Calculated osmolality=2 Na+ (mM/L) + glucose (mM/L) + Urea nitrogen (mM/L)

Small rise in toxic substances increase osmolality significantly. Hence, it becomes very easy to detect the toxicity in the body based on this test.

#### 3.1.2. Uncompetitive inhibition

Uncompetitive inhibition occurs when instead of enzyme, inhibitor binds with enzyme substrate complex to inhibit the reaction. The binding of inhibitor is possible only after the binding of substrate to the enzyme. The binding site of the inhibitor forms when the substrate binds with enzyme. This type of inhibition is rare where inhibitor binds with the enzyme substrate complex [7, 52]. This can be represented in the form of Cleland notation as,

Kinetic Modelling of Enzyme Catalyzed Biotransformation Involving Activations and Inhibitions http://dx.doi.org/10.5772/67692 97

$$\begin{aligned} E + A \overset{k1}{\underset{k2}{\rightleftharpoons}} EA \overset{k2}{\rightarrow} E + P\\ + \\ I \\ \uparrow \downarrow \\ EAI \end{aligned} \tag{52}$$

can also be represented as,

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

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

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

Small rise in toxic substances increase osmolality significantly. Hence, it becomes very easy to

Uncompetitive inhibition occurs when instead of enzyme, inhibitor binds with enzyme substrate complex to inhibit the reaction. The binding of inhibitor is possible only after the binding of substrate to the enzyme. The binding site of the inhibitor forms when the substrate binds with enzyme. This type of inhibition is rare where inhibitor binds with the enzyme substrate complex [7, 52]. This can be represented in the form of Cleland

to binding of first substrate, e.g. aminotransferase.

96 Enzyme Inhibitors and Activators

haemorrhage. This can be treated by haemodialysis.

detect the toxicity in the body based on this test.

Serum osmolal gap = Measured osmolality-calculated osmolality

Calculated osmolality=2 Na+ (mM/L) + glucose (mM/L) + Urea nitrogen (mM/L)

osmolality and calculated osmolality.

3.1.2. Uncompetitive inhibition

notation as,

$$A + E \underset{k\_{-1}}{\overset{k\_1}{\rightleftharpoons}} EA \overset{k\_2}{\rightarrow} E + P \tag{53}$$

$$
\Box E A + I \stackrel{k\_i}{\rightleftharpoons} E A I \tag{54}
$$

The Michealis Menten equation for the uncompetitive inhibition becomes,

$$\upsilon = \frac{V\_{\text{max}}[\text{S}]}{K\_{\text{m}} + [\text{S}](1 + \frac{[\text{S}]}{K\_{\text{i}}})} \tag{55}$$

The Lineweaver Burk equation can be written as,

$$\frac{1}{\upsilon} = \frac{K\_{\text{m}}}{V\_{\text{max}}[S]} + \frac{(1 + \frac{|I|}{K\_i})}{V\_{\text{max}}} \tag{56}$$

The plot is shown in Figure 13.

Figure 13. Graphical representation of uncompetitive inhibition.

The binding with ES complex yields parallel lines wherein both slope and intercept change. The apparent K<sup>m</sup> and Vmax include division by (1+ [I]/Ki). This type of inhibition is rarely observed in single substrate reactions. The classical example of this type of inhibition is an intestinal alkaline phosphatase which is inhibited by l-phenylalanine.

#### 3.1.3. Non-competitive inhibition

Non-competitive inhibition is observed when inhibitor can bind with both enzymes and enzyme-substrate complex. The inhibitor bears no structural resemblance to substrate and bind to distinct site than the substrate. There is no competition between substrate and inhibitor for the active site of the enzymes. This type of inhibition cannot be overcome by increasing the substrate concentration. This may bind to enzyme or enzyme-substrate complex making both of them catalytically inactive [8, 80]. This can be denoted as,

$$A + E \underset{k\_{-1}}{\overset{k\_1}{\rightleftharpoons}} EA \overset{k\_2}{\rightarrow} E + P \tag{57}$$

$$E + I \stackrel{k\_i}{\rightleftharpoons} EI \tag{58}$$

$$EA + I \stackrel{k\_i}{\rightleftharpoons} EAI \tag{59}$$

The Cleland notation is denoted for the non-competitive inhibition.

$$E + A \underset{k2}{\underset{k2}{\rightleftharpoons}} EA \overset{k2}{\to} E + P + I \underset{I}{\rightleftharpoons} EI + I \underset{I}{\rightleftharpoons} EAI \tag{60}$$

The double reciprocal plot for the non-competitive inhibition is represented in Figure 14.

