In the last lesson we learned
about an important and interesting family of ion channels:
the voltage-gated ion channels.
For a voltage-gated ion channel,
the open probability depends upon the membrane potential.
Furthermore, we can see that there's a complicated situation
where the opening and closing of the voltage-gated ion channel
changes membrane potential,
and that change in membrane potential
in turn affects the open probability.
And so, we can envisage complex interactions
between the voltage-gated ion channel function
and membrane potential.
The dynamics of those interactions depend upon the channel kinetics,
how rapidly it is changed in its open probability
by the membrane potential.
The voltage-gating of the ion channel
depends upon changes to the 3D conformation,
the structure of the protein ion channel itself,
and this does not occur instantaneously.
The opening and closing of the ion channel,
the individual opening and closing,
they occur on the microsecond time scale.
The voltage gating, the change in the open probability of the ion channel,
occurs on slightly longer time scales
and it's those dynamics that we're going to study in today's lesson.
We're going to focus again
on the voltage-gated sodium and potassium conductances
that we began to study in the last lesson.
These, as we remember, are largely closed
at resting membrane potentials of around -70 mV.
They only become activated as we depolarize,
as we go beyond -40mV and above, the open probability
of the voltage-gated sodium potassium conductances increases dramatically
causing an inward sodium current and an outward potassium conductance.
In order to understand how they dynamically interact
on the cell membrane in real cells,
we need to know about the gating kinetics.
If we rapidly change the membrane potential,
what happens to the sodium current in time?
For the voltage-gated sodium conductance,
we can imagine a situation where we have a patch clamp electrode
sitting on a piece of membrane,
we suck a bit of membrane into the patch electrode,
and in this patch would be voltage-gated sodium channels.
For a given membrane potential we can, using the patch clamp amplifiers,
change that membrane potential.
We can then activate these voltage-gated sodium conductances.
We know that the current/voltage relationship for a sodium conductance
is something like this:
a reversal potential right here, at around +60 mV
activating somewhere around -40 mV and enclosed, basically,
at hyper-polarized potentials relative to this.
So let's take a situation where we start at -70 mV.
At some given time we jump the membrane potential to 0 mV
and we're going to be studying  the single-channel currents
flowing through an individual ion channel
inside the patch electrode.
So as we go from -70 mV to zero mV,
initially, the open probability is very low.
The ion channel is closed at -70 mV.
We then jump to zero mV.
Now we have an inward driving force,
so we're expecting an inward current to happen.
Initially, nothing happens, but then, after a short delay,
this ion channel opens, stays open for a brief period of time,
closes again, and then remains closed
for the duration of the depolarization to zero mV.
On the next trial when we repeat this
again, -70 mV, no current flow,
we depolarize to zero mV, short delay, ion channel opens,
stays open, closes, and then again, remains closed for the duration.
In this case here, the ion channel is open for a slightly longer duration here
with some stochastic opening and closings.
And you can imagine repeating this over and over again
for hundreds of trials, or alternatively,
summating that current across a whole cell membrane
and doing just a single voltage step
and seeing that summated average currents across the sodium channels,
and either way, we get the same picture.
We make the voltage step from -70 to zero mV.
After a brief delay, inward current is activated.
This takes, maybe some ten microseconds or so,
and then the sodium conductance remains high
for a period of about 200 microseconds,
and then it closes.
The voltage-gated sodium channel inactivates rapidly
on that time scale of hundreds of microseconds.
Fast, brief, transient voltage-gated sodium conductance
is activated by a prolonged step to zero mV.
For the voltage-gated potassium conductance,
things are rather different. 
Again, envisage a situation
where we have a glass patch electrode sucking a bit of membrane inside it
and inside this membrane we now have a potassium conductance.
We can choose the membrane potential through the patch clamp amplifier,
and again we take a situation where we start at -70 mV,
the ion channel is closed, we have our current/voltage relationships
that are characteristic, which are closed
until somewhere around -40mV.
We jump to zero mV,
we have an outward driving force
and we now study what happens at the level of single channels
as we make that jump in voltage from -70 to zero mV.
Here we're looking at the single channel current through our patch electrode,
we make the voltage jump, and initially, nothing happens.
