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Identifying type of inhibitor from $K_m$ and $V_{max}$

Identifying type of inhibitor from $K_m$ and $V_{max}$


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Apparently it is possible to identify whether an inhibitor is competitive or non-competitive from graphs of substrate concentration (x axis) and rate of reaction (y axis).

There needs to be a line for with inhibitor (constant concentration) and without inhibitor. The difference in $K_m$ and $V_{max}$ can then be interpreted to find out whether the inhibitor is competitive or not.

I know that if the effect of the inhibitor decreases with an increase in substrate concentration then inhibitor is competitive.

However I don't understand how to tell from the graphs mentioned earlier and $K_m$ and $V_{max}$. Could someone explain.

I have tried to google this but most of what comes up is scholarly articles which are beyond my level of understanding…


Competitive inhibitor competes for the active site. Therefore it will interfere with the binding of the substrate thereby increasing the apparent KM.

A strictly non-competitive inhibitor does not compete for the active site. It however inhibits the catalysis by reducing the available molecules of active enzyme, E0 (if it is a perfect inhibitor), thereby lowering the Vmax.

There can be mixed inhibitors too and there can be different kinds of mixed inhibition. For example an inhibitor that interferes with catalysis and can also compete for the active site.

Depending on how you define KM, a non-competitive inhibitor may or may not change it. If such inhibitor can bind to the enzyme at non-active site and reduce its kcat, it changes the KM as well as Vmax in case of Briggs-Haldane kinetics.


I think it is possible to identify the type of inhibition from (initial) velocity vs substrate-concentration curves, but it is difficult. The usual way this is done is by using a linear transformation of the Michaelis-Menten equation, such as the Lineweaver-Burk plot.

But you are right: for a reversible inhibitor, the way to identify the inhibition pattern (that is, to determine whether a reversible inhibitor is competitive, uncompetitive, mixed, or non-competitive) is to inspect the changes to the kinetic constants (usually Km and Vmax, but see below)

Before we get into how that is done, there are a few points we need to be aware of.

  • The following only applies to reversible inhibitors. Irreversible inhibition, such as the inhibition of acetylcholinesterase by the nerve-gas sarin, is treated differently. (By 'reversible', it is simply meant that if the inhibitor is removed, by dilution for example, the inhibition goes away). In addition, tight-binding inhibitors are not considered.
  • The following also only applies to single-substrate enzymes that obey the Michaelis-Menten equation. (But the analysis may be extended, without too much difficulty, to multi-substrate enzymes).
  • We need to be very careful about the term 'non-competitive'. It means different things to different people. It is also often the least interesting pattern of inhibition.
  • When analyzing inhibition patterns, it is often easier to analyzed the effect on Vmax and Vmax/Km (the specificity constant), rather than on Km and Vmax. The reason for this is that Km is a complex kinetic constant and (as Dalziel and Fersht have shown), it should be thought of as the ratio of Vmax and the specificity constant (Vmax/Km). In this respect, enzyme kineticists have 'messed things up' by considering the specificity constant to be the ratio of the maximum velocity and the Michaelis constant: it is the Michaelis constant that is the ratio. However, the paradigm of considering the specificity constant as Vmax/Km is now so ingrained, I'll stick with it. But the 'trick' in analyzing inhibition patters is to think in terms of Vmax and Vmax/Km.
  • Much of what follows may also be applied to reversible activation, but I am not going to go into that at all.

1. Reversible Inhibitor Patterns

We can now define our inhibition patterns, independent of any mechanism that gives rise to them, as follows:

  • A competitive inhibitor has no effect on Vmax but decreases the apparent value of Vmax/Km. We can also say, in 'old school terms', that a competitive inhibitor has no effect Vmax but increases the apparent Km value. Or, if we are going to 'visualize' things in terms of Lineweaver-Burk plots (see this wikipedia article), we can say that a competitive inhibitor has no effect on Vmax but increases the apparent value of Km/Vmax

  • An uncompetitive inhibitor decreases the apparent value of Vmax but has no effect on Vmax/Km. Or, thinking in terms of reciprocals, an uncompetitive inhibitor increases the apparent value of 1/Vmax but has no effect on Km/Vmax. In many ways, 'uncompetitive' is a a very poor term. Cornish-Bowden (2004) suggests the term 'catalytic inhibitor', and Laidler and Bunting use the term 'anti-competitive' to describe this type of inhibition.

  • A mixed inhibitor decreases the apparent value of Vmax and decreases the apparent value of Vmax/ Km. Or, thinking in terms of reciprocals, a 'mixed' inhibitor increases the apparent value of 1/Vmax and increases the apparent value of Km/Vmax.
  • A non-competitive inhibitor is best thought of as a special case of mixed inhibition where the apparent values of Vmax and Vmax/ Km are decreased to the same extent. There is an interesting consequence of this: as the Michaelis constant may be thought of as the ratio of these two kinetic constants, it is unchanged in non-competitive inhibition. But it is difficult to envisage a realistic kinetic mechanism that results in this type of behavior. Cornish-Bowden (2004, pp 118-119) is very strong on this point (There is also a fourth edition of this great book).
  • We now come to a 'tricky' bit. Some authorities, notably Cleland, do not distinguish between 'mixed' and 'non-competitive' inhibition, but instead call all cases where both Vmax and Vmax/ Km are decreased 'non-competitive inhibition'. We need to be very careful on this one. As someone once said, enzyme kineticists would rather use each other's toothbrushes rather than use each other's nomenclature.

So there we have it: the two cases that 'demarcate' reversible inhibition are where only the apparent Vmax is changed (uncompetitive inhibition) and where only the apparent Vmax/Km (the specificity constant) is changed (competitive inhibition). 'Mixed' inhibition is where the apparent values of both these kinetic constants are affected, and a special case of 'mixed' inhibition is where the the apparent values of both kinetic constants are decreased to the same extent, resulting in no change to the Michaelis constant.

