Enzyme Technology
Enzyme inhibition
A number of substances may cause a
reduction in the rate of an enzyme catalysed reaction. Some of these (e.g., urea)
are non-specific protein denaturants. Others, which generally act in a fairly
specific manner, are known as inhibitors. Loss of activity may be either
reversible, where activity may be restored by the removal of the inhibitor, or
irreversible, where the loss of activity is time dependent and cannot be
recovered during the timescale of interest. If the inhibited enzyme is totally
inactive, irreversible inhibition behaves as a time-dependent loss of enzyme
concentration (i.e., lower Vmax), in other cases, involving incomplete
inactivation, there may be time-dependent changes in both Km and
Vmax. Heavy metal ions (e.g., mercury and lead) should generally be
prevented from coming into contact with enzymes as they usually cause such
irreversible inhibition by binding strongly to the amino acid backbone.
More
important for most enzyme-catalysed processes is the effect of reversible
inhibitors. These are generally discussed in terms of a simple extension to the
Michaelis-Menten reaction scheme.
[1.13]
where I represents the reversible inhibitor and the
inhibitory (dissociation) constants Ki and Ki' are given
by
(1.74)
and,
(1.75)
For the present purposes, it is assumed that neither EI nor
ESI
may react to form product. Equilibrium between EI and
ESI is allowed, but makes
no net contribution to the rate equation as it must be equivalent to the
equilibrium established through:
[1.14]
Binding of
inhibitors may change with the pH of the solution, as discussed earlier for
substrate binding, and result in the independent variation of both Ki
and Ki' with pH.
In order to simplify the analysis substantially, it is
necessary that the rate of product formation (k+2) is slow relative to
the establishment of the equilibria between the species.
Therefore:
(1.76)
also:
(1.77)
where:
(1.78)
therefore:
(1.79)
Substituting from equations (1.74), ( 1.75) and (1.76), followed by simplification,
gives:
(1.80)
therefore:
(1.81)
If the
total enzyme concentration is much less than the total inhibitor concentration (i.e.
[E]0<< [I]0),
then:
(1.82)
This is the equation used
generally for mixed inhibition involving both EI and
ESI
complexes (Figure 1.8a). A number of simplified cases exist.
Competitive inhibition
Ki' is much greater than
the total inhibitor concentration and the ESI complex is not formed. This occurs
when both the substrate and inhibitor compete for binding to the active site of
the enzyme. The inhibition is most noticeable at low substrate concentrations
but can be overcome at sufficiently high substrate concentrations as the
Vmax remains unaffected (Figure 1.8b). The rate equation is given
by:
(1.83)
where Kmapp is the apparent Km for
the reaction, and is given by:
(1.84)
Normally the competitive inhibitor bears some
structural similarity to the substrate, and often is a reaction product
(product inhibition, e.g., inhibition of lactase by galactose),
which may cause a substantial loss of productivity when high degrees of
conversion are required. The rate equation for product inhibition is derived
from equations (1.83) and (1.84).
(1.85)
A similar
effect is observed with competing substrates, quite a common state of affairs in
industrial conversions, and especially relevant to macromolecular hydrolyses
where a number of different substrates may coexist, all with different kinetic
parameters. The reaction involving two co-substrates may be modelled by the
scheme.