Examples:

• Enzymes with sulfhydryl group that participate in maintenance of three-dimensional confirmation of the molecules are non-competitively inhibited by heavy metal ions such as silver (Ag), lead (Pb) and mercury (Hg).

$$\rm ESH + Hg^{+2} \rightleftharpoons \rm ESHg^{+} + H^{+} \tag{61}$$

Heavy metal ions react with S-, O- and N-containing ligand. Hence, they can inhibit enzymes in the metabolic pathway (see Table 4).

#### 3.2. Irreversible inhibition

Irreversible inhibition occurs, when inhibitor molecule bind with enzyme so strongly that it does not dissociate from the enzyme. This kind of inhibitor binds rapidly with the enzyme and deactivated the enzyme completely. The activity decreases exponentially with binding of the inhibitor, at saturating levels of inhibitor concentration. At lower concentration, the rate of reaction decreases linearly. The covalent modification and tight binding (Kd< 10�<sup>8</sup> M) are two

Figure 14. Graphical representation of noncompetitive inhibition.

types of irreversible inhibitions; for practical purposes, there is no dissociation of E and I. Thus, physical separation processes are ineffective in removing the irreversible inhibitor from the enzyme [33, 75, 81]. Reaction is written as,

$$E + I \underset{k\_{-1}}{\overset{k\_1}{\rightleftharpoons}} EI \overset{k\_2}{\rightarrow} EI^\* \tag{62}$$

#### 3.2.1. Transition state analogues

The binding with ES complex yields parallel lines wherein both slope and intercept change. The apparent K<sup>m</sup> and Vmax include division by (1+ [I]/Ki). This type of inhibition is rarely observed in single substrate reactions. The classical example of this type of inhibition is an

Non-competitive inhibition is observed when inhibitor can bind with both enzymes and enzyme-substrate complex. The inhibitor bears no structural resemblance to substrate and bind to distinct site than the substrate. There is no competition between substrate and inhibitor for the active site of the enzymes. This type of inhibition cannot be overcome by increasing the substrate concentration. This may bind to enzyme or enzyme-substrate complex making both

E þ P (57)

EI (58)

EAI (59)

E þ P þ I⇄EI þ I⇄EAI (60)

ESH <sup>þ</sup> Hgþ<sup>2</sup> ⇄ ESHg<sup>þ</sup> <sup>þ</sup> <sup>H</sup><sup>þ</sup> (61)

A þ E⇄ k1 k�<sup>1</sup> EA! k2

> E þ I⇄ ki

EA þ I⇄ ki

The double reciprocal plot for the non-competitive inhibition is represented in Figure 14.

• Enzymes with sulfhydryl group that participate in maintenance of three-dimensional confirmation of the molecules are non-competitively inhibited by heavy metal ions such as silver

Heavy metal ions react with S-, O- and N-containing ligand. Hence, they can inhibit enzymes

Irreversible inhibition occurs, when inhibitor molecule bind with enzyme so strongly that it does not dissociate from the enzyme. This kind of inhibitor binds rapidly with the enzyme and deactivated the enzyme completely. The activity decreases exponentially with binding of the inhibitor, at saturating levels of inhibitor concentration. At lower concentration, the rate of reaction decreases linearly. The covalent modification and tight binding (Kd< 10�<sup>8</sup> M) are two

intestinal alkaline phosphatase which is inhibited by l-phenylalanine.

of them catalytically inactive [8, 80]. This can be denoted as,

The Cleland notation is denoted for the non-competitive inhibition.

E þ A⇄ k1 k2 EA! k2

3.1.3. Non-competitive inhibition

98 Enzyme Inhibitors and Activators

Examples:

(Ag), lead (Pb) and mercury (Hg).

in the metabolic pathway (see Table 4).

3.2. Irreversible inhibition

Transition state is a state in which substrate is strongly bound and interacting with enzyme for short period (in picosecond). Therefore, the transition state analogues bind tightly with transition state enzyme and cannot be easily dissociated from the enzyme [82–84, 94, 102, 103, 104, 105]. The rate expression for such type of inhibition is represented as,

$$E\_{\mathbf{t}} = E e^{-\frac{k\_{\mathbf{\hat{l}}} |\mathbf{l}|}{|\mathbf{l}| + k\_{\mathbf{\hat{i}}}}} \tag{63}$$

#### 3.2.2. Suicide inhibition

The suicide substrate binds covalently with an active site of the enzyme and blocks the enzyme completely. The mechanism of binding of suicide substrate with the active site of the enzyme gives the understanding of enzyme mechanism [84–86].

$$\begin{aligned} E + I \overset{k\_1}{\underset{k\_{-1}}{\rightleftharpoons}} EI \overset{k\_2}{\rightarrow} EI^\* \overset{k\_3}{\rightarrow} E + I^\*\\ \downarrow k\_{+4} \\ E - I \end{aligned} \tag{64}$$


Table 4. List of examples of different types of inhibitions.

