2. Study of enzyme mechanism and kinetics

#### 2.1. Study of enzyme mechanism

To study the mechanism of enzyme catalysis, one should be able to estimate the inferences of the experimentally observed effects with respect to the change in molecular events. The basic mechanism can be predicted and validated for the enzymatic reaction under investigation by analysing the data available from a number of techniques. Combination of the basic physicochemical properties with steric structure and quantum mechanical calculations gives solid foundation for the prediction of mechanism [36]. The kinetic data and graphical representation validate the data and play a crucial role in establishing the mechanism of the enzyme. Additionally, the study of enzyme inhibition not only unveils the mode of action of enzyme but also opens up other crucial information which is boon to the other fields of science. Some of the methods that are used for the prediction of the mechanism of the enzymatic catalysis are isotope exchange, irreversible inhibition, pH dependence, fluorescence labelled substrates, etc. [37].

#### 2.2. Study of enzyme kinetics

To upscale the laboratory level research to an industrial scale with improved productivity and reduction in cost of the process, it is very necessary to study the kinetic models of the desired biocatalytic reactions, which facilitate process designing and intensification [38, 39]. The understanding of enzyme kinetics is also essential to design modulator that can help in designing various drugs. Transient-state kinetics, steady-state kinetics and rapid-equilibrium kinetics are the three major classes of kinetic studies [40–42]. Transient-state kinetics is applied to the very fast reactions of which mechanisms are dependent on the enzyme structure [43, 44]. The steady state of enzyme kinetics is derived with the hypothesis that each enzymatic step is in steady state and remains in steady state, even though the outer environment continuously changes in a given catalytic system [36, 45]. For rapid equilibrium kinetics, the reaction components of the step, preceding to the rate determining step, are in equilibrium with various enzyme forms like the enzyme, enzyme-substrate complex and substrate [46–48]. The initial velocity of the enzyme catalysed reaction gets affected by the modifiers [49]. The addition of single type of modifier changes the kinetics and yields two rate constants, whereas addition of two types of modifiers in two different reactions; five independent equilibrium conditions and three routes for synthesizing products are observed [50]. The chemical equilibrium is significantly affected by the external conditions such as drugs, activators, metals, toxins and pH, some of which were discussed earlier in Section 2. However, the enzyme kinetics can differ marginally in a cellular environment because of the dynamic nature of system [41].

#### 2.2.1. Single substrate kinetics

In 1902, Brown found that at high concentration of sucrose, reaction follows zero-order reaction. Therefore, he proposed that the reaction is composed of two elementary steps. (1) Presteady-state: the formation of ES complex (2) At steady state: formation of product. This initiated the study of enzyme kinetics and derivation of the relevant rate expression (6 and 7). The next significant efforts were put forth by Michaelis and Menten in 1913 which were further improved by Briggs and Haldane [3, 7]. The reaction rate is directly proportional to [E] if excess of free substrate concentration is present. At low substrate concentration, reaction follows first-order kinetics. Enzyme substrate interaction obeys the mass action law. For given [E], reaction velocity increases initially with increasing substrate concentration up to certain maxima and further addition does not change the velocity anymore. Plotting and shaping of rectangular hyperbola characterize the shape of non-allosteric enzymes [8, 33]. The progress curve for the simple enzyme for catalysed reaction is represented in Figure 1.

Figure 1. Progress curve for simple enzyme for catalysed reaction [7].

Unfortunately, steady-state kinetics measures are incapable of revealing the number of intermediates. It is referred as 'black box'. Perhaps, it provides phenomenal description of enzymatic behaviours. The nature of intermediate remains indeterminate. Hence, even though steady-state kinetics is not helpful for predicting the mechanism, it is useful to eliminate the proposed mechanisms [8, 51]. This developed expression relates initial rate of reaction with the substrate concentration and rate constants. The representation of reaction is as follows:

enzyme forms like the enzyme, enzyme-substrate complex and substrate [46–48]. The initial velocity of the enzyme catalysed reaction gets affected by the modifiers [49]. The addition of single type of modifier changes the kinetics and yields two rate constants, whereas addition of two types of modifiers in two different reactions; five independent equilibrium conditions and three routes for synthesizing products are observed [50]. The chemical equilibrium is significantly affected by the external conditions such as drugs, activators, metals, toxins and pH, some of which were discussed earlier in Section 2. However, the enzyme kinetics can differ

In 1902, Brown found that at high concentration of sucrose, reaction follows zero-order reaction. Therefore, he proposed that the reaction is composed of two elementary steps. (1) Presteady-state: the formation of ES complex (2) At steady state: formation of product. This initiated the study of enzyme kinetics and derivation of the relevant rate expression (6 and 7). The next significant efforts were put forth by Michaelis and Menten in 1913 which were further improved by Briggs and Haldane [3, 7]. The reaction rate is directly proportional to [E] if excess of free substrate concentration is present. At low substrate concentration, reaction follows first-order kinetics. Enzyme substrate interaction obeys the mass action law. For given [E], reaction velocity increases initially with increasing substrate concentration up to certain maxima and further addition does not change the velocity anymore. Plotting and shaping of rectangular hyperbola characterize the shape of non-allosteric enzymes [8, 33]. The progress

marginally in a cellular environment because of the dynamic nature of system [41].

curve for the simple enzyme for catalysed reaction is represented in Figure 1.

Figure 1. Progress curve for simple enzyme for catalysed reaction [7].

2.2.1. Single substrate kinetics

78 Enzyme Inhibitors and Activators

$$\mathcal{S} + E \underset{k\_{-1}}{\overset{k\_1}{\rightleftharpoons}} ES \overset{k\_2}{\to} E + P \tag{8}$$

In the given rate expression, the first step is reversible, whereas second step became irreversible. The second step is not reversible as the sufficient amount of energy is not available to cross the barrier as the energy liberated during the reaction. To derive the rate expression for the desired single substrate enzymatic reaction, following assumptions are made [3, 4].

