Welcome, today we continue our discussion on Protein Structures and just to recap on
what we done so far. Initially we studied about the different Ao Acid structures and
their properties. We considered the Hydrophobicity as the most important property of the ao acid
and constructed hydropathy plots to detere which regions of the Protein ao acid sequence
are actually hydrophobic in nature, which would occupy the core of the Protein.
Then we considered where not to the Protein hierarchy meaning the different structural
properties of proteins from the ao acid sequence to the final quaternary structure which some
proteins adopt. Then we considered the Secondary structure elements which may be the Alpha
helices and the beta sheets and their different properties as to how they interact and what
are their specific features be at the backbone or the hydrogen bonding properties. And then
we constructed a helical wheel and to figure which regions of the a-helix would be facing
inside the surface of the protein. Finally we went to the certain properties of the proteins
and predictions of secondary structures.
Now we know something about Proteins. We have to consider the different classes of proteins
that are formed based on their structure and solubility. Initially we have gone though
some of these, for example if we look at Mioglobin where it is a Globular protein so it is more
or less shape like a Globule which is the case with the most proteins.
Now we understand that we will have hydrophilic residues on the surface and we will have hydrophobic
residues within the core which tend to remain away from the solvent as far as possible.
Here you can see the structure of the Heme. Here We have Membrane Proteins on the right
hand side, as we studied earlier the Membrane Proteins are embedded in phospholipid bilayer
that forms the cell membrane. And we have studied about the Transmembrane helices and
we also did hydropathy plots to figure out how we can actually detere which of these
helices are, where they are going to spam the membrane.
We also learned that it is likely to have hydrophobic ao acid residues on the surface
of these helices so that they can interact with the hydrophobic tales of these lipids.
There is another class of proteins that are Fibrous proteins. From the name itself you
can figure out what thus construction of it will be, they are more or less fibers. And
they are adopted to give strength to the structure of the protein. So what we have in fibrous
proteins is as you can see here you can have a single a-helix or you can have a coil of
two helices or you could have a triple helix.
So here the interactions would result in a fiber. These long fibers or large sheets that
are actually formed our parts of structures that required mechanical strength. a-Keratin
and Collagen are two such examples of fibrous proteins. For example you can find them in
hair or in muscles because of their strength or because of their structure. And because
of they are fibrous in nature they form as long parallel structure along a single axis
so they give this longitudinal structure and they give a mechanically strong nature to
this.
For example a-keratins, they are found in hair and their sequence consists of long alpha
helical rod segments. ß-keratins which we can see here are formed as ß- sheets, they
are found in silk which is also a fiber. But over here if you look carefully, you can see
Alanine and Glycine repeat sequences as they are called.
So you can have alternating Glycine and Alanine. The reason being is that they are small in
size and they can be accommodated in the ß-sheet structure of ß-keratins. So the a-keratins
are the ones that forms the alpha helices, ß-keratins are the ones that forms these
beta sheets that consists of a Gly Ala repeat sequence. And in the a-keratins that are found
in hair we will see longitudinal parallel alpha helices that give mechanical strength
to the fibers that are found.
Now considering the Globular Proteins, usually they are classified according to the type
in the arrangement of the Secondary structure. So what you find is you will probably see
anti parallel a-helix proteins that consist of only alpha helices. You might find ß-sheet
proteins, you might find a + ß or a/ß proteins. There are different types of nomenclatures
depending on how the protein actually looks.
So in this case you would have a largely alpha helical protein. For example when you look
at a Globular Protein you are looking at essentially the globular structure of the protein. Now
if you look at this case these are all globins, they are all globulin proteins. This one is
from plant, the middle one is from the insect and the last one is from a mammal.
What do you notice here? You notice that each of them have very similar structure. The reason
being is they are going to perform the same function. So whether it is from a plant or
an insect or a mammal these globins perform similar functions because they have similar
structures.
now today what we mean to study is what keeps the structure together because now we know
that the only types of covalent bonds that we have in proteins or the linkages between
the ao acids that give the peptide bonds and the disulfide linkages that are covalently
linked together which can bring different parts of the chain together.