There's a long delay, and then at some time,
the channel opens, stays open, briefly closes,
opens, briefly closes, opens again,
and this ion channel will remain open
as long as we keep the plasma membrane depolarized to zero mV.
In another trial we do the same.
We jump from -70 to zero mV with a delay, the ion channel opens,
closes, opens, and stays open for as long as we care
to keep the patch of membrane depolarized.
We can, again, summate this across multiple ion channels
that are present in the cell membrane,
or we can repeat at the level of individual ion channels
and get the mean current flow for the potassium conductance.
And either way we get the same picture, we jump from -70 mV to zero mV.
There's a delay, nothing happens for a few hundred microseconds,
so about 200 microseconds,  nothing happens,
and then the open probability
of the voltage-gated potassium conductance increases
and we see an increase in the current flow
through the voltage-gated potassium channels.
We can directly compare the kinetics of the voltage-gated sodium
and potassium currents by putting them on the same graph.
So again, we imagine going from our hyper-polarized
to our depolarized state  that activates both
the voltage-gated sodium
and the potassium conductances are both activated
somewhere positive to -40 mV,
but the major difference is in the time course.
The voltage gated sodium conductance is fast and transient.
The voltage-gated potassium conductance is delayed and long lasting,
without inactivation.
The transient sodium conductance lasts something like 200 microseconds,
and the potassium conductance is delayed by that same order of magnitude,
some hundreds of microseconds
delay the activation of the potassium conductance
that then remains active and doesn't inactivate,
whereas here, the sodium conductance has fully inactivated
after just a few hundred microseconds of the depolarization.
However, the voltage-gated sodium channel
doesn't remain inactivated forever.
We can take that membrane potential,
hyper-polarize it again, say, to -70 mV,
and under those circumstances, the sodium channel de-inactivates
and can go through another round of this while we can make a step activation
and will again see the transient  voltage-gated sodium conductance.
The de-inactivation doesn't occur instantaneously,
but again, takes some time.
We can study the recovery from inactivation
by doing two pulse experiments.
And so, as before, we go from our hyper-polarized
to our de-polarized state.
We see the transient voltage-gated sodium current
that becomes activated by this depolarizing step
and then at some later time, after we've re-polarized again
back to -70 mV,
we can then study how long it takes before we recover our full sodium current.
If we wait half a millisecond, we get some recovery, but not much.
If we wait one millisecond, the recovery is already better.
and after about five milliseconds, we're almost back to the full
voltage-gated sodium current that we had from controlled conditions.
And so, we can plot an exponential recovery time course
for the voltage-gated sodium conductance
if we think of this as the second peak,
and this as the control, first peak,
we can look at the ratio
of the second activated voltage-gated sodium conductance
compared to the first one,
and we find that there's a recovery time constant
with an exponential form here,
and the exponential for the recovery from inactivation
is on the seven millisecond time scale.
So we've seen some important features of the kinetics
of the activation and inactivation of the voltage-gated
sodium and potassium conductances.
Both voltage-gated sodium and potassium conductances
are interactive at resting membrane potential,
around -70 mV.
Above -40 mV the open probability of both sodium and potassium conductances
increases dramatically,
but the sodium conductance is rapidly activated in the time domain
lasting a few hundred microseconds is then inactivated,
whereas the potassium conductance is delayed.
It takes some hundreds of microseconds before it even opens,
and then, it doesn't inactivate, but remains open
for as long as the membrane is depolarized.
Now, this is true in general of the voltage-gated sodium
and potassium conductances that one sees,
but there's also some diversity as one goes across different species
and across different cells in the same species,
and we'l have a little look at the basis of that in the next slides.
The voltage-gated sodium channels are encoded by a family of nine genes
that are given the nomenclature NaV1.1 through to NaV1.9.
All of them encode the voltage-gated sodium channel in a single gene,
so it's one long string of amino-acids that has transmembrane domains
and it has four subunits that are all part of the same string of amino-acids
so this would be the N terminal, the C terminal,
and here's subunit I, II, III, and IV
and these are then the trans-membrane regions
that will ultimately sit in the plasma membrane
and will then form the four subunits of the ion channel,
the center of which forms the ion conducting channel pore.
Associated with this so-called alpha subunit
of the voltage-gated sodium channel
is a much smaller Beta subunit
that sits somewhere tightly associated to the ion channel proteins
encoded by the Alpha subunit.
