Multi-Substrate Enzyme Kinetics
Kinetics of Multi-Substrate Enzymes
* Single substrate/product enzyme-catalyzed reactions of the type we’ve been
studying, i.e.
S <==> P
are useful for gleaning kinetic principles, but are actually very rare.
* Most enzymes have two or more substrates and frequently multiple products, i.e.
A + B <==> P + Q
so the kinetics are more complicated than the 1-substrate Michaelis-Menten systems.
* Multi-substrate kinetics can be simplified somewhat by holding one substrate constant
and varying the other, but to really understand the enzyme mechanism you have to
consider all of the substrates (and even the products).
Terminology
Substrates:
Products:
Enzymes:
A, B, C, D
P, Q, R, S
E, F, G
Inhibitors:
I, J
Transitory Complexes:
With multi-substrate enzymes you often have to
invoke more than one enzyme form; E always
represents free enzyme-- the form before any
substrate is bound.
Like enzyme-substrate complex, but there are more types with a multisubstrate enzyme, i.e. for A + B <=> P + Q enzyme you could have
EA, EB, EAB and even EP, EQ, EPQ
Not all enzymes make all of these transitory complexes. Some can even
make combined enzyme-substrate-product transitory complexes such as
EAP, EBQ
Central Complexes:
These are transitory complexes that are full, i.e. all substrates are bound
or all products are bound. For A + B <=> P + Q the central complexes
could be the following (usually in parentheses):
(EAB), (EPQ)
Reactancy:
Uni, Bi, Ter, Quad
i.e., number of reactants in a particular direction.
Therefore A + B <=> P + Q is BiBi
and A + B + C <=> P + Q + R + S is TerQuad
Kinetic Mechanisms
The sequence in which substrates are bound and products are released.
(1) Sequential (a.k.a. Ternary Complex).
All substrates bind to the enzyme before the first product is released.
* Ordered
* Random
--substrates & products bound and released in obligatory sequence
--no obligatory binding sequence
(2) Ping-Pong (a.k.a. Double Displacement or Substituted-Enzyme)
At least one product is released before all substrates have bound.
We will study the distinctions between these kinetic mechanisms
Using a typical BiBi enzyme:
A + B <==> P + Q
Ordered Sequential Mechanism
Substrates bind to the enzyme in a defined sequence,
and products are released in a defined sequence.
E + A <=> EA
EA + B <=> (EAB) --central complex
The enzyme-substrate central complex is then converted to enzyme-product
central complex:
(EAB) <=> (EPQ)
The products are now released:
(EPQ) <=> EQ + P
EQ <=> E + Q
We can represent this schematically in a Cleland Plot:
Ordered Sequential BiBi
kinetic mechanism
(note parentheses are sometimes
left off of the central complexes)
Random Sequential Mechanism
Similar to Ordered Sequential except there is no specified order in which substrates
must bind or products must be released.
E + A <=> EA
EA + B <=> (EAB)
or
E + B <=> EB
EB + A <=> (EAB)
Central complex is IDENTICAL
by either path
The next step is the same as with Ordered Sequential mechanism:
(EAB) <=> (EPQ)
We now have a choice of sequences of product release:
Central complex is IDENTICAL
by either path
(EPQ) <=> EQ + P
EQ <=> E + Q
or
(EPQ) <=> EP + Q
EP <=> E + P
Random Sequential
Cleland Plot
Random & Ordered mechanisms are similar.
Why are some enzymes ordered?
-- binding of first substrate causes conformational change
that is required for binding second substrate, or
-- first substrate binds directly to second substrate.
-- kind of like Uncompetitive inhibitor binding to ES
complex.
Ping-Pong (Double Displacement) Mechanism
-- At least one product is released before all of the substrates have bound.
-- Common. Examples include serine proteases & aminotransferases.
The first substrate binds in the usual way, except that the EA complex in this case is
actually a central complex. The active site is full because substrate A will be converted to
product before the second substrate can bind:
E + A <=> (EA)
The next reaction is the key to the whole process:
(EA) <=> (FP)
In this reaction a part of the substrate has been removed from substrate A,
converting it to product P. The removed section has become covalently bound
to the enzyme to create a new form of the enzyme, enzyme F.
