10/8/2013
ION CHANNELS AND ELECTRICAL ACTIVITY
Colin Nichols
Department of Cell Biology and Physiology
Center for Investigation of Membrane Excitability Diseases
Box 8228
9611 BJC-IH
362-6630
[email protected]
http://www.nicholslab.wustl.edu/nichols.htm
http:www.cimed.wustl.edu
Many of the figures in the following notes come from Hille, B. ‘Ion Channels of Excitable
Membranes’, Sinauer Associates, Sunderland, Mass. This is highly recommended to anyone
interested in following up the lectures, and is essential reading to anyone interested in pursuing
research on ion channel structure and function. Further background material can be found in:
Lodish et al., Molecular Cell Biology, 4th ed, chapter 15 (p. 633-665) and chapter 21 (p.
925-965) and Alberts et al., Molecular Biology of the Cell, 4th ed, chapter 11 (p. 615-650)
and p. 779-780.
Overview
These notes provide additional background to the lectures. The first section is an extended
discussion of ion channel structure and function, followed by the classical description of the
action potential and the role of ion channels in it.
1
1. Electrical principles
A. Electrical properties of membranes
In order to understand the electrical properties of cells we need to review the following principles
of electricity:
1) Current,
2) Voltage,
3) Resistance/Conductance,
4) Capacitance
All matter is made up of charged particles - protons and electrons. Charge is symbolized Q and is
measured in Coulombs. The elementary charge of one electron or proton is e = 1.602 X 10-19
Coulombs. Faraday's constant (F) is the number of Coulombs per mole of particles that bear a
single + or - charge. F = 9.648 * 104 Coulombs / mole. Charged particles move. They attract and
repel each other.
1) Current (I) measures the rate of movement of the charge:
I = Q / t = Coulombs / sec = Amps (A)
2) Voltage (V) is a measure of the difference in potential energy experienced by a charged particle
in two locations. It is the work required to move a charge from point A to point B:
V = Joules / Coulomb = Volts (V)
3) Resistance/Conductance Ohm's Law states that Current through a piece of homogeneous
material is proportional to the Voltage applied across the material. Conductance (G) is the
proportionality factor between current and voltage. The unit for Conductance is the Siemen (S).
Resistance (R) is the inverse of conductance. It is measured in Ohms (). G
=
1
/
R
Conductance = 1 / Resistance
Ohm's Law
I = G  V or
1 Amp = 1 Siemen * 1 Volt
V=IR
1 Volt = 1 Amp * 1 Ohm
Resistance and Conductance depend on the size and shape of the object that you are passing
current through.
Resistivity (units = cm) is an intrinsic property of a homogeneous material that reflects its
ability to carry current. For a right circular cylinder: R = Resistivity  (Length / Area of a Cross
Section)
Sample Calculation - Consider a cylindrical pore 10 Angstroms in diameter and 50 Angstroms
long that spans a lipid bilayer. The pore contains saline with resistivity of 60 cm (the resistivity
of the bilayer is about 1015 cm). What is the resistance of this pore to axial current?
2
(Remember: 1 Angstrom = 10-10 m = 10-8 cm = 0.1 nm)
60   cm  50  10 -8 cm
R = 3.1416  (5  10 -8 cm) 2 = 4 X 109  or 4 Giga
For Resistors "In Series"
RTot = R1 + R2 + R3 . . . . + Rn
For Resistors "In Parallel"
1 / RTot = (1 / R1) + (1 / R2) + (1 / R3) . . . . . + (1 / Rn)
Separation of + and - charges produces a potential difference or Voltage.
4) Capacitance (C) is a measure of how much charge must be separated to give a particular
voltage.
C (Farads) = Q (Coulombs) / V (Volts) or Q = C  V And
I = Q / t = C  V /
Since Q = C * V, for a 1 cm2 region of membrane to be charged to 60 mV would require:
1.0 µF * 0.060 V = 6 X 10-8 Coulombs
or 375 X 109 ions or 0.622 pico moles.
t
The capacitance of a physical object depends on its geometry.
For a parallel plate capacitor: C =   o  Area / distance between the plates
where  is the dielectric constant of the material between the plates and o is the permittivity of
free space (8.85 X 10-12 Coulomb / Volt  Meter). Capacitance increases with increasing surface
area and decreases as the separation between the plates becomes greater. The cell membrane with
saline on both sides is very similar to a parallel plate capacitor. The lipid bilayer of most cells has
a specific capacitance of 1.0 µFarad / cm2. By separating charge on either side of the membrane
you develop a potential difference across the membrane. Only a small number of charges must be
separated to result in a significant voltage.
A simple model cell: Consider a spherical cell with several conducting pores. The cell contains
saline and is bathed in saline. The equivalent circuit is a capacitor and a resistor in parallel. If we
inject a square pulse of current into the cell with a microelectrode, some of it will charge the
membrane capacitance and some will pass through the resistance of the conducting pores.
ITot = IR + IC
(RC))
where
IR = Vm / R
and
IC = C  Vm / t

