Kinetics of Bi substrate enzyme Video Lecture - Biotechnology Engineering (BT)

so far we have been talking about the
kinetics of single substrate enzyme
catalyzed reactions and as we all know
that in the living cells a large variety
of enzymes interact with the multiple
substrates in fact most of the enzyme
catalyzed reactions that do take place
in a living cell involve two substrates
in most cases and we have also seen that
under certain set of conditions the
classical Michaelis Menten kinetics
which has been proposed for single
substrate and nematic reactions can also
be applied to bi-substrate reactions of
course certain conditions apply but
those conditions are by and large
extreme conditions that is you have to
have one of the substrate in a very
large excess concentration now those
situations may not really exist in a
living cell in a living cell the
concentration of the two substrates that
are to interact with the enzyme may be
almost in a equal or neighboring
concentration levels they may not be
extremely different and therefore it is
necessary to look at the actual effect
of the bi-substrate reactions on the
reaction rate now two of the examples
which I have chosen here are one on
alcohol dehydrogenase which had which
oxidizes ethanol to acetaldehyde
involving a coenzyme nad and the other
is EXO kinase catalyzed phosphorylation
of glucose or any other EXO's to the
corresponding phosphorylate sugar now as
a matter of fact if you look at bulk of
the bi-substrate reactions do fall in
the category of either oxidoreductases
or transferases or like ages most of the
hydrolytic enzymes isomerizes are often
can be analyzed using
classical Michaelis Menten kinetics the
the oxidoreductases represented by the
first reaction or a transfer is
represented by hexokinase or in many
cases like it is are the real true y
substrate reactions which in general
should not be treated or analyzed with
the Michaelis Menten kinetics now to
account for the rate of reaction for
such reactions taking example of a
typical bi-substrate reaction as I have
shown here in general
now we must I have left certain dots in
between in between the substrate as well
as the product stream basically there
signifies that the interaction the
dynamics of the interaction between the
enzyme and the substrate molecule may be
quite varied unlike in the case of a
Michaelis Menten kinetics where you have
single substrate it has to bind on the
bindings on the active sites of the
enzyme molecule and former Indian
substrate complex now we are here
because the substrates are more than one
there are many possibilities for
interaction between the substrate and
enzyme molecule and so therefore these
dotted figures indicate a variety of
interactions that are involved but in
general the action of enzymes on a
reaction involving two substrates a and
B giving rise to products X and bi is
expressed here now a very generalized
rate expression for this was proposed by
Albert II based on steady state
hypothesis I mean again the similar
considerations as we talked about in the
case of Michaelis Menten kinetics he
proposed the initial reaction rate for
such a reaction can be given by an
expression given here let us say this is
expression one that is v naught is equal
to VM into a into B VM is the maximum
reaction velocity where both the
substrates a and B are saturating
concentrations that means both the
substrates are in large quantity and
they have
they are able to saturate the enzyme
which is in concentration terms is much
much smaller than the a or B the
concentration of enzyme essentially is
much much smaller than either A or B
almost the same assumption that we made
in case of Michaelis Menten kinetics and
the a and B can reach to a saturating
level provide a maximum reaction
velocity and the denominator term
indicate gives you another three
parameters and other three kinetic
parameters KS a essentially is a
dissociation constant of binding of e to
a e
so minded that this is essentially a
dissociation constant now some amine and
KB and ka indicated here are essentially
the concentration of substrates
concentration of the substrates a and B
respectively at which the reaction
velocity is half the maximum reaction
velocity at saturating level of the
other substrate that means when we talk
of kV KB that concentration of B at this
the reaction velocity V is half of that
of DM at a saturating concentration of a
similarly for ka that concentration of a
at least the reaction velocity is half
that of VM at the saturating
concentration of B now I think so or in
other words they are analogous to our
classical Michaelis Menten constant for
the substrate that means you can
consider that essentially KB is the
Michaelis Menten constant with respect
to be at saturating concentration of a
and same analogous is that now there
might be some confusion about ka + k - e
que des a the decision constant for
binding of a to the enzyme KA is there i
am the the corresponding Michaelis
Menten constant with respect to a now
the distinction between the two will be
more
clarified or clear when we proceed ahead
and but so this situation exists in the
case of I substrate reactions in most
cases that this is Susan constant is
different than the apparent Michaelis
Menten constant unlike in the case of
single substrate reaction where there
two are almost identical well you will
notice that the apparent Michaelis
Menten constant will depend upon the
concentration of the other substrate
also and this dissociation does not
depend upon the other substrate and of