2. Reversible Inhibitor Mechanisms

So far, I have said nothing about the mechanisms that might give rise to these inhibition patterns. Preliminaries:

  • In what follows, $K_m$ is the Michaelis constant, $V_{max}$ is the maximum velocity, $s$ is substrate concentration, $i$ is inhibitor concentration, and $K_{i}$ and $K_{ii}$ are inhibition constants. Both $v$ and $v_i$ refer to the initial velocity.
  • Inhibition patterns are analyzed using the Lineweaver-Burk plot. This is convenient as in such a plot (see this wikipedia article), the y-axis intercept equals $1$/$V_{max}$ and the slope equals $K_m$/$V_{max}$. Changes to the apparent value of $V_{max}$ are manifested as a y-axis-intercept effect, and changes to the specificity constant ($V_{max}$/$K_m$) are manifested as a slope effect. In addition, the x-axis intercept equals $-1$/$K_m$, so that changes to the apparent $K_m$ value, or lack of such a change, is easily recognized.
  • The Lineweaver-Burk plot is not the only linear transformation of the Michelis-Menten equation, or even the best one (see here). Other plots are the Hanes-Woolf plot and the Eadie-Hofstee plot. As someone else once said, biochemists worship at the alter of the straight line. I use the Lineweaver-Burk plot because, IMO at least, it is the most intuitive.
  • It needs to be borne is mind that many kinetic mechanisms may give rise to an inhibition pattern. Many kinetic mechanisms may give rise to competitive inhibition, for example. What follows are illustrative examples.
  • All of the plots below (generated using Mathematica) were created with $V_{max}$ = 100 and $K_m$ = 10. When only one inhibition constant was required ($K_i$), it was set to 100. When two were required, the second ($K_{ii}$) was set to 20 (All 'arbitrary units'). The plots, of course, are very easy to generate and may be done with many software applications.

(a) Competitive Inhibition

Let's consider reversible inhibition in single-substrate enzyme described by the mechanism shown above, where both the inhibitor and substrate compete for the 'free' enzyme.

Derivation of the rate law for this mechanism using either the equilibrium or steady-state assumption, leads to an equation of the following form (nice derivations are given in Segel, 1975):

$$ v_{i} = { {{{V_{max}}} s }over{K_{m}(1 + {iover{K_{i}}})} + s} (1)$$

Representative plots of Eqn (1), showing the effect of increasing inhibitor concentrations:

Taking reciprocals of Eqn (1) followed by rearrangement leads to the Lineweaver-Burk linear transformation:

$${1over{v_i}}=frac{K_m}{V_{max}}(1 + {iover{K_i}})( {1over{s}}) + {1over{V_{max}}} (2)$$

It is immediately obvious that the inhibitor increases the apparent value of $K_{m}$ / $V_{max}$ but does not effect 1 / $V_{max}$.

That is, it effects the specificity constant ($V_{max}$ / $K_{m}$) but not $V_{max}$. Inhibition is therefore competitive

Plots of Eqn (2) predict a family of straight lines intersecting on the y-axis at $1$/$V_{max}$, and the competitive inhibition pattern is easily recognized:

In terms of the Lineweaver-Burk transformation, a competitive inhibitor causes the slope to increase but does not change the y-axis intercept.

We can also go a step further. The slopes of the above lines are given by the following Eqn:

$$slope = frac{K_m}{V_{max}} + frac{K_m}{V_{max} K_{i}}{i} (3)$$

Thus a plot of slope vs inhibitor-concentration is predicted to be a straight line which intersects the x-axis at -$K_i$

Such replots serve two functions. Firstly, they allow determination of the $K_{i}$ value. In this case, the x-axis intercept is -100, which is not too surprising as 100 was the value of $K_i$ chosen in the simulation. Secondly, they check for unexpected kinetic complexity. A curved slope replot, for example, might be indicative of partial competitive inhibition, where the EI complex can perhaps breakdown to give product. Such kinetic complexity is probably rare with single-substrate enzymes, but may occur in multi-substrate enzymes (and may require the rejection of a simple kinetic mechanism as an explanation of kinetic data). Segel (1975) is very strong on partial inhibition, and the mechanisms that may give rise to it. When the slope replot is linear we may speak of linear competitive inhibition (see Cornish-Bowden, 2004).

A number of points may be made about competitive inhibition:

  • One of the 'hallmarks' of competitive inhibition is that the inhibitory effect may be overcome by adding excess substrate.
  • A competitive inhibitor need not bind the the active site. All that is required is that it binds to the free enzyme in a manner that prevents substrate binding. An allosteric inhibitor, for example, may be competitive. But, of course, competition between the substrate and inhibitor for the same active site is one way that competitive inhibition may arise (assuming that binding of inhibitor prevents substrate binding). Segel (1975) is very strong on this point.
  • A good example of a competitive inhibitor is malonic acid, which inhibits succinate dehydrogenase (see Segel, 1975). In the world of two-substrate kinetics, pyrazole is a competitive inhibitor, with respect to ethanol, of horse liver alcohol dehydrogenase, and a classic paper (Li and Theorell) showing this is available here

Finally, let's reiterate this point: Eqn (1) describes one mechanism that gives rise to a competitive inhibition pattern. It is certainly not the only one.

(b) Uncompetitive Inhibition

Now let's consider a mechanism, described by the diagram above, where the inhibitor cannot bind to the 'free' enzyme, but instead bind to the enzyme-substrate complex (to give an abortive EAI ternary complex)

Derivation of the rate law his mechanism (again by making either the steady-state or equilibrium assumption; see Segel, 1975) leads to an equation of the following form:

$$ v_{i} = { {{{V_{max}}} s }over{K_{m}} + (1 + {iover{K_{i}}}) s} (3)$$

Transformation to the Lineweaver-Burk form:

$${1over{v_i}}=frac{K_m}{V_{max}}( {1over{s}}) + {1over{V_{max}}}(1 + {iover{K_i}}) (4)$$

In this case, the inhibitor increases the apparent value of 1 / $V_{max}$ but does not effect $K_{m}$ / $V_{max}$

In other words, it effects the apparent value of $V_{max}$, but has no effect on the specificity constant ($V_{max}$ / $K_{m}$). Inhibition is therefore uncompetitive.

Furthermore, unlike the case of competitive inhibition, increasing the substrate concentration does not abolish inhibition.

An uncompetitive inhibitor causes the slope of a Lineweaver-Burk plot to increase, but does not change the y-axis intercept of such a plot.