Now we also know the alpha helices and the beta sheets that also bring parts of the structure
together and they are connected by the hydrogen bonds but not by covalent bonds.
So now we need to know what the forces are going to drive protein folding. Because now
we do not have polypeptide chain anymore we have only a folded protein structure. And
what we need to know is how this protein folded structure is found.
Here there are certain terologies that we have. In which one is called hydrophobic collapse.
This means you know the core of the protein is hydrophobic in nature so it may so happen
that initially when the polypeptide chain is formed then there is a hydrophobic collapse
which means there is a hydrophobic core formed first and then the rest of the protein chain
will gradually forms alpha helices or beta sheets or interconnectors such as are loops
or turns to bring about the structure.
So initially you will have a collapse, the polar surface is going to interact with the
solvent. And we will have gradual formation of the alpha helices. There may be another
case where the alpha helices are formed first. So first they would be local interaction followed
by gradual collapsing of the overall structure.
Here what you are looking is for imum volume where you do not have very large cavities
because that would open up the protein. The Disulfide bond formation will stabilize the
protein because it will bring different parts of the polypeptide chain close to one another.
Then you have Hydrogen bonds which will bring different part of the protein structure together.
Again we have polar electro static interactions. Then we will consider how actually form these
ionic interactions or other polar type hydrogen bonding between ao acid residues.Now what
we have is an unfolded form that was the polypeptide chain and we have a native folded form of
the polypeptide chain.
If we look at the hydrogen bond see how it stabilizes the interactions. For example in
alpha helices and beta sheets you recognize that here we do have a lot of hydrogen bonds
and what happens is the accumulation of these hydrogen bonds renders a large amount of stability
to the protein. Because you have not just one hydrogen bond you have a series of hydrogen
bonds both in alpha helices as well as in beta sheets. And also you can recognize that
in anti parallel case the hydrogen bonding is between similar ao acid residues.
And what happens in the parallel case is they are between different ao acid residues. So
what are the structure stabilizing interactions? The Covalent Interactions but now we also
know that we have these Disulfide bonds which are actually formed from the link of two Cysteine
ao acid residues in forg a cysteine bond where we have this SS linkage. These can be very
far apart in the structure and bring the polypeptide chain close to one another.
So we would have a structure stabilizing interactions in the form of covalent bonds which are in
the form of disulfide bonds of Cysteine residues. The other cases are The Van der Waals forces
that are weak electrical interactions, they are transient in nature. We have hydrophobic
interactions where they are clustering of non polar groups together like we form hydrophobic
core of the protein. Then we have Hydrogen bonding. What do have in that case? We have
a donor atom that has hydrogen attached to it and we have an acceptor atom. We have hydrogen
atom that is sort of partially shared because of the acceptor atom and the donor atom having
partially d- charges and the hydrogen being d+ charges.
So now what are all these interactions? All these interactions are non covalent in nature,
there is no covalent linkage. But what happens is when you add up all these you will have
a substantial amount of energetic favorability for the folded conformation.
Now what do we have here is the hydrophobic collapse or a hydrophobic effect. When we
have the non polar solute then there is no possibility of hydrogen bonding because we
do not have any polar group or any group that can act as a donor. We should have a donor
and an acceptor. But in the case of a polar solute we see that there is a possibility
of hydrogen bonding .
So what would be expected on the surface of the protein is all these polar residues that
can interact with the solvent with preferentially be on the surface of the protein. However
the non polar solutes that have no such interaction with the solvent around it would tend to be
in the central part of the protein or rather in the hydrophobic core of the protein.
This is an example of a Structure Stabilizing Interactions. What do we have here? We have
an ion pair. An ion pair would link a Lysine and an Aspartic acid together. It is not always
possible for all the Lysines or all the Aspartic acids or all the Basic and Acetic charged
ao acid residues to be on the surface.
The reason being is that it follows a large hydrophobic region so that would tend to be
in the core. Then the Covalent bond is not going to break. But the Lysine is there so
what it is going to have is an ionic interaction or an ion pair formation with a charge of
an opposite kind in the protein chain itself. So that will effect the folding because the
Lysine is going to be looking for an Acetic ao acid residue closed to it so that it can
form this ion pair. So that is going to change the folding in a sense, it is going to effect
the folding. For say you had all of these hydrophobic in nature then the nature of the
folding would definitely have been slightly different than what you see here.