course in one of the mechanisms as we
talked out of the several mechanism in
one of the mechanisms this case a may
equal to K and the rate expression will
accordingly get modified and under those
conditions you will notice that if you
take this expression first in general
you will notice that this can also be
considered almost like a as we mentioned
earlier while looking at the validity of
Michaelis Menten kinetics for my
substrate reaction that if we put one of
the substrate concentration in excess
the expression can represent the
bi-substrate reaction kinetically with
respect to other substrate so therefore
if you put let us say if your if let us
say V is very large we tend to infinity
then V naught will become equal to VM
into a upon km plus a both from a
numerator and denominator divided by V
you will end up some of the terms will
be cancelled and you will end up with
simple expression which is essentially
like a microwave and similarly when a
tend to infinity analog expression will
emerge VM into V upon km or so rather I
would say this will be K a and KB plus B
naught km okay so you get a similar
expression in the case of excess
concentration of or large concentration
of one of the reactant and that was also
the understanding we had when we discuss
michaelis-menten kindly now you can also
look at you can rearrange this general
expression what we I talked earlier by
taking certain factors and divide both
and you can end up at a constant
concentration of B if you consider let
us say V and a constant at some value of
V the expression will turn out to be
analogous to Michaelis Menten constant V
M into a into B upon so if this becomes
a constant parameter you get you will
end up in the term at constant B you can
write V naught equal to V M into a into
V upon KB plus B whole / K - a into KB
plus ka into be this whole divided by K
B plus B plus a now this is now this is
essentially we have realized the the
general equation in the form of
michaelis-menten expression so therefore
at any constant value of B you can
consider that the apparent value of ka
the apparent value of km for a KA is
your K - a KB plus ka into B upon kV
plus B so this is essentially the
apparent km with respect to a I mean by
rearranging about general equation so
therefore essentially you notice that
our K now you can realize the
relationship between the apparent K M
for a and K a - I mean although they are
related but it also an
all the concentration terms
concentration term of the other
substrate which is B and a similar
relationship will exist when you
consider constant concentration of a and
the apparent km for B now our or you or
in other words if you also consider that
if you also go further and if you say
that when K - a becomes equal to K a and
in a very special case when gate as a
becomes K your K a a parent will
essentially become independent of B will
become equal to K be the km a parent
sorry km a parent will become equal to
KB and it will be independent of B
therefore essentially the relationship
between these two terms
essentially applies that when they have
same as the the Michaelis Menten
constant with respect to a it does not
interfere or when ka - becomes equal to
ka it has no effect on the binding of B
so it is independent of concentration of
B in the reaction mixture and similar
situation will apply when if you
consider km a parent for V will be equal
to your K - a KB plus KB into a upon ka
plus a and again here also similarly you
will notice that at K - a equal to K a
you will have km a parent for B will be
your KB
sorry no this is here on the K prime is
equal to ka it is with respect to only
the first substrate binding yes under
this condition no this is just I am
trying to give you a analogy or an
explanation how are KNK - a related you
see if you consider the single substrate
reaction the dissociation constant of
substrate with the enzyme is analogous
to km value now whereas in the case of a
bi-substrate reaction that situation is
not true there is only a special case of
a bi-substrate reaction under which the
km apparent for B will become equal to
KB when these two become equal otherwise
the value will be this magnitude
although they will have a relationship
but they will be a function of other
substrate concentration the other
substrate concentration will influence
the magnitude of km apparent in the case
of a bi-substrate reaction whereas in
the case of a single substrate reaction
the km value was a was almost analogous
of course under the assumption that the
term turnover number that this k2 term
is not very very small that was the only
assumption otherwise if if it is very
small
yes they have a difference but if it is
not very small the two are and all of us
so basically this ka and in the first
case as you are right this should be
keen
now you can also look at these
expressions in a graphical mode and to
have a better visualization now in the
first case when we are talking of
constant B your profile will be
something like this this is your maximum
reaction velocity and your half BM will
be this one where k a apparent will be
equal to the DMACC the km value for the
with respect to substrate a apparently
will be K - a KB plus K into V upon kV
plus B and similarly here this situation
will come of v-0 when the value of b is
saturating it will be vm when the value
of e saturating at any other v value of
v the rate profile will be a hyperbolic
profile analogous to that of a Michael
is maintained constant similarly in the
case of constant a constant you will
