Hello and welcome to today’s lecture.
So, in the last class we were discussing how
to go about quantifying or characterizing
the properties of ECM networks and in that
regard, we had the you know introduced the
terms of rheology which is the field of that
study is how materials deform when subjected
to force.
We had also discussed for the different types
of deformation we can impose on a material.
So, these include tension, compression, shear
and bending.
So, tension, compression is very clear bending
is where instead of something straight you
exert forces so that the final configuration
is something like this.
And shear, we had discussed in great details
where if you have a block where you insert
tangential forces on the top surface as a
consequence of which the block deforms to
a shape like this, and this delta x, so delta
x by l this is my length l and this is delta
x this is what is given by your shear.
Now, we also said that how what is the difference
between behavior of a solid, perfect solid
versus a perfect liquid, and the main difference
is for a solid you write down this expression
well shear stress is given by G times gamma,
G is called the shear modulus and, G, for
incompressible materials we have shown that
Young’s modulus if elasticity.
So, this is shear you can write sigma is equal
to E epsilon for normal stresses.
So, E is given by 3 times G for incompressible
materials.
So, tau is equal to G gamma for solids, and
for liquids you have Newton’s law of viscosity
which is tau is equal to mu into du/dy and
what is du dy.
So, du/dy is nothing, but d/dt of dx/dy.
So, dx by dy is nothing, but the definition
of shear which is gamma.
So, this is nothing, but d/dt of gamma this
is equal to gamma dot.
So, this equation is same as writing tau is
equal to mu gamma dot.
So, the main difference is in a solid tau
is proportional to shear for a liquid tau
is proportional to shear rate the constant
of proportionality here is the shear modulus
the constant of proportionality here mu is
viscosity right.
So, for tau is equal to mu gamma dot, mu is
viscosity and we showed so units of mu is
Pascal.second in mks units, and in CGS units
we call it as poise or simple P, we write
it as simple P. So, mu of water is one centipoise
at room temperature.
So, also important to say that mu has a dependency
on the temperature.
Now for materials where mu is constant independent
of shear rate this is called a Newtonian fluid,
mu is constant and does not change with gamma
dot.
So, I had shown this slide in last class saying
that ECM networks are viscoelastic.
So, as opposed to let us say this is my stress
strain curve for linear elastic materials
my stress strain is linear, for non-linear
elastic materials, so this is non-linear that
is E is not constant and here E is constant
why because the slope of the line is E.
For viscoelastic materials like ECM networks,
this is a simple example of how the stress
strain curve would look if you make a collagen
gel and put it in a uniaxial tester which
kind of keeps on pulling it repeatedly.
So, what you see is so the repetition is corresponds
to the cycle number and what you see is the
path by which it follows in the stress strain
curve when you exert when you stretch it and
when you relax it is different and also the
average slopes of these lines keeps on increasing
with the increasing passage of cycle number.
Suggesting that there are some dynamic rearrangements
which happen.
So, this is what we want to focus now as to
what are those attributes of an ECM network
which dictates is functional properties.
And you would remember this picture I drew
from last class saying that the scaffold that
you create in terms of its organization here
I have drawn one as random and one has aligned
these have robust effects on how cells process
these cues.
So, for example, on a random matrix cells
will tend to migrate in a random fashion without
any persistent motion.
While on an align matrix like that the cells
will not only stretch itself along the alignment
direction of these fibers, but also tend to
migrate along these aligned fibers taking
them as a directional cue.
So, how do we characterize the properties
of these random versus align matrices?
And what I suggest is the properties of these
collagen scaffolds depends on two things cross:
linking and alignment.
So, alignment is very clear in this, but for
the same network.
So, imagine I had raised this analogy of cooked
chowmein right.
So, when you try to extract one strand of
noodles from the entire bunch, so this does
not come out so easily even though there is
no chemical glue which is bonding them together
there is relative friction ok.
So, even a random network will exhibit some
resistance, which means it has some bulk stiffness.
But if I for this random network let us say
I had this random network in one case if this
network is just that these fibers are put
together and I exert force on this fiber.
So, I will lead to a configuration, but this
might slowly come out of this network leaving
the remaining two fibers like this.
So, in this case the properties of the network
will change dynamically versus if you had
fixed all these points together in other words
you had cross linked the network then when
you exert a force here this gets transmitted
to the entire network.
So, the network resists that force as a whole.
So, the response that you would observe for
such a network is drastically different if
it was not cross-linked purses it was cross-linked,
similarly, the case of alignment.
So, what would be an equipment with which
we might be able to probe these properties
note that these networks are super soft.