#### Examples:

Sr.

Competitive inhibition 1. Cytochrome c oxidase

100 Enzyme Inhibitors and Activators

Dehydrogenase

2. Succinate

3. HMG-CoA reductase

5. Influenza neuraminidase

6. Dihydropteroate synthetase

7. Dihydrofolate reductase

9. Cytochrome P450 enzyme

2. Enzyme requiring divalent ions

> (magnesium and manganese complexes

Uncompetitive inhibition Inositol

monophosphatase

3. Enolase

Non-competitive inhibition 1. Porphobilinogen synthase and ferrocene lactase

no. Enzyme Substrate Inhibitor Mechanism of action Reference

Succinate Malonate, oxaloacetate, oxaloacetate

deoxynojirimycin

8. Xanthine oxidase Hypoxanthine Allopurinol Competes with active site to

Biapigenin (hypericum perforatum extracts)

Ethylenediamine tetracetate

dimethylaminocyclohexanol,

Inositol Lithium Interfere with

(hydroxyphenyl) trimethylammonium derivatives

(EDTA)

4. Sucrase Sucrose Acarbose, nojirimycin, and

p-Aminobenzic

acid

Range of substrate

Heme group synthesis pathway

Magnesium and calcium

phosphoglycerate

2-

4. Acetylcholinesterase Acetylcholine cis-2-

Table 4. List of examples of different types of inhibitions.

Oxygen Cyanides Competes with active site [92]

HMG-CoA Lovastatin Competes with active site [54]

Sulfonamides Competes with active site

Neuraminic acid Oseltamivir carboxylate Competes with active site

Folate Methotrexate Competes with active site

Competes with active site [93, 94]

Competes with active site [95]

[96, 97]

[98]

[98]

[99, 100]

[102, 103]

[105, 106]

[108, 109]

and prevent escape of viral flu particles (Influenza)

(bacterial infection)

therapy)

enzyme

pathway.

Lead (Pb) Bind with sulfuryl group of

Fluorides Competes with magnesium

and prevent rapid DNA synthesis (HIV)

block formation of uric acid (Gout, hemotological disorders, antineoplastic

Competes with active site [101]

Chelates the metallic ion [104]

Binds with esterase active site [107]

and manganese complexes and prevent glycolysis

polyphosphoinositide metabolism in brain


#### 3.3. Inhibition in combination with each other

The kinetics expression for mutually exclusive inhibitors is studied for single substrate system. The overall reaction velocity for the system in presence of types of inhibition is given by,


Table 5. Examples of irreversible inhibitions.

$$\frac{1}{v\_{1,2,\ldots,n}} = \sum\_{i=1}^{n} \frac{1}{v\_i} - \frac{n-1}{v\_0} \tag{65}$$

Wherein, v<sup>0</sup> is the velocity in the absence of inhibition and 'n' is the number of inhibitors used in combination. Similarly, the kinetic expression is derived for the two substrate systems. For example, two substrate reaction with two inhibitors: ping-pong Bi-Bi mechanism.

Two inhibitors: I<sup>1</sup> is competitive with respect to the substrate A (binds to E) and uncompetitive with respect to the substrate B; I<sup>2</sup> is competitive with respect to the substrate A (binds to E) and uncompetitive with respect to the substrate B.

$$\frac{1}{v\_0} = \frac{(AB + K\_\text{b}A + K\_\text{m}B)}{VAB} \tag{66}$$

$$\frac{1}{\upsilon\_1} = \frac{(AB + K\_\text{b}A + K\_\text{m}B(1 + \frac{l\_1}{K\_{l\_1}}))}{VAB} \tag{67}$$

$$\frac{1}{v\_2} = \frac{(AB + K\_bA + K\_mB(1 + \frac{I\_2}{K\_{l\_2}}))}{VAB} \tag{68}$$

$$\frac{1}{\frac{1}{\upsilon\_{1,2}}} = \frac{(AB + K\_{b^\*}A + K\_{\text{m}}B(1 + \frac{I\_1}{K\_{l\_1}} + \frac{I\_2}{K\_{l\_2}}))}{VAB} \tag{69}$$

Kinetic Modelling of Enzyme Catalyzed Biotransformation Involving Activations and Inhibitions http://dx.doi.org/10.5772/67692 103

Overall velocity of the reaction is given as,

$$\frac{1}{v\_{1,2}} = \frac{1}{v\_1} + \frac{1}{v\_2} - \frac{1}{v\_0} \tag{70}$$

Synergism:

$$\left(\frac{1}{v\_{1,2}}\right)\frac{1}{v\_1} + \frac{1}{v\_2} - \frac{1}{v\_0} \tag{71}$$

Antagonism:

1 v1,2,…<sup>n</sup>

example, two substrate reaction with two inhibitors: ping-pong Bi-Bi mechanism.