What do we observe here is a Lysine which is a basic ao acid residue have an ionic interaction
and ion pair formation with an Aspartic acid residue. This is a case where you can have
hydrogen bonding. Here we do not have an ion pair formation but we have a donor that is
Serine and we have an acceptor that has the carbonyl oxygen of the amide group of the
Asparagine.
So this would be the formation of a hydrogen bond, this would be the formation of an ion
pair. Both of these are extremely important in forg a final protein folded structure.
Now, we are considering the energy terms. We lets just look at what energy terms we
can have. If we are looking at energy then we can have the total energy can be covalent
or we can also have a non covalent component to this.
Now under the covalent ones we have normal bond formation that is going to contribute
so we have bonds. What else we have? There is a contribution from angles and there is
a contribution from torsional angles. So we have energy contributions from these three
components under the covalent set because these are formed from direct linkages. Under
the non covalent ones we have listed a hydrogen bond, we listed an ionic interaction and we have listed Van der Waals interaction.
So these are the three that we could have in case of a non covalent formation and these
are three that we are going to have in case of covalent bond formation. And sumg these
together we are going to get the total energy.
Now what we do we want this total energy for the protein to be? We want this to be a imum.
So we have a stable structure. So we have to get an imum of total energy which is going
to result in a stable structure and this structure is a final native folded form of the protein.
Now what are these in terms of energetics? If we look at the bonds, how do you represent
bonds normally for a compound? You represent them as springs. So in case of bonds we represent
these as springs and they follow Hooke’s law. The Hooke’s law is when you have two
masses connected by a spring they are going to give some energy. So that is this energy.
What is this energy due to? It is due to stretching energy, this follows Hooke’s law. Here r
is the variation that you will get because the bond is not going to stick to one specific
distance. It acts like a spring because it is going to form certain interactions. So
it has to acts like a spring where it is going to have some favorable interaction which will
try to adopt or it will have some unfavorable interaction which is trying to get away from.
So what do we have here is we have covalent in which we have a bond and this bond is going
to give us an energetic contribution to the total energy in the form of Hooke’s law.
We have a Bending for the angles that is going to contribute to the energy also. These are
called energy terms that is added to the total energy that the protein is going to have.
Now you understand that this is going to get extremely complicated if you want to do a
computation because the number of atoms is huge. But nevertheless these are the components
that found the total energy. Then we also have the Torsional energy. You need to know
what the contributions are. You need to know that the covalent terms are come from the
Stretching, the Bending and the Torsional. Then we need to know about how the non covalent
terms are going to come. In these we will have an ionic interaction, we are going to
have a Van der Waals interaction and we are going to have hydrogen bonding.
So for Van der Waals interaction all of you know about Leonard Jones potential curve where
we have an attraction due to the negative part of this. This is called as a six twelve
potential where we have a contribution for attraction and a contribution for repulsion
because you know that these atoms have repulsive force acting on them when they get too close
to each other. Then we have the Coulomb interaction which is due to the ionic interaction between
the two ion pair formers.
Finally we have the hydrogen bonding. So this is another feature where we have the hydrogen
bonding and again we have ten twelve potential in the case.Here we are about the total energy
that a polypeptide would have based on its energy terms? Now what are these energy terms?
We have energy terms contributions from the covalent component and contributions from
a non covalent component.
The covalent component is comprised of three parts and these three parts you have to remember
from the name itself. These are covalent because they are directly linked. You have to remember
that if we are talking about a spring means the two atoms are directly linked to one another,
if we are talking about an angle bending energy these are linked to one another, if we are
talking about a torsional energy the atoms are linked to one another. But none of them
are linked in a non covalent formation. I do not have any bonds linking the two atoms
that have been drawn in the non covalent set.
So when we are talking about a covalent contribution we are talking about energy contribution from
the parts of the protein structure that are linked to one another in which one is the
bond, second is the angle and the third is the torsional part. We have the Van der Waals
interaction, the coulomb interactions and the hydrogen bonding for the non covalent
set.