have another km value km a parent will
be equal to K - a KB plus KB into a upon
K a plus a and essentially here also
this is your constant a this will be the
maximum reaction velocity when a becomes
saturating and such a situation and can
be conceived as a simplification of
Michaelis Menten system now another way
to look at
effective meetings another way to look
at the these kinetic expression is just
like we have been looking and of all the
cases of single substrate reaction
double reciprocal plot because they will
also give us as a matter of fact the
magnitude of all the kinetic parameters
that are involved now what will be the
kind of a double that's were plot in the
case of a generalized rate expression
one can just write 1 upon V naught equal
to 1 plus K a upon a plus K V upon V
Plus K - a KB upon AV this whole divided
by V M now that is a double let's go
plot if you divide both human retur and
denominator by into B you will get the
next expression now here if you plot
this and say for example at a constant
value of B just like in the first case
then we take a constant value of V and
you will get a profile be increasing at
different constant values of V if B
increases you will get a slope of ka
plus ka - kV upon K beep upon V am sorry
ka plus K - K B upon we gave me this
will be upon B upon B M and the
intercept on this factor will be 1 plus
K V upon V upon V M so you will notice
that both slope and intercept will
decrease slope as well as intercept of
the profiles will decrease as you
increase the value of B and ultimately
you will end up when this B becomes a
gyrating it almost comes to a Michaelis
Menten
it will typical k value for the
substrate a and now from the essentially
experimentally to determine the
magnitudes of k a.kb
k desu and vm can be determined by
analysis by SS will plot analysis as we
saw essentially just like when we if you
recall what we did in the case of the
inhibition patterns that we took that
doubled as well the smoker plots and
then took slopes and intercept and made
several secondary plot similarly here
can we done that if you plot your 1 upon
V versus say slope the magnitude of
slope you will get again a straight line
with the slope is equal to ka - kb / vm
and intercept of ka upon vm in the case
of intercept the slope will be K V upon
BM and intercept of 1 upon V M so
therefore by a double the circle plot at
different concentrations of B and
plotting again the 1 upon B versus the
slope and intercept one can determine
the values of the four parameters
kinetic parameter that are involved in a
white substrate reaction that is k a.kb
k - kb + v n essentially the other four
kinetic parameters unlike in the case of
a single substrate reaction where we are
concerned only with two currently
parameters and km and VM so one can
determine experimentally the various
various kinetic parameters in the case
of a bi-substrate reaction
now I think you'll notice that while
looking at the generalized expression of
the bi-substrate reactions rate
expression we have assumed that we have
not really bothered about the dynamics
of enzyme substrate interaction we have
just kept in a black box some
interaction takes place by which the
products are formed and some general
rate expression have been arrived at
which involves certain kinetic
parameters which have been considered an
analogy to single substrate reaction
because the kinetic analysis of enzyme
catalyzed reactions have been so much
dominated by the Michaelis Menten
kinetics that any any new mechanism or
any proposed mechanism must be
interpreted in the light of those km and
VM as parameters and that is what we
have done now essentially we must also
look at that what are the possible kind
of interactions that are likely to take
place and of course almost all the
interactions between enzyme and
substrate for bi-substrate reaction have
been classified into some general forms
the first form of the first complex
formation can be considered as the
random ternary complex formation I think
when we are talking of enzyme and two
substrates there is quite a logical
choice that we might end up instead of a
binary complex a ternary complex that
will where e a and B all the three have
combined together before a product
formation takes place minded that when I
talk of ternary complex formation I am
referring to a ternary complex formation
before the product is formed and in the
case of a random ternary complex
formation the enzyme can form binary
complexes EA and EB to start with and
also the ternary complex EAB with no
restriction on the order in which a and
B bind to the enzyme I mean it can start
by binding first with a and then B will
account to that or it can start with EB
and then a will poke on to that
and or or in other words and you will
notice that just like in the case of a
non-competitive inhibition the a and we
both have separate binding sites on the
enzyme molecule and therefore they don't
interfere each other and randomly they
can bind and result and once the ternary
complex formation has taken place the
product formation will begin now
essentially you can express it in a net
in a mechanistic way the ends I'm going
to ei or EB and essentially again EAB
and so obviously I mean these for this
little can in a cyclic form and the EAB
then goes to form your EEP lusts ex plus
bi and of course they'll be rate
constant at he just stays k1 K minus 1 K
2 K minus 2 K 3 K minus 3 K 4 K minus 4
now the basically the but what is either
reaction can go in this direction or in