Vm / t = (ITot / C) - (Vm /
The solution of this differential equation is:
Vm = ITot  R  (1 - exp(-t
/ ))
where  = R  C is the membrane time constant, the membrane potential of the cell will change
along an exponential time course that is governed by . At equilibrium, when t >>  Vm = ITot 
R , where R = 1 /  Gpores is called the Input Resistance of the cell.
3
Sample Calculation - Consider a spherical cell,
100 µm in diameter, that has 200 open channels, each
with a conductance of 10 pS.
Surface Area of a Sphere of Radius r is
4    r2
A=
R = 0.5 GOhms
= 4  3.1416  (50 X 10-4cm)2
= 3.1 X 10-4 cm2
and C = 3.1 X 10-4 µF
GTot = 200  10 pS
so Rin = 1 / GTot = 5 X 108  and
 = Rin  C
= 155 msec
Area
-4
C = 3.1 X 10 µF
t = 155 msec
Vm
(mV)
I = 5 pA
time (msec)
Modeling changes in Vm in a cell membrane
Physical diagrams and electrical equivalence circuits showing how current injection from an
electrode (left) or current entry through channels selective for sodium (right) can change the
membrane potential.
4
The figures below, taken from Jack, Noble and Tsien Electric Current Flow in Excitable Cells
(1983), illustrate the change in potential across a resistor and capacitor in parallel. The dashed
and dotted lines in the figure on the right show the fraction of total current that is flowing through
the resistor (IR) and charging the capacitor (IC), respectively. We said above that IR = Vm / Rm so
the time course of IR will be identical to the change in membrane potential. I C = ITot - IR shows
that initially all of the current goes to charging the capacitor. As charge builds up on the
capacitor, the rate of addition of more charges decreases exponentially. Notice that at the end of
the current pulse IC has the opposite sign.
B. The Resting Potential
An undisturbed cell at rest contains a slight excess of anions that produces a steady membrane
potential, called the resting potential. The resting potential is usually in the range from -30 mV to
-90 mV or so.
Why do cells have ion channels and a resting potential?
Cells live in an environment of dilute
salt water. They contain within their cytoplasm a variety of impermeant solutes, including
proteins and nucleic acids, but also smaller metabolites like amino acids, Kreb's cycle
intermediates and so on. The sum total charge of these impermeant solutes is negative. Ion
channels allow the cell to cope with the osmotic difficulties that result from confining these large
charged ions inside the plasma membrane. The resting potential is an unavoidable consequence of
the cell's strategy for handling changes in osmolarity. A cell needs to accommodate two physical
facts 1) The osmolarity of the cell's contents and the solution it is bathed in must be the same,
otherwise water will flow into or out of the cell causing it to swell or contract. Cells will
tolerate a bit of swelling, but not much. Since the environment may change at any
moment, the cell needs to be able to adjust its internal osmolarity quickly.
2) There must be bulk neutrality of the two solutions - separation of tiny amounts of charge
produce a substantial voltage across the membrane. An imbalance in the millimolar range
is not physically sustainable.
Let's examine several possible strategies the cell could use:
1) The cell could simply make its membrane impermeable to everything - this will not work
because then slight changes in the external or internal osmolarity would exert great
pressure on the membrane
5
2) The cell could be equally permeable to all ions - that won't work either because it would
lead to osmotic imbalance. Ions will enter, causing the cell to expand and eventually
burst.
If impermeable and freely permeable will not work then the membrane has to be selectively
permeable to a subset of ions. In order to allow for rapid adjustment of osmolarity, while
preserving bulk neutrality, the membrane should be permeable to a cation and an anion. Most cell
membranes are selectively permeable to potassium and chloride, but nearly impermeable to
sodium ions, at rest.
Consider the distribution of ions that might be typical for a frog neuron:
(Concentration in mM)
Out
In
Na+
117
30
K+
3
90
Cl
120
4
Anions
0
116
In addition to osmotic balance and bulk neutrality there is an additional thermodynamic
restriction: All permeable ions will move toward electrochemical equilibrium. At equilibrium,
there will be no net flux of ions across the membrane and no change in membrane potential. As
the name electrochemical equilibrium implies, there are two components we need to consider:
a chemical component and an electrical component. A charged ion in solution wants to flow
down its concentration gradient but it also wants to flow down any electrical gradient that may be
present. In our case the electrical gradient would be across the membrane in the form of a
membrane potential. For K+ ions the concentration gradient indicates that they want to flow from
inside to outside. However, the outward movement of K+ ions will produce an excess of negative
charges inside and an excess of positive charges outside - an electrical gradient will develop that
will tend to counteract the chemical gradient.
Once the two gradients are equal and opposite, there will be no more net movement of K+
ions. At that point the charge separation across the membrane capacitance will be stable and will
result in a resting membrane potential. The Nernst Equation gives the membrane potential at
which a given ion will be in electrochemical equilibrium. At electrochemical equilibrium the total
energy for a K+ ion inside will equal the total energy outside. There is an electrical term (z *F*V)
and a chemical energy term (RT*ln [K+]). Where z is the charge valence (+1 for Na and K, +2 for
Ca and Mg, -1 for Cl); R is the gas constant (8.315 joules /  kelvin mole); and T is the
temperature in  kelvin.
z.F.Vin + R.T.ln[K+]in = z.F.Vout + R.T.ln[K+]out

z  F  (Vin - Vout) = RT  (ln [K+]out - ln[K+]in)

Vin - Vout = EK = (RT/zF) ln ([K+]out / [K+]in)

EK = (RT/F) ln ([K+]out / [K+]in) = 2.303  (RT/F) log10 ([K+]out / [K+]in)
EK = 60 mV log ([K+]out / [K+]in)
The Nernst Equation @30°C
Given the concentrations shown above.
6
EK = 60 mV  log (3/90) = -1.477 * 60 = -89 mV.
ECl = (60 mV / -1) log ([Cl-]out / [Cl-]in) = -89 mV
Both Cl- and K+ are in electrochemical
equilibrium when Vm = -89 mV. Any
ion species that is freely permeable and
passively distributed (not pumped) must
be in equilibrium at steady state - if it
were not initially in equilibrium, the ions
would pass into or out of the cell until
electrochemical
equilibrium
was
achieved. Earlier, we calculated that
only a minute amount of charge must
cross the membrane to produce a
significant potential. There will be no
or
Intracellular and extracellular ion concentrations must measurable change in the internal
+
satisfy osmotic balance and bulk neutrality. If the cell external concentrations of K or Cl .
is permeable to ions, there will be a membrane But, the potential across the membrane
is great enough to prevent any further
potential.
net efflux of K+ or influx of Cl-, down
their respective concentration gradients.
In this simple system, K+ and Cl- are equally permeable and are the only permeable ions.
However, this does not mean that both ions are equally important in determining the resting
potential. Consider the effect of doubling external [K+] from its initial value of 3 mM to 6 mM.
Then we will consider what happens if we instead reduce external [Cl-] from 120 mM to 60 mM.
Since both K+ and Cl- must be at electrochemical equilibrium
EK = ECl
or
log ([K+]out / [K+]in) = - log ([Cl-]out / [Cl-]in)
or
K 
K 