[1.15]
Both substrates compete for the same
catalytic site and, therefore, their binding is mutually exclusive and they
behave as competitive inhibitors of each others reactions. If the rates of
product formation are much slower than attainment of the equilibria (i.e., k+2 and k+4 are very much less than k-1 and
k-3 respectively), the rate of formation of P1 is given by:
(1.86)
and the rate of
formation of P2 is given by
(1.87)
If the substrate concentrations are both small relative
to their Km values:
(1.88)
Therefore, in a competitive situation using the same
enzyme and with both substrates at the same concentration:
(1.89)
where and
> in this simplified case. The relative rates of reaction are in the
ratio of their specificity constants. If both reactions produce the same product
(e.g., some hydrolyses):
(1.90)
therefore:
(1.91)
Uncompetitive
inhibition
Ki is much greater than the total inhibitor
concentration and the EI complex is not formed. This occurs when the inhibitor
binds to a site which only becomes available after the substrate (S1)
has bound to the active site of the enzyme. This inhibition is most commonly
encountered in multi-substrate reactions where the inhibitor is competitive with
respect to one substrate (e.g., S2) but uncompetitive with respect to
another (e.g., S1), where the reaction scheme may be represented by
[1.16]
The inhibition is
most noticeable at high substrate concentrations (i.e., S1 in the scheme
above) and cannot be overcome as both the Vmax and Km are
equally reduced (Figure 1.8c). The rate equation is:
(1.92)
where
Vmaxapp and Kmapp are the apparent
Vmax and Km given by:
(1.93)
and
(1.94)
In
this case the specificity constant remains unaffected by the inhibition.
Normally the uncompetitive inhibitor also bears some structural similarity to
one of the substrates and, again, is often a reaction product.
Figure 1.8. A schematic diagram showing the effect of reversible
inhibitors on the rate of enzyme-catalysed reactions. —— no
inhibition, (a) —— mixed inhibition ([I] = Ki = 0.5 Ki'); lower Vmaxapp (=
0.67 Vmax),
higher Kmapp (= 2 Km). (b) —— competitive
inhibition ([I] = Ki); Vmaxapp unchanged (=
Vmax), higher Kmapp (= 2 Km). (c) ——
uncompetitive inhibition ([I] = Ki'); lower Vmaxapp (=
0.5 Vmax) and Kmapp (= 0.5 Km). (d) ——
noncompetitive inhibition ([I] = Ki = Ki'); lower
Vmaxapp (= 0.5 Vmax), unchanged Kmapp
(= Km).
A special case of
uncompetitive inhibition is substrate inhibition which occurs at
high substrate concentrations in about 20% of all known enzymes (e.g., invertase
is inhibited by sucrose). It is primarily caused by more than one substrate
molecule binding to an active site meant for just one, often by different parts
of the substrate molecules binding to different subsites within the substrate
binding site. If the resultant complex is inactive this type of inhibition
causes a reduction in the rate of reaction, at high substrate concentrations. It
may be modelled by the following scheme
[1.17]
where:
(1.95)
The assumption is made that ESS
may not react to form product. It follows from equation (1.82) that:
(1.96)
Even quite high values for KS lead to a
levelling off of the rate of reaction at high substrate concentrations, and
lower KS values cause substantial inhibition (Figure
1.9).
Figure 1.9. The effect of substrate inhibition on the
rate of an enzyme-catalysed reaction. A comparison is made between the
inhibition caused by increasing KS relative to Km. —— no inhibition, KS/Km >> 100; ——
KS/Km = 100; —— KS/Km = 10; —— KS/Km = 1. By the nature of the binding causing
this inhibition, it is unlikely that KS/Km < 1.
Noncompetitive
inhibition
Both the EI and ESI complexes are formed equally well (i.e.
Ki equals Ki'). This occurs when the inhibitor binds at
a site away from the substrate binding site, causing a reduction in the
catalytic rate. It is quite rarely found as a special case of mixed inhibition.
The fractional inhibition is identical at all substrate concentrations and
cannot be overcome by increasing substrate concentration due to the reduction in
Vmax (Figure 1.8d). The rate equation is given by:
(1.97)
where
Vmaxapp is given by:
(1.98)
The diminution in the rate
of reaction with pH, described earlier, may be considered as a special case of
noncompetitive inhibition; the inhibitor being the hydrogen ion on the acid side
of the optimum or the hydroxide ion on the alkaline side.
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This page was established in 2004 and last updated by Martin
Chaplin on
6 August, 2014
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