Biology for Engineers:
Cellular and Systems Neurophysiology
Christopher Fiorillo
BiS 521, Fall 2009
042 350 4326, fiorillo@kaist.ac.kr
Part 3: Dynamic Regulation of Membrane Voltage
Reading: Bear, Connors, and Paradiso
Chapter 4
The Action Potential
• Graded changes in current cause graded changes in voltage.
• If voltage is depolarized beyond a threshold (about -50 mV), an action
potential is triggered.
An Action Potential is “All-or-None”
•
At a brief moment in time (~1 ms), an action potential either occurs or it does not
•
The shape of an action potential is always the same (almost)
•
The magnitude of the current and depolarization that triggered the action
potential do not matter (but the depolarization must reach threshold)
Firing Rate Depends on Current Magnitude
• The frequency of action potentials (“firing rate”) depends on
the magnitude of depolarizing current (assuming that the
current lasts long enough).
Why Do Neurons Have
Action Potentials?
• Current that enters the cell at one point will spread passively through
the cytosol of a dendrite.
• Because of membrane permeability, current leaks out of the neuron as
it travels along a dendrite.
• Thus information cannot be conveyed over long distances through
passive spread of current.
• An action potential is “regenerative” and therefore it can reliably carry
information over long distances.
• Trade-off: Digital (action potential) versus Analog (membrane voltage)
• Most neurons have action potentials.
• Many neurons that do not need to transmit information over long
distances do not have action potentials.
Phases of the Action Potential
•
•
•
•
Rising phase
Overshoot
Falling phase
Undershoot
Properties of the Action Potential
•
Threshold
–
–
•
Rising phase
–
•
K+ conductance greater than before start of action
potential
Absolute refractory period
–
•
Inactivation of Na+ conductance
Activation of K+ conductance
Undershoot (After-Hyperpolarization)
–
•
Positive membrane voltage (no functional significance)
Falling phase
–
–
•
Increase in Na+ conductance
Overshoot
–
•
Caused by positive feedback among Na+ channels
Requires high density of Na+ channels
Na+ channel inactivation makes it impossible to elicit
another action potential
Relative refractory period
–
High K+ conductance means that a large depolarizing
current is necessary to elicit another action potential
The Hodgkin-Huxley Model
•
•
•
Hodgkin and Huxley described the ionic basis of the action
potential (1952)
This is considered the most important single achievement in
cellular neurophysiology.
Their approach: Experiments on the squid giant axon
–
–
–
•
•
•
•
•
•
•
Two electrode voltage clamp (1 mm diameter axon)
Measured the voltage-dependence and kinetics of sodium and
potassium currents
Ion substitution experiments
They derived a relatively simple but detailed mathematical
and biophysical model of the action potential
Their model is still the “textbook” model
The utility of their model extends beyond the action
potential. It is useful for understanding all voltage-dependent
ion channels
Their model predicted some of the key properties of ion
channels
It was about 30 years later (~1980) that scientists were able
to identify and record single ion channels
It was about 10 years after that (~1990) that people began to
clone ion channels (to discover their amino acid sequence)
It was about 10 years after that (~2000) that the 3dimensional structure and function of ion channels began to
be understood (Rod Mackinnon)
The Patch Clamp Method
• Developed by Erwin Neher
• Very useful for electrophysiology
• Enables the recording of single channels
Recordings of Single Na+ Channels
• Channels exist in discrete states: Open or closed
• The channels “behavior” will not be the same, even
under identical conditions. It is “stochastic.”
• Inactivation occurs after the channel opens
Relationship between single channel and
cellular currents
• Macroscopic currents in the cell result from the
summation of many microscopic single channel
currents
• Although single channel currents are stochastic,
currents within the cell are not. They are highly
reproducible.