out
in

Cl 
Cl 


in
out
or
[K+]out * [Cl-]out = [K+]in * [Cl-]in
This relationship is sometimes referred to as the Donnan Equilibrium. First raise [K+]out to 6
mM, and lower [Na+]out by 3 mM to compensate. K+ will want to enter the cell, making the
inside more positive and causing Cl- to enter as well. How much KCl will come in? - enough to
achieve a new equilibrium state. How can we calculate it?
6 * 120 = (90 + X) * (4 + X) or 720 = 360 + 94 * X + X2
this is a quadratic equation - the solution is for
a * X2 + b * X + c = 0 ,
X = (-b + (b2 - 4 * a * c)1/2) / (2 * a)
in our case
X = (-94 + (942 + 4 * 360)1/2) / 2 so X = 3.685
that means initially [K+]in = 93.685 and [Cl-]in = 7.685 and
[K+]in * [Cl-]in = 720, just as outside.
7
However, now the total ion concentration inside is 30 + 93.685 + 7.685 + 116 = 247.37
compared to 240 outside. Water will enter to bring the osmolarity into balance. The cell will
swell to 247.37/240 = 1.031 times its original volume and the contents will be diluted by a factor
of 240/247.37 = 0.970. So the final concentrations are:
Na+ = 29.10
K+ = 90.87
An- = 112.52
Cl- = 7.45
[total] = 239.94
Or are these the final concentrations? Let's check for equilibrium 90.87 * 7.45 = 677 which is
not 720 so we need to repeat the cycle
720 = 677 + 94 * X + X2 which gives X = 0.435 (the correction is getting smaller!) so [K+]in =
91.305 and [Cl-]in = 7.885 initially. The volume increased by 240.81/240 = 1.003 fold, so dilute
by 0.997 to give
Na+ = 29.01
An- = 112.18
[total] = 240
+
K = 91.03
Cl = 7.86
91.03 * 7.86 = 715.5 which is much closer to 720
What is the new membrane potential?
EK = 60 * log (6/91) = -71 mV
ECl = -60 * log (120/7.9) = -71 mV
Doubling [K+]out caused a significant depolarization. What if we cut [Cl-]out in half by replacing
it with some impermeant anion. K+ and Cl- will flow out until
3 * 60 = (90 + X) * (4 + X) or X2 + 94 * X + 180 = 0
X = -1.96 so [K+]in = 88.04 and [Cl-]in = 2.04
and 236.08/240 = 0.984 is the relative volume after shrinkage
which means a concentration by 1.016 fold to give
Na+ = 30.5
An- = 117.9
[total] = 240
+
K = 89.5
Cl- = 2.1
89.5 * 2.1 = 188 which is not far from 3 * 60 = 180
EK = 60 * log (3/89.5) = -88 mV
ECl = -60 * log (60/2.1) = -87 mV
This dramatic change in [Cl-]out has had almost no effect at all on the resting potential. We have
shown by our calculations that the resting membrane potential is much more sensitive to a change
in [K+]out than to a change in [Cl-]out. It is commonly said that potassium determines the resting
potential while chloride is passively distributed. Can we explain in words why this is so?
Consider these four points 1) The equilibrium potential for any ion depends on the ratio [Ion]out / [Ion]in.
2) [K+]in is high, so small changes in [K+]in will not change [K+]out / [K+]in.
3) [Cl-]in is low, so small changes in [Cl-]in will change [Cl-]out / [Cl-]in.
4) The external environment is so large that ion flux across the cell membrane will not change
external concentrations. (We will always assume this for our calculations but in a real tissue it
8
may not be true.)
Notice that for the situation we have discussed so far, in which only K+ and Cl- ions are
permeable, the magnitude of membrane permeability to K+ and Cl- does not affect the resting
membrane potential. When both ions have reached electrochemical equilibrium, any change in
permeability will not change the ion distribution or the membrane potential.
Now consider Na+.
ENa = 60  log (117/30) = +36 mV
Therefore Na+ is very far from electrochemical
equilibrium when the membrane potential is at
the resting potential of -89 mV. Both the
concentration gradient and the electrical
gradient will tend to drive Na+ into the cell.
Since all cells have a finite permeability to
sodium, this calculation illustrates the necessity
for a pumping mechanism to actively maintain
the sodium gradient.
In some cells the resting permeability to
sodium is great enough to have a significant
influence on the resting membrane potential
(see inset figure). In this case, the resting
potential will not be equal to the Nernst
potential for potassium. The steady inward
leak of Na+ ions will be balanced by a steady
outward flow of K+ ions, and inward
movement of Cl-. The resting potential will be
the steady-state potential at which there is no
net inward or outward current - it can be calculated
with the Goldman, Hodgkin, Katz equation.
Goldman, Hodgkin, Katz equation. To derive this equation we make two assumptions:
1) The ions pass across the membrane independently.
2) Their movement involves passive diffusion along a potential gradient.
It is important to point out that the Nernst Equation is for an equilibrium situation - there is no net
flux and the mechanism of permeation does not matter. For the GHK Equation, the relative
permeabilities and the permeation mechanism are important. There is net flux of the individual
ions but there is no net current at the resting potential.
The GHK Equation:
 pK  [K]out  pNa  [Na]out  pCl  [Cl]in 

Vm = 60 mV * log 
 pK  [K]in  pNa  [Na]in  pCl  [Cl] out 
9
A second way to describe the ionic basis of the resting potential is the competing batteries model,
which is derived from Ohm’s law, applied to each separate ion conductance:
Ohm's Law: Vm = I.R, or I = Vm.G
so
INa = (Vm-ENa).gNa
IK = (Vm-EK).gK
ICl = (Vm-ECl).gCl
at rest there is no net current :
INa + IK + ICl = 0