So, typically a collagen network might have
a stiffness order of 1 kPa.
So, this is super soft.
So, you cannot use traditional instrument
used in material science like indentures which
can only probe the material properties of
stiff materials.
So, that brings us to what we called a rheometer.
So, what is the rheometer?
This is a picture of a rheometer where you
have a sample which is placed between two
things one portion of switch the bottom portion
of switch is fixed and the top portion of
switch is rotated.
So, imagine a mortar and pestle in which the
top thing you keep on rotating.
So, if you put a sample in between when you
exert this rotation the sample is essentially
being sheared.
So, you can essentially probe its shear properties
shear modulus and if you knew the poisons
ratio of the material you can backtrack what
is the Young’s modulus of elasticity.
So, several things I wish to say about the
rheometer.
So, you have what you can do.
So, you can do two things first is you can
change.
So, you have this set up where you have a
sample.
So, this one you are rotating.
So, you have control over the rate at which
you are rotating you have also control over
how much you can indent, you can push into
the sample.
So, this is called, so this is your imposing
a strain with how much your pushing the sample
and your controlling the amplitude of rotation
the frequency of rotation.
So, strain amplitude is one thing we are controlling
and we are controlling the frequency.
So, again for a pure solid we have T is equal
to G gamma for pure fluid we have T is equal
to mu gamma dot.
So, in general if I were to apply an oscillatory
field, in other words I can write if I were
to write gamma as gamma naught sin of omega
T if you exert an oscillatory strain then
your stress field can be written as sigma
0 sin of omega T plus delta.
So, if you expand this equation, this sigma
is then written as gamma dot into; so it has
two components G prime sin omega 2 and G double
prime cos omega T this term G prime is called
the storage modulus.
So, G prime and G double prime is called the
loss modulus.
So, if I were to pictorially depicted you
would have a curve like this.
If this is your gamma function you have a
phase shift this is what delta is, this is
gamma and this is sigma this is time.
So, you have one component, so you have sigma
is equal to gamma dot into G prime sin omega
T plus G double prime cos omega T. So, you
have this component which is in phase with
the applied strain field which means that
as soon as you exert the strain immediately
the material deforms.
So, G prime or the storage modulus corresponds
to the elastic component this corresponds
to the elastic component and it is called
the storage modulus because this energy can
be retrieved when you release it you again
go back to the original configuration.
The G double prime is the viscous component
and hence it is called the loss modulus because
this is dissipated, this is dissipated.
So, how, as I said that when I make this ECM
networks what can I say about G prime and
G double prime.
What is known in the literature and has been
shown by many groups that if you make gels
of various concentrations.
It means that if you vary the concentration
that say 1 mg per mil 2 mg per mil etcetera.
So, your G prime will scale as concentration
cubed, x is roughly 3 for collagen gels, for
collagen gels G prime will scale as concentration
cubed which means that in order to stiffen
a matrix you can increase its concentration;
however, since cells directly bind to this
material when your changing the concentration
your changing the bulk stiffness, but at the
same time you are changing ligand density.
So, this is one problem of working with collagen
gels if you want to probe the independent
effect of ligand density keeping stiffness
constant that is why people tend to use synthetic
substrates where they can control its stiffness
and then independently functionalized ECM
proteins like collagen onto those substrates.
So, this is one aspect, other aspect again
coming back to the linear versus you know
non-linear materials.
So, what I have shown here is how cells would
spread on materials of different stiffnesses
if it was a linear material, linear elastic
material case of polyacrylamide hydrogel or
a non-linear material.
So, what you see of cells spreading in linear
materials is that when you increase the stiffness
cells spread more and more and beyond a certain
threshold there is no change in cells spreading
it saturates.
But if you take a non-linear material no matter
what concentration you start from whatever
is this initial stiffness you see that the
cell spreading does not have any dependents
on stiffness.
So, suggesting again that there are these
rearrangements which can happen which can
drive this increase in stiffening.
So, this is saying that whatever be the starting
stiffness when you put cells on it which pull
on these matrices the matrices deform and
becomes differ in the process.
So, this is called strain stiffening, this
is called strain stiffening and for fibrin
similar to fibrin collagen gels also have
been shown to exhibit this profile.
So, if I plot the storage modulus as a function
of strain what you find is at a given concentration
first your storage modulus is constant and
beyond a certain strain it starts to increase.
So, it becomes non-linear in nature ok.
So, this phenomenon is called strain stiffening.
And then the red line, you have another variable
because we are called just by the concentration
alone, but playing with the concentration
alone you can get more and more stiffening
also.