	- a. Sufficient time has passed, which is needed to build the concentration of the ES complex after mixing of E and S.
	- b. Adequate time has been given to the reaction for the rate of formation of ES complex resulting into the depletion of substrate.
	- c. If it is k<sup>2</sup> >> k�1, ES complex breakdown occurs as rapidly as it is produced to form product and thus steady state can never be achieved. When k<sup>2</sup> << k�1, the concentration of ES can build up inside the system and then,

$$\text{Rate of formation of ES complex} = \frac{d[ES]}{dt} = k\_1[E][S] \tag{9}$$

$$=k\_1([E\_\Gamma - [ES])[\mathcal{S}]\tag{10}$$

$$\text{Rate of breakdown of ES complex} = \frac{d[ES]}{dt} = k\_{-1}[ES] + k\_2[ES] \tag{11}$$

Under steady state conditions,

Rate of formation of ES complex = rate of breakdown of ES complex

$$k\_1([E\_T] - [ES])[S] = (k\_{-1} + k\_2)[ES] \tag{12}$$

Rearranging the Eq. (12)

$$\frac{([ET] - [ES])[\mathbb{S}]}{[ES]} = \frac{k\_{-1} + k\_2}{k\_1} = K\_m \tag{13}$$

Wherein, K<sup>m</sup> = Michealis Menten constant which is a ratio of rate constant and not an equilibrium constant.

$$\mathbb{E}\left[\mathbb{S}\middle|\left[E\_T\right]-\left[\mathbb{S}\right]\middle|ES\right]=\mathbb{K}\_m\left[ES\right]\tag{14}$$

$$[S][ET] = (K\_{\rm m} + [S])[ES] \tag{15}$$

$$[S] = \frac{[ES]}{[E\_\mathrm{T}]} (K\_\mathrm{m} + [S]) \tag{16}$$

At any point of time, it is very difficult to measure the concentration of enzyme-substrate complex in the system. Hence, Eq. (16) is not useful experimentally to deduce any quantitative results. On the contrary, various experimental methods can be used for quantify the velocity (v) and maximum velocity (Vmax). Therefore, Vmax is the limiting value, if ½S� ! ∞. In this case, all enzymes are bound to the substrate and [E] = 0, [ET]=[ES]. Thus,

$$w = k\_2[ES] \tag{17}$$

$$V\_{\text{max}} = k\_2 [E\_\Gamma] \tag{18}$$

$$k\_2 = \frac{v}{[ES]}\tag{19}$$

$$\mathbf{k}\_2 = \frac{V\_{\text{max}}}{[E\_\text{T}]} \tag{20}$$

$$\frac{v}{V\_{\text{max}}} = \frac{[ES]}{[E\_{\text{T}}]} \tag{21}$$

So, after putting these substitutes, Eq. (16) becomes,

$$\mathbb{E}\left[\mathcal{S}\right] = \frac{\upsilon}{V\_{\text{max}}} (K\_{\text{m}} + [\mathcal{S}]) \tag{22}$$

This expression is known as Michealis Menten equation for the prediction of enzyme kinetics. This is the most widely accepted and applied enzyme kinetics to the various systems in vitro and in vivo.

Deductions derived from the Michealis Menten expression:

Under steady state conditions,

80 Enzyme Inhibitors and Activators

Rearranging the Eq. (12)

rium constant.

and in vivo.

Rate of formation of ES complex = rate of breakdown of ES complex

ð½ET��½ES�Þ½S�

<sup>½</sup>S� ¼ <sup>½</sup>ES� ½ET�

enzymes are bound to the substrate and [E] = 0, [ET]=[ES]. Thus,

So, after putting these substitutes, Eq. (16) becomes,

<sup>½</sup>ES� <sup>¼</sup> <sup>k</sup>�<sup>1</sup> <sup>þ</sup> <sup>k</sup><sup>2</sup>

Wherein, K<sup>m</sup> = Michealis Menten constant which is a ratio of rate constant and not an equilib-

At any point of time, it is very difficult to measure the concentration of enzyme-substrate complex in the system. Hence, Eq. (16) is not useful experimentally to deduce any quantitative results. On the contrary, various experimental methods can be used for quantify the velocity (v) and maximum velocity (Vmax). Therefore, Vmax is the limiting value, if ½S� ! ∞. In this case, all

<sup>k</sup><sup>2</sup> <sup>¼</sup> <sup>v</sup>

k2 <sup>¼</sup> <sup>V</sup>max

This expression is known as Michealis Menten equation for the prediction of enzyme kinetics. This is the most widely accepted and applied enzyme kinetics to the various systems in vitro

<sup>¼</sup> <sup>½</sup>ES�

v Vmax

<sup>½</sup>S� ¼ <sup>v</sup> Vmax k1

k1ð½ET��½ES�Þ½S�¼ðk�<sup>1</sup> þ k2Þ½ES� (12)

½S�½ET��½S�½ES� ¼ Km½ES� (14)

½S�½ET�¼ðK<sup>m</sup> þ ½S�Þ½ES� (15)

ðK<sup>m</sup> þ ½S�Þ (16)

v ¼ k2½ES� (17)

Vmax ¼ k2½ET� (18)

<sup>½</sup>ES� (19)

<sup>½</sup>ET� (20)

<sup>½</sup>ET� (21)

ðK<sup>m</sup> þ ½S�Þ (22)

¼ Km (13)


$$K\_{\mathbb{S}} = \frac{[E][\mathbb{S}]}{[ES]} = \frac{k\_{-1}}{k\_1} \tag{23}$$

$$K\_{\mathfrak{m}} = \frac{k\_{-1} + k\_2}{k\_1} \tag{24}$$

$$K\_{\rm m} = \frac{k\_{-1}}{k\_1} = K\_{\rm S} \quad k\_{-1} \gg k\_2 \tag{25}$$

vii. When k<sup>2</sup> >> k�1, the rate of dissociation is low so that the rate of product formation is high, reaction sequence becomes irreversible at both steps.

$$E + S \xrightarrow{k\_1} ES \xrightarrow{k\_2} E + P \tag{26}$$

As overall rate of reaction is determined by the concentration of ES complex,


complex leads to the formation of product. When [S] >> Km, the turnover number for the enzyme is calculated. It can be determined under saturation conditions as,

$$\frac{dP}{dt} = V\_{\text{max}} = k\_2[ES] = k\_2[E\_\Gamma] \tag{27}$$

If [ET] increases x-times, while concentration of substrate is established at the saturating levels as compared to the total concentration of enzyme, then Vmax increases x-times. The rate of reaction is proportional to the concentration of total enzyme concentration. The reaction tends to become first order.

In saturation condition, the rate of reaction is maximum. The rate constant k<sup>2</sup> is denoted as kcat at saturation levels and gives the value of turnover number. It ranges from 1 to 104 per second. Sometimes, it reaches to 105 . Upper limit to the value of kcat/K<sup>m</sup> cannot be greater than k<sup>2</sup> i.e. decomposition of ES complex to E and P. The most efficient catalyst has values of kcat/k<sup>m</sup> near the controlled diffusion limits of 10�<sup>8</sup> –10�<sup>9</sup> m�<sup>1</sup> s �1 . These enzymes catalyse reaction almost every time they colloid with substrate and achieve virtual catalytic perfection.

$$k\_{\rm cat} = \frac{V\_{\rm max}}{[E\_{\rm T}]} \tag{28}$$

The ability of enzyme to produce a given amount of product to use in given time is changes proportionally with turnover number and total amount of enzyme present in cell. However, turn over number is measured for purified enzymes. Hence, the enzyme activity is measured as a specific activity (μmol of substrate converted per minute per mg of enzyme to form product). That is also denoted as Katal (kat). It is defined as concentration of enzyme that transforms 1 mol of substrate into product per second. As for most of the clinical disorders, activity is measured in biological fluids. It is redefined as 1 μmol of substrate to product per minute at optimal conditions (IU).

ix. When concentration of substrate is far less that the value of Km, the product formation rate rises linearly with rise in substrate concentration and reaction becomes first order with reference to the concentration of substrate.

