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Enzyme Kinetics. The aims of enzyme kinetics studies are to: Measure the rates of enzyme catalyzed reactions Examine enzyme specificity Identify selective and potent enzyme inhibitors Determine the kinetic mechanism of an enzyme. Enzyme Activity Measurements.

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enzyme kinetics
Enzyme Kinetics
  • The aims of enzyme kinetics studies are to:
  • Measure the rates of enzyme catalyzed reactions
  • Examine enzyme specificity
  • Identify selective and potent enzyme inhibitors
  • Determine the kinetic mechanism of an enzyme
enzyme activity measurements
Enzyme Activity Measurements

The rate of an enzyme-catalyzed reaction is measured by an activity assay where the formation of product (or the disappearance of substrate) is determined over a given time period

The formation of product can be measured continuously or by sampling the reaction mixture at different time intervals

Typical means of determining product (or substrate) concentrations are absorption or fluorescence spectroscopy for continuous assays or HPLC, GC or radiolabeled sampling for fixed time assays

If neither the substrate nor the product of an enzyme have spectral signals then a coupled assay can be designed where the product is converted to something with a signal by using another enzyme

coupled enzyme activity assay

















Coupled Enzyme Activity Assay

[A340 = 6.2 mM-1 ]

In this case the formation of a product (ADP) with an identical spectral signal as the substrate (ATP) can be measured by following the disappearance of a substrate for a coupling enzyme (NADH) with a unique spectral signal

enzyme kinetics4
Enzyme Kinetics

The velocity of an enzyme-catalyzed reaction is described by the Michaelis-Menten equation

Plotting v vs. [S] yields a hyperbola

Vmax is the maximum velocity

This is the rate of the reaction at saturating substrate concentration

Km is the Michaelis constant

This is the concentration of substrate [S] that gives half of Vmax

enzyme kinetics7
Enzyme Kinetics

It is not easy to extrapolate a hyperbola to its limiting value to determine the maximum velocity

The Michaelis-Menten equation can be recast into a linear form

The y-intercept give the Vmaxvalue

and the slope gives Vmax/Km


Enzyme Kineticstwo substrate enzymes

The Michaelis-Menten equation for an enzyme with two substrates has a similar form to the one substrate equation

The major difference is the presence of some additional terms

What does Km measure ?


Enzyme KineticsWhat does Km measure ?

If catalysis (k3) is rate limiting, only then does Km Ki and the Km value is a reasonable measure of substrate affinity


Enzyme Kineticstwo substrate enzymes

If an enzyme has two substrates then they can bind to the active site in an obligatory order or they can bind in a random order

An ordered kinetic mechanism

Horizontal line represents the enzyme (E)

A and B are the substrates

P and Q are the products

The brackets ( ) represent the conversion of substrates to products


Enzyme Kineticstwo substrate enzymes

A fully random kinetic mechanism

Reactions can also be partially ordered

1. Ordered addition of substrates, random release of products

2. Random addition of substrates, ordered release of products


Enzyme Kineticsdetermining kinetic parameters

This is a plot of 1/velocity vs. 1/[substrate A] at different levels of substrate B

We can’t simply extract the kinetic constants from this plot

In order to get these values we have to replot the data


Enzyme Kineticsdetermining kinetic parameters

From a replot of the intercepts we can determine Vmax and Kb

From a replot of the slopes we can determine Ka and Kia

We cannot distinguish between an ordered and a random kinetic mechanism from this initial velocity data analysis

There is another type of kinetic mechanism in which the catalytic reaction can start without both substrates being present


Enzyme Kineticsping-pong mechanism

In this example the first substrate (A) is converted to product (P) and the product departs before the second substrate (B) binds

This leaves the enzyme in a modified form (F) which can now bind (B) and convert it to product (Q)


Enzyme Kineticsping-pong mechanism

This plot gives parallel lines that are diagnostic of this mechanism

Replots are again needed to determine the kinetic parameters


Enzyme Kineticsping-pong mechanism

Again, the intercept replot gives us Vmax and Kb

However, since all the lines have the same slope this replot only gives us Ka

Kia is zero for a ping-pong mechanism


Enzyme Kineticsinhibition studies

Inhibition studies will help to identify:

The detailed kinetic mechanism of an enzyme (ordered or random, order of substrate addition)

New potent inhibitors of an enzyme that can be developed into drugs


Enzyme Kineticsinhibition studies

To conduct these studies we vary the concentration of a potential inhibitor and then plot the rates in the presence of inhibitor vs. the substrate concentration

The presence of the inhibitor can affect either the slope or the intercept of the linear reciprocal plots

If there is an intercept effect this means that the inhibitor combines with a different form of the enzyme than does the substrate that is being varied

If there is a slope effect then the inhibitor combines with the same enzyme form as the varied substrate


Enzyme Kineticscompetitive inhibition

A competitive inhibitor binds to the same enzyme form(E) as the varied substrate

The slope replot gives the Ki value for the inhibitor


Enzyme Kineticsuncompetitive inhibition

An uncompetitive inhibitor binds to a different enzyme form (ES) from that of the varied substrate (E)

The intercept replot gives the Ki value for the inhibitor


Enzyme Kineticsnoncompetitive inhibition

A noncompetitive inhibitor can bind to more than one enzyme form (E and ES)

The replots gives the Kis and Kiivalues for the inhibitor


Enzyme Kineticsproduct inhibition studies

Product inhibition studies can be used to distinguish between the various possible kinetic mechanisms

* becomes NC for any substrate-product pair that can bind simultaneously to the enzyme (dead-end complex)

enzyme kinetics terreactant mechanisms
Enzyme Kineticsterreactant mechanisms

Some enzymes have three substrates and/or three products

1. Synthetases

2. Hydroxylases

enzyme kinetics terreactant mechanisms24
Enzyme Kineticsterreactant mechanisms

3. Certain Dehydrogenases

4. Carboxylases


Enzyme Kineticsterreactant mechanisms

The Michaelis-Menten equation for an enzyme with three substrates has a similar overall form to the one or two substrate equation

For enzymes with terreactant mechanisms we must use replots of the replots to separate and determine all of the kinetic parameters

There are eight different terms in the rate equation and the presence or absence of these terms are indicative of different kinetic mechanisms

enzyme kinetics terreactant mechanisms26
Enzyme Kineticsterreactant mechanisms
  • Reciprocal plots are made vs. 1/C at several levels of A
  • This pattern is then repeated at difference B levels
  • The slopes and intercepts of these plots are replotted vs. 1/A
  • The slopes and intercepts of these replots are then replotted vs. 1/B
  • A zero slope or zero intercept in these secondary replots indicate the absence of that term from the rate equation
enzyme kinetics27
Enzyme Kinetics
  • The kinetic mechanism of an enzyme gives the order of addition of substrates and release of products
  • Mechanisms can be ordered, random, or ping-pong
  • Plots (and replots) are used to determine the kinetic parameters (Vmax, Km, Vmax/Km) for each substrate
  • Inhibition studies help to sort out complex kinetic mechanisms, identify new enzyme inhibitors, and measure their potency (Ki)