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Hi! My name is Eve Marder,
and I'm head of the Division of Science at Brandeis University
and a professor in the Biology department.
And today I would like to, in this module,
discuss with you a problem that's fundamental to all nervous systems,
but in particular to human nervous systems.
And that is to say, you have to build your brain early in development.
And then, the circuits that are important for behavior
have to remain stable throughout the animal's life...
throughout your own life.
And so I'm going to talk you through
a combination of experimental and computational work
that addresses the problem of neuronal homeostasis, as we call it.
So, I'm just going to set up with an example from
lobsters -- my laboratory works with lobsters and crabs.
This now, is a juvenile lobster. It's about a year or year and a half old.
And about so big.
And this is your chicken lobster
one and a quarter pounds.
The ones that those of you who eat lobsters eat.
I don't eat lobsters because I think it's cruel.
Actually, it's because this lobster has spent 7 years fighting
the North Atlantic oceans, and therefore I can't bring myself to eat them.
But, what you see here
is that the small lobster and the large lobster
basically have the same job.
The small lobster has to eat, grow, and molt.
And the large lobster has to eat, grow, molt, and reproduce.
Now, that tells you that the nervous system that's important for eating --
which the stomatogastric nervous system is --
has to be functional both in the small lobster
and in the large lobster.
Now, in the next slide, I'm showing you a filled neuron
(a PD neuron that was filled by Dirk Bucher)
in a juvenile lobster and in the adult lobster --
a neuron in the stomatogastric ganglion. And you can see 2 things here.
Number 1: the ganglion itself has increased enormously in size.
And number 2: all the parts of the neuron itself have increased in size.
So, the cell body has gotten much bigger.
The thickness of the branches has gotten much bigger.
That's telling you that the physical instantiation of the PD cell has changed enormously
over the 4 years or the 5 years that the animal has grown.
But, nonetheless, the solution that this cell has to have found
to be a good PD cell and the solution that this cell
has to have found to be a good PD cell
have to be consistent with there being a good pyloric rhythm
throughout the animal's life.
So the question you're going to ask me now
is, If the cell has grown so much,
its membrane capacitance has changed,
it's added a lot more membrane, it's added a lot more channels,
and so first of all, what do the motor patterns look like,
and then second of all, how can it manage to maintain (if it does)
constant function throughout the lifetime while it's doing this?
So, these recordings that Dirk made...
The top three were from a juvenile animal,
and the bottom three were from an adult animal.
And I think you can see that, by eye,
the motor patterns that small baby lobster were producing
and that the adult was producing are virtually indistinguishable.
And they are statistically basically indistinguishable.
So, this tells you that, as the cell is growing,
as the membrane is getting larger, as channels are being added,
as the whole physical nervous system is changing,
there have to be mechanisms that are working to maintain constant function.
And so, that is the problem that we're going to be thinking about
in the next few minutes.
So, most of you know that the components of functional circuits
are not static, but are constantly turning over rapidly
during the lifetime of a neuron.
Now, neurons -- your neurons -- are all hopefully going to live 100 years,
but receptors and ion channels hang out in the membrane for
minutes or hours or days or maybe weeks,
but certainly every neuron which is living for a long time
is constantly turning over every single receptor and ion channel
in its membrane.
So, you can see that the neuron is not sitting there with a constellation
of sodium channels and potassium channels and calcium channels.
Instead, it has to be rebuilding itself while maintaining dynamic function correctly.
Now, if you think about it,
this is as if you were flying an airplane,
and while you were flying the airplane,
you had to swap out every single part multiple times
while the airplane is in the air.
And that's what your brain is doing
in a sense. When you build the circuits for you to be able to recognize a tree
when you're young and be able to name the tree,
you somehow or other have to be
maintaining the structure of those circuits for 80 or 100 years,
while every single ion channel receptor is being replaced.
So, how can we think about this?
I first want to remind you that
here we have a very simple neuron.
This is just sort of an isopotential model neuron.
But it's a little complicated in that it has 8 different kinds
of voltage- and ligand-dependent channels.
It has a hyperpolarization-activated inward current,
three different kinds of potassium channels,
two calcium channels, a sodium channel,
a leak, and a calcium buffer.
And all of you know what ion channels are.
They're membrane proteins in the membrane that open and close
as a function of either binding a transmitter or voltage.
Now, the number and kind of each kind of ion channel
in the membrane determines its activity.
And, this now is an example from a model that
Zheng Liu who was a graduate student in Larry Abbott's lab
made a number of years ago
just for the purposes of this talk.