Together this provides some diversity.
There are nine different sodium channel proteins,
there are four different Beta supplements,
and they can then encode slightly different functions
in terms of the single-channel conductance
and the detailed kinetics and the voltage activation.
Another very important aspect
that's different between the different isoforms
is the cell types in which they are expressed,
and also the sub-cellular localization of the voltage-gated sodium channel.
As we'll learn in the next lesson,
the density of the voltage-gated sodium channel
is regulated very precisely, and some small subregions of neurons
have very high densities of voltage-gated sodium channels
and that makes a big difference to the functioning of neurons.
There's also some diversity in terms of the time course
of the voltage-gated sodium channel,
and in particular, some subtypes of voltage-gated sodium channels
have much less inactivation than what we've discussed.
Potassium channels are an even more diverse family of ion channels.
There's something like 80 different genes in the mammalian genome
that encode potassium channels.
Not all of the potassium channels are voltage-gated.
They are an important family of the potassium channels,
and are certainly the ones that are most interesting to us
in terms of thinking about the complex dynamics of membrane potential
but they're not the only ones.
There are also potassium channels that are gated by the intracellular
calcium concentration, calcium activated potassium channels
that are so-called BK and SK channels,
and there's another family of proteins, of potassium channels,
that are so-called G-protein coupled ion channels,
these are the so-called GIRK channels,
and there are the Tandem pore potassium channels
that are involved in setting the resting membrane potential.
The voltage-gated potassium channels in themselves
have extensive diversity.
Some of the voltage-gated potassium channels
have some degree of inactivation but on a much longer time scale
than what we saw for the voltage-gated sodium channels.
The potassium channels are also different in the sense that they encode
individual subunits rather than the whole potassium channel in itself
and so, one gene will encode the six transmembrane regions
of the potassium channel, but it will only encode one subunit of that,
so one gene will encode one subunit and another gene might mix
together with that and form other parts of the subunit of the potassium channel,
so we can generate even more diversity by mixing different proteins together
to form the voltage-gated potassium channels.
The diversity in the voltage-gated potassium channels
causes a great deal of the diversity in terms of how neuronal
membrane potential changes in different cell types
and in different compartments of the same cell.
So now we've learned a bit about the voltage activation
of the sodium and the potassium conductances.
We have the voltage activation of the sodium conductance,
and we have the voltage activation of the potassium conductance,
both of which are activating somewhere positive to -40 mV
and closed at resting membrane potentials.
We also know something about the dynamics
of the opening of the voltage-gated sodium conductance.
It opens rapidly and then inactivates, whereas for the potassium conductance,
we have a slower rise that takes some hundreds of microseconds.
We can then begin to think about what happens inside a cell
that might express both the sodium and the potassium conductances.
If we think now about the different time courses of these,
you can imagine that if we take the membrane potential
a little bit depolarized and we get into this regime
where the sodium channel begins to activate,
we could then get this brief activity of the voltage-gated sodium conductance
that will drive a depolarization for the inward current
through the sodium conductance.
This will then inactivate, and at the same time,
while the sodium conductance inactivates,
the potassium conductance is activating, driving a hyper-polarization.
We'll see it's exactly this dynamic interaction
between the sodium and the potassium conductances
giving rise to brief transient excursions in the membrane potential with time
that drives the so-called action potential.
That action potential is what we'll be studying in the next lesson.
So to summarize this lesson, we've learned some interesting details
about the kinetics of activation and inactivation
of voltage-gated sodium and potassium channels.
The voltage-gated sodium channel activates rapidly,
then inactivates rapidly,
and remains inactivated until the membrane potential
hyper-polarizes again, and then, after a few milliseconds,
it's de-inactivated and ready for the next voltage pulse.
The voltage-gated potassium channels, on the other hand,
are slowly activated by depolarization.
It takes them a few microseconds before their open probability increases,
but then they remain open for as long as the membrane potential is depolarized.
The complex interplay between time, space and membrane potential
and the opening of these voltage-gated ion channels
causes very interesting and complex dynamics in membrane potential,
and ultimately underlie the action potential signal,
which is the 0 and 1 signal
that we'll go on to study in the next lesson.