(Vm-ENa).gNa + (Vm-EK).gK + (Vm-ECl).gCl = 0
Which rearranges to:
Vm =
The Competing Batteries Equation:
g Na  E Na  g K  E K  g Cl  E Cl
g Na  g K  g Cl
The equivalent circuit analysis and the GHK
equation give similar results for VRest.
It is important to realize that the relationship
between current and voltage is linear in the
equivalent circuit model:
Iion = gion * (Vm - Eion)
Current through real ion channels, however, may
not be linear due to unequal distribution of ions on
the two sides of the membrane.
If the
concentration of the permeant ion is low enough,
the current through the channel will be limited by
the rate of ion entry.
10
Circuit Diagram for the Competing Batteries
Model
2. Channel Structure and diversity
1. ION CHANNELS ARE (1) PORES, WITH (2) GATES.
Introduction
You probably know that action potentials are the electrical signals in excitable tissues. You may know
that currents carried by sodium, potassium and other ions underlie them, and that the currents flow
through specific conductance pathways called channels. We will now consider the functioning of ion
channels from a theoretical perspective and see how the analysis of single channel function relates to
the macroscopic analysis of currents and the generation of action potentials. The aim is to gain an
understanding of the principles of analysis and interpretation to allow you to read the original literature
on ion channels.
Ion channels and carriers serve essentially the
same function. They facilitate the passive
movement of ions across membranes. however,
they do so in very different ways:
Since the 1970's it has become universally
accepted that ion channels allow ion flow
by forming a pore. Ion channels are
essentially passive catalysts for ion
movement across the membrane. They
cannot determine the direction of ion
flow. The direction of ion flow is
determined by the concentration and
electrical gradients existing across the
membrane, defined by the Nernst
equation. The rate, on the other hand, is
determined by the pore properties. In
thermodynamic terms, the channel
effectively lowers the activation energy of
2
the transfer.
The nature of the channel pore
For a simple analogy, we may consider an ion channel as being like a drain in the ground. The drain
allows only certain sized particles to flow through it (it has selectivity), and it may have a lid over it (it
can be gated). When the lid is open, the selected particles can flow through. Thus when we consider an
ion channel, there are two fundamental components of its function : (1) Its pore properties conductance, and selectivity; (2) Its gating - what causes the lid to open and close. External agents drugs, temperature, pressure, act essentially on one component or the other, or both. We will now
examine mechanistically these two components of ion channel function. We will consider them from a
'classical' view as separate components but as you read more about ion channels it will become
apparent that these properties are not completely unrelated.
In the 'simplest' of channels, exemplified
by the 'gap junctional' channels that allow
ion passage between one cell and another,
the pore is literally a water filled hole:
There is one major limitation to such
channels - they are unable to select
between ions. So how do channels select
for one ion over another? One obvious
way would be to make the pore diameter
small enough to discriminate on the basis
of ion radius:
Good idea, but cannot be the whole
answer. We know that there are channels
highly selective for Na over K, but there
are also channels highly selective for K
over Na. So, this would be alright for a Na
channel, but not for a K channel:
Ions are soluble in water because of electrostatic interactions with the dipolar water molecules. On the
other hand, the almost non-existent interaction of ions with lipids makes phospholipid bilayers (as in
3
biological membranes) virtually impermeable to ions. In solution, ions are constantly binding and
unbinding with water at rates of around 109 per second. Water molecules make and break bonds with
each other about 100 times faster. Smaller ions, due to a higher charge density, bind water more tightly
than do larger ions. Thus larger ions, such as K, can 'shed' their waters of hydration more 'easily' than
can smaller ions such as Na.
Selectivity is achieved by a combination of a pore
diameter that is only just wide enough for a
dehydrated ion to pass through, and a pore lining
with polar groups placed appropriately to aid the
ion of choice in 'shedding' its waters of hydration,
since an ion will not dehydrate spontaneously.
The lining of the pore provides polar groups,
appropriately placed so that the ion of choice is
compensated for the loss of the water of
hydration. Thus even though a Na ion could flow
through a K channel, the channel does not provide
an energetically favorable environment for the Na
ion to dehydrate. Conversely, the Na channel does
specifically provide an energetically favorable
environment for the dehydration of the ion:
4
3. Channel Structure and function
Ion channel nomenclature
The naming of ion channels is not systematic. As you will learn, Hodgkin and Huxley recognized three
different components of currents in the squid axon action potential, and today Na channel and K
channel are used to refer to the respective current carrying pores in the membrane. It should be
realized that although the term leak current and leak channel are also used, the leak current is probably
carried by many distinct channels. Channels are typically named, as above, on the basis of the major ion
carried by the channel. However, some channels discriminate poorly, or not at all between ions, and
frequently several distinct channels conducting the same ion will be present and distinguishable only by
their kinetics, conductance, or pharmacology. In these cases, various names and subscripts to names
will be found. This functional nomenclature has been developed over the last forty years. In the last 15
years, since ion channel proteins have been cloned, the individual clones have been given names. This
nomenclature generally parallels the functional nomenclature, but only in a few cases can a specific
current from a given cell or tissue be attributed to a specific cloned channel. The cloning and
sequencing of ion channels has shown that ion channels generally belong to families that have diverged
into certain branches evolutionarily. Thus, most potassium channels are related to one another, and
then more distantly to the Na and Ca channels. Similarly, many receptor-operated synaptic channels are
shown to be structurally related.
Ion channel structure – The Cation
channel superfamily
The voltage-gated Na, Ca and K channels
are both made up of four homologous
domains (Na, Ca channel) or subunits (K
channel). In each case the N- and C-termini
are intracellular and each domain or subunit
contains 6 transmembrane helices. The most
coserved region in each case is the S5
through S6 helix, the S5-S6 linker consisting
of a large loop with some hydrophobic
character (B).
Hydropathy analysis suggested that
each subunit consists of six hydrophobic
regions (termed S1-S6 in the K channels),
each long enough to span the membrane as
an alpha-helix. The additional region
between S5 and S6 originally conceived as
a large extracellular loop (P-loop or H5)
has been shown to be the site of internal
and external TEA block of the pore of K
channels as well as the binding sites for a
number of pore blocking toxins in both Na
5
and K channels.
The crystal structure of KcsA – the prototype K channel structure
We now know that the simplest K channels contain only 2
transmembrane helices (termed M1 and M2, and equivalent to
S5 and S6). In eukaryotes, ‘inward rectifier’ K channels (to be
discussed below) have this structure. 1998 saw a breakthrough
in understanding of ion channel structure with the
determination of the first crystal structure of a bacterial 2
transmembrane domain K channel (KcsA), by Rod MacKinnon
and colleagues. The crystal structure reveals critical features
that are likely to be common to all K channels, Na, and Ca
channels.
Fig. 3. Views of the tetramer. (A) Stereoview of a ribbon
representation illustrating the three-dimensional fold of the KcsA
tetramer viewed from the extracellular side. The four subunits are
distin-guished by color. (B) Stereoview from another perspective,
perpendicular to that in (A).
Fig. 4. Mutagenesis studies on Shaker: Mapping onto the KcsA
structure. Mutations in the voltage-gated Shaker K 1 channel
that affect function are mapped to the equivalent positions in
KcsA based on the sequence alignment. Two subunits of KcsA
are shown. Mutation of any of the white side chains
significantly alters the affinity of agitoxin2 or charybdotoxin for
the Shaker K 1 channel (12). Changing the yellow side chain
af-fects both agitoxin2 and TEA binding from the extracellular
solution (14). This residue is the x-ternal TEA site. The
mustard-colored side chain at the base of the selectivity filter
affects TEA binding from the intracellular solution [the internal
TEA site (15)]. The side chains colored green, when mutat-ed
to cysteine, are modified by cysteine-reactive agents whether
or not the channel gate is open, whereas those colored pink
react only when the channel is open (16). Finally, the residues
colored red (GYG, main chain only) are absolutely required for
6
K 1 selectivity (4). This figure was prepared with MOLSCRIPT and RAS-TER- 3D.
The open K channel – the mechanism of gating..?
KcsA
MthK
of the permeation pathway by these M2 motions.
In 2002 MacKinnon-s group published
the structure of another bacterial K
channel (MthK), in which the
cytoplasmic domain structure, which
confers Ca-dependent gating is visible
as well as the pore. Intriguingly, the
pore structure differs from that of
KcsA in only one important respect –
the M2 helix splays open at the
conserved glycine residue in the middle
of the helix. It is proposed that MthK is
open and KcsA is closed, and that the
fundamental ‘gate’ in K channels and
other cation channels is a pinching off
Glutamate receptor channel structure
analogs) actually contain a Koriented on the intracellular
which establishes a likely 4channel and gives rise to
Ach
receptor
channel
The subunit composition and
nicotinic Ach receptors were
in the early 1980’s, based on
purification from the Torpedo
channel toxin bungarotoxin as
have been viewed using
The major excitatory neurotransmitter in the CNS is glutamate,
which binds to a whole class of receptors, that are themselves ion
channels. Since the cloning of these channels and the determination
of transmembrane topologies and localization of binding sites has
revealed that these channels combine a large receptor domain joined
to a transmembrane domain that forms the ion channel. Intriguingly,
these glutamate receptor channels (functionally classified as AMPAkainate- and NMDAreceptors due to their
pharmacological
sensitivity to activation by
these three glutamate
channel-like P-loop that is
face of the membrane,
fold symmetry to the
cation selectivity.
structures
amino acid sequence of
the first to be established
classical
protein
electroplax using the
a ligand. The channels
electron micrographs, in
7
which it is clear that these channels are pentamers, consisting of a  subunits arranged
around a central axis. Hydropathy plots suggest that there are 4 transmembrane domains, and that the
N-terminus encodes the ligand binding domain.
Other channel structures
Although there are clearly ion channels
that fall into the major cation and anion
channel families described above, there
are also ion channels that do not. In
every case, they seem to be formed with
membrane spanning alpha helices, but
that is probably the only consistent
feature. Ion channels that do not fall
into the families above include CFTR,
the cystic fibrosis transmembrane
regulator, which form anion channels
and may be a monomer with 12
transmembrane helices. Others are the
bacterial toxins and Bcl-family of
proteins that seem to induce, or protect
against, apoptosis by forming ion
channels in the mitochondrial outer
membrane. Although we will not
consider them here, many ion channels,
including members of the above families
are associated with beta-subunits which may modulate pore properties, ligand- or voltagesensitivities, or both. An important class of ion channels, that mediate ion and solute flow between
cells, are the Gap Junctions, which are formed from two adjoining ‘hemi-channels’, each of which
is a hexameric structure spanning the bilayer of one cell, and directly facing a hemi-channel in the
bilayer of the communicating cell:
4. Channels are gated pores
How can we measure ion channel activities?
Ion channel activities were first directly measured 60 years ago with the two microelectrode voltage
clamp circuit used by Andrew Hodgkin and Alan Huxley. In this circuit, two microelectrodes are
impaled into a cell, one microelectrode senses the membrane potential which is compared to a desired
voltage and the difference used as the command signal to inject current into the cell through a second
electrode and hence control the voltage at the desired level. Approximately 20 years ago, the field was
revolutionized by the development of the patch clamp by Erwin Neher, Bert Sakmann and colleagues.
8
Only one electrode is required for
the patch clamp, and it can be
applied to essentially any cell type
for measurement of membrane
currents. Two major developments
were necessary for the patch clamp
to
work.
Firstly
glass
microelectrodes made of soft
borosilicate glass had to be
developed that could form very
high resistance (>109 ohm) seals
when the glass is placed against a
cell membrane. Secondly very low
noise (electrical) amplifiers had to
be developed for amplification of
the tiny (<10-11 amp) currents that
are generated by single channels.
Four different arrangements of the
patch clamp are shown in the
figure. In the on-cell, inside-out
and outside-out configuration, we measure the currents flowing through the small patch of membrane
at the tip of the electrode and this is where we see single channels. In the whole-cell mode, we
measure currents flowing across the whole cell membrane, and obtain macroscopic records like those
seen with the two microelectrode clamp.
How does the patch clamp work?
Below is a simplified diagram of the two microelectrode circuit and the patch clamp circuit. In the two
microelectrode circuit, the membrane potential (vm) is sensed, compared to a desired voltage (vc), and
then clamped by current injection through a second electrode. In the patch clamp, the potential
actually being clamped
is the input to the
amplifier. The clamp
works because there is
negligible
resistance
between this point and
the membrane, so the
potential
at
the
membrane is the same
as that at the amplifier
input (vm=vc).
9
In the whole-cell mode, macroscopic currents are recorded across the whole cell membrane. In the
other three patch modes, only currents through the patch of membrane at the tip of the electrode are
measured. You might wonder how the on-cell configuration manages to measure only the patch
current. It is because the patch resistance is very high relative to the rest of the cell membrane. Thus
almost all of the voltage drop between the electrode and the bath occurs across this membrane. Hence
the rest of the cell membrane is not clamped and no currents are measured.
Let's look at a recording of the current flowing through a single ion channel in an inside-out membrane
patch (Fig.1, above). It is apparent that the channel can exist in two functionally distinguishable states:
(1) Open - i.e. conducting ions, (2) Closed - i.e. not conducting. When open, the current is constant
under constant conditions.
The switch between open
and closed occurs very
rapidly,
essentially
instantaneously over the
time scale that we are
seeing channel activity.
The probability that the
channel will be open (Po)
is the ratio of time spent in
the open state to the total
time:
Po = O/(O+C)
[1],
where O = fractional time spent in open state, C = fractional time spent in the closed state.
The macroscopic current (I) corresponding to current flowing through many channels is related to the
single channel currents:
I = N * Po * i
[2],
where N = the number of channels present, i = single open channel current.
10
4. Channel gating – voltage gated channels
The Theory of analysis
Radioactive decay - Macroscopic kinetics
The simplest chemical reaction is an irreversible change from one state to another, exemplified by
radioactive decay:

