stimulus is depolarizing and large enough to evoke an action potential, a full action potential appears at each of the
recording sites. However, the action potential arrives at the most distant sites with increasing delay.
Voltage-clamp and space-clamp of a single nerve fiber
Dissection of Na+ and K+ currents by voltage-clamp analysis and pharmacology. A, In a typical voltage-clamp experiment, a
sudden hyperpolarization from 80 to 140 mV results in a transient capacitative current, but no ionic currents. B, In a voltageclamp experiment, a sudden depolarization from 80 to 20 mV results in a transient capacitative current followed first by an inward
ionic current and then by an outward ionic current. C, Blockade of the outward current by tetraethylammonium leaves only the
inward current, which is carried by Na+. Conversely, a blockade of the inward current by tetrodotoxin or saxitoxin leaves only the
outward current, which is carried by K+.
Voltage dependence of ionic currents.
Proteins also have a bonded structure that helps them resist
the constant bombardment caused by Brownian motion.
Small protein ubiquitin
A cartoon representation
The Bonded structure is dynamic, as it gets bombarded,
the structure bends and bonds break and reform
How often does Brownian motion overcomes the energy
barrier and causes an ion channel to open ?
E
kT
t  t0  e
E
kT
t0 ~ 10-12 seconds
How long do we have to wait for Brownian motion
to overcome an energy barrier ?
pico seconds
seconds
Brownian death
E=0
kT
3
Biology
3 kT
35 kT
1067years
Too strong
300 kT
Control in Biology is accomplished by
reducing energy barriers. Then, unlikely events
will occur over short time periods
DE
Local current loops during action-potential propagation. A, The currents flow at one instant in time as a result of the action potential
("active" zone). In the "inactive" zones that are adjacent to the active zone, the outward currents lead to a depolarization. If the
membrane is not in an absolute refractory period and if the depolarization is large enough to reach threshold, the immediately
adjacent inactive zones will become active and fire their own action potential. In the more distant inactive zones, the outward current
is not intense enough to cause Vm to reach threshold. Thus, the magnitudes of the outward currents decrease smoothly with
increasing distance from the active zone. B, In this example, the "active" zone consists of a single node of Ranvier. In a myelinated
axon, the currents flow only through the nodes, where there is no myelin and the density of Na+ channels is very high. Current does
not flow through the internodal membrane because of the high resistance of myelin. As a result, the current flowing down the axon is
conserved, and the current density at the nodes is very high. This high current density results in the generation of an action potential
at the node. Thus, the active zones jump in a "saltatory" manner from one node to another. The internodal membrane (i.e.,
underneath the myelin) may not ever fire an action potential.
Passive cable properties of an axon. A, The axon is represented as a hollow, cylindric "cable" that is filled with an electrolyte
solution. All of the electrical properties of the axon are represented by discrete elements that are expressed in terms of the
length of the axon. ri is the resistance of the internal medium. Similarly, ro is the resistance of the external medium. rm and cm
are the membrane resistance and capacitance per discrete element of axon length. B, When current is injected into the axon, the
current flows away from the injection site in both directions. The current density smoothly decays with increasing distance from
the site of injection. C, Because the current density decreases with distance from the site of current injection in B, the
electrotonic potential (V) also decays exponentially with distance in both directions. Vo is the maximum change in Vm that is at
the site of current injection.
The space constant l is given by
l for a 1 mm squid axon is
11 mm.
l for a 1 mm mammalian nerve
is 0.2 mm.
Conduction velocity for a giant axon q = 20m/s
q~a