So, that is why the red curve is above initial
again flat and then it rises.
So, you see that there are two independent
ways in which you can in which cells can different
collagen gels.
So, first is for a given ligand density just
by exerting forces the gels becomes stiffer
and stiffer, and the other is that just by
playing with the concentration alone you can
generate materials of difference differences.
So, this brings us to the question that what
is driving this behavior of strain stiffening
and what it turns out is as I was drawing
before when you have increase in strain then
individual fibers tend to align along the
direction of strain.
So, as opposed to having a network like this
when everything gets aligned then the fibers
then the effective stiffness increases in
that direction.
So, an isotropic thus stiffness is an isotropic
invention in one direction it is very stiff
and it can be experimentally probed by shaking
the orientation of fibers within a gel.
So, if I take a collagen gel let us say where
you have fibers in all directions and I align
them actually I pull this matrix along the
long axis.
So, if I draw the average orientation as a
function every orientation of fibers what
I will find is, I will find a uniform distribution
a normal distribution, which suggests that
there is equal propensity to find fibers which
are oriented in one direction or the other
direction, but as I align more and more.
So, as I align more and more you will see
they will generate this kind of geometries
eventually where everything is aligned in
one direction.
So, your average axis, your average angle
will change and from here in this particular
case you will see that everything will align
along 0.
This is 0, close to 0 you will see everything
will align along 0.
So, this is what drives differing.
However, one of the things about this network
is if it was not cross linked, if it was not
cross linked when you remove the force the
alignment of these fibers remains in the final
configuration.
So, from here you do not go back to this configuration.
So, how would you do that and the way to do
that is essentially cross linking.
So, the way to do this is to cross link it.
So, when you have two fibers if they are cross
linked at this point when you tend to force
along this direction they will align, but
as soon as you remove the force they will
come back to its original configuration.
So, this suggests that you can do these experiments
in which you can track the angle distribution
as a function of pulling and as a function
of cross linking.
So, you will see that if it was an uncrossing
gel that you made your angle evolves and then
stays put as the final configuration, but
if you take a network which was cross linked
wanting to see that if it was 100 percent
crosslinked, first it will even its basal
stiffness will be increasing, the other thing
is it will keep on returning to the same position.
So, if you do it 
in an oscillator way, let us say what I am
doing is I am doing it in a Sin wt fashion.
So, my strain is some gamma naught into sin
wt along the accesses.
So, what you will see is the angle distribution
will keep on changing like.
So, let us say your angle increases and when
you really release at this point you release
relax the angle will keep on coming to the
same position again you increase.
So, this in this stage you stretch here you
relax.
So, your angle will keep coming back to the
same configuration after you remove.
So, that is about it for our discussion of
collagen and their material properties.
I would ask you to read these two papers - one
on which and how cells can sense non-linear
stiffness and how they change their properties
in response to non-linear stiffness and the
other one this paper, the other paper is about
this orientation and effect of cross linking
and alignment on these fibers.
So, both these papers are in; have been published
in plus one which is an open access journal
which means that you can download these papers
anywhere you do not need any special access
to be able to download these papers.
So, in this course I will give you reading
assignments in which I would recommend you
to read certain papers.
So, it is mandatory if you want to follow,
if you want to follow up of what we are doing
in class then it is mandatory that you 
read these papers even the quiz questions
that will be asked in the course will be posed
from these particular papers and the content
which has been covered in the class.
So, that brings us to close on our discussion
about collagen, we would discuss about one
more protein, so I do not have much time today
I will just introduce this protein is fibronectin.
So, fibronectin is a protein which has dimers
of 2 similar polypeptides which are linked
by disulfide bonds.
And fibronectin has that RGD sequence which
is critical for cell addition, and that has
led to peptides, adhesive peptides of RGD
being alone used for sustaining cell spreading
or cell addition.
So, fibronectin is known to bind to collagens,
proteoglycans and other things, it plays very
important role in migration and differentiation
wound healing and it is secreted by many adherent
cells.
So, if I were to draw the structure of fibronectin
so you will have multiple units like this
and at the end you have these disulfide bonds.
So, these individual domains are referred
to as FN I, FN II and FN III domains.
So, you know for any protein which has multiple
domains for its function it folds into one
particular structure.
So, the question that I am going to ask is
how does folding of the protein participate
in regulating signaling and how does forces
influence the folding kinetics of this protein
and its role in subsequent function.
So, this 
is just to give you 
an intro to Fibronectin.
We will start discussing in detail about fibronectin
in next class.
Thank you.