The first product of the reaction is now released and the second substrate binds:
(FP) <=> F + P
F + B <=> (FB)
F = covalent enzyme-adduct
Now the stored section of the first substrate is transferred to the second substrate to create the second product,
which is then released:
(FB) <=> (EQ)
(EQ) <=> E + Q
Ping-Pong Mechanism: The Movie
Cleland Plot for Ping-Pong BiBi Mechanism:
Remember--(EA), (FP), (FQ), &
(EQ) are CENTRAL COMPLEXES
Note: Ping-Pong is an ordered kinetic mechanism, of necessity!
Effects of Substrate Concentration in Multi-Substrate Systems
For a single-substrate enzyme, i.e. A <=> P, a kinetic experiment measuring v as a function
of [A] gives you a hyperbolic, Michaelis-Menten-type curve, which can be analyzed via
any of the kinetic plots discussed previously, such as Lineweaver-Burk, Hanes, etc.
With a multi-substrate enzyme, i.e a typical BiBi enzyme: A + B <=> P + Q
you can get the same result by holding one substrate constant and varying the other, so if
A = variable substrate
B = fixed substrate
then a plot of v vs. [A] will give a hyperbolic MichaelisMenten curve, and vice-versa. Analysis would be the same
as with a single-substrate system.
Now consider what would happen if you repeat the experiment with an increased conc. of
the fixed substrate, B in this case.
-- reaction rate will be faster at any given conc. of variable substrate, A.
-- kinetic parameters will change to reflect changes in velocity.
-- if you did this at several fixed concentrations of B and plotted the data
sets on a Lineweaver-Burk plot, you would get a series of lines.
Here is a typical Lineweaver-Burk pattern
obtained for a BiBi enzyme
A + B <=> P + Q
at different fixed concentrations of
substrate B.
The actual pattern of lines obtained will vary
according to the way in which the enzyme
interacts with the two substrates, and enables
us to distinguish between sequential and
ping-pong enzymes.
In discussing graphs of this type we'll consider changes in V and in the slope of the line.
-- A change in V indicates the effect that a change in the concentration of the fixed substrate
would have on the velocity at very high concentrations of the variable substrate.
-- A change in slope indicates the effect that a change in concentration of the fixed substrate
would have on the velocity at very low concentrations of the variable substrate. Remember
that the 1/slope of LB plot is the rate constant at low substrate concentrations (V/Km).
Substrate Concentration Assays with Sequential Enzymes
Consider a BiBi ordered sequential reaction: A + B <=> P + Q
The Cleland plot for such a reaction would be:
We'll discuss the results of a set of enzyme assays in which substrate A is used as the
variable substrate and substrate B as the fixed substrate.
At very low [A]:
-- the rate limiting step of the reaction would be the binding of A to the enzyme as the substrate is in very short
supply.
-- an increase in the concentration of B would reduce the concentration of the EA complex in the reaction mixture by
binding to it to form EAB complex. Reducing the concentration of the product of the E + A <=> EA reaction will
pull it to the right by the Law of Mass Action. So the increase in B has increased the speed of the rate limiting step,
and therefore of the overall reaction. As we're looking at effects at low A concentrations this would be seen as a
change in the slope of the Lineweaver-Burk plot.
At very high [A]:
-- the rate limiting step would be the EAB <=> EPQ, which is the inherently slowest reaction, or EA + B <=> EAB
at low B levels.
-- an increase in B would increase the speed of either of these as a reactant in the second reaction and by the effect of
generating more EAB for the central reaction to occur. This would be seen as a change in V as we are considering
the effects at high A concentration.
Ordered Sequential Reaction:
Change in concentration of fixed substrate
brings about a change in both the slope
and intercept of Lineweaver-Burk plots.
Increasing V and V/Km
A similar result would be obtained if the assay was reversed and B used as the variable
substrate or if the enzyme used a random sequential mechanism.
Substrate Concentration Assays with Ping-Pong Enzymes
Consider a BiBi ping-pong reaction: A + B <=> P + Q
The Cleland plot for such a reaction would be:
We'll discuss the results of a set of enzyme assays in which substrate A is used as the
variable substrate and substrate B as the fixed substrate.