At low substrate concentrations, reaction rate is proportional to the total enzyme concentration. Reaction velocity at low concentration of substrate can be represented as,

$$w = k'[E][\mathbb{S}] \tag{29}$$

$$k' = \frac{k\_{\text{cat}}}{K\_{\text{m}}} \tag{30}$$

Therefore, the rate equation must specify a second-order dependence on the concentration of substrate and total enzyme. When concentration of substrate is small there is first order dependence in concentration of total enzyme alone. When concentration of substrate is large, rate constant is kcat for first order and kcat/K<sup>m</sup> for second order in which <sup>K</sup><sup>m</sup> is the value of the concentration of substrate. When <sup>v</sup> <sup>¼</sup> <sup>1</sup> <sup>2</sup> Vmax, kcat/K<sup>m</sup> measures total activity of the enzyme, which includes the ability of enzyme to bind with a particular substrate.

x. When K<sup>m</sup> = [S], results in the velocity that is Vmax/2,

$$\frac{V\_{\text{max}}}{\text{2}} = \frac{V\_{\text{max}}[\text{S}]}{K\_{\text{m}} + [\text{S}]} \tag{31}$$

$$K\_m + [S] = \mathcal{Z}[S] \tag{32}$$

Initial velocity increases with increase in Vmax at constant concentration of the substrate and K<sup>m</sup> and Initial velocity decreases with increase in K<sup>m</sup> at constant concentration of the substrate and Vmax.


complex leads to the formation of product. When [S] >> Km, the turnover number for the

If [ET] increases x-times, while concentration of substrate is established at the saturating levels as compared to the total concentration of enzyme, then Vmax increases x-times. The rate of reaction is proportional to the concentration of total enzyme concentration. The

In saturation condition, the rate of reaction is maximum. The rate constant k<sup>2</sup> is denoted as kcat at saturation levels and gives the value of turnover number. It ranges from 1 to 104

greater than k<sup>2</sup> i.e. decomposition of ES complex to E and P. The most efficient catalyst has

catalyse reaction almost every time they colloid with substrate and achieve virtual cata-

The ability of enzyme to produce a given amount of product to use in given time is changes proportionally with turnover number and total amount of enzyme present in cell. However, turn over number is measured for purified enzymes. Hence, the enzyme activity is measured as a specific activity (μmol of substrate converted per minute per mg of enzyme to form product). That is also denoted as Katal (kat). It is defined as concentration of enzyme that transforms 1 mol of substrate into product per second. As for most of the clinical disorders, activity is measured in biological fluids. It is redefined as 1 μmol

kcat <sup>¼</sup> <sup>V</sup>max

ix. When concentration of substrate is far less that the value of Km, the product formation rate rises linearly with rise in substrate concentration and reaction becomes first order

tration. Reaction velocity at low concentration of substrate can be represented as,

v ¼ k 0

> k 0 <sup>¼</sup> <sup>k</sup>cat K<sup>m</sup>

At low substrate concentrations, reaction rate is proportional to the total enzyme concen-

Therefore, the rate equation must specify a second-order dependence on the concentration of substrate and total enzyme. When concentration of substrate is small there is first order dependence in concentration of total enzyme alone. When concentration of substrate is large, rate constant is kcat for first order and kcat/K<sup>m</sup> for second order in which

dt <sup>¼</sup> <sup>V</sup>max <sup>¼</sup> <sup>k</sup>2½ES� ¼ <sup>k</sup>2½ET� (27)

. Upper limit to the value of kcat/K<sup>m</sup> cannot be

–10�<sup>9</sup> m�<sup>1</sup> s

<sup>½</sup>ET� (28)

½E�½S� (29)

�1

. These enzymes

(30)

enzyme is calculated. It can be determined under saturation conditions as,

dP

values of kcat/k<sup>m</sup> near the controlled diffusion limits of 10�<sup>8</sup>

of substrate to product per minute at optimal conditions (IU).

with reference to the concentration of substrate.

reaction tends to become first order.

lytic perfection.

82 Enzyme Inhibitors and Activators

per second. Sometimes, it reaches to 105

It is very tedious to quantify the velocity of the enzyme which can catalyse the multiple reactions. In other cases, the enzyme may be inactivated by its substrate or impurities in it. The enzyme that consists of several components and velocity-substrate relationship depend upon their ratios (e.g. urease). In these cases, the use of Michealis Menten equation cannot be accurately predicted.


For enzyme catalysis the data mostly fit into a rectangular hyperbola wherein the initial velocity of reaction is plotted against the concentration of substrate in the system [52, 53]. It can be represented as follows (Figure 2):

Figure 2. Initial velocity of reaction versus the concentration of substrate [4].

In the direct diagram, Vmax and K<sup>m</sup> are calculated by extrapolating the graph. As from the given data points, there are numerous ways to represent the data. Secondly, as the experiment is conducted at the saturation level, it is often that velocity is overlooked and therefore Km. Also, the inhibitory effect of the excessive substrate or the limited solubility of the substrate causes the misinterpretation of the values of kinetic parameters. Practical prediction of this error prone data becomes more tedious as it becomes very difficult to predict and evaluate the experimental error from data. Hence, the need of accurate prediction of the data resulted into development of various types of reciprocal and logarithmic plots derived on the basis of Michealis Menten equation. Because straight lines are easier to evaluate, the efforts have been taken to interpret that hyperbolic data in the form of a straight line by various ways like Lineweaver Burk plot, Eadie Hofstee plot, Hanes plot, Dixon plot, etc. [47, 53].

• Lineweaver Burk plot (Double reciprocal plot)

It is based on the reciprocal of the Michealis Menten Equation and represented as,

$$\frac{1}{v} = \frac{1}{V\_{\text{max}}} + \frac{K\_{\text{m}}}{V\_{\text{max}}} \frac{1}{[S]} \tag{33}$$

The plot is developed by plotting the inverse of velocity of reaction against the inverse of concentration of substrate with abscissa at 1/Km. This method is the most frequently used method for the prediction of kinetic parameters. The major disadvantage is the irregular distribution of data. The reciprocal action causes distortion of equally distributed substrate concentrations either in the compressed form towards the co-ordinates or over-extended in the other direction. To overcome the limitation, if the analysis is carried out at small range for uniform dispersal of data, the results do not cover the range of study at satisfactory levels. The tangible advantage of the linear graph is that the variables (v and [S]) are displayed on the separate co-ordinators from each other. The external disturbances and change in mechanism pattern cause the deviations from straight lines nature of the plot. This plot serves as primary step to distinguish the inhibition in the system as well as it is useful to understand the mechanism followed by the reactions [7, 8, 54].