this direction there's no constraint on
the order of the ternary complex
formation and such a system essentially
is a typical examples in the enzymes are
either East alcohol dehydrogenase follow
such a kind of mechanism and when it now
you will notice another typical feature
that when we say that the kinetic
parameters of the same enzyme which
catalyzes the same reaction from two
different sources are different and you
will notice that for example East
alcohol dehydrogenase follows a random
ternary complex formation in product
form in the I mean as a part of the
dynamics of their enzyme substrate
interaction whereas the same enzyme
alcohol dehydrogenase from mammalian
cells forms Devon followed this kind of
mechanic
it follows an ordered mechanism where it
can find only do one of the substrate
first before the second substrate can
bind and that's why the kinetic
parameters will automatically turn out
to be different one of the regions in
such cases is based on the different
reaction mechanisms that are involved
similarly each tell extra plane is also
follows this kind of mechanism where the
ternary complex formation is obtained
yes they may be equal to in some cases
or they may not be equal to because
ultimately the multiplication of the two
decision constant in reaching to EAB
will be same now they may or may not be
equal to in some cases yes in a specific
case it could be equal to also but we
have just put the different rate
constants the second case again with
respect to ternary complex formation is
ordered ternary complex formation here
the ternary complex EAB can be formed
from only one of the complex EA I mean
just I've taken hypothetically EA it
could be EB also and only one of the
binary complex has to start the trigger
of the enzyme substrate interaction and
then the other substrate will interact
with the EA complex to form that here
essentially in other words if you write
down the reaction mechanism EA which is
K 1 K minus 1 and then this will go to
EAB
K 2 K minus 2 now obviously the reaction
in this direction B cannot bind to the e
3 E and essentially the reaction has to
proceed in a anti-clockwise fashion that
means after year bound to e
we will mount the AEA we will be formed
and ultimately this will form you a by
releasing one of the product let us say
X and then this will release another
product by and they will be let us say
k3 k4 but the product formation will
take place only after the ternary
complex formation has begun the process
in this direction is not feasible
now the ordered ternary complex
formation as I mentioned is a typical
example is your liver alcohol
dehydrogenase which is obtained in the
mammalian or mammalian systems and also
lactate dehydrogenase is another example
of ordered ternary complex formation and
you can see that the same alcohol
dehydrogenase can follow different
mechanisms and that is they now in
special case of ordered ternary complex
formation is thorolund chance mechanism
because in many of the enzyme catalyzed
reaction thorolund chance observed that
very often the ternary complex is not a
very stable entity and it exists only
for a short period of time a special
case of ordered ternary complex
formation when B reacts with EA of
course the order is important we can
only react with enzyme only when a has
bound to it to form and the one of the
product is released and the modified
enzyme substrate complex is generated
that means a modified enzyme substrate
complex is generated and a first product
has been released without the formation
of a stable ternary complex of kinetic
significance that means the half-life of
the ternary complex is very very small
in this case although they never defined
then they never said that the ternary
complex formation does not take place
they agreed that ternary complex
formation is taking place but the
half-life of the ternary complex is
essentially very small and before that
the second reaction the second substrate
can interact with the EA to form the
first product all in other words you can
have e again going to EA and then this
EA can then convert into key by
relieving a product X and then this e bi
can give you back EA releasing the
product another product Y and you can
have K 1 K minus 1 K 2 K 3 and such a
kind of a system where although the the
second substrate B reacts with the EA to
give you the first product and the
ternary complex is not a very stable
entity is classified into the tunnel and
trans mechanism a typical example of
such a reaction is
glyceraldehyde-3-phosphate dehydrogenase
which you also come across in the case
of glycolysis so that is but it is only
a special case of an ordered mechanism
where order one is ternary complex
formation is not denied we still me this
is not one can also consider it either
as a special case of ternary complex
formation or a special case of binary
complex formation that means but Winery
complex cannot lead to a product yeah
the third the the second substrate has
to interact with the binary complex
before the first product can arrive at
but the stable intermediates are only EA
and ey the fourth two mechanism which
essentially represents the binary
complex formation essentially is
ping-pong mechanism you will also notice
in many books is written as ping-pong
bye-bye mechanism now it's term bye-bye
refers to substrate and product
the I mean by way referred to by means
to substrates and to products now in
case of many of the luggages this will
maybe by unique that means the product
may be one and substrates may be too