If we look at the interactions and their approximate bond strength in kJ/mole you will see that
Covalent bonds are extremely strong, Ionic bonds are 20 to 40 kJ/mole, Hydrogen bonds
are approximately 5 to 10 kJ/mole, hydrophobic interactions are 8 kJ/mole and Van der Waals
are approximately 4 kJ/mole. But when we consider the combination of the large number of hydrogen
bonds, Van der waals, hydrophobic interactions that are possible they are add up together
making it a strong folded structure because of the multitude of interactions that are
possible.
Now what I have listed here is an energetic contribution. Suppose you have to do a calculation
to figure out what the total energy of a protein was then you would use a force field. Since
we consider the different energetic terms, I just want to emphasize here that when you
are calculating the total energy you have to find the summation of all the possible
variations from equilibrium bond length for bonds.
So now we are looking at all the possible covalent interactions the bonds, the angles,
the dihedrals. In this is case this is a very crude one because here I have not considered
hydrogen bonds. What do I have here is this is for Van der Waals and this is for Coulombic
interactions. but here I am missing out hydrogen bonds because you understand that when you
are doing a computational calculation it is going to be extremely difficult to try and
calculate all the bonds because as soon as you form a dipeptide you can recognize how
it is going to change or increase the number of bonds, increase the number of angles and
increase the number of dihedrals.
So we have an extremely large number as we go from a single ao acid to a dipeptide to
a tripeptide. If you consider even the smallest protein that would have approximately thirty
ao acid residues would be extremely difficult to compute. Because you can understand the
multitude of interactions that are going to form based on the number of atoms that the
protein is going to have.
So we have a final native structure. What is this native structure? We have a well defined
3D structure, it has a specific function and we remembered we spoke about the specific
Isoelectric point due to the type and number of ao acid residues it has.
So what are we going from? We are going from a relatively unfolded structure to a folded
structure. So basically I spoke earlier about levinthals paradox where they were a multitude
of open conformations that was possible for the polypeptide chain but it forms the single
native structure. So what is happening now is when it forms the native structure we have
all these interactions that are taking place which are hydrogen bonds in the alpha helices.
Hydrogen bonds between the strands of the beta sheets. Then we can have the other interactions
that are going to form the covalent interactions are disulfide interactions, hydrophobic interactions,
Van der Waals interactions and other Electro static and Coulombic hydrogen bonds and all
others between the different ao acids in the protein
Now we will consider the Thermodynamics of protein folding. If we consider an initial
and final state, what do we have is a ?G. What is this ?G? We want to find out the free
energy change due to folding of the protein. So initially we had an unfolded state that
is G initial. Then we have a folded state so that is G final. So how we find the ?Gfolding?
We know that the G final which is Gfolded us G initial which is Gunfolded. We all know
that ?G is ?H – T?S.
So I have a ?Hfolding - T?Sfolding. So the ?Hfolding is again going to be the H final
us H initial so it is Hfolding - Hunfolding. Now I am doing this at a particular temperature
so the temperature here is constant.The ?S are Sfolding - Sunfolding because the unfolded
is again my initial state and the final is folded state.
Now we are going to look at the specific terms of these. What happens to the ?S which is
Sfolding - Sunfolding when I consider the entropy. We know the entropy is the disorder
of the system. If I have an unfolded protein and now I am having the protein fold I am
bringing ordered into the system. Now if I will bring order into the system then will
be ?S is negative it is not positive any more because I have ordered the disordered polypeptide
chain into an ordered folded native structure. So the ?Sfolding is negative. So what happens
to T?S? Therefore -T?S is a positive quantity because my ?Sfolding is negative. So -T?S
is a positive quantity which is I have drawn here.
So if we look the energy on the Y-axis and just this axis is the energy axis here. We
have an unfolded form here and a folded form here. Now obviously the entropy of an unfolded
form is going to be much more than entropy of a folded form. So the overall -T?S is going
to be positive but the enthalpy or the folding interactions that are found are all favorable.
Because the hydrophobic interaction is going to be favorable, a hydrogen bond is going
to be favorable and ionic interaction is going to be favorable.