Therefore double-reciprocal plots of $1$/$v_i$ vs $1$/$s$ at different $i$ form a family of parallel lines.

In this case, the $K_{i}$ may be determined from an intercept-replot, where the x-axis intercept is -$K_i$.

$$intercept={1over{V_{max}}} +{iover{V_{max} {K_i}}} (5)$$

(c) Mixed Inhibition

Now let's consider a mechanism where the inhibitor may bind to either the 'free' enzyme or the enzyme-substrate complex and (to keep things somewhat realistic) where the substrate may bind to either the free enzyme or the enzyme-inhibitor complex.

Under certain simplifying assumptions (see Segel, 1975) the mechanism shown above may give rise to the following rate law:

$$ v_{i} = { {{{V_{max}}} s }over{K_{m}(1 + {iover{K_{i}}})} + (1 + {iover{K_{ii}}}) s} (6)$$

In this case, there are two inhibition constants, one 'governing' the binding of inhibitor to the 'free' enzyme ($K_{i}$) and one 'governing' the binding of inhibitor to the enzyme-substrate complex ( $K{ii}$).

Taking reciprocals, the corresponding Lineweaver-Burk transformation may be expressed as follows: $${1over{v_i}}=frac{K_m}{V_{max}}(1 + {iover{K_i}})( {1over{s}}) + {1over{V_{max}}}(1 + {iover{K_{ii}}}) (7)$$

The inhibitor increases both apparent the value of 1 / $V_{max}$ and (by not necessarily the same factor) and the apparent value of $K_{m}$ / $V_{max}$. Inhibition is therefore mixed.

Eqn (7) predicts a family of straight lines that intersect at a single point:

$$({x, y})= (-frac{K_{ii}}{K_i K_m}, frac{K_{i} - K_{ii}}{K_i V_{max}}) = (-0.02,0.008) (8) $$

In this case, slope and intercept replots may be used to determine the values of $K_i$ and $K_{ii}$. A detailed analysis of such plots is given in Segel (1975).

(d) Non-Competitive Inhibition

We now come to the case of non-competitive inhibition, which (as stated above) is best considered a special case of mixed inhibition. When $K_i$ = $K_{ii}$, Eqn (6) simplifies to the following:

$$ v_{i} = { {{{V_{max}}} s }over(1 + {iover{K_{i}}})(K_{m} +s)} (9)$$

The Lineweaver-Burk transformation:

$${1over{v_i}}=frac{K_m}{V_{max}}(1 + {iover{K_i}})( {1over{s}}) + {1over{V_{max}}}(1 + {iover{K_{i}}}) (10)$$

Eqn (10) predicts a family of lines where increasing $i$ affects both the slope and intercept to the same extent, and which intersect on the x-axis at $-1$/$K_m$

But why should $K_i$ equal $K_{ii}$ in any realistic case?

Notes

Fersht now owns the copyright to his book, and is distributing it free of charge

All issues of Acta Chem Scand (1947 - 1999), including many classic papers, are available on-line

An example of a steady-state rate law derivation is given in this Biology This Site answer

References

Cook, P. F. & Cleland, W. W. (2007). Enzyme Kinetics and Mechanism. Garland Science Publishing (Taylor & Francis Group). London & New York.

Cornish-Bowden, A. (2004). Fundamentals of Enzyme Kinetics. 3rd edn. Portland Press Ltd, London.

Dalziel, K. (1957). Initial steady state velocities in the evaluation of enzyme-coenzyme-substrate reaction mechanisms. Acta Chem. Scand. 11, 1706 - 1723. [pdf]

Dalziel, K. (1975). Kinetics and mechanism of nicotinamide-nucleotide-linked dehydrogenases. In The Enzymes, 3rd edn., Vol. 11. Boyer, P. D., Ed. pp 1 - 60. Academic Press, New York.

Fersht, A. (1999). Structure and Mechanism in Protein Science. A Guide to Enzyme Catalysis and Protein Folding. W. H. Freeman, New York. [pdf]

Li, T. - K. & Theorell, H. (1969). Human liver alcohol dehydrogenase: Inhibition by pyrazole and pyrazole analogs. Acta Chem. Scand. 23, 892 - 902. [pdf]

Lineweaver, H. & Burk, D. (1934). The determination of enzyme dissociation constants. J. Am. Chem. Soc. 56, 658 - 666.

Segel, I. H. (1975). Enzyme Kinetics. Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems. John Wiley & Sons, Inc., New York.


Introduction to Food Enzymes

1.5.5 Effect of Inhibitors

Enzyme inhibitors are molecules that interact with enzymes (temporary or permanent) in some way and reduce the rate of an enzyme-catalyzed reaction or prevent enzymes to work in a normal manner. The important types of inhibitors are competitive, noncompetitive, and uncompetitive inhibitors. Besides these inhibitor types, a mixed inhibition exists as well. Competitive enzyme inhibitors possess a similar shape to that of the substrate molecule and compete with the substrate for the active site of the enzyme. This prevents the formation of enzyme-substrate complexes. Therefore, fewer substrate molecules can bind to the enzymes so the reaction rate is decreased. The level of inhibition depends on the relative concentration of substrate and inhibitor. This is a reversible process (temporary binding). In the case of competitive inhibition, Km is increased but Vmax is not altered. Noncompetitive enzyme inhibitors bind to a site other than the active site of the enzyme, called an allosteric site. Due to this binding, it deforms the structure of the enzyme so that it does not form the ES complex at its normal rate, and it prevents the formation of enzyme-product complexes, which leads to fewer product formations. Because they do not compete with substrate molecules, noncompetitive inhibitors are not affected by substrate concentration. In the case of noncompetitive inhibition, Vmax is lowered but Km is not altered. Uncompetitive inhibitor cannot bind to the free enzyme, but only to the ES complex. The resulting ES complex is enzymatically inactive. This type of inhibition is rare but may occur in multimeric enzymes. Some enzyme inhibitors covalently bind to the active site of the enzyme and inhibit its total activity, thus known as enzyme poison. This type of inhibition is irreversible (permanent). Some enzyme inhibitors can be used as a medicine or as metabolic poison in the treatment of a particular disease.