X -> Y
The rate (dX/dt) at which X atoms decay is directly proportional to the number of X atoms remaining:
dX/dt = -X
Thus this simplest possible chemical reaction is described mathematically by a function whose
derivative is proportional to the function itself. Integrating this function w.r.t. time gives:
X(t) = Xoe-t,
where Xo
constant' in units of atoms per second.
 = 1/,
where  is the time constant in seconds per atom.
Biological reactions are series of chemical reactions, and are thus described as sums of exponentials.
The kinetics of ion channels are very well described as sums of exponential chemical decays.
Radioactive decay - Microscopic kinetics
Above we considered what happens to radioactive material with time, and saw that the amount of 'hot'
material remaining declines exponentially with time towards zero. Now consider an individual atom. It
remains 'hot' until the point in time that it decays to cold. Thus it has a lifetime as a 'hot' atom. Since
the decay of any given atom occurs randomnly, then the lifetime of a given 'hot' atom cannot be stated.
However, we can say that, on average, the lifetime in the 'hot' state will be equal to the macroscopic 
(time constant). If we measured the lifetime of many 'hot' atoms and plotted the frequency of
observation of a particular lifetime versus the lifetime duration (Fig. 2) we would see that the
distribution of the lifetimes falls along an exponential with the same time constant as that observed for
the total radioactivity remaining in the lump of material.
11
At this point, it is perhaps worth thinking about what is the significance of the average (or mean)
lifetime of an individual member of an exponential distribution as opposed to the mean value in a
Gaussian, or normal, distribution. Only in the latter case is the mean value also the most frequently
observed value.
Reversible reactions - Simple channel gating
Let us consider the simplest model of the gating (opening and closing) of an ion channel. This is
equivalent to a chemical reaction, such as isomerization, in which form A can change reversibly to form
B:


C
=O


k
1
A
=B
k
-1
where  and , and k1and k-1, are rate constants for the indicated transitions.
We can consider the reaction from a thermodynamic viewpoint. The two states of the channel (closed C and open - O) are each associated with a potential energy level and there is an energy barrier to be
overcome in changing from one state to the other: The rate constants for the transitions are inversely
dependent on the chemical energy (G) needed to make the transition:
G() = -RT(ln ), G() = -RT(ln ),
The rate of the forward reaction is [C], where [C] is the concentration (i.e. the number) of closed
channels; the rate of the back reaction is [O]. At infinite time, this system will reach equilibrium, and
[C] = [O],
so:
12
[O]/[C] = /
The useful number is the fraction of channels in the open state at equilibrium. We'll call this O (this is
also the open probability, Po):
O = [O]/([C]+ [O])
= (/) * [C] /([C]+ (/) * [C])
= (/) /(1 + (/))
O=  /(+)
(from eqn. *)
(divide by [C])
[3]
(multiply by )
Now, let us consider the time course of the approach to this final state, i.e. the kinetics of the process.
The rate of change of the fraction (O) of open channels is the forward rate minus the backwards rate:
dO/dt = C - O,
If we consider C and O as fractions of the total (C = 1-O), then we can write:

O,
=  - ( + )*O,
which is a differential of the general form:
dx/dt = A-Bx, where A and B are constants.
1/(A-Bx).dx = dt
ln(A-Bx) + C = -bt
A-Bx = c.e-Bt,
 - (+)*Ot = c.e-(+)t
(+)*Ot = -c.e-(+)t
Ot = -c.e-(+)t + d
O = 0 + d = d
Oo = -c*1 + d,
c = O - Oo
Hence:
Ot = -(O - Oo).e-t/ + O [4]
where
13
 = 1/(+)
[5]
Equations 3 and 5 can then be solved simultaneously to obtain the rate constants.
In conclusion, the simple reversible reaction described above causes exponential changes in current
(and number of open channels) when it proceeds. The exponential can be analyzed to get  and , the
forward and backward rate constants.
Microscopic analysis of more complex channels
If a channel is described correctly by the simple 2-state model discussed, then we can directly measure
 and , since in the steady-state the  (opening rate) = 1/closed time, and (closing rate) = 1/open
time. Experimentally, one can measure the durations of openings and closings, then bin them and plot
number of observations against the bin duration:
Real channels, such as the Na and K channels in the nerve action potential, are rarely, if ever as simple
as the model above. It is clear that there are for many channels multiple closed states, prior to opening,
and these are indistinguishable experimentally. Multiple closed states preceding the channel opening
would be the current explanation for the four gates in the H-H descriptions. A further complication
occurs, when multiple exit pathways from a given state exist. In this case, the mean open time is equal
to the reciprocal of the sum of the rate constants leaving the state. This is a general rule for the lifetime
of any state with mutiple exit pathways. A fuller description of these and other complications can be
found in Colquhoun and Hawkes (1984).
1 