But what is not going to be favorable is if I have a specific hydrophobic interaction
trying to make with the solvent. That is going to give an unfavorable situation. But for
most of the cases in the folded protein I am going to have a large number of interactions
contribute to the enthalpy and this multitude of interactions which makes this a high negative
number.
So what happens is these more or less compensate one another and I eventually have a favorable
?G of folding. We have a ?G of folding and ?G of folding is going from an unfolded state
to a folded state. So I have to consider in the thermodynamic quantities ?Hfolding - T?Sfolding.
I know that the entropy of a polypeptide chain in the open form will be much more than when
it will be in its closed folded form. So the Sfolding is negative which makes my - T?Sfolding
is a positive quantity. Then I have ?Hfolding which compensates for this positive ordering
of the system because of the large number of favorable interactions that are formed
on protein folding. And we have a ?Gfolding that is a small negative quantity which means
that this is a favorable spontaneous process. So I am going to get from the unfolded form
to the folded form in a spontaneous process because the ?S is not going to make it spontaneous
it is the enthalpy that is going to make it spontaneous.
Now we move on to the Thermodynamics of the Protein Folding. If we have considered the
?Gfolding we have the initial part which is an unfolded part and the final part which
is the folded part.So when we are considering the ?G we go from an initial unfolded form
to a final folded native structure. So the ?G is G final that is Gfolded us G initial
that is Gunfolded. If we consider the form of ?Hfolding - T?Sfolding we recognize that
we can also open up these into the initial and final components. So the ?Hfolding is
going to be H final that is Hfolded us H initial that is Hunfolded. Similarly for ?S we can
have Sfolded - Sunfolded.
Now we considering the entropical considerations if we go from an unfolded form which is disordered
to a folded native conformation so the entropy contribution ?S will be a negative quantity
because we are ordering the system. A positive quantity is when we have more disorder. A
sciatic situation would give you favorable entropy. But we are bringing order into the
system because we are folding the polypeptide chain. So our ?S is negative so -T?S is a
positive quantity which is what we have here it is positive in its energy contribution.
But the ?Hfolding is a negative quantity due to the different interactions that give favorable
energy to the folded conformation. We have this positive energy which is due to the entropical
considerations compensative by the enthalpy due to the large number of interactions possible.
So the over all ?Gfolding is very small but negative quantity meaning that you have favorable
spontaneous folding from the unfolded to the folded native protein. Now we will consider
the native state and the denatured state, this is in an equilibrium situation. The beginning
of the proteins begins at N and it ends at C so here we have a disordered orientation
which is also called as an unfolded state or a denatured state and we have a native
state in this case.
So if we have a ?G associated with it then we are going to have an equilibrium associated
with it. So we have a K that is -RTln[K], the K being the equilibrium between the denatured
state and the native state. So the stability of the native state defined as difference
in free energy between the native and the denatured states.
So what do we have in the native state? We have a compact structure, intra molecular
non bonded interactions. And the entropy significantly decreased because of the well ordered conformation.
What the features do we have for the denatured states? We have a non compact structure, we
have inter molecular non bonded interactions and we have a large ?S due to the large number
of different conformations.
All of these contribute to the ?G of the system, the ?Gfolding which is going to be a small
but negative quantity because we are going to have spontaneous folding from denatured
state to the native state. Now we will consider the different interactions
that we had. What were the different interactions that we had? We had Hydrogen bonding, we had
Electro static interactions, we had Van der Waals interactions and we had Hydrophobic
type interactions.
I can denature the protein if I add certain denaturants to it or increasing the temperature.
We have to consider that the disrupting the actual interactions that were holding the
protein folded together in the process of denaturing.
So if I look at all the different conformations that I had so if I had a protein helix structure
and I had some sheets then in this folded structure as I add a denaturant say I add
Urea where Urea disrupts the hydrogen bonding. Now if I disrupt the hydrogen bonding of an
a-helix what is the eventually going to do is it is going to open up the helix because
the hydrogen bonds that were present here would preferably found with urea. So urea
sort of gets into the protein structure disrupts the interactions that were holding the folded
or the protein polypeptide chain together.