12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering

Timothy Van Daele , . Ingmar Nopens , in Computer Aided Chemical Engineering , 2015

3 Results

The Michaelis-Menten equation (see Equation 1 ) will be used to illustrate the different core functionalities of the package by following the stepwise approach of Figure 1 . The following results were achieved by using only 25 lines of code from model definition until OED (ignoring loading of packages and comments), this illustrates the power and accessibility of the package. This limited number of lines gives the user access to advanced functionalities. In the following part only the results and figures of the different steps are shown, the code will be made publicly available prior to the conference. A (local) identifiability analysis was performed by using collinearity analysis, and showed no identifiability problems.

3.1 Model calibration

First the parameters Vmax and KS of the Michaelis-Menten reaction have to be estimated by use of some data. Six data points were generated in silico, using the parameter values of the paper published by Johnson and Goody (2011) . For each of these data points relative noise was added, what means that higher model output values of v can have a higher absolute noise compared to low values of v. This noise was randomly sampled from a normal distribution with mean zero and a standard deviation of 0.05. The six data points were taken at substrate concentrations S of 5, 10, 20, 30, 75 and 100 mM. By using a WSSE with relative weights more weight/certainty was given to low v values. This resulted in the fit shown in Figure 2 . The estimated parameter values were slightly different from the real parameter values (a Vmax value of 0.746 mM/min and a KS value of 17.55 mM). This is due to the normal noise that was added. To assure that the objective function is not prone to local minima, it is considered good practice to repeat a parameter estimation multiple times with different starting points to assure that the same values are always retrieved. If this is not the case, one should use global minimisation methods (e.g. particle swarm optimisation) or verify whether the model is (practical) identifiable.

Figure 2 . The in silico data with noise was used to estimate the parameters Vmax and KS of the Michaelis-Menten model ( Equation 1 ). The minimisation of the objective function yielded a Vmax value of 0.746 mM/min and a KS value of 17.55 mM. These results are slightly different from the real parameter values, because of the normal noise which was added.

3.2 Estimate parameter confidence

After finishing the parameter estimation the confidence levels for the different parameters can be calculated using the FIM. Using the built-in function ‘get_parameter_confidence’, the different parameter and corresponding 95 % confidence intervals are retrieved: Vmax = 0.746 ± 0.094 mM/min and KS = 17.55 ± 4.55 mM and were both considered as reliable based on the Student’s t-test.

Figure 3 . By using optimal experimental design and the D-optimality criterion, the experiments are optimised and the confidence intervals are decreased for both parameters. In the two lower figures, the local parameter relative sensitivity is showed for both Vmax and KS.

3.3 Optimal Experimental Design for parameter estimation

Instead of ignoring available knowledge reported in the paper of Johnson and Goody (2011) , it is possible to take this knowledge into account when designing experiments. The total number of experiments is still equal to six and the only experimental degree of freedom is the sucrose concentration S, which can be varied between 5 and 100 mM. The minimum sucrose concentration was set to 5 mM to assure sufficiently high reaction rates. An extra optimisation constraint was added, i.e. the difference in sucrose concentration between two experiments should be at least 5 mM. This allows to make the design less dependent on the actual parameter values. This optimisation led to lower confidence intervals for both parameters. For Vmax the optimised experimental design led to a 95 % confidence interval of only 0.070, a decrease of 25.5 %. For KS the 95 % confidence interval decreased to 3.73, which is 18.0 % lower compared the the original experimental setup. This illustrates that OED is a powerful technique which can improve the confidence levels of the models without requiring an additional experimental effort.


Identifying type of inhibitor from $K_m$ and $V_{max}$ - Biology

Enzyme inhibitors function as an important mechanism for regulating enzymatic activity.

The cell uses specific molecules to regulate enzymes in order to promote or inhibit certain chemical reactions. Sometimes it is necessary to inhibit an enzyme to reduce a reaction rate, and there is more than one way for this inhibition to occur. In competitive inhibition, an inhibitor molecule is similar enough to a substrate that it can bind to the enzyme’s active site to stop it from binding to the substrate. It “competes” with the substrate to bind to the enzyme.

In noncompetitive (allosteric) inhibition, an inhibitor molecule binds to the enzyme at a location other than the active site (an allosteric site). The substrate can still bind to the enzyme, but the inhibitor changes the shape of the enzyme so it is no longer in an optimal position to catalyze the reaction.

Mixed inhibitors bind at a site on the enzyme other than the active site, so they do not prevent the substrate from binding. Their name is inspired by the fact that they can bind to either the enzyme alone or the enzyme-substrate complex. Most types of mixed inhibitors have a preference for one or the other, which dictates the effect on Km and Vmax. Mixed inhibitors that act like competitive inhibitors by binding primarily to the enzyme before the substrate is associated increase Km (like competitive inhibitors). In contrast, mixed inhibitors that act more like uncompetitive inhibitors by preferring to bind to the enzyme-substrate complex lower Km. All mixed inhibitors lover Vmax to some extent.

Uncompetitive inhibitors bind at a site other than the active site. Regulatory molecules can also bind to a site other than the active site and exert a positive feedback effect (as opposed to an inhibitory effect). Uncompetitive inhibitors do not bind to the enzyme until it has associated with the substrate to form the enzyme-substrate complex. Once the uncompetitive inhibitor has bound, the substrate remains associated with the enzyme. The apparent affinity of the enzyme for the substrate increases, meaning that Km decreases. Because the uncompetitive inhibitor only affects enzymes that have already bound the substrate, adding more substrate does not overcome the effect of the inhibitor. The Vmax is lowered because the substrate stays bound to the enzyme for a longer period of time. Uncompetitive inhibitors decrease the Vmax and Km proportionally.

Characteristics of Enzyme Inhibitors

Type of Inhibitor Binding Site Inhibits Binding of Substrate? Effect on Km Effect on Vmax
Competitive Enzyme (active site) Yes Increase No change
Uncompetitive E-S complex No Decrease Decrease
Mixed E-S complex or enzyme No Increase OR decrease Decrease
Noncompetitive E-S complex or enzyme No No change Decrease

Graphing experimental data from reactions with and without an inhibitor in a Lineweaver-Burk plot allows for the identification of the type of inhibition, based on how the best-fit line changes. Then the changes in Km and Vmax can be calculated. For example, a competitive inhibitor will change the Km, but not the Vmax – so the slope and x-intercept of the Lineweaver-Burk plot will be different from the original reaction but the y-interecept (Vmax) will remain the same. The addition of an uncompetitive inhibitor decreases both the Km and Vmax, but it does so proportionally such that the slope of the Lineweaver-Burk plot (Km/Vmax) does not change.