#### • Eddie-Hofstee plot

Eddie-Hofstee plot is more equally placed in comparison with Lineweaver Burk plot. The equation can be obtained as,

$$v(\frac{k\_m + [S]}{[S]}) = V\_{\text{max}}\tag{34}$$

$$
v \left(\frac{k\_{\rm m}}{[S]}\right) + v = V\_{\rm max} \tag{35}$$

$$\upsilon = V\_{\text{max}} - K\_{\text{m}} \left( \frac{\upsilon}{[S]} \right) \tag{36}$$

Plotting v against v/[S] gives Vmax from the ordinate intercept and –K<sup>m</sup> from the slope. This method of linearization is not only associated with distortion of error limits at higher concentrations of substrates but also there is no separation of variables from each other [3, 55].

#### • Hanes plot

In the direct diagram, Vmax and K<sup>m</sup> are calculated by extrapolating the graph. As from the given data points, there are numerous ways to represent the data. Secondly, as the experiment is conducted at the saturation level, it is often that velocity is overlooked and therefore Km. Also, the inhibitory effect of the excessive substrate or the limited solubility of the substrate causes the misinterpretation of the values of kinetic parameters. Practical prediction of this error prone data becomes more tedious as it becomes very difficult to predict and evaluate the experimental error from data. Hence, the need of accurate prediction of the data resulted into development of various types of reciprocal and logarithmic plots derived on the basis of Michealis Menten equation. Because straight lines are easier to evaluate, the efforts have been taken to interpret that hyperbolic data in the form of a straight line by various ways like

Lineweaver Burk plot, Eadie Hofstee plot, Hanes plot, Dixon plot, etc. [47, 53].

It is based on the reciprocal of the Michealis Menten Equation and represented as,

The plot is developed by plotting the inverse of velocity of reaction against the inverse of concentration of substrate with abscissa at 1/Km. This method is the most frequently used method for the prediction of kinetic parameters. The major disadvantage is the irregular distribution of data. The reciprocal action causes distortion of equally distributed substrate concentrations either in the compressed form towards the co-ordinates or over-extended in the other direction. To overcome the limitation, if the analysis is carried out at small range for uniform dispersal of data, the results do not cover the range of study at satisfactory levels. The tangible advantage of the linear graph is that the variables (v and [S]) are displayed on the separate co-ordinators from each other. The external disturbances and change in mechanism pattern cause the deviations from straight lines nature of the plot. This plot serves as primary step to distinguish the inhibition in the system as well as it is useful to understand the

Eddie-Hofstee plot is more equally placed in comparison with Lineweaver Burk plot. The

k<sup>m</sup> þ ½S�

v ¼ Vmax � K<sup>m</sup>

Plotting v against v/[S] gives Vmax from the ordinate intercept and –K<sup>m</sup> from the slope. This method of linearization is not only associated with distortion of error limits at higher concentrations of substrates but also there is no separation of variables from each other [3, 55].

v ½S� 

vð

v km ½S�  1

<sup>½</sup>S� (33)

<sup>½</sup>S� Þ ¼ <sup>V</sup>max (34)

þ v ¼ Vmax (35)

(36)

1 <sup>v</sup> <sup>¼</sup> <sup>1</sup> Vmax þ K<sup>m</sup> Vmax

• Lineweaver Burk plot (Double reciprocal plot)

mechanism followed by the reactions [7, 8, 54].

• Eddie-Hofstee plot

84 Enzyme Inhibitors and Activators

equation can be obtained as,

The expression is derived by simple multiplication of the concentration of the substrate with the reciprocal Michaelis-Menten equation. It is represented as,

$$\frac{[\text{S}]}{\upsilon} = \frac{K\_{\text{m}}}{V\_{\text{max}}} + \frac{[\text{S}]}{V\_{\text{max}}} \tag{37}$$

Plotting of [S]/v against [S] gives Km/Vmax (ordinate intercept) and 1/Vmax (slope). The error limits are only slightly deflected at low substrate concentrations when simple linear regressions can be applied. However, substrate concentrations variable is represented on both the coordinates [7, 33].

• Eisenthal and Cornish-Bowden plot

Eisenthal and Cornish-Bowden have derived over a period of time in various forms. The final equation of this type of direct linearization is represented as,

$$\frac{1}{K\_{\rm m}} = \frac{V\_{\rm max}}{K\_{\rm m}v} - \frac{1}{[S]} \tag{38}$$

By entering 1/v against 1/[S], 1/K<sup>m</sup> is quantified from the intercept and Vmax/K<sup>m</sup> from the slope of the graph. The reciprocal transformation of the equation leads to the distortion of scale. The deviation of the graph from the ideal behaviour is difficult to trace as it is overlapped by the distortion error and gives the false values of kinetic constants [52, 56, 57].

• Dixon plot

In a Dixon analysis, two types of graphs are plotted to evaluate the type of inhibition that is caused by the addition of the inhibitor in the reaction system. In 1953, the first Dixon plot of 1/v versus concentration of inhibitor at static substrate level was studied. Based on the nature of lines, this plot can be used to differentiate between the partial and complete inhibition (Table 1).

In some cases, the plots create confusion in the prediction of non-competitive and competitive inhibition. This led to the development of second Dixon plot ([S]ν�1 is plotted versus [I]) (1972), which requires change in the turnover rate with respect to the inhibitor concentration at a static saturating concentration of the substrate. In this case, the enzyme activity follows hyperbolic decrease reaching to zero at complete inhibition. In case of the competitive inhibition, the lines plotted remain parallel to each other while in case of uncompetitive inhibition, the Dixon plot showed the presence of intersecting lines [33, 55].


Table 1. Analysis of Dixon plots.

There are some generalized methods that are used for determining various rate and inhibition constants along with the prediction of mechanism that is followed by the reaction under particular set of conditions.