Now what happens if I heat it? Again if I heat this, for example you know that if you
heat albu like egg what happens you form a solid mass. Basically what you are doing is
you are denaturing the protein. So if you have a solid globular albu structure when
you heat it up so you are decreasing the solubility or aggregating it because you are opening
up the polypeptide chain. You will have this mass form by opening up the polypeptide chain.
And so each of these structures that are supposes to look identical are opening up into a denatured
form forg a solid mass of aggregate. And you have now a denatured protein. This is a denaturation
due to the temperature. So here essentially what we are doing in protein denaturation
is we are disrupting all the interactions that were possible. And these interactions
were Hydrogen bonding, Van der Waals interactions and Ionic interactions.
We can be denatured the Proteins by increasing the temperature. We can also add different
denaturants for example we could add Acid or we could add urea or we could add Guadinium
Hydrochloride. What is acid going to do? How is acid going
to change the components? How is going to disrupt the interactions?. So if I add Acid
means I am adding H+. What happens when I add H plus? For example all the groups are
acidic groups which comprise for example Aspartic acid or Glutamic acid so what is going to
happen to them is they will get protonated. So if they get protonated on addition of acid then we will get this.
Now if this Aspartic acid or Glutamic acid happens to be involved in ionic interaction
with say Lysine then it would disrupt the ionic interaction. So now we are adding acid
to our protein. When we add acid to a protein any acidic group that had the free carboxylic
acid group in its ionized form would get protonated. And what happens is if this Aspartic acid
or Glutamic acid that could form an ionic interaction with basic residues they would
no longer form. Once I get into this form it is not possible for the ionic interactions
to form.
So any folded structure that would have this ionic interaction with an Asp and say Lys
what would happen is this would no longer formed so that would open the chain. So eventually
the idea here is that when you have a denatured structured you are disrupting the energetics.
Usually denaturation does not mean that you are disrupting the covalent bond formation.
So if you had a disulfide linkage you would not actually disrupting unless you would put
in same ß-Mercaptoethanol or you would have some other reagents that would break the SS
linkages because that you are remembered as a covalent linkages.
Also you are not breaking the peptide bond. The polypeptide chain is intact so what we
can do is we can go from a folded form to an unfolded form by denaturing the protein
by adding Urea. You can also renature the protein in some cases. So, what you would
have to do is you would have to remove the Urea if you want the get back here and in
some cases you can reform the Folded Protein.
So you are going from the native folded structure to an unfolded structure and you reform this
back. So this would be +urea and this is –urea. Here again you could form folded structure
back. So what we learned today was we learnt about the Protein folding, The Energetics
of Protein folding where we have Covalent and Noncovalent contributions where the Covalent
contributions comes from bonds anything that is connected that are bonds, angles, dihedrals
and Noncovalent contributions come from Ionic, Van der Waals, Hydrogen bonds. These all are
going to contribute to the Energetic of Protein folding.Then when we have considered the Thermodynamics
of Protein folding in which we have a ?G associated to the folding, we have a ?H associated to
it and we have a ?S associated to it.
So all of these fall under the per view of protein folding where we are considering the
Thermodynamics the ?G, the ?H and the ?S and we have an equilibrium consideration here
as well. We will stop here. Thank you.
We started discussion on enzymes. We have considered, what proteins are, we studied
protein structures, the constituents of proteins that are the amino acids and their properties.
What we are going to start today is a study on enzymes which will cover about 3 lectures
and we will be studying the enzyme mechanisms of a few enzymes which will be basically ribonuclease,
lisozymes and a cerin protease. As we go along, you will see what they mean. Now, you would
have heard about enzymes, you know that you need them in the body for digestive purposes
and you need them actually for any process that goes on in the body. So, whether it is
your respiratory process or your digestive process or whatever the other process is going
on, all of them are enzymatic processes. There are specific enzymes that bring about specific
reactions and we will see how specificity is extremely important in the way enzymes
act.
Basically, all enzymes are protein catalysts, that is there are catalytic in nature but
they are proteins. What we have here? You know about catalyst, what do they do? They
alter the rate of a chemical reaction without undergoing a permanent change in structure.