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• In competitive inhibition, an inhibitor molecule competes with a substrate by binding to the enzyme ‘s active site so the substrate is blocked.

• In noncompetitive inhibition (also known as allosteric inhibition), an inhibitor binds to an allosteric site the substrate can still bind to the enzyme, but the enzyme is no longer in optimal position to catalyze the reaction.

• Mixed inhibitors bind at a site on the enzyme other than the active site, so they do not prevent the substrate from binding. Their name is inspired by the fact that they can bind to either the enzyme alone or the enzyme-substrate complex.

• Uncompetitive inhibitors bind at a site other than the active site. Uncompetitive inhibitors do not bind to the enzyme until it has associated with the substrate to form the enzyme-substrate complex.

allosteric site: a site other than the active site on an enzyme.

noncompetitive inhibition: inhibitor molecules bind to the enzyme at a location other than the active site

competitive inhibition: an inhibitor molecule is similar enough to a substrate that it can bind to the enzyme’s active site to stop it from binding to the substrate

substrate: a reactant in a chemical reaction is called a substrate when acted upon by an enzyme

inhibitor: a molecule that binds to an enzyme and decreases its activity

Vmax: The maximal velocity, or rate of a reaction, at saturating substrate concentrations.

Km: the michaelis constant is a measure of the affinity of the enzyme for the substrates

positive feedback: is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance

affinity: how strongly an enzyme binds to a substrate

Lineweaver-Burk plot: A method for experimentally determining the kinetic parameters of an enzymatic reaction. The slope is equal to Km/Vmax.


Contents

[S]: substrate concentration. The independent axis of Lineweaver- Burk plot is the reciprocal of substrate concentration. [2]

V0 or V: initial velocity of an enzyme inhibited reaction. The dependent axis of the Lineweaver- Burk plot is the reciprocal of velocity. [5]

Vmax: maximum velocity of the reaction. The y-intercept of the Lineweaver- Burk plot is the reciprocal of maximum velocity. [2]

KM: Michaelis-Menten constant or enzyme affinity. The lower the KM the higher the affinity. Graphically the x-intercept of the line is -1/KM. [5]

Kcat: turnover number, or reactions per unit time. The lower the Kcat the slower the reaction. Kcat=Vmax/[Enzyme]. Graphically this can be evaluated by looking at Vmax. [2]

Catalytic Efficiency= Kcat/KM . A fast catalyst and high affinity results in best catalytic efficiency. [5]

The plot provides a useful graphical method for analysis of the Michaelis–Menten equation, as it is difficult to determine precisely the Vmax of an enzyme-catalysed reaction:

Taking the reciprocal gives:

The Lineweaver–Burk plot puts 1/[S] on the x-axis and 1/V on the y-axis. [6]

When used for determining the type of enzyme inhibition, the Lineweaver–Burk plot can distinguish competitive, pure non-competitive and uncompetitive inhibitors. The various modes of inhibition can be compared to the uninhibited reaction.

Competitive Inhibition Edit

Vmax is unaffected by competitive inhibitors. Therefore competitive inhibitors have the same y-intercept as uninhibited enzymes (since Vmax is unaffected by competitive inhibitors the inverse of Vmax also doesn't change).

Competitive inhibition increases the KM ,or lowers substrate affinity. The KM inhibited is α >> KM. [5] Graphically this can be seen as the inhibited enzyme having a larger x-intercept. [2] The slopes of competitively inhibited enzymes and non-inhibited enzymes are different. Competitive inhibition is shown on the far left image.

Pure Noncompetitive Inhibition Edit

With pure noncompetitive inhibition Vmax is lowered with inhibition. Vmax inhibited is α >> Vmax. [5] This can be seen on the Lineweaver–Burk plot as an increased y-intercept with inhibition, as the reciprocal is plotted. [7]

Pure noncompetitive inhibition does not effect substrate affinity, therefore KM remains unchanged. Graphically this can be seen in that enzymes with pure noncompetitive inhibition intersect with non-inhibited enzymes at the x-axis. [2] The slopes of pure noncompetitive inhibited enzymes and non-inhibited enzymes are different. [7] Pure noncompetitive inhibition is shown in the image far right image.

Mixed Inhibition Edit

Pure noncompetitive inhibition is rare, meaning mixed inhibition is more likely to result. In the case of mixed inhibition Vmax and KM are both effected at non-proportional rate. In most cases Vmax is decreased, while KM is increased, meaning affinity usually decreases with mixed inhibition. The lines of mixed inhibition and no inhibition intersect somewhere between the x- axis and y- axis, but never on an axis with mixed inhibition. [5]

Uncompetitive Inhibition Edit

Vmax decreases with uncompetitive inhibition. Vmax inhibited is α >> Vmax. [5] This can be seen on the Lineweaver–Burk plot as an increased y-intercept with inhibition, as the reciprocal is plotted. [7] This relationship is seen in both uncompetitive inhibition and pure competitive inhibition. [5]

Substrate affinity increases with uncompetitive inhibition, or lowers KM. The inhibited KM is KM / α >> . Graphically this means that enzymes with uncompetitive inhibition will have a smaller x-intercept than non inhibited enzymes. [5] Despite the x-intercept and y-intercept of uncompetitive inhibition both changing, the slope remains constant. Graphically uncompetitive inhibition can be identified in that the line of inhibited enzyme is parallel to non-inhibited enzyme. Uncompetitive inhibition is shown in the middle image.

While the Lineweaver-Burk is useful for determining important variables in enzyme kinetics, it is prone to error. The y-axis of the plot takes the reciprocal of the rate of reaction, meaning small errors in measurement are more noticeable. [8] Additionally because most points on the plot are found far to the right of the y-axis. large values of [S] (and hence small values for 1/[S] on the plot) are often not possible due to limited solubility. [8]


H + + HbO2 ←→ H + Hb + O2

The observed cooperativity of oxygen binding to hemoglobin can be explained by changes in shape to the hemoglobin molecule upon oxygen attachment. What kind of change would this be considered?