C
C2

1 O


14
For this scheme the rate of leaving the open state
= - [O] – [O]
= - ( + [O]
and hence o, the mean open time = 1/( + 
15
5. Na and K channels of nerve – Action potential generation
The Action Potential
Although we now know excruciating detail
about the structure and function of ion
channels, their existence as discrete
conductance pores was only demonstrated in
real cells about 20 years ago using the patchclamp technique. However, action potentials
have been measured using intracellular
microelectrodes for 50 years, and it is now 50
years since Andrew Huxley and Alan Hodgkin
described the mechanistic basis in terms of
gated Na and K selective channels, after
analysis of macroscopic currents from the
squid giant
axon, using the two
microelectrode technique.
The development of a classical description of
the action potential began with the realization
of Cole and Curtis (1939, Fig. 3), that total
cellular conductance increased during the action
potential, rather than decreasing. Since the
action potential overshoots zero (typically
nerve action potentials peak at around +40
mV), then this implies a selective increase in Na
conductance (since ENa is ~+50 mV). This
interpretation was
supported by the
experiments of Hodgkin and Katz (1949, Fig.
4), who showed that the peak of the action
potential was reduced, when ENa was reduced
by lowering the external [Na].
The voltage clamp allowed Hodgkin and
Huxley to dissect the underlying conductance
changes. To voltage-clamp means to control
the voltage across the cell membrane. Under
such conditions, conductance changes generate
ionic current. In the giant axon, the resting
potential is around –65 mV, so the current is
zero at around –65 mV under voltage clamp.
Hodgkin and Huxley observed that when the
membrane was depolarized from this potential,
16
there was an initial inward current, followed by an outward current (Fig. 6). With successive
depolarizations, the inward current component first becomes larger, then declines, while the
outward current gets larger with each successive depolarization. By removing the external Na, it
was shown that the inward current is carried by Na ions (Fig. 8).
By convention, inward current is defined (contrary to normal electronic conventions) as the
inward movement of positive ions, or the outward movement of anions.By measuring the current
amplitude at each point in time, and dividing by the driving force, H and H calculated the
conductance change as a function of time and voltage (Fig. 11, 12).
Modeling the conductance changes - The Hodgkin-Huxley equations
The earlier discussion showed how a single reversible reaction leads to exponential kinetics. However,
neither the Na+ current nor the K+ current have simple exponential kinetics. Following a step in voltage
to a potential at which the currents activate (i.e. channels open) the Na+ current first activates in a nonexponential (actually approximately sigmoidal) manner, and then decays (Fig. 14). In order to describe
the current time course mathematically, Hodgkin and Huxley needed a function that provided a
sigmoidal rise and then a fall back to zero. They chose the function m3h where m is a rising exponential
and the h-term is a falling exponential. The K+ current activates in an even more sigmoidal manner, and
this current is maintained. Hodgkin and Huxley chose the
17
function n4 where n is a rising exponential to describe the K+ current kinetics. Each of the three m, four
n and one h were considered to be Na+ and K+ selective ion gates described by simple closed-open
kinetics as for the hypothetical channel we considered in detail above. Hodgkin and Huxley did not
know what the physical reality of the gates was, there was no knowledge of what ion channels were at
the time, and although they went to some pains to point out that theirs was a mathematical formulation
without implying any physical reality, a mechanism is implicit in the equations.
18
The K current is easiest to understand, and (in modern parlance) can be described as resulting from the
action of 4 independent gates, each of which opens and closes as single exponential function of voltage
as in the examples above. Hence
IK = n4.gK (Vm – EK),
where IK is the K current, gK is the activated K conductance. Macroscopically, n is the ‘openness’ of
each gate, i.e. it is the probability that any one of the 4 gates will be open. In the above equation, n is
raised to the 4th power since every gate must be open for the channel to conduct.
The gating state of each subunit is either open
(probability ‘n’), or closed (probability ‘1-n’),
and the equilibrium in the steady-state will be
determined by rate constants n and n, which
are functions of voltage, such that n increases
with depolarization, and n decreases (Fig.
16).
n
‘1-n’ <-> ‘n’
n
As above, such a system will relax as a single
exponential, if the parameters n and n are
changed stepwise, as will follow a change in
voltage.
19
A little more complex than for the K channel, the original HH explanation of the Na channel also
involved 4 gating ‘particles’, but instead of identical ‘n’ probabilities, there are 3 ‘m’ probabilities that
increase with depolarization, and 1 ‘h’ probability that decreases with depolarization. In this way the
product m3h is very small at both positive and negative voltages in the steady state. However, the rate
constants for movement of the h gate (h and h) are much smaller than for the m gates (Fig. 17), so
that following a step depolarization, the increase in m occurs more quickly than the decrease of h,
allowing a transient increase in channel opening before closure.
The motivation for the H-H analysis was to explain the action potential. Therefore, having derived
differential equations to explain the time-and voltage-dependence of the underlying conductances, they
could, and people still do, integrate these equations to generate the electrical response of an unclamped
membrane.
In the example in Fig. 18, action potentials are generated in a model membrane that contains the H-H
K and Na channels, and a brief depolarizing current is injected to initiate the action potential at various
distances along the axon. To the right is illustrated the behavior of the H-H parameters for a single
non-voltage-clamped AP. (A) AP itself. (B) Underlying voltage-dependent conductances (gm is the
sum of K and Na conductancesThe non-sigmoidalinactivation of the Na conductance and the
prolonged elevation of the K conductance helps give rise to the undershoot and the prolonged
refratoriness (C) The probability parameters that underlie the conductance changes. Note that both h
and n remain different from rest for more than 6 msecs (the refractory period).
It is important to realize that the action potential is an ‘all or nothing’ event. Once initiated, it continues
through the same sequence of voltage changes and over the same time course each time. This is
because of the voltage- and time-dependence of the Na channel gating. At the resting potential, m gates
20
are almost completely closed (i.e. the probability of being in the ‘open’ state for each subunit is very
low, but the slow moving ‘h’ gate is open. When depolarization is initiated by a stimulus, m gates open
and the channels conduct inward Na current. This inward movement causes further depolarization, and
the ‘m’ probability increases further. A positive feedback situation is generated, and the membrane
potential moves towards ENa very rapidly. More slowly, the probability n increases, and h decreases,
resulting in increased (outward) K conductance and decreased (inward) Na conductance. The
membrane then repolarizes back towards EK.
Hodgkin and Huxley were aiming for the
minimal model to describe their data, the Na
activation could just as easily have been
explained by 4 exponentials. We now know that
the Na channel is made up of four homologous
domains, and that the K channel is made up of
four homologous subunits, each equivalent to a
domain of the Na channel. It is then a simple
conceptual jump to imagine that each domain of
the Na channel, or subunit of the K channel,
must 'gate' independently, for the channel to
conduct (i.e. for the whole channel to be 'open).
Such a mechanism is diagrammed here:
One might then ask, what about the h-gate? If there is an h-gate on each subunit, why shouldn't
inactivation be described by h4? If not, then where is it? We now have a very interesting explanation for
this phenomena based on the structure of the channel - namely that it is the N-terminal ‘ball’ region of
the channel that enters the pore and blocks it.. It appears that only one of the 'inactivation balls' needs
to be in place to inactivate the channel. The kinetics will thus appear as the kinetics of a single ball,
only four-fold faster.
21
6. Additional V-gated currents – Frequency coding
In the above classical discussion of the action potential, we limited ourselves to discussing generic
sodium channels, delayed rectifier potassium channels and rather poorly defined 'leak' channels. It is
now obvious that there are many sub-types of sodium and potassium channels, and that leak channels
come in many flavors. Na channels have essentially one function in the nervous system, and in other
cells, to generate a rapid upstroke of the action potential, and hence show relatively little functional
diversity. On the other hand, potassium channels, while universally causing hyperpolarization and
reduced excitability, can be recruited under different conditions to serve quite different roles. As a
consequence, the functional variability among potassium channels is enormous. Post-synaptic ion
channels, gated by neurotransmitters, cause the post-synaptic depolarization that initiates the action
potential. Diversity of response to synaptic input is generated by diversity of functional properties of
these channels.
Potassium channel diversity
As we said initially, an ion channel is defined by its pore properties, and its gating. Potassium channels
show an almost bewildering variability of both.
Gating of potassium channels generates diversity of function: Inactivating IA channels allow
frequency encoding
Probably the greatest functional diversity among potassium channels is generated by differences in
gating. There are potassium channels that gate (i.e. open) in response to voltage, but other channels are
almost insensitive to voltage and require chemical ligands to cause them to open. Among the voltagegated potassium channels, we have become familiar with delayed rectifier channels (HH channels), and