So, this is exactly what the protein is going to do also. It is going to change. We will
see how it exactly does that? It is going to change the rate of chemical reaction but
the protein itself is not going to undergo any change, even though it is going to bring
about a drastic change in the reaction. Now, this is a typical picture that all of you
have seen, a typical diagram that gives you the free energy of A+B, what are these? These
are the reactants and your p+q in these case are the products.
So, what do you have? You have delta G of reaction which is the G of p plus the G of
q minus the G of A and the G of B. It is g final minus g initial. This is your transition
state, your activation state that has to be or this activation barrier has to be overcome
to get you from the reactance to the products. Now, if you look at this as a specific nomenclature
that we have put here, which sometimes called as the dagger sign. So, we have a delta G
dagger that tells us that this is the energy of activation for the reactance to go to this
transition state. Now, if we have a catalyst, how does this reaction profile change?
It changes in such a manner that for the reaction A+B going to p+q, we have now a catalysed
portion of the reaction or a catalysed reaction in which our activation energy has decreased.
In decreasing, what does it do? The reaction is catalysed; it means that the rate has been
enhanced.
Now, K is for equilibrium always and k is always for the rate. So, we have a k for uncatalysed
reaction, I have a small k for the catalysed reaction. How do I determine it? All I have
to do is plug in the values here. Here A and if we consider the pre exponential factor
to be the same. So I have to be careful about units here which are kilojoules 8.314 and
by default we usually use 298. What about my catalyzed? A e- 46000/8.314x298 remember
to use the right R also 298.
So, I can find out, how the rate has increased for the catalysed reaction as compared to
the uncatalysed reaction. It turns out that this is approximately 5 into 10 to the 10.
So, what am I saying? I am saying that, when I reduce this energy of activation and increase
the rate, 10 to the 10, 10… basically. So, I have uncatalysed reaction and catalysed
reaction and then I have associated with it, the change in the rate due to the reaction
being catalysed. Whether the catalyst happens to be an enzyme or any other catalyst, it
is the same thing. So, what do we have here? We have our enzyme plus substrate and we have
our enzyme plus product. So, what is our catalyst? Our catalyst is the enzyme. If you notice,
what do we have in the beginning? In the first slide that I showed you, we had A+B going
to p+q. Now, what do I have here?
I have E+S going to E+P. So, what is my E? My E is my catalyst that is transforming the
substrate to the product but itself, is remaining unchanged. So, it is not like a normal reaction
where you have A+B going to P+Q, it is E+S going to E+P. E remains as it is in this reaction.
So, what do enzymes do?
They are certain quantities that you have measured, it is your experiment. What do you
know? You know the amount of substrate you have added. You know the amount of total enzyme
you have added. But you do not know at what time the amount of enzyme or substrate is
actually being formed. So, what you know is S and you also know the total enzyme concentration
is.
So, at any time T, the total enzyme concentration is going to be what? Whatever free enzyme
is left plus whatever has formed the enzyme substrate complex, because the enzyme cannot
go anywhere else. Either it is free or it has formed an enzyme substrate complex. So,
that is what our ET amounts to. So, now if I change the expression and instead of the
enzyme concentration, I write ET minus ES, I can write this, for free enzyme. Where do
I have this quantity in my expression? Here,.
So this is where, now we are going to substitute. So, do that. So, if you do that we get, k-1
plus k2 into ES is equal to k1ET. That is what I have. So, what can I now do? I have
another expression for ES here, which I can take over onto the left hand side. So, if
I do that I will amount on the right hand side to k1 ET S. If I take this part ES over
onto the left hand side, what will I land up with on the right hand side? K1 ET S and
what will I have on the left hand side? Let us just do it. I will have on the left hand
side k-1+ k2 + k1 [S]) [ES] = k1…
We continue our discussion on enzymes and enzyme kinetics. What we discussed last time
was Michaelis-Menten enzyme kinetics. Now, for this we have a particular reaction scheme
where we have the enzyme react with the substrate to form what is called as the enzyme substrate
complex. In the sense enzyme substrate complex, we have an equilibrium as to what is called
a pre equilibrium step which then finally dissociates into the products E+P.