#### 2.2.2. Kinetics of two substrate reaction

The study of enzyme kinetics was initiated with the single substrate molecule which can be further applied to study the bisubstrate reactions which constitute 60% of biochemical bisubstrate reactions in nature [8].Two substrate reactions are more complex than single substrate reactions. For example, most of dehydrogenase and aminotransferase follow bisubstrate enzyme kinetics. The Cleland notation is used for the representation of higher order enzymatic reactions. According to which, the substrates are assigned with A, B, C and D letters based on the sequence of binding to the enzyme, products are assigned by letters P, Q, R and S on the basis of release sequence. Enzyme is designated with letter E, and sometimes with F, which is a slightly modified form of a stable enzyme observed in double-displacement reaction [58–60]. Hence forward, this notation is used for the representation of bisubstrate reaction. To study reaction kinetics by applying Michaelis Menten kinetic to bisubstrate enzyme reactions, concentration of one of the substrates (B) is kept constant, whereas another one (A) is varied and vice versa. As concentration of substrate B is kept arbitrarily constant, the obtained values of the kinetic parameters for concentration of substrate A can be erroneous. On the other hand, varying the concentration of both the parameters at a single point of time intricates large complexity in data acquisition and analysis. Bisubstrate reactions can be broadly classified into two groups, namely, sequential and double-displacement reactions. In sequential reaction mechanism, both substrates bind to the enzyme which leads to the development of transition state complex followed by the product. The binding of substrate decides further classification of sequential reaction mechanism. When binding of one substrate A becomes obligatory prior to other substrate B, then the reaction follows ordered sequential mechanism (Figure 3). On the other hand, the sequence of binding of the substrates to the enzyme has very less importance, the reaction undergoes random sequential reaction mechanism (Figure 4) [8, 33, 61].

These types of sequential mechanisms are further bifurcated into different sub-groups based on the location rate limiting step. In case of a rapid equilibrium mechanism, the rate-limiting step is chemistry of the reaction; on the other hand, step except chemistry of reaction controls the rate of reaction for a steady-state ordered mechanism. In Theorell-Chance mechanism, every step is fast except the release of the second product, Q, in a reaction pathway. For steady-state random mechanism, the substrate binds with the enzyme in any order [55, 62].

Figure 3. Ordered sequential mechanism.

As the name suggests, a double-displacement mechanism occurs when a catalytic process can proceed with binding of one of the two substrates to the enzyme (Figure 5). On completion of first catalytic event, first product (P) leaves from the active site leaving some of its portion inside the active site. After the release of first product, some chemical group of substrate A left behind in the catalytic site of the enzyme creating new form of stable enzyme (F). After binding of second substrate, the catalysis proceeds further to produce product Q with the regeneration of an original enzyme E. The plot of initial velocity and substrate concentration does not signify any noticeable change in different types of mechanisms by visual inspection and hence, not helpful in assigning any proper rate equation. However, the double-reciprocal plot, i.e. 1/v<sup>0</sup> versus 1/[A] at the different concentrations of B, significantly distinct between a sequential or ping-pong mechanism [13, 63, 64].

In case of sequential mechanism (ternary complex mechanism) of reaction, the lines on the double reciprocal plot intersect with each other on the left of the x-axis (Figure 6), while that of the double-displacement mechanism (ping-pong mechanism), the double reciprocal plot is represented by the parallel lines (Figure 7) [58, 65, 66].

Thus, the double reciprocal plot gives clear indication of mechanism of reaction with some exception [67]. The different rate equations and plot information are presented in Table 2.

The rapid-equilibrium random, steady-state ordered and Theorell-Chance mechanisms are represented with the same rate expression and the primary plot or the double reciprocal plot cannot differentiate between these mechanisms from each other. They only differ at the location of rate limiting step and can be differentiated on the basis of kinetics studies such as deadend inhibition studies, isotope effects and pre-steady-state kinetics [55, 59, 68]. The bisubstrate

Figure 4. Random sequential mechanism.

There are some generalized methods that are used for determining various rate and inhibition constants along with the prediction of mechanism that is followed by the reaction under

The study of enzyme kinetics was initiated with the single substrate molecule which can be further applied to study the bisubstrate reactions which constitute 60% of biochemical bisubstrate reactions in nature [8].Two substrate reactions are more complex than single substrate reactions. For example, most of dehydrogenase and aminotransferase follow bisubstrate enzyme kinetics. The Cleland notation is used for the representation of higher order enzymatic reactions. According to which, the substrates are assigned with A, B, C and D letters based on the sequence of binding to the enzyme, products are assigned by letters P, Q, R and S on the basis of release sequence. Enzyme is designated with letter E, and sometimes with F, which is a slightly modified form of a stable enzyme observed in double-displacement reaction [58–60]. Hence forward, this notation is used for the representation of bisubstrate reaction. To study reaction kinetics by applying Michaelis Menten kinetic to bisubstrate enzyme reactions, concentration of one of the substrates (B) is kept constant, whereas another one (A) is varied and vice versa. As concentration of substrate B is kept arbitrarily constant, the obtained values of the kinetic parameters for concentration of substrate A can be erroneous. On the other hand, varying the concentration of both the parameters at a single point of time intricates large complexity in data acquisition and analysis. Bisubstrate reactions can be broadly classified into two groups, namely, sequential and double-displacement reactions. In sequential reaction mechanism, both substrates bind to the enzyme which leads to the development of transition state complex followed by the product. The binding of substrate decides further classification of sequential reaction mechanism. When binding of one substrate A becomes obligatory prior to other substrate B, then the reaction follows ordered sequential mechanism (Figure 3). On the other hand, the sequence of binding of the substrates to the enzyme has very less importance,

the reaction undergoes random sequential reaction mechanism (Figure 4) [8, 33, 61].

These types of sequential mechanisms are further bifurcated into different sub-groups based on the location rate limiting step. In case of a rapid equilibrium mechanism, the rate-limiting step is chemistry of the reaction; on the other hand, step except chemistry of reaction controls the rate of reaction for a steady-state ordered mechanism. In Theorell-Chance mechanism, every step is fast except the release of the second product, Q, in a reaction pathway. For steady-state random mechanism, the substrate binds with the enzyme in any order [55, 62].

particular set of conditions.

86 Enzyme Inhibitors and Activators

2.2.2. Kinetics of two substrate reaction

Figure 3. Ordered sequential mechanism.

Figure 5. Double-displacement reaction mechanism.

Figure 6. Double reciprocal plot for double-displacement mechanism (at different levels of B).

Figure 7. Double reciprocal plot for double-displacement mechanism (at different levels of B).