so all those cases are collab clubbed
under ping-pong mechanism and in this
case of ping-pong mechanism the basic
hypothesis is that the note ordinary
complex is formed as soon as the first
substrate binds to the enzyme it can
react to form the B to form a product or
claim split off to a product II I mean
something similar you know you will
notice that the two things like coral
and trans mechanism and the ping-pong
mechanism in some way might show analogy
that means as soon as the EA of the
first binary complex is formed the the
attack or the interaction with the
second substrate forms a product first
product or it splits off to a product
and a modified enzyme substrate complex
which then in turn reacts with the B to
form by and therefore your e EA this is
let us say K 1 K minus 1 will now right
at this state itself the product will be
formed sorry X and this will be your EA
- and this is K 2 then EA does then is
interacted with B to give you e a - B
and then this gives you a product again
by K 3 K 4 now basically the name
ping-pong is just you know as soon as
the first binary subjects complex is
formed over the product is released then
the next substrate redirects
the next product is released so and that
is what happens in such cases and a
large number of transfer areas large
number of transfers is most of the bulk
of the transparencies fall in the
category of a ping-pong reaction
excepting those of the east source most
of the million extra kindnesses and all
that they form under the category of
ping-pong
they example they leap to the
classification of ping-pong mechanism so
these are the variety of now you'll
notice that when we look into these
mechanisms and develop steady state rate
expressions specifically in today and
you will end up in quite complex
situations yes now obviously this year -
essentially is something which is
hypothetical in the sense it may not be
a binary complex it is it all you can
write D - E - I will I think it will be
better more clear he does anam in the
modified form the first substrate has
reacted and released a product enzyme is
modified second substrate attached that
really is related another product I
think that will be a better
interpretation and we are in the case of
the tourism Chung cancel this will be a
binary complex this will not be a
modified in yet now and you will notice
that when we look at these reaction
mechanisms with the increased order of
complexity between the dynamics of
enzyme substrate interaction the rate
expression also will be quite complex if
you put them in terms of individual rate
constants as you can notice that each of
the reaction mechanism involved
particularly the random ternary complex
formation will involve eight rate
constants eight and nine rate constant
for reversible and one irreversible step
nine rate constants and the expression
will be quite complex and a I mean in
practice to derive expression may be
quite complex and of course we are
talking only a binary substrate complex
formation that might be an emetic
reaction which may involve three
substrates system will be still more
complex now I think before I go to that
give you the rate expression for these
different mechanisms I'd like to
introduce you to a simplified
methodology for writing a rate
expression under steady state
offices of course the steady state
hypothesis is valid the method was
proposed by a king and Artman
way back in 1956 they gave a method
in fact they analyzed number four the
action mechanisms and using matrix
algebra they wrote down rate expression
for different kinetic mechanisms and
proposed a method that okay you can
solve obviously with all use a matrix as
ever all steady state I mean expressions
can be solved out ultimately taking
making some generalizations from those
matrix algebra and Wong and hints in
1962 proposed certain set of simplified
rules almost like empirical rules
although they are based on hardcore
mathematics mathematics algebra but he
just analyzed certain rules so that by
observation of the reaction mechanism as
long as you can write a reaction
mechanism you one can arrive at a rate
expression in a simplistic way so I will
probably try to introduce you with that
kind of a system taking a simple example
so that that can be applied to over
these complex binary substrate system to
arrive at the actual rate expressions
now the kind of system we will take for
simplicity will be a tooth of two enzyme
substrate complex formation yes going to
ET going through a plus P we can take a
reversible system K 1 K minus 1 K 2 K
minus 2 K 3 K minus 3 so let us assume
just to illustrate the the procedure
what they follow I mean I I just chose
this
I mean reaction mechanism now the very
first step in such a reaction such a
procedure as proposed by Wong and Hans
that very first thing is what we need to
do is then write any reaction mechanism
in a cyclic form reaction mechanism in a
cyclic form cyclic form means you will
have inter convergence of the enzyme
substrate complexes now for example here
as you note notice and young species can
exist in the form of e ES and et in
three form so the the whole action
mechanism can be interpreted in the form
of a triangle with three vertices each
vertex representing one of the enzyme
species and so therefore you can write
such a reaction mechanism as e es ET now
so the inter conversion of each of the
enzyme species say for example es ET es
to a T and let us say this is your s K 1
K minus 1 then I'll explain that I'll
explain that then you have K 3 sorry K 2
and K minus 2 K 3 and P into K 3 K minus