• The critical difference about a ping-pong reaction is that a product leaves the enzyme before all the
substrates have bound. This is going to change the way in which the substrates interact with each
other, kinetically.
• Remember that in normal enzyme assays we are measuring the initial velocity - i.e. the rate
immediately after addition of enzyme to the substrates. Under these conditions the concentration of
products is zero - no product has had time to be produced yet - and the reaction:
FP <=> F + P
which is normally a readily reversible reaction, is effectively irreversible since the back reaction
would require a supply of product P. We'll see how this affects the kinetics of the reaction when we
examine the influence of B, as the fixed substrate, at low concentrations of A.
Effects of Substrate Concentration on Ping-Pong Kinetics, Cont’d
At very high [A]:
-- V increases with increasing concentration of fixed substrate as with sequential, so intercept of LB
plot decreases.
At very low [A]:
-- Like sequential, at low [A] the reaction E + A <=> EA will be rate limiting.
-- Increasing the [B] will convert more F to FB and thereby decrease the concentration of enzyme
form F. At this point you might expect the Law of Mass Action to take over. The reduction of F would
pull the FP <=> F + P reaction to the right reducing the concentration of FP which, in turn, would
pull EA <=> FP to the right which would have the same effect on the rate limiting step.
*** But remember that FP <=> F + P is effectively irreversible due to initial velocities!***
-- The reduction in F would seem to pull this to the right because the loss of F would decrease the
speed of the back reaction. However it has no direct effect on the speed of the forward reaction.
-- The speed of this back reaction is already zero under initial velocity conditions so it can't be slowed
down any more.
-- Effectively then the irreversibility of the reaction isolates the rate limiting step from the influence
of B and a change in the concentration in B has no effect on the speed at low A concentrations.
Upshot: The slope of the line is unchanged.
Ping-Pong Reaction:
Change in concentration of fixed substrate
brings about a change in the intercept but
NOT the slope of Lineweaver-Burk plots.
Increasing V;
V/Km unchanged
As with a sequential enzyme, a similar type of graph would be obtained if the
substrates were reversed with B as the variable and A as the fixed substrate.
Effects of Substrate Concentration Distinguish Sequential
vs. Ping-Pong Kinetic Mechanisms in Multi-Substrate Enzymes
Increasing V;
V/Km unchanged
Increasing V and V/Km
For further details we need to look at the effects of
product inhibition…
Uses of Product Inhibition in Multi-Substrate Kinetics Analyses
(1)Determine whether a sequential mechanism is random or ordered.
(2)If it is ordered, determine the order of substrate binding and product release.
(3)Can yield useful information about the mechanism of ping-pong enzymes.
Single Substrate Systems:
A <=> P
-- Product inhibition is always competitive since A & P bind to the same site.
-- Usually never see it due to initial velocity studies.
Multi-Substrate Systems, e.g.: A + B <=> P + Q
-- Also unseen in initial velocity measurements, unless you manipulate the reaction by adding
a product to the initial mixture.
-- Things are more complex, and inhibition is not always competitive.
-- With multi-substrate, it may be possible for one of the substrates and one of the products to
bind to the active site at the same time, depending on the enzyme. Therefore a substrate and
product are not necessarily in direct competition with each other.
-- In fact all of the reversible inhibitor types (competitive, classic non-competitive, mixed,
uncompetitive) that we saw with single substrate kinetics may occur as product inhibitors in
multi-substrate systems, and it is the pattern of product inhibitor types which gives us the
information we need to determine the kinetic mechanism.
Inhibition Refresher:
Inhibitor Type
Inhibits At
Lineweaver-Burk Plot
--------------------------------------------------------------------------------------------------Competitive
Low [substrate]
Changes slope not
intercept
Non-competitive
Low & high [substrate]
Changes slope and
intercept
Uncompetitive
High [substrate]
Changes intercept
not slope
Experimental Approaches in Product Inhibition Studies
* Simple extension of substrate concentration effects on multi-substrate systems.
