Transcript Cellular Neuroscience (207) Ian Parker

Cellular Neuroscience (207)
Ian Parker
Lecture # 4 - The HodgkinHuxley Axon
http://parkerlab.bio.uci.edu
The Action Potential
An electrical depolarization that propagates rapidly (up to 10s of m per sec) along
nerve axons
record
stimulate
+ 50 mV
overshoot
0 mV
Rising phase
depolarization
Falling phase
repolarization
- 70 mV
hyperpolarization
Afterpotential (undershoot)
Stimulus artifact
Conduction delay
Basic mechanisms of the action potential
The action potential is a brief time when the
membrane potential is ‘flipped’ – positive
rather than negative inside. This arises
because the cell membrane becomes
transiently permeable to Na+ ions, which
rush into the cell down their concentration
gradient, depolarizing it toward ENa.
RISING PHASE
1. Depolarization (e.g. excitatory
synaptic input) opens voltagedependent Na channels.
2. Na+ ions enter cell causing…
FALLING PHASE
1.
Na channels inactivate, so depolarizing,
inward Na+ current stops.
2.
Voltage-gated K channels open
3.
Efflux of K+ ions down their electrochemical
gradient repolarizes the cell toward Ek
4.
Repolarization causes K channels to shut, but
slow gating may cause ‘undershoot’ below
normal resting potential.
3. Depolarization
Some properties of the action potential
•
1. Action potentials are all-or-none events. Once a stimulus exceeds threshold (ca. -45 mV) an
action potential is triggered. Size of the action potential (peak ~ + 50 mV) is fixed, and does not
depend on stimulus strength.
•
2. Action potentials propagate without decrement at a finite speed. Speed is fast by biological
standards (several m per sec vs. um per sec for ‘chemical;’ signals), but much (million-fold)
slower than an electrical signal along a wire.
•
3. Refractory period. After one action potential there is a short time (ms) when an axon cannot be
stimulated to give another action potential. Primarily due to the time for Na channels to recover
from inactivation. This is important because it;
a. Stops action potentials from traveling ‘backwards’
b. Sets a limit to the maximum frequency of action potentials an axon can transmit.
•
•
Hodgkin - Huxley analysis of the action potential
(early 1950s)
Voltage-clamp
Technique that allows the voltage across an axon membrane to be held at any
desired level, while measuring the resulting current flow across the membrane.
Used with giant (1 mm diameter) squid axon, that allows easy insertion of
intracellular electrodes.
Feedback circuit – compares the actual membrane potential with the desired command voltage. Any
difference (error) is amplified and inverted, and fed back into the axon as a current to bring the
potential to the desired level (like cruise control on a car). Current flowing from the circuit thus gives a
direct measure of current flowing acros the axon membrane.
Currents flowing across a squid axon in response to voltage
steps
Depolarization to voltages more positive than
about -25 mV evokes a complex series of
currents. A transient current –usually inward-,
followed by a slower developing , maintained
outward current. The initial transient current at
first becomes larger (more inward current) with
increasing depolarization, then reduces to zero
at ~ +60 mV, and inverts to become outward at
yet more positive voltages. The slower current
is always outward, and becomes increasingly
large at more positive potentials.
Depolarization to -35 mV evokes
only passive responses
Hyperpolarization evokes only
passive, leakage currents
Resting potential
depolarize or
hyperpolarize
How to make sense of this – pharmacologically dissect the
transient and maintained currents into their ionic
components
Total currents evoked by a
range of depolarizing stimuli
Blocking Na channels with tetrodotoxin
abolishes the initial transient current,
leaving only the slower, maintained
outward K current.
Blocking K channels with TEA abolishes the slow
outward current, leaving just the fast, inward Na
currrent
Current/voltage relationships for the initial and maintained current
components
Current amplitudes measured at their peaks
The delayed, outward current
increases progressively at
increasingly positive voltages
Both currents begin to activate
at about -35 mV.
The initial transient current
increases with voltages up to about
+20 mV, then declines to zero at
about +50 - +60 mV, and becomes
outward at voltages > +60 mV
Currents through Na and K channels reflect both the Ohmic dependence of
current flow through single channels, and the voltage-dependence of channel
open probability
We can separate these two effects by calculating whole-cell conductance as a function of voltage
e.g. for transient Na current
IM
ENa = +50 mV
0 mV
VM
Ichannel
Current across the axon
membrane is the product of
the single-channel Na current
and the number of Na
channels open at a given
voltage. We can estimate the
latter by calculating Na
conductance;
Sigmoid relationship reflecting
voltage-dependent activation
of Na channels
g Na
gNa = IM/VM-ENa
VM
VM
-50 mV
0
+50 mV
The conductance/voltage relationship for K
channels looks very similar, except that the initial
‘turn-on’ is a little less steep
Equivalent circuit diagram for an axon membrane
The Na and K channels can be thought of as variable resistors, whose values depend on
voltage, and which determine the importance of their respective ‘batteries’ (Na and K
equilibrium potentials) in setting the final voltage across the cell membrane.
Changing the membrane potential involves charging the membrane capacitance, so the
voltage changes during an action potential depend on the time course (kinetics) of the Na
and K conductance changes as well as their peak values.
So, what are the kinetics of gNa and gK?
0 mV
VM
-60 mV
gNa
gK
During depolarization, gNa shows both time-dependent activation and inactivation.
gK shows only activation. During the falling phase of an action potential, gK declines
because the membrane potential repolarizes, NOT because K channels inactivate
The kinetics of Na channel activation and inactivation, and the kinetics of K
channel activation all become faster at more positive potentials
- 20 mV
+20 mV
gNa
gK
Time course of K channel activation and closing
VM
Sigmoid rise
Exponential decay
gK
H-H expained the openinng of a K channel as being controlled by movement of
several independent ‘particles’ (voltage sensors). The channel is open only if all
are in the ‘ON’ position.
Suppose 4 particles, each with probability n of being in the ON position.
Probability of channel opening is then given by n4
Further suppose that probability n changes exponentially with time following a voltage step
VM
gK (varies as n)
n
gK (varies as
n4)
More about gating particles
The K channel molecule has 4 charged ‘particles’ that move according to the voltage
across the membrane. [In the 1950s these particles were merely postulates – we
now know they correspond to the S4 regions of the channel molecule]
Out
+ + + + + + + + + +
- - - - - - - - - - - - +
OFF
position
In
+
+
+
+
- - - - - - - - - - - - -
+
+
+
+ + + + + + + + + +
n varies with voltage and with time. H-H characterized it by two
parameters;
ninfinity probability of being in the ON state after holding at a given voltage for a
very long time
tn the rate at which n changes following a step to a new voltage.
From their experimental data H-H could derive empirical values for these
parameters.
ON
position
What about Na channels?
H-H described Na channel activation in the same
way as for K channels, by movement of gating
particles.
For the Na channel, these are referred to as m (not
n), and movement of only 3 (not 4) was required
to give the best fit to the data.
Also, another gating particle (h – only one per
channel) was introduced to account for the
inactivation of the Na channel
The Hodgkin Huxley Equation
Ionic currents across the axon membrane can be described in terms of three components;
IM = m3hgNa(E-ENa) + n4gK(E-EK) +gL(E-EL)
Na current
K current
‘leak’ current
[Don’t worry; you wont be asked to remember this in an exam! ]
All of the electrical excitability of the membrane is embodied in the timeand voltage-dependence of n, m and h.
The model accurately predicts observed action potentials in many
species, and is one of the few cases where we can reduce biology to an
equation. But, like any other model it cannot prove the existence of
underlying mechanisms.