0:22

What we found was that both cellular geometry and enzymatic activity

of negative regulators are needed for the formation of these micro domains.

You might remember in one of the last slides of the previous lecture.

I showed you that ten dendrites, de, dendrites with the small

diameter favored the formation of sharp gradients of cyclic AMP.

As compared to thick dendrites.

So we explored this property further with thin and thick dendrites

but now adding another variable which was, reading concentrations.

Or reading levels of the negative regulator phosphodiesterase [LAUGH].

Also called PDE or PDE4 in this case, varying levels of the phophodiesterase.

So when there is no phosphodiesterase or negative regulator there's a lot

of cyclic AMP can be formed and then loss signal flows through.

So there are no gradients really observable.

At moderate levels of phosphodiesterase, one starts to see nice sharp gradients.

And at high levels of phosphodiesterase all the cyclic AMPs

dissipate, and all the gradients get to be dissipated, as well.

Now, you can see that the, the key in, this happens,in the case

of the thin dendrites, but not so well in the case of thick dendrites.

Although at one particular concentration of phosphodiesterase

there is some gradient that's seen here.

This effect of the phosphodiesterase which degrades cyclic AMP.

on, on which is out here, on MAP kinase, which is down here

it's sort of distill prediction of how this network is configured.

And so, we try to use this prediction to test the whether one could see

this in real life experimentally and for this we used brain slices.

Stimulated the slices with a bit [INAUDIBLE] receptor ligand.

And ask the question, does, is their MAP kinase

activity in the dendrites, or, or the cell body.

And as you can see that when the phosphodiesterase

is inhibited, with the chemical inhibitor, there are no gradients.

Similar to the condition here and there is for a

MAP kinase both in the cell body and the dendrites.

Otherwise, the MAP kinase is largely localized to the dendrites

and there is very little in the cell body of each.

Here are the corresponding simulations for this.

Okay.

So if these micro domains sort of require both enzymatic

activity of the negative regulators and the shape or size of the cell.

One can sort of ask the question.

Is this, are these conditions enough to transmit the

spatial information from upstream components to downstream components?

So in, in this particular set of simulations we

follow the flow of spatial information within the dendrite.

And it's this one white dendrite in this particular neuron.

And starting with cyclic AMP the signal goes to protein kinase A.

And from there it goes down to MAP kinase and to to a couple of pathways.

So you can see that the PKA gradient is similar to the MAP kinase gradient.

However, when the signal that goes to the Mac.

Neither RAF nor MEK show good gradients.

In contrast, the protein kinase A gradient,

is recapitulated by this second negative regulator, PTP.

Which is which is phosphotyrosine phosphatase, which is the

regulator of the tyrosine phosphorylation side of MAP kinase.

So you can see that the gradient, this

looks similar to this this looks similar to this.

Indicating that the flow of gradient was likely to be to this PTP pathway.

Again since although there was a cyclic

PKA gradient because there was no MEK gradient.

We tested whether this was observable in experimentally.

And we saw indeed that MEK is activated both

in the dendrites and the cell body in these experiments.

So, from these experiments what one can sort of conclude

is that the flow of information regarding the activity state.

Which means protein kinase A activates RAF.

B-RAF activates MEK.

MEK activates cyclic AMP forced through this RAF MAPK kinase pathway.

However, the flow of special information.

That is how much MAP kinase is activated at a certain location.

In response to the similar spatially

restricted activation of PKA flows through PTP.

You can again clearly see this is the same simulation as before.

The PKA gradient matches the PTP gradient that matches the MAP kinase gradient.

So what does simulation which was indeed a very surprising finding

was that the flow of spatial information is through a different arm.

As compared to the flow of information with regard to the activity.

Of course, the model of the computation predicts, the

per that PTP is going to be very important.

And we tested, therefore, the importance of PTP for loo, by looking at

what happens when you ablate the PTP by using antisense oligos.

And what we found is that when you

knock out the PTP, the MAP kanise gradient disappears.

And you get MAP kinase all over the cell body,

which is what is shown here, as well as the dendrites.

