And we will work out a second case next class.
So, here for example,remember we were talking
about the cytoskeletal filaments, actins and
microtubules.
So, here is an actin , so this was this actin
filaments ah.
So, there is a class of problems which are
called diffusion and captured which are called
diffusion and capture with the idea is that
you have this fault this very long molecule,
this actin molecule which is growing ok over
in that screen is probably better ,which is
growing in time and its growing by the addition
of these subunits.
It is growing by this addition of subunits
the g-act; the globular actin subunits which
come and bind and causes this polymerization.
So, the idea is that this globular actin molecules
must diffuse.
So, here is my actin which is growing, this
is all my subunits.
So, I have these individual monomers in solution,
many many such monomers, let us say these
monomers must somehow diffuse and find the
tip of this growing filament in order for
it to attach and grow by a unit right.
So, it must diffuse and then be captured by
this growing tip.
Its true generically also for microtubules,
so this is true for actin, this is also true
for microtubules.
So, for example, here is, here is a cartoon
for microtubules where you have all these,microtubules
remember form the fundamental unit is thisdimer
the tubule in dimer which consists of alpha
tubulin and beta tubulin this together forms
an unit, so which is this red and this green
thing over here.
So, they come and they come and they must
form find this growing tip of the microtubule
and they are captured and then the microtubule
grows or it can disassemble and then in depolymerizes
ok ah.
This this process has various implications
one one of the more interesting being that,
if you look at when the cell divides it forms
a spindle which is called the mitotic spindle.
And that spindle ah.
So, ok this video is not very nice.
So, well all these green fluorescent objects
that you see these are the microtubules, they
polymerize and de polymerize and until they
find the chromosomes which are shown in orange
over here.
So, here is my nuke, here is my chromosomes
over here ah.
The microtubules start polymerizing from these
two objects, thespindle poles and they polymerize
and depolymerize until they find this chromosome
and one another microtubule from this end
finds the corresponding sister of that chromosome.
Once it finds this chromosomes it pulls them
apart and all these chromosomes are then segregated
and then one copy goes to each daughter cell
ok.
So, this polymerization, its of course, important
in various other contexts as we will describe
, but this mitotic spindle for example, is
crucial to cell division.
So, this is then this class of problems called
diffusion and capture, where you have this
growing polymer or filament and you have many
many subunits which are these individual monomers,
they are diffusing in space and then they
must find the growing tip of this polymer
whether it be an actin or a microtubule or
so on and be captured over there.
You could also think of this in the context
of chemo reception ah.
For example, I will show you this movies in
a bit but.
So, here is an E. coli cell ah, here is an
E. coli cell,it has these proteins on the
surface of it which are called chemo receptors.
And, so this is one particular chemo receptor
I think this TlpB probably ah, but I am not
sure.
So, this is one particular chemo receptor.
So, these chemo receptors are these things
which are shown on the surface of this cell
and they detect various chemical concentration
gradients that the E. coli can respond to
.
For example, if some chemical is a food for
the E. coli and you produced that chemical
at some point.
So, you are releasing chemical over here and
you have and you have your E. coli over here
then the E. coli will try to swim towards
the great, towards its food source.
If you give some chemical which is harmful
to the E. coli ah, so a repellent basically
then the E. coli will try to swim in the other
way.
How does it do this, how does it sense this
gradient? it sense senses these gradients
through these chemo receptors which are on
the surface of this E. coli and then it it
sort of modifies this this diffusion of this
random walk process that it undergoes according
to the concentration of this chemo attractants
or chemo repellents.
So, this is called the cell signaling problem
. So, this is called the cell signaling problem
. And again this is something which we will
look at next class , its called the cell signaling
problem
This can lead to very nice sort of experiments
I will just show you a couple of movies from
an experiment over here ,ah let us see ok
let me stop this.
So, this is one particularbacteria which is
called H. pylori,this is a gut bacteria ah.
If I remember correctly this is, its often
not harmful, but it can cause its responsible
for stomach ulcers.
So, this H. pylorisenses urea as an attractant
ok.
So, its an attractant through a chemo receptor,
a particular chemo receptor called TlpB.
So, here is an experiment; these are two species
of this H. pylori, this is the wild type which
means its the normal bacteria.
Here is a modified genetically modified version
of pylori where this receptor TlpB is not
present, so its a delta TlpB.
So, this is the start of the experiment after
some time what you will find is that somebody
introduces a pipet over here and over here.