Hemoglobin reacts with an allosteric change to oxygen binding, because the shape of the molecule changes. In fact, oxygen is considered a "homotropic" allosteric regulator because it is the normal substrate for hemoglobin, and affects its changes on that molecule by binding to its active site.

Example Question #1 : Enzymes And Enzyme Inhibition

Cryptosporidium is a genus of gastrointestinal parasite that infects the intestinal epithelium of mammals. Cryptosporidium is water-borne, and is an apicomplexan parasite. This phylum also includes Plasmodium, Babesia, and Toxoplasma.

Apicomplexans are unique due to their apicoplast, an apical organelle that helps penetrate mammalian epithelium. In the case of cryptosporidium, there is an interaction between the surface proteins of mammalian epithelial tissue and those of the apical portion of the cryptosporidium infective stage, or oocyst. A scientist is conducting an experiment to test the hypothesis that the oocyst secretes a peptide compound that neutralizes intestinal defense cells. These defense cells are resident in the intestinal epithelium, and defend the tissue by phagocytizing the oocysts.

She sets up the following experiment:

As the neutralizing compound was believed to be secreted by the oocyst, the scientist collected oocysts onto growth media. The oocysts were grown among intestinal epithelial cells, and then the media was collected. The media was then added to another plate where Toxoplasma gondii was growing with intestinal epithelial cells. A second plate of Toxoplasma gondii was grown with the same type of intestinal epithelium, but no oocyst-sourced media was added.

Where is the likely site of the neutralizing toxin synthesis in cryptosporidium cells?

Smooth endoplasmic reticulum

The passage specifies that the neutralizing agent is a peptide. Ribosomes synthesize peptides. Nuceloulus may have been a tempting answer, but is where ribosomes are synthesized, not peptides.

Example Question #1 : Enzymes And Enzyme Inhibition

Of the following statements, which is true regarding the change in free energy (ΔG) of a reaction?

ΔG predicts the rate of a reaction.

Two of these answers are correct.

ΔG is a measure of whether a reaction is spontaneous.

When ΔG is zero, the system is at equilibrium.

Two of these answers are correct.

Gibbs Free Energy (G) is a measure of the capacity of a system to do useful work as it proceeds to equilibrium. ΔG measures the spontaneity of a reaction a negative value for ΔG indicates a spontaneous reaction, a positive value indicates a non-spontaneous reaction, and a value of zero indicates a reaction at equilibrium. ΔG does not predict enzyme kinetics it only predicts thermodynamics, thus, two of the answers are correct.

Example Question #5 : Enzymes And Enzyme Inhibition

Drain cleaners a common household staple, used to open clogged drains in bathtubs and sinks. Human hair is a common culprit that clogs pipes, and hair is made predominately of protein. Drain cleaners are effective at breaking down proteins that have accumulated in plumbing. Drain cleaners can be either acidic or basic, and are also effective at breaking down fats that have accumulated with proteins.

A typical reaction—reaction 1—which would be expected for a drain cleaner on contact with human hair, would be as follows in an aqueous solution:

Another reaction that may occur, reaction 2, would take place as follows in an aqueous solution:

Protein that forms the hair discussed in the preceeding passage is considered strucutral protein. Functional proteins, such as enzymes, are the other major class. Which of the following is true of enzymes?

They raise activaiton energy to prevent the reverse reaction from occuring as quickly.

They only lower activation energy of the original reaction mechanism.

They lower activation energy by providing an alternate reaction mechanism.

They lower activation energy by changing the equilibrium position of a reaction.

They lower activation energy by changing the products of a reaction.

They lower activation energy by providing an alternate reaction mechanism.

Enzymes are biological catalysts that function to lower activation energy via an alternative reaction pathway. They never alter the equilibrium of the reaction they impact.

Example Question #1 : Enzymes And Enzyme Inhibition

Drain cleaners a common household staple, used to open clogged drains in bathtubs and sinks. Human hair is a common culprit that clogs pipes, and hair is made predominately of protein. Drain cleaners are effective at breaking down proteins that have accumulated in plumbing. Drain cleaners can be either acidic or basic, and are also effective at breaking down fats that have accumulated with proteins.

A typical reaction—reaction 1—which would be expected for a drain cleaner on contact with human hair, would be as follows in an aqueous solution:

Another reaction that may occur, reaction 2, would take place as follows in an aqueous solution:

Protein that forms the hair discussed in the preceeding passage is considered strucutral protein. Functional proteins, such as enzymes, are the other major class. Which of the following is expected in an enzymatic biological reaction?

I. Faster rate than non-enzymatic reaction

II. Enzymatic coupling to hydrolysis reactions

III. More product generation relative to amount of reactant than non-enzymatic reaction

Enzymatic reactions will always proceed faster than if there was no enzyme present. They will also often be coupled to hydrolysis reactions to drive them forward thermodynamically, such as ATP hyrodlysis to make an otherwise unfavorable reaction proceed. The equilibrium constant of an enzymatic reaction is never different than the constant for the same reaction without enyzme, however, and thus choice III is incorrect.

Example Question #1 : Enzymes And Enzyme Inhibition

A student observes an enzymatic chemical reaction that normally takes place in human blood. She performs an experiment to see how certain conditions affect the reaction with the enzyme fully saturated with substrate. What should she do to speed the reaction up?

Increase the enzyme concentration

Increase the temperature to 40 degrees Celsius

Remove some of the enzyme

Increase the enzyme concentration

Adding more enzyme is the only way to make this reaction proceed faster. Since this is a reaction that takes place in the blood, the optimal conditions are 37 degrees Celsius and a pH of 7.4. Adding more substrate could help in certain conditions, but we know from the question that there is no free enzyme in the reaction so adding more would not help. Removing enzyme would obviously sow the reaction down.