Table 2. Rate expressions for different type of bisubstrate mechanisms.

kinetic study also reveals which form of enzyme can exist and which cannot, which has significant implications in the study of dead-end inhibition and therapeutic application [68, 69]. The rapid equilibrium ordered mechanism is a unique sequential mechanism as the chemistry step is the slowest step along the reaction pathway. This results in the absence of kinetic term Ka[B] from the rate of expression.

$$\upsilon\_0 = \frac{V\_{\text{max}}[A][B]}{K\_{\text{ia}}K\_b + K\_b[A] + [A][B]} \tag{39}$$

This mechanism cannot be differentiated from other on the basis of double-reciprocal patterns.

$$\frac{1}{w\_0} = \frac{1}{[A]} \frac{K\_{\text{ia}} K\_{\text{b}}}{V\_{\text{max}}[B]} + \frac{K\_{\text{b}}}{V\_{\text{max}}[A]} + \frac{1}{V\_{\text{max}}} \tag{40}$$

As discussed previously, both the slope (KiaKb/Vmax[B]) and intercept (Kb/Vmax[B] + 1/Vmax) terms reveal a dependency on the concentration of substrate B. In this instance, the graph of intercept will not differ much. By contrast, the slope value (y = 1/[B](KiaKb/Vmax)) when plotted as the slope versus 1/[B], a line that passes directly through the origin as Ka/Vmax does not exist. However, the slope-of-the-slope value reflects free enzyme and is equivalent to KiaKb/Vmax. Similarly, the implications are valid when bisubstrate reaction is studied by varying concentration B at various levels of the concentration of A, are kept constant.

This distinctive character works as a diagnostic tool to distinguish rapid-equilibrium ordered mechanism from all the other double-reciprocal plots. For various rate expressions for other mechanism, please refer the above section. The double-displacement or ping-pong mechanism, which represents the other type of bireactant mechanism, has symmetrical equation as it can be broken into two separate equations representing each half of the complete reaction [70]. For example, at saturating concentrations of substrate, the equation can be simplified as,

$$w\_0 = \frac{V\_{\text{max}}[A]}{K\_\text{a} + [A]} \quad \text{at starting concentration of } B \tag{41}$$

$$w\_0 = \frac{V\_{\text{max}}[B]}{K\_a + [B]} \text{at starting concentration of } A \tag{42}$$

The diagnostic double-reciprocal pattern for a double-displacement mechanism is a series of parallel lines. When varying the concentration of A, the double-reciprocal equation becomes,

Figure 7. Double reciprocal plot for double-displacement mechanism (at different levels of B).

Figure 6. Double reciprocal plot for double-displacement mechanism (at different levels of B).

88 Enzyme Inhibitors and Activators

Rapid equilibrium random sequential mechanism <sup>v</sup> <sup>¼</sup> VAB

Rapid equilibrium ordered sequential mechanism <sup>v</sup> <sup>¼</sup> VAB

Double-displacement mechanism <sup>v</sup> <sup>¼</sup> VAB

Table 2. Rate expressions for different type of bisubstrate mechanisms.

Mechanism Rate equation Double reciprocal plots

Steady state ordered sequential mechanism <sup>v</sup> <sup>¼</sup> VAB <sup>ð</sup>KiaKbþKbAþKaBþAB<sup>Þ</sup> Intersecting lines Theorell-Chance mechanism <sup>v</sup> <sup>¼</sup> VAB <sup>ð</sup>KiaKbþKbAþKaBþAB<sup>Þ</sup> Intersecting lines

<sup>ð</sup>KiaþKbAþKaBþAB<sup>Þ</sup> Intersecting lines

<sup>ð</sup>KiaKbþKbAþAB<sup>Þ</sup> Intersecting lines

<sup>ð</sup>KaBþKbAþAB<sup>Þ</sup> Parallel lines

$$\frac{1}{v\_0} = \frac{1}{[A]} \frac{K\_\mathrm{a}}{V\_{\mathrm{max}}} + (\frac{K\_\mathrm{b}}{[B]} + 1) \frac{1}{V\_{\mathrm{max}}} \tag{43}$$

When the intercept of intercept is plotted, it provides the values of Kb/Vmax and 1/Vmax. By contrast, the slope value from the primary plot is defined as y = (Ka/Vmax).

When reaction mechanism is predicted based on the initial velocity data, one has to be sceptical as value of Kia is much greater than that of Ka, rapid-equilibrium random mechanism gets degenerated into a rapid-equilibrium ordered mechanism. If the value of Kia is very less, then the sequential mechanism degenerates into a ping-pong mechanism [11, 45, 55, 61].

#### Examples

— Ternary complex mechanism

Cinnamyl acetate is a major ingredient of food and cosmetic products as a flavouring or fragrance agent [71]. Yadav and Devendran [71] discuss transesterification of cinnamyl alcohol with vinyl acetate to produce cinnamyl acetate. The parameters were optimized to minimize the errors in the prediction of kinetic constants due to change in temperature and solvent system. The mass transfer resistance was removed to accurately estimate the kinetic constant. Hence, the reaction was conducted in toluene with 10 mg novozym 435 as a catalyst. The mole ratio was maintained at 1:2 of cinnamyl alcohol to vinyl acetate. Under these optimized conditions, the reaction kinetics was studied. The detailed experimental process is explained in the section below. The kinetics was predicted by systematically changing the concentrations of reactants on a wide range of the concentrations keeping others constant. The Lineweaver Burk plot was plotted with the initial velocities of reaction (Figure 8). It was observed that for given system under given set of conditions, reaction followed ternary complex mechanism as the plot showed the lines intersecting with each other [71].

The formation of dead-end complex with alcohol at saturating level of cinnamyl alcohols is observed in double reciprocal graph with linear increase in slope and intercept with rise of concentration of cinnamyl alcohol (Figure 8). The equation obtained with this mechanism is represented as,

$$\upsilon = \frac{V\_{\text{max}}[A][B]}{(K\_{\text{ia}}K\_{\text{mb}}(1 + ([B]/K\_{\text{ib}})) + K\_{\text{mb}}[A] + K\_{\text{mu}}[B](1 + ([B]/K\_{\text{ib}})) + [A][B])} \tag{44}$$

Where v is the velocity of reaction, Vmax is the maximum velocity of reaction and [A] and [B] represent the initial concentration of vinyl acetate and cinnamyl alcohol, respectively. Kma and

Figure 8. Lineweaver Burk plot of initial velocity versus concentration of vinyl acetate.

Kmb are the Michaelis constants for vinyl acetate and cinnamyl alcohol, respectively; Kia and Kib are the inhibition constants for vinyl acetate and cinnamyl alcohol, respectively. The kinetic constants were predicted using Polymath 5.1 software. The model was validated by plotting the simulate versus experimental rate of reactions for proposed reaction mechanism.

#### Ping-pong Bi-Bi mechanism

Examples

represented as,

— Ternary complex mechanism

90 Enzyme Inhibitors and Activators

the plot showed the lines intersecting with each other [71].

<sup>v</sup> <sup>¼</sup> <sup>V</sup>max½A�½B�

Figure 8. Lineweaver Burk plot of initial velocity versus concentration of vinyl acetate.