so-called IA channels, which activate very quickly upon depolarization, but then inactivate, like Na
channels.
Axons that contain only Na channels and
delayed rectifier K channels tend to repolarize
after an action potential, and then remain
refractory, or fire at high rates (HH at about
200 Hz) with steady-depolarizing currents.
many membranes in the nervous system must
encode, i.e. generate a signal that reflects an
input stimulus intensity. They normally do this
by varying the frequency (1 to 100 Hz range)
of firing (Fig. 1), and such encoding requires
IA channels.
When present, IA channels play little
role in the action potential since they rapidly
inactivate as the cell depolarizes. At the end of
the action potential, IA channels are
22
inactivated, but delayed rectifier K (KDR) channels are open, hyperpolarizing the cell. Eventually, the
maintained hyperpolarization causes KDR channels to deactivate (i.e. close, causing the membrane to
begin to depolarize). This allows the IA channels to
recover from inactivation. As the cell depolarizes, the IA channels open again, and arrest the
depolarization. Eventually, the IA
channels begin to inactivate and
allow depolarization to continue.
Thus repetitive action potential
firing is damped, allowing an
interspike interval of hundreds of
milliseconds.
23
KATP channels couple metabolism to electrical activity
Some potassium channels are not depolarization-activated (and lack S4-like segments in their primary
structure). These channels can provide a feedback modulation of membrane excitability in response to
changes in cell metabolic state or other ligands. When cells are made anoxic, it makes teleological sense
that such cells may want to become inexcitable, stopping the cell from 'working', and conserving ATP.
A mechanism to do this exists in many neurons and other cells. A class of voltage-independent K
channels (KATP) are normally closed by the binding of ATP. In conditions of anoxia, as ATP begins to
fall, these K channels open. They are time- and voltage-independent and so they act to hyperpolarize
the cell towards EK and abolish action potential firing.
Ca-activated K channels modulate bursting activity
Ca-activated K channels, known also as maxi-K, or BK (for big K), channels are high conductance
voltage- and calcium activated K channels that provide a feedback link between intracellular calcium
and membrane potential in many cells:
In bursting neurones, these channels are
activated following the rise of calcium that
occurs during a burst, and function to
terminate the burst.
Variable pore properties generate further
functional diversity
All potassium channels contain K
selectivity filters, and recent evidence
suggests that only one or two amino acids
within the pore form this filter. However,
the pore is lined by many residues,
contributing potential binding sites for
other agents which may block the channel.
Since the pore spans the voltage field,
binding of a charged ion within the pore
will be influenced by the voltage.
Depending on the direction of the voltage,
the ion will be either pulled into or pushed
out of the pore. Several pharmacological
+
agents, notably TEA and derivatives, block channels in a voltage dependent manner. While some K
channels are blocked by micromolar concentrations of TEA, others are virtually insensitive. Of
significance physiologically, is pore blockade by internal Mg2+ and polyamines, which causes steeply
voltage-dependent block of otherwise voltage-insensitive K channels:
24
Large currents are seen in the inward direction, but virtually no currents are observed in the outward
direction. These K channels shows inward, or anomolous, rectification. In zero internal Mg2+, the I-V is
linear. This figure is taken from data obtained on a cloned inward rectifier K channel from the
hippocampus. The rectification results from a voltage dependent block of the channel by internal
magnesium and polyamines. When the cell is depolarized, these cations are driven into the pore,
blocking the channel.
A
B
+100 mV
0 mV
0 mV
-100 mV
spd
Em = 0
Em = +100
spe
K
put
IN
OUT
IN
~20 A
OUT
In heart cells, these channels reduce the need for a large inward current to maintain the action potential
at a depolarized potential, and hence minimizes the energetically expensive rundown of the ion
gradients that would result from large opposing conductances during the a.p., whilst still allowing a
large K conductance to stabilize the resting potential. Having a low resting K conductance in other
cells would predispose them to depolarize and fire spontaneous action potentials of their own. Ectopic
arrhythmias disturb the rhythm and interfere with the appropriately timed spread of excitation. Most
neurons probably do not require such stability of the resting potential, obviating the need for inward
rectifiers. However, glial cells have enormous inward rectifier conductances, and it is believed that such
high conductance allows glial cells to buffer extracellular potassium concentrations against changes
resulting from neuronal activity
25
Functional variety of ligand-gated receptor activated channels
Many different neurotransmitters are employed within the nervous system, including ACh, glutamate,
glycine and GABA. In order to serve as depolarizing agents, both ACh and glutamate activate nonselective cation channels (Erev ~ 0 mV). However, each responds only to the relevant neurotransmitter.
ACh receptor channels are well studied at the structural level and in terms of the kinetics of gating (Fig.
8). It is apparent that even ACh receptor channels can show quite complex gating, with at least two
ACh binding steps and slow desensitization steps which will lead to desensitization of the neuronal
response to its input.
Differential
pore
properties
allow
coincidence detection by glutamate receptors
acting in concert
Glutamate-activated channels can be separated
pharmacologically into those which are also
activatable
by
N-methyl-D-aspartate
(NMDA), and those which are not (nonNMDA). Interestingly, the pore properties of
NMDA receptors are such that these channels
are actually well-designed, not to generate
electrical signals (although they do), but to
transduce the input signal to a rise in
intracellular calcium. NMDA receptor
channels are 5 - 10 times more permeable to
Ca than to Na or K. In normal bathing
solution, containing Mg2+, NMDA receptor channels are blocked by external Mg2+ in a voltagedependent manner. Thus at normal resting potentials, even if glutamate is released onto NMDA
receptors, the non-selective conductance
is not activated since although channels
open, they remain blocked by Mg.
When glutamate is released onto
non-NMDA receptors (which are not
blocked by external Mg), the non-specific
conductance is activated, and the cell
depolarizes. If NMDA receptors are also
activated, then the depolarization relieves
the Mg block, permitting Ca entry. Thus
only when NMDA receptors and nonNMDA receptor activation is coincident
does Ca entry and downstream signaling
occur.
Recap - What have we learned about
What have we learned about electrical
signaling and what skills do we want to
take away?
26
We have re-capped the principles of electricity, including all the common terms and physical
components, including current, voltage, resistance and capacitance. These same principles
underlie all electric signaling, both in physical and biological systems. The cell membrane acts
as a capacitor. The energy-dependent separation of ions across this capacitor, by ATP driven
pumps, generates ‘batteries’, with energy stoed in the ion gradients, partiularly for Na and Ca.
These batteries can be discharged, by the opening of ion channels, conductors, across the
membrane. The membrane potential will depend on which ion conductors are ope, and can be
estimated using the GHK or Competing batteries equations.
We have considered radioactive decay as a simple example of an exponential process which underlies
every biological reaction. Unlike radioactive decay, biological reactions, including ion channel
gating have a finite possibility of reversal, and so we consider kinetic models of ion channels from a
thermodynamic and kinetic standpoint. There are a few simple conclusions and principles from this
analysis which should be mastered. Firstly, channel lifetimes are inversely proportional to the rate of
decay of that state, and hence the rate constants for the appropriate kinetic model can, in principle,
be determined from measurements of channel lifetimes, or from macroscopic time courses of current
change in response to a step change of voltage. With this approach, Hodgkin and Huxley, without
knowledge of the channel nature of the current carriers, derived empirical equations describing the
Na and K conductances underlying the action potential. Today, these empirical descriptions can be
interpreted in terms of kinetic models and even in relation to the molecular structure of the channel.
To complement electrophysiological analysis, high-resolution structures of ion channels are now
emerging, and future studies will further relate the structure of channels to their function. You should
now be able to read these papers and understand the measurements being made. In general,
electrophysiological studies of channels measure (1) channel lifetimes or macroscopic activation,
deactivation, or inactivation. In every case the underlying drive to measure these parameters is to
develop or refine a kinetic model, or to understand the effects of a modulator on a specific part of the
kinetic scheme; (2) current-voltage relationships, conductance, selectivity. Knowing the amount of
current flowing through the open channel under given sets of conditions helps to separate channels
from one another by their relative ability to distinguish one ion from another, or to separate channels
of similar ion selectivity by their conductance under similar conditions. Frequently, channels are
distinguished by their pharmacological profile, and many papers that you come across will be aimed
at interpreting the action of the pharmacological (or physiological) modifying agent on the channel.
Vice versa, many papers dealing with channel mutations will assume the action of the agent and
interpret the experimental results in terms of defining the site of action of the agent, or the role of
specific regions or residues of the channel in the action of the agent. The approach, in all cases is
still to measure (1) kinetics, or (2) conductance properties since all pharmacological, and
physiological modifiers effectively act on one of these two parameter sets, or both.
27