3 now basically we write the rate
constant for all these steps in the
cyclic form assuming or making them in
the kind of L first-order rate constants
for example wherever there is a
substrate involved in the in for example
were in a binding of an AM to substrate
the substrate is involved the rate
constant can be written L as in to k1
where there is no substrate involve only
simple rate constant can be written
and similarly when we're there were our
productive song because ET goes into
form the product in the in the in most
reverse direction the product
concentration will be incorporated so
basically and the inter convergence of
the enzyme forms involved each step must
be described by a now these are called
Kappa Kappa I mean tubs the conversion
of the rate constant or interpreting
each of the step in terms of a first
order rate constant term is called each
each of this term is called Kappa now
the next step is yeah only the substrate
binds right will come from here and for
each enzyme species now then we consider
each enzyme species in a sequence for
example we take E and consider all the
possible pathways by which is formed in
this cyclic manner now he can be formed
by all the possible pathways involving n
minus 1 steps that means if there are
three species there are three enzyme
species number of a species are n n
minus one steps will involved in each
pathway we identify now for II can be
formed by this for example this and this
now obviously we can consider similarly
you can form this and this is that right
right all the possible pathways which
are feasible to form a particular this
is for e actually
you know what I'm trying to explain is
that for each of the enzyme is PC now
write down all the pathways which are
false involving n minus 1 steps that
means if it is a 3 enzyme species system
if there are 3 and gamma speeding system
then each pathway must consist of 2
steps which can form the enzyme species
or any name species which we ever we are
which we are considering now one of the
consideration in such a system is that
all these species are all the pathways
that converge at this enzyme species
that we then like for example systems
like this are possible that means all
the pathways which converts at a
particular Indian species are
permissible but no no pathway which
leaves the indium is specie both
directions is not permissible
that means a system like this will not
be permissible if it happens are you
clear
for each of the enzyme species we work
out the pathways by which these species
will be synthesized each pathway must
consist of n minus 1 step where n is the
number of enzyme species present and the
product of the Capas of the steps in
each pathway is determined now each of
the you can write they couples here and
you can have the cup of product for
example what is the Kappa product for
this pathway k minus 1 and PK minus 1 K
minus 3 this pathway is represented by
this and this so the cup of the product
of these compile this now in this case
it is a k minus 2 and K minus 1 K minus
1 K minus 2 for this one and the third
pathway will be your k2 and e K 2 K
minus 3
now you will find that that similarly
you will write down thee you see ya -
we're talking of e we are at the in this
expression we are writing for the
formation of the engine is VCE this one
these on these arrows represent your
this and this known the formation will
not be SK one doesn't fall e SK one form
yes but by IES it will form e what we
mentioned that we are considering only
pathways which have two steps n minus 1
steps and any steps which lead to
formation of e involving two steps will
be considered first pathway involving
two steps this one and this one
no not pathway in the tour metabolic
pathway that where they are all linked
but we have only the steps which are
involved in formation of E and all the
steps involving to never ever think they
are just generalized rules and they are
not really
otherwise you have to go to the matrix I
will never have to solve the
simultaneous equations and even arrive
at the same thing what what wrong and
Hayes did was he simplified the whole
matrix algebra did wai-king and ultimate
and forms of temples and he said that
you form a cyclic rate expression
silence a cyclic reaction mechanism and
write down the visual pathway for each
of the enzyme is PC or off for example
we can take in a simpler case let us
take the classical
the simpler case of ki plus s going to
es away probably which will which is
much more the probably simplest case E +
P k1 I think try to write this one using
the same you will arrive at the same
expression as Michaelis Menten equation
of course for such a simple system
writing my observation will look to be
more difficult than solving the steady
state equation but if you you if you
have let us say more than one enzyme
substrate complex it may look to be
simpler to write by observation so I
think n represents the number of enzyme
species involved in the mechanism that
yeah so whereas in the in the case of
what I thought we have three enzyme
species
ye-es and ET so it will be expressed in
the cyclic form by a triangle each
enzyme species represented on the vortex
of a triangle and each of the pathway
which should be considered for formation
of the enzyme is PC must have n minus 1
steps is not a question of this is not
this is how to define a pathway is not a
pathway in the sense of metabolic
pathway it's a number of steps involved
in formation of that each having n minus
1 step so I think we'll stop at this
point
Oh