What he did is he started out with a model that had
(and I apologize for the symbols down here)...
It had a couple of calcium channels, 3 potassium channels,
a sodium channel.
And what you see on the y-axis
are the conductance densities,
or the maximal conductances for each of those channels in the membrane.
Now one set of conductances
gives rise here to a neuron that's silent.
Another set of conductances gives rise to a neuron that's tonically active.
It's just firing single action potentials.
A different set of conductances gives rise to a neuron that's firing in bursts,
where it's depolarizing, firing a burst of action potentials,
then hyperpolarizing.
And, I think many of us grew up with the intuition
that the number and kind of ion channels determines its activity.
But, now we have to start thinking about
how do you maintain an activity pattern
throughout the lifetime of an animal?
And perhaps be useful for you to know why it was
that we came to thinking about this.
And this goes back to, in the early 1990s,
when Jorge Golowasch was a graduate student in the lab,
and he wanted to build a computational model
of an LP neuron based on voltage clamp data.
He measured a whole bunch of conductances,
and we assembled the model, and the model was very, very unforgiving.
It would crash all the time.
And, I had a very smart graduate student
and a very smart post-doc, and they were working on tuning this model,
and it was a very, very difficult problem.
And I couldn't understand why the problem was so difficult
when the LP cell always had it right.
And the LP had it right day, after day, after day,
But when we started changing the number of ion channels in the membrane,
the model would crash all the time.
And so I said, well, what kind of simple rules
could the LP cell be using to get the right balance of conductances?
And at the time, people were thinking that there would be a very simple rule
controlling the regulation of sodium channels
and another set of rules controlling or processes controlling potassium channels
or calcium channels, but what mattered was getting the right set of conductances,
not the right value for them one by one.
And so, Larry Abbott, with whom I was then working,
came up with a very simple idea,
which is that the neuron might not be controlling the number
of sodium channels or calcium channels or potassium channels
independently, but it might be controlling its activity,
so it would have a target activity level.
And then a very simple negative feedback /
homeostatic rule might then be useful,
if the cell had a way of monitoring its own activity.
And we reasoned that intracellular calcium concentrations
fluctuated with activity, so intracellular calcium concentrations
might be used as a way of sensing the cell's own activity
and then might be used as a feedback for a simple homeostatic mechanism.
And so those are the models which we built.
These models are models in which neurons self-tune their
conductance densities to maintain a target activity level.
And these models basically stipulate that the activity is a controlled variable,
not the actual number of any one kind of ion channel.
And the premise behind these models
is that the target activity level would be set during
determination and would be a characteristic of that neuron's cell type
or its identity.
And so we built two generations of these models.
In the first generation, a single intracellular calcium sensor was used
to tune all of the conductances -- the idea being
if the cell became too active, then calcium would rise,
and you would downregulate the inward currents
and upregulate the outward currents.
In a second generation model, we had 3 different sensors --
a fast, a slow, and a DC sensor
of the calcium current, and then these would influence
different ion channels in different ways.
But, in all of these models,
the important thing is that the regulation of conductance density
is slow, relative to the dynamics of the neuronal activity.
So, how do these models work?
This is an example -- one of my favorite examples --
from Zheng Liu's paper.
And, he started out a model, as you see up there,
with a model neuron in a bursting regime.
And these were the conductance densities
that gave rise to this activity.
And then, Zheng shifted Ek from -80 to -60mV.
This is, if you will, the model equivalent of going into high potassium solution,
and you can see the model instantly change its activity.
And then slowly, the neuron's sensors detected the fact that it was no longer bursting,
and the cell rebuilt itself back into a bursting
activity pattern by changing the sodium conductance,
and the potassium conductance in the model.
And then Zheng shifted Ek back from -60 to -80mV,
the model instantly changed its activity pattern,
and then slowly, over time, it rebuilt itself back into a bursting mode,
and it did so by again, changing the balance of conductances.
Now, you can see it recovered its bursting target activity level.
So these models made a set of predictions
and they said, basically, that neurons would sense
a target activity level and then alter
the density of their ionic conductances accordingly.
So, this set in motion a great deal of experimental work,
both in our lab and in many other labs around the country.
Some of the nicest work directly testing this kind of model
came from Gina Turrigiano's lab,
This is a paper that Niraj Desai did.
And in this work, what Niraj did is he took
some control cells -- these are cortical neurons that he placed in culture --
and he depolarized them.
And you can see here, they fire some action potentials.
And then he activity-deprived sister cultures
by putting them in TTX for 48 hours.
And the prediction would be that when you activity-deprive the neurons,
they would upregulate their inward currents.