• Single sodium channels do not have a threshold
voltage at which they open
• The action potential threshold depends on
positive feedback between many sodium
channels
• Action potentials require a high density of
sodium channels
– A sufficient number of channels must be
deinactivated (ready to be opened)
Structure of Ion Channels
• The Voltage-Gated Sodium Channel
– Four subunits
•
•
•
•
Each has 6 transmembrane alpha-helices
Voltage sensor (positive charges) on S4
Selectivity filter
K+ channel
Gate
Na+ channel
The Voltage-gated Sodium Channel
• Structure – gating and pore selectivity
– Positive charges move with changes in voltage
• Conformational change in protein
• Gating current can be measured
• Ion selectivity is possible because of the difference
in size between sodium and potassium
An Ion Channel Has Many States (Conformations)
• States of a glutamate-gated ion
channel (4 subunits) are shown
• Open states require that
glutamate is bound
• There are many desensitized
(inactivated) states
• Gray states are seldom visited
• This is typical of many ion
channels, including voltagegated ion channels
• This is probably more simplistic
than reality
Three Key Properties of Voltagegated Ion Channels
• Ion selectivity
• Voltage-dependence
• Time-dependence (Kinetics)
Voltage-Dependence of Ion
Channels in HH model
• ‘n-infinity’ is the steady-state
probability that a K+ channel subunit
“gate” is in the “open” conformation
• The channel is only open when all four
subunit gates are in open conformation
– Thus, the steady-state probability that a
channel is open:
• Po = ninfinity4
• The Na+ channel has three activation
gates (m) and one inactivation gate (h)
– Thus, the steady-state probability that a
channel is open:
• Po = minfinity3h
Summary of Voltage-Dependence of Parameters in HH model
Diversity of K+ Channel Kinetics
ventricular
myocytes
200 ms
Kv4.3
2000 ms
Kinetics of Ion Channels Underlying the Action Potential
• Sodium channels activate and inactivate quickly
• Potassium channels activate slowly
The Spread of Current Through Neurons
• Passive spread of current
DVx = DV0e-x/l
l = square root (rm/ra)
• Lambda is the “length constant”
• At a distance lambda, the change
in voltage will be 1/e of the
original change in voltage
• Actual length constants are 0.1 1.0 mm
Action Potential Conduction
• Propagation of the
action potential
– It is an active,
regenerative process,
but it still relies upon
the passive spread of
current
– Orthodromic: Action
potential travels from
soma to terminal
– Antidromic
(experimental):
Backward propagation
(towards soma)
Conduction Velocity
• Conduction velocity (0.5-80 m/s)
• Two means of increasing velocity
– Diameter of axon (or dendrite)
• Increases speed by decreasing axial
resistance
• Squid Giant Axon: 1 mm
– Insulation
• Myelination by glia
• Increases membrane resistance and decreases
membrane capacitance
• Some information needs to be
transmitted quickly, some does not
• Large axons and myelination are each
costly
• Some axons are small and unmyelinated
Myelination
• Some axons are insulated by
glial cells
• Node of Ranvier
– Gap in myelin sheath
– High density of Na+ channels
• Current decays as it passes
from one node to another
• Multiple sclerosis is caused by
degeneration of myelin
Initiation and propagation of action potentials
• Requires a high density of sodium channels
• High density is found in:
– Axon
– Nerve endings of primary somatosensory neurons
– Dendrites have lower density, but some dendrites can have
action potentials
• Dendritic action potentials are not always all-or-none
• Forward and backward propagation
Beyond the Action Potential
• We have focused on action potentials, but the HH model
can be extended (by changing parameter values) to
include many other types of voltage-gated ion channels
• Voltage-gated ion channels do not only mediate the
action potential. They also influence the pattern of
action potentials.
• Different neurons express different sets of voltageregulated ion channels
– Therefore, different neurons have different firing patterns in
response to the same excitatory input
Measuring the Current-Voltage Relationship
• The Current-Voltage relationship of a cloned Na+ channel
– At very negative potentials, the channels are closed
– At very positive potentials, the current is small, or positive, because of
inactivation and the sodium reversal potential
– It would be useful to measure the I-V curve when the sodium channels are
open
• A “tail current” protocol can be used for this purpose
Measuring the Current-Voltage Relationship
•
A “Tail Current” protocol activates channels
and then measures the I-V function at a brief
moment in time
– A voltage protocol is delivered that is
designed to strongly activate the channels
– The voltage is then stepped to different
potentials, and the instantaneous “tail”
current is measured at each potential
– An I-V curve is constructed
– Another I-V curve can be constructed
without the first “activating” voltage protocol
– The second I-V curve is then subtracted from
the first. The resulting curve shows the I-V
relationship of the isolated current.
– In this example (from glial cells), the
reversal potential of the current matches the
theoretical K+ reversal potential
•
The I-V function is linear because it follows
Ohm’s Law.
– no time is allowed for the channels to open
or close at the “new” voltage
Voltage-regulated ion channels
• Na+ channels
– depolarization activated
• Ca2+ channels
– depolarization activated
– L-type, T-type, N-type, P-type, Q-type, R-type
• Cl- channels
– depolarization activated
– not common
• Cation channel (non-selective; Na+ and K+)
– Hyperpolarizaton activated
– “H” current
• K+ channels
–
–
–
–
Depolarization activated
Most diverse
A-type, M-type, delayed rectifier, inward rectifier, etc.
Multiple types of calcium-activated K+ channels (BK, SK, etc)
K+ channel diversity
•
This shows only genetic diversity (~100 genes)
•
There is great diversity created by non-genetic mechanisms, such as alternative splicing
of mRNA, post-translational modifications, varying subunit composition, and
phosphorylation
•
There are probably hundreds, or even thousands, of functionally distinct K+ channels
•
A typical neuron might express about 10 types, or more
Diversity of K+ Channel Kinetics
ventricular
myocytes
200 ms
Kv4.3
2000 ms
The AfterHyperpolarization
in Hippocampal
Pyramidal
Neurons
• Three components to the AHP, mediated by 4 K+ channel types
– Fast
• BK-type K+ channels, activated synergistically by calcium and voltage
– Medium
• M-type K+ channel, voltage-activated
• Calcium-activated K+ channel
– Slow
• Calcium-activated K+ channel
H-current (HCN channels)
• HCN channels are hyperpolarization activated, nonselective cation channels that underlie the “H-current”
Representation of Space and Time
•
Inputs to a neuron:
–
–
Non-synaptic, voltage-regulated ion channels carry information from the past
•
The conductance of these channels depends on the history of a neuron’s voltage
•
Different types of channels represent different periods of the past, depending on their kinetics
Synaptic inputs represent points in space
•
•
Different synapses represent different points in space
A neuron’s output depends on integration of the conductance of all of its ion channels