So, these are two corresponding experiments
running side by side and through this pipet
you introduce urea ok, which is an attractant
for the pylori.
So, the bacteria are happily doing their own
thing you introduce the pipet and through
this pipet you introduce urea.
So, this wild type bacteria which has this
chemo receptive, sort of tends to aggregate
you will see that the here nothing changes,
it goes on doing whatever it was doing earlier,
because that chemo receptor is missing, but
here all the bacteria which was outside of
your field of view, they sort of tend to congregate
towards this pipet over there and you will
see that the num the concentration of bacteria
near the pipet increases right, Compared to
this other version where the chemo receptor
was absent.
You can do various fun sort of things with
this for example, a version of this experiment
is.
So, again this is similar two bacteria;the
wild type and this bacteria which does not
have this chemoreception TlpB, but now you
introduce two two signals.
Earlier you just introduced urea, now you
introduced urea plus HCl hydrochloric acid.
So, it so happens that urea is an attractant
which means bacteria try to move towards the
source, HCl is a repellent ok, so it tries
to move away from it.
And so what would happen for the wild type
what would you guess.
So, if I introduce this pipet here and this
pipet introduces urea plus HCl; one of which
is an attractant the other is a repellent,
what would the bacteria tend to do?
any guesses, huh stay where they are, stay
away.
If you had a lot more attractant then and
very very little HCl, would it still trying
to stay away .
What it does?
So, its difficult to sort of a, what it does
is that it sort of tries to come to this source
until it reaches some sort of a critical radius
and then it sort of turns back away.
So, it does not really complete its journey.
So, let me see I can clear this ah.
So, here I introduce the pipetwhich is injecting
this urea plus HCl.
And 
you see that the bacteria does not come close
to the pipet, but not does it go far away
from the field of view as well.
It comes until a certain radius somewhere
over here and then it sort of reflects back.
You can change the radius to which it approaches
by changing the ratio at which you produce,
at which you inject urea plus HCl.
The more urea you give so the more chemo attractant
you give the closer it will approach.
The more chemo repellant you give the further
away it will get.
Whereas, for the other one that delta TlpB
the mutant version of that only the repellent
is sort of , because this the mutation is
delta TlpB when this TlpB chemoreception only
senses urea.
So, it cannot sense the urea, but it cannot,
can sense HCl, so all of that gets, all the
bacteria tend to move away from the source
let me see if I can yes.
Sirwhat will be on the ratio you (Ratio Time:
09:47) absolute value .
The ratios if I remember correctly.
So, if I increase both urea and HCl by a factor
of 2, I think the radius to which it approaches
remains the same.
So, if youif you look at thisthe second panel
of the movie which is delta TlpByou will see
that.
So, this TlpB, because it senses only the
the urea.
The receptor for the HCl is a different receptor
I have forgotten its name, but that is still
there in the mutant version . So, all of those
bacteria would sort of tend to go away ah.
So, you will see that the whole field of view
will become clear, there will be you will
see almost no bacteria after some amount of
time.
So, in the second panel all the bacteria have
sort of moved away, because its sensing the
HCl, but its not sensing the urea because
that particular receptor is absent.
So, this is the cell signaling problem, how
to cell sort of sense signals and again there
is something will look at in the next class.
So, here is still images,these are still images
of that.
So, for example, for this 50 milli molar plus
5 milli molar HCl plus 5 milli molar urea
you can measure a sort of depletion zone where
there are no bacteria enters of around 60
microns and then you can change that.
Whereas, for this delta tlpB at the whole
field of view is cleared because it only senses
the HCl ok.
So, we look at this next class ok .
So, let me come to this question that let
us say things are diffusing ok.
So, we we are since we are talking about diffusion,
let us say objects are diffusing in some context
. I have some cell and in, I have some cell
and maybe in that cell I have a protein and
that protein is happily diffusing away ok.
To produce any sort of quantitative predictions
what I need is an estimate of what this diffusion
constant D is going to be right preamble.
So, its the motion of this object is described
by the diffusion equation del rho del t is
D nablus del square rho and how fast or how
slow it diffuses that is measured by the diffusion
coefficient; that is measured by the diffusion
coefficient .
You could try to if you knew the size of this
protein, could you estimate what the diffusion
coefficient would be?
what is the Einstein's relation in terms of
the size of a size of an object, what is D?
yes that is right kbT by 6 pi eta R right
and you can of course, use that for a sort
of first estimate.
The problem often is that determining this
eta is often problematic, because the inside
of a cell is not water, its in fact, a very
complicated viscoelastic sort of medium.