* For any given assay one substrate will be chosen as the variable substrate with the
other kept at a fixed concentration.
* This time though the enzyme will be assayed in the presence and absence of a
fixed amount of a chosen product.
* With a typical BiBi enzyme four experiments of this kind can be carried out.
-- Both substrates can be used as the variable substrate, with the other one fixed.
-- Both products can be used as inhibitors.
* The results can be plotted using LB or any of the other kinetic plots.
We'll start by looking at the results that would be expected with an
ordered sequential enzyme.
Product Inhibition in Multi-Substrate Systems:
The Ordered Sequential Mechanism
(1) Variable substrate A, Product inhibitor Q
• Substrate A and product Q are both capable of combining with the free enzyme, E.
• Because this is an ordered reaction they can only bind to free enzyme, so whichever ligand binds first will
prevent the other one from binding.
• This is a classic case of competitive inhibition and will appear as such on an LB plot.
(2) Variable substrate A, Product inhibitor P
• Product P can't bind to free enzyme but it can bind to the EQ complex, driving the reaction backwards by
the law of mass action.
• Since product P is incapable of binding to free enzyme large amounts of substrate A will have no effect on
the inhibition as the loss of free enzyme is irrelevant to binding of P.
• Therefore P will inhibit at both low and high concentrations of the variable substrate, and we'll see a noncompetitive/mixed form of inhibition.
(3) Variable substrate B, Product inhibitor P
• P inhibits for the same reason as in the last experiment.
• The variable substrate, B, can only combine with the EA complex as this is an ordered reaction, and P can
only combine with the EQ complex.
• Again there is no direct competition between the inhibitor and variable substrate and non-competitive/
mixed inhibition will be found.
(4) Variable substrate B, Product inhibitor Q
• Q inhibits for the same reason as in the first example.
• This time however the variable substrate is incapable of binding to free enzyme and doesn't compete
directly with the inhibitor.
• The product will still inhibit then at high B concentrations and we'll see another example of noncompetitive/mixed inhibition.
Effects of the Fixed Substrate on Product Inhibition Patterns
(Ordered Sequential BiBi)
In two of the experiments the type of inhibition changes if the assay is repeated at very high
(saturating) concentrations of the fixed substrate.
(1) Variable substrate B, Product inhibitor Q, Saturating levels of A
* Normally this would show non-competitive inhibition.
* But, if large amounts of substrate A are present, this will compete with the product inhibitor
as they both bind to free enzyme. Under these circumstances no inhibition will be
observed as the inhibitor is competed out by the fixed substrate.
Ordered Sequential BiBi (Cont’d)
(2) Variable substrate A, Product inhibitor P, Saturating levels of B
* In any reaction sequence there is a rate limiting step which determines the overall reaction speed. To
slow down the overall reaction speed an inhibitor must slow down the rate limiting step. Normally the
rate limiting step would be the EAB <=> EPQ reaction as this involves a true covalent change and is
chemically more difficult. Product P slows this down as described previously.
* At low A concentrations the rate limiting step becomes the E + A <=> EA reaction. Normally P would
inhibit this by an extension of the mass action effect. Inhibition therefore occurs at both low and high
levels of the variable substrate (non-competitive/mixed).
* However if the fixed substrate B is present at very high levels it will drive the EA <=> EAB reaction
completely to the right, making this step effectively irreversible. This acts as a barrier between the
inhibitor and the rate limiting step.
* Under the circumstances described here product P inhibits at high concentrations of the variable
substrate but not at low ones, giving rise to an uncompetitive inhibition pattern.
SUMMARY: Product Inhibition Patterns for Ordered Sequential BiBi
Inhibition at
Inhibition at
Variable
Product
Normal Levels
Saturating Levels
Substrate
Inhibitor
of Fixed Substrate
of Fixed Substrate
---------------------------------------------------------------------------------------------------------A
P
Non-competitive
Uncompetitive
A
Q
Competitive
Competitive
B
P
Non-competitive
Non-competitive
B
Q
Non-competitive
None
Product Inhibition in Multi-Substrate Systems
The Random Sequential Mechanism
Substrates bind in no specified order;
Products release in no specified order.