8:09

And in this study, the researchers, mostly in Julie Theriot and Alex Mogilners

lab were interested in understanding a pretty high level question.

Which is how do moving cells determine their shape.

As cells move along a gradient or even swim randomly, they,

they are capable of preserving their shape even though they are moving.

And the question is how do they do this?

For this the researchers used fish skin epithelial cells.

These are called keratocytes.

People use these cells to study these kinds of

stuff because they are fast moving cells and cultures.

And when they move, even during the

movement, they maintain both their shape and speed.

So one can study these cells in a way that is mm, we

can look at the shape of the cell and also look how they're moving.

And ask the question what are the processes that are

involved in sort of preserving this shape during the dynamics of movement.

9:14

So there are four characteristics that provide a nearly

complete description of the shape of these ce, cells.

And the four characteristics are shown here.

There are cells that are D shaped.

There are cells that are elongated and canoe shaped.

There are sev, the third mode tells you something

about where the position of this cell body is.

Which is down here, with respect to the leading edge

and the final mode tells you something about right left symmetry.

So by looking at all the characteristics that go with cell shape.

One can identify the four top, if you

want to call that characterize a population of these keratocytes.

So what these authors also found that for sharp, for [LAUGH] fast moving cells.

The speed of the cell could be correlated with the shape of the cells.

So here is a correlation between area and time.

Here is a correlation between aspect ratio.

Which is the long, which is the short access on time.

Here is correlation between the front of the cell and with respect to time.

And here is a correlation of the speed of

the cell with which it moves with respect to type.

12:13

A, B, and C, sort of show the

quantification of shape and actin filament density.

And indeed the shape is maintained by the actin filament density.

So what they did was for they develop some equations to describe this

relationship between the filaments and the shape and so on.

And then, they plotted the comparison between the model

which is in the red line and the experiments.

The simulations which is in the red [LAUGH] line a, a, a,

and the experiments the which are the smooth mean and the blue line.

And you can see that the match between the

calculated values and the experimentally observed values is pretty good.

This is done for a very large number

of cells and these individual dots represent individual cells.

So this mathematical formulation allows them to correlate the shape of

the leading edge, along with the speed of the, with which the cell moves.

So even a model such as this has a number of assumptions.

And these authors have published a very nice

Table of Model Assumptions, the rationale for their assumptions.

The level of confidence they have in assuming this, and

how critical their assumption is, both in the model and experiment.

I'm just going to draw your attention to one of them which warrants us speculation.

And here we can see that this is speculation that the growing

filaments are stored or indeed buckled at the sides of the cell.

14:03

They clearly state that this is a speculative assumption.

And since the model calculations agree with experimentally observed

relationships it is reasonable to sort of assume that this speculative.

Assumption is likely to be correct.

However I should caution you there is no direct experimental proof just

visualization of stored or buckled filaments at the, the sides of the cells.

So this is something we need to wait further

to understand how whether it really occurs within these cells.

At the next level, what they did was to now that they were able to

calculate out the sort of protruding shape.

They started to look at whether they could use for

each cells both are measured, shape and a calculated shape.

And what the relationship between the two were for a good,

695 cells and they found that this relationship is very good.

And then, they were able to take this shape calculate out the aspect

ratio then look at the relationship between the shape.

As denoted by the aspect ratio and the speed at which they move.

And they have a predicted behavior and they find that experimentally.

Observed system behaves very closely, enter for this very same behavior.

There's been compelling experiments and, model.

15:42

They found the match was actually very good.

And so, one could say that they had sort of like a predictive understanding

of how cell shape is related to the, the speed of cells in these moving cells.

So what are the conclusions from this cell spreading model?

The conclusions are, that relatively simple mathematical

models can accurately describe complex cellular behaviors.

In this case, they did not actually

build a differential equation based dynamical model.

But rather they, they, they found values and use relatively

simple relationships, simple models to relate one parameter to the others.

All of these models however simple or

complex they are, they all have underlying assumptions.

And like, like how these researchers had done in their, in their paper.

It is good to clearly state

the assumptions, underlying assumptions for the model.

And let the reader judge for herself or himself, whether

this is appropriate and how the model is to be interpreted.