Cinnamyl acetate is a major ingredient of food and cosmetic products as a flavouring or fragrance agent [71]. Yadav and Devendran [71] discuss transesterification of cinnamyl alcohol with vinyl acetate to produce cinnamyl acetate. The parameters were optimized to minimize the errors in the prediction of kinetic constants due to change in temperature and solvent system. The mass transfer resistance was removed to accurately estimate the kinetic constant. Hence, the reaction was conducted in toluene with 10 mg novozym 435 as a catalyst. The mole ratio was maintained at 1:2 of cinnamyl alcohol to vinyl acetate. Under these optimized conditions, the reaction kinetics was studied. The detailed experimental process is explained in the section below. The kinetics was predicted by systematically changing the concentrations of reactants on a wide range of the concentrations keeping others constant. The Lineweaver Burk plot was plotted with the initial velocities of reaction (Figure 8). It was observed that for given system under given set of conditions, reaction followed ternary complex mechanism as

The formation of dead-end complex with alcohol at saturating level of cinnamyl alcohols is observed in double reciprocal graph with linear increase in slope and intercept with rise of concentration of cinnamyl alcohol (Figure 8). The equation obtained with this mechanism is

Where v is the velocity of reaction, Vmax is the maximum velocity of reaction and [A] and [B] represent the initial concentration of vinyl acetate and cinnamyl alcohol, respectively. Kma and

<sup>ð</sup>KiaKmbð<sup>1</sup> þ ð½B�=KibÞÞ þ <sup>K</sup>mb½A� þ Kma½B�ð<sup>1</sup> þ ð½B�=KibÞÞ þ ½A�½B�Þ (44)

The reaction between ethyl-3-phenylpropanoate and n-butanol was studied using novozyme 435. The reaction conditions of transesterification are optimized for maximum conversion and initial rates to understand the kinetics and mechanism. There is synergism between enzyme catalysis and microwave irradiation. The reaction kinetics was studied after eliminating the external mass transfer limitation. The Lineweaver Burk plot showed that the lines are parallel to each other. The reaction follows the ping-pong bi-bi mechanism with inhibition by n-butanol as the double reciprocal graph represents the data in the form of parallel lines (Figure 9) [72].

With experimental data analysis and Lineweaver Burk plot, the reaction rate equation was predicted as,

$$\upsilon\_0 = \frac{V\_{\text{max}}[A][B]}{K\_{\text{mb}}[A] + K\_{\text{ma}}[B](1 + \frac{[B]}{K\_i}) + [A][B]} \tag{45}$$

where Kma and Kmb are the respective Michaelis constants for ethyl-3-phenylpropanoate and n-butanol. v<sup>0</sup> and Vmax represent the respective initial and maximum velocity of the reaction. The data are validated with a parity plot.

Figure 9. Lineweaver Burk plot of initial velocity versus concentration of ethyl-3-phenylpropionate.

#### Ordered Bi-Bi mechanism

For the production of perlauric acid, Novozyme 435 was used as catalyst in toluene solvent. The conversion and initial velocity are optimized with reference to the different parameter of reaction. Lineweaver-Burk plots indicated the formation of a ternary complex. The reaction undergoes ordered bi-bi mechanism based on which the kinetic parameters were calculated (Figure 10) [73].

Reusability studies indicated that there was enzyme deactivation and from the preliminary study of the deactivation, it was observed that the deactivation obeys a pseudo first-order model. The deactivation was observed at higher levels of hydrogen peroxide wherein the methionine and cysteine amino acid got oxidized due to the hydrogen peroxide. The ordered Bi-Bi mechanism showed the best fit for the given data and it is represented as,

$$\upsilon = \frac{V\_{\text{max}}[A][B]}{(K\_{\text{ia}}K\_{\text{mb}}(1 + ([B]/K\_{\text{ib}})) + K\_{\text{mb}}[A] + K\_{\text{mu}}[B](1 + ([B]/K\_{\text{ib}})) + [A][B])} \tag{46}$$

Some of the examples for the bisubstrate reaction are presented in Table 3.

#### 2.2.3. Termolecular reaction

Termolecular reactions are the reactions wherein three reactants react simultaneously to form a desired product. They are unusual because the simultaneous collision of three molecules is a rare event. Fourth and higher-order reactions are unknown. These types of reaction are given in literature [74].

Figure 10. Lineweaver Burk plot of initial velocity versus concentration of lauric acid.


Table 3. List of bisubstrate reaction with their mechanism and inhibition.

### 3. Enzyme inhibition

Ordered Bi-Bi mechanism

92 Enzyme Inhibitors and Activators

2.2.3. Termolecular reaction

in literature [74].

(Figure 10) [73].

For the production of perlauric acid, Novozyme 435 was used as catalyst in toluene solvent. The conversion and initial velocity are optimized with reference to the different parameter of reaction. Lineweaver-Burk plots indicated the formation of a ternary complex. The reaction undergoes ordered bi-bi mechanism based on which the kinetic parameters were calculated

Reusability studies indicated that there was enzyme deactivation and from the preliminary study of the deactivation, it was observed that the deactivation obeys a pseudo first-order model. The deactivation was observed at higher levels of hydrogen peroxide wherein the methionine and cysteine amino acid got oxidized due to the hydrogen peroxide. The ordered

Termolecular reactions are the reactions wherein three reactants react simultaneously to form a desired product. They are unusual because the simultaneous collision of three molecules is a rare event. Fourth and higher-order reactions are unknown. These types of reaction are given

<sup>ð</sup>KiaKmbð<sup>1</sup> þ ð½B�=KibÞÞ þ <sup>K</sup>mb½A� þ Kma½B�ð<sup>1</sup> þ ð½B�=KibÞÞ þ ½A�½B�Þ (46)

Bi-Bi mechanism showed the best fit for the given data and it is represented as,

Some of the examples for the bisubstrate reaction are presented in Table 3.

<sup>v</sup> <sup>¼</sup> <sup>V</sup>max½A�½B�

Figure 10. Lineweaver Burk plot of initial velocity versus concentration of lauric acid.

The inhibition of enzymes is a naturally occurring phenomenon that control and regulate body's defence and repair system along with various other essential functionalities. It also helps in regulating the optimal use of limited resources available within the cell. Naturally occurring inhibition processes are blood coagulation, blood clot dissolution, complement activation, connective tissue turnover, inflammatory reaction, etc. [57]. Hence, it is very essential to study the nature of inhibitor, mode of action, quantitative estimation of the inhibitory effect of the inhibitor on the enzyme. Such mechanistic and kinetic observations provide the information for the designing of various inhibitors. The inhibitors are usually classified into two groups namely, reversible and irreversible. In case of reversible, inhibitors bind with the enzyme with non-covalent interaction which can be reversed at any point of time by dilution or dialysis. In second class of inhibitors, i.e. irreversible inhibitors, the inhibitors bind covalently or tightly with the enzyme which cannot revert back causing permanent damage to the catalytic site [68, 75, 76]. The detailed classification of the inhibition is shown in Figure 11.

