Download What enzymes do do!! Increase the rate of a reaction by lowering the

MBLG1001_lecture6
What enzymes do do!!
Increase the rate of a reaction by lowering the activation energy ∆G#
Reaction specificity and the activation energy of a reaction
Enzymes have evolved special active site pockets which recognise only certain substrates
and allow them to bind. This makes enzymes generally more specific than non-protein
catalysts with respect to the range of substrates they will work on. However, the active
site is not exactly complementary to the substrate, like a key in a lock. If it were, this
would stabilise the substrate through hydrophobic, electrostatic, hydrogen bond and van
der Waals interactions, making the activation energy even higher. Instead, while the
active site will accommodate the substrate, it is more complementary to the transition
state with respect to shape and noncovalent interactions.
In general, the active sites in enzymes: occupy a relatively small part of the protein; is
three-dimensional and formed by disparate parts of the protein chain; substrates are
bound by weak forces; are crevices or clefts; specificity is defined by the precise threedimensional arrangement of groups in the active site.
In real enzymes some weak interactions are formed with the substrate in order that it
becomes localised in the enzyme active site and then correctly oriented. The full
complement of interactions, however, only occurs between the enzyme and the transition
state. One reason why enzymes are so large and complicated is the need for various
amino acid side chains to provide chemical groups for these non-covalent interactions
which stabilise the transition state.
Can reactions for which the free energy change is positive be catalysed by
enzymes?
In this case the enzyme has to resort to using a coupled reaction. The most common of
these is the hydrolysis of ATP to yield ADP + Pi. This yields a large amount of energy
which can offset the positive ∆G of the reaction to be catalysed. The requirement is that
the energy is not lost in the intermediate step. A simplified example is that of the
phosphorylation of glucose by hexokinase. If the enzyme were required to inorganic
phosphate, PI, directly to glucose the reaction would have an overall positive value.
glucose + Pi --> glucose 6-phosphate, ∆G0 > 0
glucose + ATP -->glucose 6-phosphate + ADP, ∆G0 < 0. The latter can actually be
thought of as the sum of two separate reactions:
1. ATP --> ADP + Pi ∆G0 < 0
2. glucose + Pi --> glucose 6-phosphate, ∆G0 > 0
Having discussed what enzymes can and can’t do let’s now consider how to measure
enzyme activity and what parameters govern this measurement.
The rate of a reaction is measured as the #moles of product produced per unit
time. The most user friendly units are µmol/min.
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Reaction rates are increased by:
• Temperature
• [reactant]
• A catalyst
If the temperature is kept constant let’s consider the effect of [reactant] on a simple first
order reaction (a first order reaction is one where the reaction rate is dependent on the
concentration of one reactant). If you plot the reaction rate on the y-axis and the
[reactant] on the x-axis you would obtain a straight line with a slope of k, the rate
constant. In a second order reaction the rate is dependent on the concentration of two
reactants. Analysis of these reactions is much more difficult (and beyond the scope of this
course). Often in biochemical analysis these reactions are converted to pseudo first order
reactions by putting in a vast excess of one reactant.
Now let’s add an enzyme to the reaction. The plot of initial velocity, v, versus substrate
concentration [S] is described now by a rectangular hyperbola. The initial velocity
reaches a maximum value, Vmax, at high substrate concentrations and does not increase
any higher. This makes sense, since there should be some point at which all the enzyme
molecules are saturated with substrate and addition of further substrate will not increase
the rate of the reaction.
At saturating values of [S] the rate is only dependent on the enzyme concentration [E].
Thus the enzyme catalysed reaction is said to be pseudo first order in [E].
If we look at the time-course of the reaction we can see that after an initial lag phase, the
rate of product formation d[P]/dt is a constant until at some time it begins to decline.
How do we explain the exact shape of the curve?
In 1913, Michaelis and Menten proposed a very simple model to account for this kinetic
behaviour. The key point of their theory was that a specific enzyme - substrate complex
(ES) is formed prior to the catalytic reaction and furthermore that the rate-limiting step in
the overall reaction was governed by the breakdown of the ES complex to give the
product.
The model they proposed is the simplest that accounts for the kinetic behaviour of many
enzymes. An enzyme, E, combines with substrate, S, to form an ES complex with rate
constant k1. The ES complex has two possible fates. It can dissociate back to E + S with
rate constant k-1, or it can proceed to product with rate constant k2. It is assumed for the
purposes of the model that none of the product is converted back to substrate, a condition
that is likely to be true in the early stages of a reaction when the concentration of product
is negligible. This is known as the initial velocity assumption.
How do we measure Vmax and KM?
A series of reactions is set up, each with the same enzyme concentration but different
substrate concentrations (in all cases [S] >> [ET]). The initial velocity is then measured
MBLG1001_lecture6
from the linear part of the reaction curve, which plots [P] versus time of reaction. The
initial velocity, v, is the slope at the origin.
Then v is plotted against [S] to give the curve we saw before. The Michael-Menten
equation can be fitted to the experimental curve using non-linear regression. A simpler
way to extract the parameters, Vmax and KM is to transform the equation into form that
will yield a linear plot. First take the reciprocals of both sides of the equation.
1/v = {[S] +KM}/Vmax[S] = 1/Vmax +KM/Vmax[S]
Thus a plot of 1/v versus 1/[S] will give a straight-line plot with a slope of KM/Vmax and
an intercept on the ordinate of 1/Vmax. This double reciprocal plot is known as a
Lineweaver-Burk plot. We will now go on to look at the physical significance of the
kinetic parameters. and various models for the ways in which enzymes can be inhibited.
Meaning of Vmax and KM
For most enzymes, the KM lies between 0.1 M and 0.1 mM. The KM depends on
environmental conditions such as pH, ionic strength and temperature. While KM is
trivially interpreted as the substrate concentration, which gives half-maximal velocity, it
can also have more physical significance under certain circumstances.
KM is equal to the dissociation constant of the ES complex. In other words, KM, is a
measure of the affinity of the enzyme for substrate. A low KM indicates tight binding of
the substrate by the enzyme, whereas a high KM indicates weak binding. It is a useful
measure of the relative strengths of the binding of an enzyme for different substrates.
This might be very useful information if one is trying to design an inhibitor for example.
The KM is independent of the enzyme concentration.
The turnover number of the enzyme, kcat, is the number of substrate molecules
that are converted into product by the enzyme per unit time when it is fully saturated with
substrate. This can vary greatly between enzymes. For example, catalase has a turnover
number of 40,000,000 s-1 whereas lysozyme has a turnover number of 0.5 s-1. However,
the KM for catalase is 25 mM while that for lysozyme is on 6 mM. Clearly the rate at
which an enzyme works is not dependent on how tightly the substrate binds.
The use of Vmax
Vmax is dependent on the [enzyme]. This means that by performing assays under Vmax
conditions ([S] > 10*KM) you can measure the amount of enzyme in a sample. If one
sample has twice the amount of enzyme in it than another sample then the Vmax rate will
be double. This has big implications in pathology, biochemistry and molecular biology.
Enzyme assays are used to measure everything from tissue damage and diagnosis to the
induction of enzymes by transcription factors in molecular biology.