Example Question #8 : Enzymes And Enzyme Inhibition

In order to catalyze a reaction, an enzyme is required to __________ .

decrease the activation energy

be saturated with substrate

increase the equilibrium constant

increase the activation energy

decrease the activation energy

Enzymes are biological catalysts that are responsible for the acceleration of the rate and specificity of many metabolic reactions. In order for rate acceleration to occur, an enzyme lowers the activation energy of a reaction. This allows for products to be formed more quickly and reactions to reach equilibrium more rapidly. Substrates bind to the active site of an enzyme and, in the presence of a large concentration of substrate, enzyme active sites become saturated and the reaction rate reaches a maximum constant. The equilibrium constant is calculated from the expression for chemical equilibrium, and is not affected by enzymes. Thus, the correct answer is to decrease the activation energy.

Example Question #9 : Enzymes And Enzyme Inhibition

Fetal hemoglobin has a higher binding affinity for oxygen than does adult hemoglobin.

In comparison to the adult oxyhemoglobin dissociation curve, the fetal oxyhemoglobin dissociation curve will __________ .

be shifted to the right and display a higher Km

be shifted to the right and display a lower Km

be shifted to the left and display a lower Km

be shifted to the left and display a higher Km

be shifted to the left and display a lower Km

Fetal hemoglobin is associated with a left-shift due to its greater binding affinity for oxygen. The Michaelis constant, Km, is defined as the substrate concentration at which the reaction rate is 0.5 * Vmax. A low Km indicates high substrate affinity.

Example Question #1 : Enzymes And Enzyme Inhibition

Which of the following is NOT a class of enzyme?

The correct answer is pyrimidine complex. A pyrimidine refers to a type of nucleotide base. Enzymes commonly have the suffix -ase at the end of their name.

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EXPERIMENTAL PROCEDURES

Materials—

All chemicals were obtained from Sigma (St. Louis, MO) catalog numbers are indicated. Household chemicals were purchased at local grocery and retail discount stores.

Library Preparation—

The library consists of a wide variety of household substances, ranging from over-the-counter drugs to beauty products to spices (Table I). These substances are prepared as 10% (v/v) aqueous solutions for liquid items and 5% w/v aqueous stock solutions for solids and given an identifying code. The latter solutions are centrifuged to remove any particulate matter. To aid in dispensing the library to students, the samples are distributed both in screw cap tubes and in 96-well dispensing plates, leaving one well in each column blank for controls (Table II). Students use multichannel pipetmen to dispense the samples into the test plates. In the outreach version, disposable plastic droppers are used for all solution additions.

Enzyme Inhibition Assay—

Wheat germ acid phosphatase previously prepared by students in previous weeks or commercially available acid phosphatase (1 U/ml Sigma P 3627) is used. For each test compound, 20 μl of substance, 12 μl of 5 mm pNPP (0.3 mm final concentration Sigma N 3254), 100 μl of 100 mm sodium acetate buffer, pH 4.7, and 48 μl of water are mixed in a well of a 96-well plate. Then 20 μl of enzyme solution was added to start the reaction. After 5 min, 100 μl of 1 m NaOH was added to stop the reaction, and the absorbance was measured at 405 nm using a SpectraMax plate reader. The Path Check function was used to reduce error due to variations in volume. A blank reaction with no enzyme is used as a measure of background hydrolysis of the pNPP, and 5 mm sodium phosphate buffer, pH 4.7, was used as a known inhibitor. By simply changing the buffer system to pH 8.0 Tris buffer, the assay is easily adapted for use with alkaline phosphatase as a target enzyme.

In the outreach version of the experiment, five drops of the substance, five drops of phosphatase, and five drops of 1 mm pNPP are mixed. After 5 min, two drops of 0.1 m NaOH are added to the wells. Inhibition is determined visually. If a substance inhibits the enzyme, the sample is colorless if there is no inhibition, the sample is yellow.

PH Screen—

A universal indicator composed of 0.025 mg/ml thymol blue (Sigma T9887), 0.063 mg/ml methyl red (Sigma M7267), 0.5 g/liter phenolphthalein (Sigma P 9750), and 0.25 mg/ml bromthymol blue (Aldrich 11441-3), in 50% (v/v) ethanol is adjusted to green with 0.5 m NaOH. Alternatively, red cabbage indicator, prepared by mixing chopped red cabbage with hot water, may be used. For each substance, 20 μl of substance, 160 μl of water, and 20 μl of indicator solution are mixed in a well of a 96-well plate. The color is compared with standards [1 m HCl (red), 1 m acetic acid (orange), distilled water (green), 1 m NaOH (blue/purple)].

Folding Assay—

Phycocyanobilin, a fluorescent blue protein from Spirulina, is used to test the effect of the test substances on protein folding. A crude preparation of phycocyanobilin proteins is prepared as described previously [ 15 ] in conjunction with the protein folding laboratory exercise. Briefly, each student pair grinds 1 g of Spirulina (available at health food stores or Sigma S 9134) with 0.1 g of sand for 5 min, then adds 25 ml of 0.04 mg/ml lysozyme (Sigma L 6876) in 100 mm sodium phosphate buffer, pH 7.0, and incubates the samples for 15 min at 37 °C. The mixture is centrifuged at 20,000 × g for 10 min. The supernatant is filtered through cheesecloth, and ammonium sulfate is added to give a 50% saturated solution. The solution was centrifuged at 12,000 × g for 15 min to collect the precipitated phycocyanobilin, and the pellet was dissolved in 2 ml of 100 mm potassium phosphate buffer, pH 7.

For each trial, 20 μl of substance, 170 μl of 100 mm sodium phosphate buffer, pH 7.0, and 10 μl of phycocyanobilin extract are mixed in a well of a 96-well plate. The color is compared with a blank in which water was substituted for substance, and to an unfolded control in which 8 m urea in 100 mm sodium phosphate buffer, pH 7.0, is used instead of buffer. Because the urea solution is an irritant, gloves should be worn. Samples are mixed well, and then allowed to equilibrate for 10 min before reading the absorbance at 625 nm. The red fluorescence of the protein is lost upon unfolding, and the intensity of the blue absorption is decreased.