So, you can try to measure the diffusion coefficient
of these objects directly and that is what
I will that is one there are many such experiments
which do thisfrap, which is this thing fluorescence
recovery after photobleaching which is the
slide.
There are others for example, so this is a
method called fluorescence recovery after
photo bleaching which is called FRAP, FRAP
which is what I will talk about.
There are other methods for example, through
fluorescence correlation spectroscopy FCS,then
there is something which is called FLIP which
I have forgotten the full form of, they are
roughly similar principles.
So, I will describe one of the simplest which
is called FRAP and simplest and yet used a
lot ah.
So, what what is the basic idea of this FRAP?I
will play the video later.
So, here is what we do ah, let us say this
is my cell okwhere I have some sort of fluorescent
protein.
So, maybe I have tagged GFP tagged which is
a green fluorescent protein to my protein
of interest.
So, all my proteins of interest are fluorescent
green light ok
What I do is that, I shine a laser, a very
intense laser on a small region of this cell
ok.
What that does is that it photo bleaches the
fluorescent molecules.
So, if you think about a fluorescent molecule
that has a limited number of photons it can
emit ok.
So, its continuously emitting photons and
that is why you are seeing the light, but
overall it is some limited number of photons
it can emit.
So, if we shine very intense light you cause
all the photons to be emitted and that molecule
becomes dark ok
So, what you do is that you shine a very intense
laser light on a small patch, what that causes
is that the fluorescent molecules in this
region become dark, they do not fluoresce
anymore ok, now you wait.
So, this is my start of the experiment when
I have when I do this this is called photobleaching
ok ah.
So, then I wait what happens is that fluorescent
molecules which are outside this bleached
region they will tend to come inside right.
So, if you wait long enough, so you will see
that again there is an uniform fluorescence
everywhere right.
So, when you, so this is now that this is
a cartoon this is the actual cell.
So, this is pre- bleach where you have some
fluorescent intensity.
Now you bleach a particular region and that
becomes dark and then as you wait fluorescent
molecules come in from the rest of the cell
into this region and then if you wait long
enough you will get again some sort of a uniform
fluorescent intensity.
You can measure how long it takes for this
recovery process and that will tell you how
fast this molecule is diffusing right.
So, that is the basic idea yes .
.
So, by bleaching I mean that I take this fluorescent
molecule and I strip away all the photons
away from it, so that it cannot fluoresce
any more ok.
So, .
.
So, you shine a very intense laser light ok.
When you shine that laser light, so generally
what you do is that you shine a low level
light and you observe this proteins you shine
a very intense light all the available photons
that were there in this protein they are all
emitted ok.
So, now it has no more photons left to emit,
so it becomes dark.
So, that is what I call that a photobleached
a molecule ok.
And then I wait that is called the recovery
period and I see how fast it recovers, how
fast it recovers fluorescents simply because
there is other molecules which are outside
the bleach region they are coming back into
this region.
So, here for example, is an experiment, this
is on a sort of very elongated, I think this
is an E. coli cell I am not sure, you bleach
this region.
Now, you will immediately see the differences
between this and this.
For example, here this boundaries of this
region were very sharp right.
Here in an its quite sort of diffused, there
is not a very sharp boundary, but this is
the region where you shine the laser light,
the laser light has some width basically the
intensity drops away that there is an intensity
profile.
So, for example, let us say you have a Gaussian
intensity profile for your laser which means
all molecules here are completely bleached,
but maybe only a small percentage here are
bleached, all right
So, initially what you see is a dark, the
maximum dark is in darkness is here and slowly
it becomes white means which means that this
is outside the fluorescent region.
So, this point I bleach thisbleach this protein
and then I wait.
As I wait it sort of recovers fluorescence
until it becomes an uniform whiteness throughout
ok.
I can quantify thisI can quantify this fluorescence
distance, so this is as a function of distancethis
is fluorescence different starting from this
end and traversing the length.
So, its the fluorescence difference is maximum
at this middle point where you have bleached
and then again it falls away.
So, this is immediately after photo bleaching
and then as you wait, it sort of flattens
out and flattens out until it becomes completely
flat.
So, you can you can measure the dynamics of
this fluorescence recovery and you can use
this to sort of say what is the diffusion
coefficient of these molecules.
So, that is what we will try to work out.
And I will do the simplest possible case which
is a 1D model.
You can generalize it to 2 D or 3 D models.
So, 1 D model of FRAP fluorescence recovery
after photo bleaching .