In a typical reaction of this type the
two substrates are bound to the
active site and a section of one
substrate is transferred to the other
to create the products:
Not allowed:
EA + P <=> (EAP)
EB + Q <=> (EBQ)
EB + P <=> (EPB) should form readily:
EA + Q <=> (EAQ) may or may not form
depending on sterics of the transferred side group:
NO
YES, but weaker?
Product Inhibition Patterns for Random Sequential BiBi
• Depend on the enzyme’s ability to form the combined
substrate-product complexes above. Both products will inhibit
the enzyme since binding of either product will prevent at least
one substrate from binding.
Variable substrate A, Product inhibitor Q
• If the EAQ complex is unable to form then a large A concentration would stop Q from binding and prevent
the inhibition. This is a classical example of competitive inhibition.
• If the EAQ complex is able to form then even saturating amounts of A will not prevent product binding,
though its ability to bind might be reduced, and inhibition will still occur at high substrate concentrations.
This is noncompetitive inhibition.
• The type of inhibition then depends on the properties of the particular enzyme.
Variable substrate A, Product inhibitor P
• The EAP complex can never be formed since A & P binding to E are mutually exclusive.
• The inhibitor will be competed out by saturating amounts of A. This is classical competitive inhibition.
Variable substrate B, Product inhibitor Q
• As in previous, EBQ complex can't be formed so this is competitive inhibition again.
Variable substrate B, Product inhibitor P
• The EBP complex can be formed easily.
• Saturating amounts of the substrate will have no effect on the binding of the inhibitor which will therefore
continue to operate at high substrate concentrations. Noncompetitive inhibition.
SUMMARY:
Product Inhibition Patterns for
Random Sequential BiBi
Variable
Product
Substrate
Inhibitor
Inhibition Type
--------------------------------------------------------------------A
P
Competitive
A
Q
Competitive or
Non-competitive
B
P
Non-competitive
B
Q
Competitive
Product Inhibition in Multi-Substrate Systems
The Ping-Pong Mechanism
Remember:
In Ping-Pong substrate A and product Q are both capable of binding to free enzyme, E.
Also, substrate B and product P are both capable of binding to the enzyme containing
the structure that's being transferred during the reaction, F.
These ligand pairs therefore compete directly with each other. The products will inhibit by
preventing access by the substrate but saturating amounts of the substrate will prevent the
product from binding and therefore inhibiting. This will show classical competitive
inhibition when the substrate is used as the variable substrate.
The other substrate-inhibitor pairs (A/P and B/Q) do not normally bind to the same
enzyme form and thus do not compete directly with each other and these pairs will show
non-competitive inhibition when tested against each other.
SUMMARY:
Product Inhibition Patterns for
Ping-Pong BiBi
Variable
Product
Substrate
Inhibitor
Inhibition Type
--------------------------------------------------------------------A
P
Non-competitive
A
Q
Competitive
B
P
Competitive
B
Q
Non-competitive
COMPARISON: Product Inhibition Patterns for BiBi Mechanisms
Variable Product
Ordered
Random
Substrate Inhibitor
Sequential
Sequential
Ping-Pong
----------------------------------------------------------------------------------------------------------------------A
P
Non-competitive
Competitive
Non-competitive
/Uncompetitive*
A
Q
Competitive
Competitive or
Non-competitive
Competitive
B
P
Non-competitive
Non-competitive
Competitive
B
Q
Non-competitive
/None*
Competitive
Non-competitive
* At very high concentrations of fixed substrate.
-----------------------------------------------------------------------------------------------------------------------
• Patterns easily distinguish between ordered and random sequential mechanisms.
• For ordered sequential, patterns establish binding order since the substrate/product
pair showing competitive inhibition represent the first substrate to bind and the last
product to leave the enzyme.
• With a random sequential mechanism the type of inhibition found with the A/Q pairing
gives us some information about the physical interaction between ligands and enzyme.
• The pattern with a ping-pong enzyme is similar to one of the possibilities with a
random sequential enzyme (two competitive and two non-competitive). However, these
mechanisms are easily distinguished by substrate concentration studies.
Siesta
Time!