Thyroid Hormone Synthesis

Peter Kopp , Juan Carlos Solis-S , in Clinical Management of Thyroid Disease , 2009

Sodium-Iodide Symporter Function, Inhibition by Competitors, and Perchlorate Test

The Michaelis-Menten constant (Km) of NIS is approximately 36 μM. 7,12 Electrophysiologic studies in oocytes have demonstrated that NIS is electrogenic because of the influx of sodium with a stoichiometric ratio of sodium to iodide of 2:1. 13 NIS is blocked by several anions, in particular perchlorate and thiocyanate, by competitive inhibition. 14,15 Although there was some controversy in the past as to whether perchlorate is a substrate for NIS, recent evidence has indicated that it is actively transported by NIS. 16,17 In contrast to the transport of iodide, the transport of perchlorate is electroneutral, indicating that NIS translocates different substrates with different stoichiometries.

Perchlorate is used for the so-called perchlorate test, which permits determination of the extent of iodide organification. 15 Under normal conditions, iodide is transported very rapidly into thyroid cells by NIS, released into the follicular lumen by pendrin and one or several other anion channel(s), and then organified on tyrosyl residues of TG by TPO. After the inhibition of NIS by perchlorate, any intrathyroidal iodide that has not been incorporated into TG is rapidly released into the bloodstream at the basolateral membrane and cannot be transported back into thyrocytes. In the standard perchlorate test, the thyroidal counts are measured at frequent intervals after the administration of radioiodine to determine the uptake into the thyroid gland. One hour later, 1 g of KClO4 or NaClO4 is administered, and the amount of intrathyroidal radioiodine is monitored longitudinally. In individuals with normal iodide organification, there is no decrease in intrathyroidal counts because the iodide has been incorporated into TG. In contrast, a loss of 10% or more indicates an organification defect common causes include thyroiditis and congenital defects with abnormal efflux of iodide into the follicular lumen, such as Pendred’s syndrome, defects of DUOX and DUOXA2, or dysfunction of TPO. 18-20 In the case of a complete organification defect (total iodide organification defect [TIOD]), such as in patients with complete inactivation of TPO, there is no meaningful organification and the tracer is completely released from the gland. In the situation of a partial iodide organification defect (PIOD), such as in Pendred’s syndrome or partially inactivating TPO mutations, the fraction of the tracer that has not been incorporated is released from the gland.


Biochemistry. 5th edition.

Before the availability of computers, the determination of KM and Vmax values required algebraic manipulation of the basic Michaelis-Menten equation. Because Vmax is approached asymptotically (see Figure 8.11), it is impossible to obtain a definitive value from a typical Michaelis-Menten plot. Because KM is the concentration of substrate at Vmax/2, it is likewise impossible to determine an accurate value of KM. However, Vmax can be accurately determined if the Michaelis-Menten equation is transformed into one that gives a straight-line plot. Taking the reciprocal of both sides of equation 23 gives

A plot of 1/V0 versus 1/[S], called a Lineweaver-Burk or double-reciprocal plot, yields a straight line with an intercept of 1/Vmax and a slope of KM/Vmax (Figure 8.36). The intercept on the x-axis is -1/KM.

Figure 8.36

A Double-Reciprocal or Lineweaver-Burk Plot. A double-reciprocal plot of enzyme kinetics is generated by plotting 1/V0 as a function 1/[S]. The slope is the KM/Vmax, the intercept on the vertical axis is 1/Vmax, and the intercept on the horizontal axis (more. )

Double-reciprocal plots are especially useful for distinguishing between competitive and noncompetitive inhibitors. In competitive inhibition, the intercept on the y-axis of the plot of 1/V0 versus 1/[S] is the same in the presence and in the absence of inhibitor, although the slope is increased (Figure 8.37). That the intercept is unchanged is because a competitive inhibitor does not alter Vmax. At a sufficiently high concentration, virtually all the active sites are filled by substrate, and the enzyme is fully operative. The increase in the slope of the 1/V0 versus 1/[S] plot indicates the strength of binding of competitive inhibitor. In the presence of a competitive inhibitor, equation 31 is replaced by

Figure 8.37

Competitive Inhibition Illustrated on a Double-Reciprocal Plot. A double-reciprocal plot of enzyme kinetics in the presence () and absence () of a competitive inhibitor illustrates that the inhibitor has no effect on Vmax but increases KM.

In other words, the slope of the plot is increased by the factor (1 + [I]/Ki) in the presence of a competitive inhibitor. Consider an enzyme with a KM of 10 -4 M. In the absence of inhibitor, V0 = Vmax/2 when [S] = 10 -4 M. In the presence of 2 × 10 -3 M competitive inhibitor that is bound to the enzyme with a Ki of 10 -3 M, the apparent KM (K app M ) will be equal to KM × (1 + [I]/Ki), or 3 × 10 -4 M. Substitution of these values into equation 23 gives V0 = Vmax/4, when [S] = 10 -4 M. The presence of the competitive inhibitor thus cuts the reaction rate in half at this substrate concentration.

In noncompetitive inhibition (Figure 8.38), the inhibitor can combine with either the enzyme or the enzyme-substrate complex. In pure noncompetitive inhibition, the values of the dissociation constants of the inhibitor and enzyme and of the inhibitor and enzyme-substrate complex are equal (Section 8.5.1). The value of Vmax is decreased to a new value called V app max, and so the intercept on the vertical axis is increased. The new slope, which is equal to KM/V app max, is larger by the same factor. In contrast with Vmax, KM is not affected by pure noncompetitive inhibition. The maximal velocity in the presence of a pure noncompetitive inhibitor, V i max, is given by

Figure 8.38

Noncompetitive Inhibition Illustrated on a Double-Reciprocal Plot. A double-reciprocal plot of enzyme kinetics in the presence () and absence () of a noncompetitive inhibitor shows that KM is unaltered and Vmax is decreased.

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This Declaration acknowledges that this paper adheres to the principles for transparent reporting and scientific rigour of preclinical research recommended by funding agencies, publishers and other organisations engaged with supporting research.

Data S1 Certificate of analysis provided by Sigma-Aldrich, the commercial supplier of benztropine used in this study (NSC63912) showing purity as determined by HPLC.

Data S2 Identity and purity of compounds used in this study provided by DTP-NCI, as determined by electrospray ionisation mass spectrometry and liquid chromatography in full scan mode at 214 nm absorption wavelength, using 500 nm as a reference. See table 1 for purity values and chemical names (NSC number shown).

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