welcome to lecture seven in this n p t e l online certification course on a bioreactors
in the last lecture we had look at the solution to a practice problem practice problem two
point one so let us continue with the material after that we had looked at the michaelis-menten
kinetics for an enzyme reaction there the mechanism was enzyme and substrate giving
us an enzyme substrate complex and the enzyme substrate complex breaks down to give you
the enzyme and the product product in the enzyme that was the mechanism that is of course
a varying simplistic mechanism and as expected many other types of mechanisms exist for
enzymatic reactions and we would look at some of those as variations from this michaelis-menten
kinetics that way it will be easier for us to put it in a certain frame work get the
appropriate parameters and so on therefore let us look at other kinetics with a single
enzymes single substrate kind of the situation with some inhibitors thrown the first inhibition
that we are going to look at is called competitive inhibition ok in this case the inhibitor inhibitor
is the one that inhibits the reaction that inhibits the reaction by binding to the enzyme
and there by providing competition ok so competitive inhibition there by providing competition
to the substrate in the process of binding to the enzyme in other words the scheme reaction
scheme is like this the substrate plus enzyme they bind together to give you the enzyme
substrate complex this is the reversible reaction k one forward rate k two the reverse reaction
rate and enzyme substrate complex gives the enzyme and the product this was the simple
enzyme michaelis-menten michaelis-menten enzyme kinetics and here in addition we have
an inhibitor molecule that interacts with the enzyme at the same time and reversibly
gives an enzyme inhibitor complex this kind of a reaction scheme is called competitive
inhibition now you can try this when you have time it is going to take a lot of time and
therefore i am not going to derive the whole thing the derivation is on the same
lines as that for the michaelis-menten kinetics it will be a little more complex than that
because there is one more reaction taking place you need to look at how things are done
if you derive it which will take you quite some time a few pages and so on we will
get v in this again this is the back system therefore the rate the volumetric rate is
a can be take into be the accumulation rate of the product d d t of p that equals v m
times s divided by k m into one plus i by k i plus s ok this is been deliberately
arranged to be of this form pirombeira are michaelis-menten kinetics was v m s by k m
plus s here we have v m s by k m into one plus i by k i plus s i is the inhibitor concentration
in other words the k m has been modified the k m earlier has been modified with this term
to give us k m into one plus i by k i therefore in the case of competitor inhibition the k
m gets modified the mechanism of course the inhibitor binds with the enzyme and that's
how it is a competing with the substrate for the enzyme and there by end us the reaction
and in the case of the rate expression the variation is only in k m v m remains infact
the k i here is nothing but k six the reverse reaction by k five the forward reaction rate
constant reverse reaction constant divided by the forward reaction rate constant as mentioned
earlier v m remains a same so k m changes so if we plot the line viewer burk plot
then we will get the appropriate things as this slope and appropriate things as the intersect
ok i will let you figure that out in fact let's sign a problem so that you can
figure that out
the next type of a inhibition the earlier was one was to competitor this one is called
the second one is called in non competitive inhibition in the non competitive inhibition
case the inhibitor binds to the enzyme as well as the enzyme substrate complex the scheme
as like this this is the michaelis-menten scheme the first reaction S plus E reversibly
E S gives u irreversibly E plus P the enzyme binds to the inhibitor to give you the enzyme
inhibitor complex the enzyme substrate complex also binds to the inhibitor reversibly to
give you enzyme substrate inhibitor complex the enzyme substrate complex also binds to
the inhibitors reversibly to give you enzyme substrate inhibitor complex so this is the
additional reaction here for non competitor inhibition in which case the inhibitor binds
to the enzyme as well as to the enzyme substrate complex you can go through a longer process
on the same lines as that for michaelis-menten the material balance and so on and if do it
right you will get v equals for a batch case k s d p d t equals v m by one plus i by k
i into s plus k m s by k m plus s as we can recognize here are michaelis-menten was v
m s by k m plus s here it is v m by one plus i by i by k i into s by k m plus s v m has
been modified k m has been not modified in the case of non competitive inhibition
v m changes k m remains the same we will look at one other kind of inhibition and then we
will and then anchored them on some matrixes it could be
a porous matrix such as
a
bead or a gel or even a bed and carried out the enzyme reaction on the immobilized or
with the immobilized enzyme they have placed enzymes on a porous matrix and we use the
matrix in bioreactors for carrying out enzyme reactions the beads and gels it is quite easy
to see you can just add them to the reactor austere environment may be austere reactor
and then the substrate gets into these beads or gels it interacts with the enzyme the
product gets made the product comes out or it could happen in a bed where we have a bed
with the this matrix the the substrate solution passes through this bed and where
comes out at the end of the bed the conversion is done so this is an example of a enzyme
immobilization this is been heavily used in the industry for a few products so it's an
industrial process they are also immobilized on a gels nano particles and small surfaces
these enzymes and when done appropriately they can be used as bio sensors for the detection
of let say pesticides or heavy metals and also as and for analysis such as glucose the
enzyme immobilization may be glucose oxides immobilized glucose oxidize can be used
as a glucose sensor in in a appropriate format that's what is typically done also so it can
be used for various different purposes not just for production purpose some examples
of industrial scale use of enzyme immobilization in the pharma industry penicillin acylase
has been immobilized and that immobilized enzyme has been used for six apa production
from penicillin g we saw that six a p a is the preferred antibiotic and the conversion
of penicillin g to six a p a is done in enzyme immobilized reactor in the industry
the food industry glucose isomerase to produce sweet invert sugar a mixture of glucose
and fructose that is also done by immobilized glucose isomerase in the energy industry lipases
to produce bio diesel from bio oil is carried out using immobilized enzymes in immobilized
lipases and this is a paper this also there in your list of references list of additional
sources you can go and take it from that we complete references here this is this is published
in twenty ten in the research journal of biological sciences this by khan and al alzohairy
the title is recent advances and applications in immobilization enzyme technologies arrive
you so if we interested knowing some details about immobilized enzymes you may want to
read that paper not just enzymes the cells that we saw earlier they can also be immobilized
that helps the cells overcome the harsh environment of a bioreactor with a lot of shear and so
on so that cells can be protected there are again some down size in terms of a rates
and so on but in terms of a concept you could use immobilized sets immobilized enzymes
are of course industrial processes immobilized cells have been studied
may be there used to with this let us look at practice problem two point two and
will finish of this lecture here in the next lecture i will tell you how to solve
this practice problem two point two before this a quick recap of the short lecture that
we had we had looked at the kinetic mechanisms for enzymes which are different from the michaelis-menten
kinetics especially we had looked at inhibition kinetics the the we looked at three types
of inhibition kinetics competitive non competitive and uncompetitive what happens during competitive
what happens during non competitive and what happen during uncompetitive in terms of the
mechanism what does a inhibitor bind to essentially that makes the difference and
the resulting kinetic expression also is different in the first case one is modified
in the second case
other one is modified in third case both are modified so that is over all what we saw and
then we saw something about immobilized enzymes being used in the industry i have said that
let us look at the practice problem two point two an enzyme normally displays michaelis-menten
behavior in converting a substrate s to a product p it gave the following data when
it's m m parameters for the above conversion were estimated in the presence of another
substance i at different concentrations determine the type of inhibition and the inhibition
constant here given the michaelis-menten parameters here v max in k m v max as millimolar per
minute and k m as millimolar and the inhibitor contraction in millimolar are given as zero
point five one five and ten so these are the michaelis-menten parameters that were obtained
v m and k m at various inhibitor
concentrations you are ask to find the type of inhibition and the inhibition constant
k i go head and do it where we meet in the next lecture we will take this forward