And so, after activity deprivation, he washed out the TTX,
(you know, TTX blocks sodium channels)
and then he depolarized them, and you can see
now the activity-deprived neurons are firing much more
heavily when depolarized with the same current pulse
than the controls.
And, in that same set of studies,
what Niraj did, is he used voltage clamp and actually measured
the conductances for the sodium current, the calcium current,
and the potassium currents.
And as expected, the sodium current was upregulated,
the potassium conductances -- two of them -- were downregulated.
Now, another very interesting example at the network level
of the effects of activity-deprivation
comes from the pyloric rhythm studies on the pyloric rhythm
of the stomatogastric nervous system.
And, in these experiments, what we've done,
is we've chronically removed the effects of descending modulatory inputs.
So, here you have some control recordings,
and you can see a robust pyloric rhythm.
You see the activity in the PD neuron on this extracellular recording of the PDN.
And then, what Jorge Golowasch did in these early experiments,
is he cut the stomatogastric nerve, thus removing
all of the descending modulatory inputs.
You can see that pyloric rhythm is lost,
and the network went silent.
However, he then waited 18 hours,
and the rhythm recovered.
And now, this rhythm is present,
although the modulatory inputs are completely absent.
And these are just pooled data that just show...
Here's the control and then the block, and the recovery.
Recovery often takes place with the networks resuming activity
in bouts of activity.
So, what we do now is we record continuously
for up to two weeks
from the same preparations as they recover their activity.
And this was a paper published by
Jason Luther in 2003 on a very slow timebase.
See the timebase here is 18 hours.
And these are data from continuous recordings.
So, on this timebase, the control
had a high pyloric frequency. After the stomatogastric nerve was blocked
removing modulatory inputs, the rhythm disappeared.
But then it came back in rhythmic bouts
until it eventually resumed again.
So, the interpretation again, of this,
is that either the loss of activity or the loss of the modulatory inputs themselves
which produce the activity
is part of a signal that causes the network
to change its properties so now it can be rhythmically active
in the absence of the descending modulatory inputs,
which were ordinarily necessary for its strong rhythmic activity.
Now, Erwan Ledoux built a very simple model of this process.
And I'd just like to talk you through it
because it makes another point that I think will be useful.
So, in this model, he started out
with modeling the 3 components of the pyloric rhythm
He has a neuron in blue representing the pacemaker kernel,
in red the LP cell, and the PY cell (in green),
and if we cut a slice through A,
you can see a really nice pyloric rhythm -- a triphasic pyloric rhythm.
Now, to represent the modulatory inputs,
what Erwan did is he put into these two cells,
a protcolin current which would represent
the effects of those descending modulatory inputs.
Then, Erwan removed that current,
and you can see the network oscillations stopped.
Here, PY continued, as you might have noticed in the biological data.
And then, because these neurons all have this self-tuning
homeostatic mechanism in them,
you see partial recovery of function here,
with bouts of activity that are similar to the bouts of activity you saw before.
And then, full recovery of activity that you see here,
with a triphasic rhythm here.
which looks very similar to the one that you see over here
although this rhythm exists because of a modulatory current,
which is completely gone here.
So, now you've got two rhythms which look very similar,
but which are arising from two entirely different mechanisms.
In this case, independent of a current, which is very important over here.
And that transition is just shown in the next slide.
That's what you've seen before.
Where now Erwan has plotted the conductance densities of
several of the currents in the model.
So, you see the H current, the A current, and the calcium-activated potassium current
during recovery of all 3 neurons.
And you can see that, during the recovery process,
these neurons are changing each of those currents.
And the important thing is that over here, at the end of the recovery process,
the balance of these conductances is different
from what we saw in the control,
although the motor patterns produced are very, very similar.
So, this tells you that there have to be multiple solutions
to producing a similar motor pattern.
Now, some very beautiful work by Muriel Thoby-Brisson in John Simmer's lab
actually went back to the experimental condition and asked,
What kinds of processes were resulting in this decentralization phenomenon?
And then they saw, as we would expect,
as the PD cells and other cells became more excitable,
there were downregulations of potassium currents,
which is exactly the same results in Niraj Desai's experiments.
So, to summarize, I'll say
that homeostatic processes can find multiple solutions
to a target activity pattern
in single neurons or networks,
provided that the mechanisms for compensation are present.
And then, the prediction from this work
-- and this prediction set up a lot of the work we're doing today --
will be that if each individual animal has found
a different solution to producing a very similar motor pattern,
you would expect there to be a considerable amount of inter-animal variability.
Thank you.