Figure 11. The classification of enzyme inhibition.

#### 3.1. Reversible inhibition

The reversible inhibition is the class of inhibitors which bind with the enzymes and this binding can be reversed with the complete regain of enzyme activity. The reversible inhibition further is mainly classified in three categories competitive, uncompetitive and non-competitive inhibition based on its binding with direct enzyme, enzyme-substrate complex or both [77].

#### 3.1.1. Competitive inhibition

The competitive inhibition occurs due to either binding of substrate or inhibitor to the active site. Both substrate and inhibiting molecule compete for the same active site on the enzyme leading to the reduction in the velocity of the reaction. The diverse set of substrate analogues studied for their activity in the presence of different kinds of inhibitors reveals immense information useful to understand the interaction of the active site and catalytic mechanism of the enzyme. The basic assumption in the study of this type of inhibition is that the inhibitor can only bind to the active site of the free enzyme [3, 74, 78].The Cleland notation for the competitive inhibition can be written as,

$$\begin{aligned} E &+ A \stackrel{k1}{\rightleftharpoons} EA \stackrel{k2}{\rightleftharpoons} E + P\\ &+ \\ I & \\ \uparrow \downarrow \\ EI \end{aligned} \tag{47}$$

which can also be represented as,

Kinetic Modelling of Enzyme Catalyzed Biotransformation Involving Activations and Inhibitions http://dx.doi.org/10.5772/67692 95

$$A + E \underset{k\_{-1}}{\overset{k\_1}{\rightleftharpoons}} EA \overset{k\_2}{\rightarrow} E + P \tag{48}$$

$$E + I \stackrel{k\_i}{\rightleftharpoons} EI \tag{49}$$

The Michealis Menten equation for the competitive inhibition can be written as,

$$w = \frac{V\_{\text{max}}[\text{S}]}{[\text{S}] + K\_{\text{m}}(1 + \frac{[I]}{K\_{i}})} \tag{50}$$

Hence, the Lineweaver Burk equation can be derived as,

enzyme with non-covalent interaction which can be reversed at any point of time by dilution or dialysis. In second class of inhibitors, i.e. irreversible inhibitors, the inhibitors bind covalently or tightly with the enzyme which cannot revert back causing permanent damage to the catalytic site [68, 75, 76]. The detailed classification of the inhibition is shown in Figure 11.

The reversible inhibition is the class of inhibitors which bind with the enzymes and this binding can be reversed with the complete regain of enzyme activity. The reversible inhibition further is mainly classified in three categories competitive, uncompetitive and non-competitive inhibition based on its binding with direct enzyme, enzyme-substrate complex or both [77].

The competitive inhibition occurs due to either binding of substrate or inhibitor to the active site. Both substrate and inhibiting molecule compete for the same active site on the enzyme leading to the reduction in the velocity of the reaction. The diverse set of substrate analogues studied for their activity in the presence of different kinds of inhibitors reveals immense information useful to understand the interaction of the active site and catalytic mechanism of the enzyme. The basic assumption in the study of this type of inhibition is that the inhibitor can only bind to the active site of the free enzyme [3, 74, 78].The Cleland notation for the compet-

> E þ A⇄ k1 k2 EA! k2 E þ P

> > (47)

þ I ↑↓ EI

3.1. Reversible inhibition

94 Enzyme Inhibitors and Activators

Figure 11. The classification of enzyme inhibition.

3.1.1. Competitive inhibition

itive inhibition can be written as,

which can also be represented as,

$$\frac{1}{v} = \frac{(1 + \frac{|l|}{K\_l})K\_m}{V\_{\text{max}}[S]} + \frac{1}{V\_{\text{max}}} \tag{51}$$

After plotting 1/v versus 1/[S], the slope and intercept will give the values of apparent K<sup>m</sup> and Vmax (Figure 12).

In this case, K<sup>m</sup> changes with Vmax unchanged. Increase in KM depends upon the concentration of I. The competitive inhibitors can be applied as targeted blockers of enzyme in the pharmaceutical industry. Product can also act as a competitive inhibitor in various regulation pathways in the cells which increases the efficiency of cellular processes by eliminating the accumulation product and diverting the substrate to another pathway [79]. Both structural analogue and in some cases, unrelated compounds act as competitor inhibitors. For example, alkaline phosphatases are inhibited by the inorganic inhibitors where both substrate and inhibitor have similar affinities. Because of high selectivity, it provides many in vivo application opportunities, e.g. penicillinase, prostaglandin cyclooxygenase.

Figure 12. Graphical representation of competitive inhibition.

The reactions requiring the presence of metal ion as co-factors compete with similar ones for the catalytic site on the enzyme, e.g. Ca ions compete with Mg requiring enzyme. Similarly, Na requiring enzymes are inhibited by the Li and K ions. In double-displacement reaction mechanism, high concentration of the second substrate acts as a competitive inhibitor with reference to binding of first substrate, e.g. aminotransferase.

Adulteration of ethanol with methanol makes it unsuitable for human consumption, commonly known as denatured alcohol. Methanol is oxidized in liver and kidney to form formaldehyde and formic acid. This causes damage to retinal cells that may cause blindness which is followed by severe acidosis which lead to death. This may also lead to depression of CNS. Retardation of first step in oxidation of methanol can be achieved by administration of ethanol. The removal of methanol is done by gastric lavage, haemodialysis and administration of exogenous bicarbonate. Ethylene glycol is an anti-freezing agent used in automobiles. Ingestion in the body leads to depression of CNS and causes metabolic acidosis with severe renal damage after oxidation by alcohol dehydrogenase which is inhibited by ethanol or 4-methyl pyrazole. Kidney damage is resulted due to the deposition of oxalate crystal into convulsed tubules. Elevated anion-gap metabolic acidosis is caused by glycolic acid and lactic acid. The shift in redox potential causes the production of lactic acid instead of pyruvate. The treatment is same as that of methanol adult injection. Fomepizole drug (4-methylpyrazole) can be used in the treatment without any side effect that is caused by the ethanol. Isopropanol is major constituent in rubbing alcohols such as hand lotion and anti-freezing preparations. If ingested accidentally is oxidized and converted into acetone, a toxic non-metabolized product by alcohol dehydrogenase. It also causes depression in CNS, coma, gastritis, vomiting and haemorrhage. This can be treated by haemodialysis.

Toxicity by these substrates is done by evaluation of following serum components: Na, K, Cl, HCO3, glucose, urea nitrogen, blood osmolality, blood gap, anion gap and metabolic acidosis along with pertinent medical history. Serum osmolal gap is difference between measured osmolality and calculated osmolality.

Serum osmolal gap = Measured osmolality-calculated osmolality