1 v0

1 v1 ¼

1 v2 ¼

1 v1, <sup>2</sup> ¼

uncompetitive with respect to the substrate B.

no. Enzyme Substrate Inhibitor

ATP

metabolism)

4. Human caspases Proteins Peptide based (4 amino acid

5. Serine proteases Proteins Phenylmethanesulfonyl

Deoxyuridine monophosphate

7. Chymotrypsin Protein Tosyl phenylalanyl

Norepinephrine, serotonin

2. Human mast-cell tryptase Benzamidine CRA-001390 inhibitor Tight binding

1. ATPase Phosphoenolpyruvate,

3. Adenosine deaminase Adenosine (purine

6. Thymidylate synthase and Cofactor methylene tetrahydrofolate

8. Monoamine oxidase (MAO)

Table 5. Examples of irreversible inhibitions.

Sr.

102 Enzyme Inhibitors and Activators

<sup>¼</sup> <sup>X</sup><sup>n</sup> i¼1

9. Cyclooxygenase 2 Arachidonic acid Vioxx, celebrex Suicide inhibition [121–123]

Wherein, v<sup>0</sup> is the velocity in the absence of inhibition and 'n' is the number of inhibitors used in combination. Similarly, the kinetic expression is derived for the two substrate systems. For

Two inhibitors: I<sup>1</sup> is competitive with respect to the substrate A (binds to E) and uncompetitive with respect to the substrate B; I<sup>2</sup> is competitive with respect to the substrate A (binds to E) and

<sup>¼</sup> <sup>ð</sup>AB <sup>þ</sup> <sup>K</sup>b<sup>A</sup> <sup>þ</sup> <sup>K</sup>mB<sup>Þ</sup>

<sup>ð</sup>AB <sup>þ</sup> <sup>K</sup>b<sup>A</sup> <sup>þ</sup> <sup>K</sup>mBð<sup>1</sup> <sup>þ</sup> <sup>I</sup><sup>1</sup>

<sup>ð</sup>AB <sup>þ</sup> KbA <sup>þ</sup> KmBð<sup>1</sup> <sup>þ</sup> <sup>I</sup><sup>2</sup>

<sup>ð</sup>AB <sup>þ</sup> <sup>K</sup>b<sup>A</sup> <sup>þ</sup> <sup>K</sup>mBð<sup>1</sup> <sup>þ</sup> <sup>I</sup><sup>1</sup>

KI1 ÞÞ

KI2 ÞÞ

KI1 <sup>þ</sup> <sup>I</sup><sup>2</sup> KI2 ÞÞ

VAB (66)

Mechanism of

inhibitions

inhibitions

Tight binding inhibitions

Tight binding inhibitions

Suicide inhibition [36]

Suicide inhibition [119]

Suicide inhibition [120]

Rutamycin, bongkrekic acid Tight binding

Fluorouracil Suicide inhibition [36]

action Reference

[116]

[113]

[117]

[118]

VAB (67)

VAB (68)

VAB (69)

1 vi

pargyline

� <sup>n</sup> � <sup>1</sup> v0

chloromethylketone

Clorgyline, deprenyl,

Deoxycoformycin, 1,6 dihydro-6-hydroxymethyl purine ribonucleoside

sequence)

fluoride

(65)

$$\frac{1}{v\_{1,2}}(\frac{1}{v\_1} + \frac{1}{v\_2} - \frac{1}{v\_0})\tag{72}$$

The expression is useful to understand the effect of inhibitors on each other's activity when used in combination. The overall velocity of the reaction is independent of mechanism of reaction, type of inhibition and number substrate used in the study [89].

#### 4. Analytical aspects of enzyme inhibition

#### 4.1. Assay conditions for single substrate enzyme kinetics

To estimate the reaction rate, it becomes very essential to quantify accurately the change in the concentration of either substrate or product or both during the progress of reaction. If the substrate and product generate different signals, the spectroscopic techniques like UV-visible spectroscopy and fluorescence spectroscopy can be applied to estimate these parameters [90]. If there is no significant difference between the products and substrate signal, then the better alternative is a discontinuous assay which measures the rates by intermittent sampling. This sampling can be done with removal of aliquots of a reaction mixture or sampling from the batch reactor. These reaction samples represent the time points of a reaction, and their respective concentration of product formed and substrate consumed. In some cases, labelling the molecules with chromophore or the fluorescent dye can serve as a better option. The estimation of amount of an ATP can be quantified by determining the amount of Pi present by the Malachite Green assay with absorbance at 660 nm [91]. Chromatography techniques can separate the substrate from the product which is then estimated with the spectroscopic method in continuous or discontinuous manner. In depth understanding, the enzyme mechanism is studied by radiolabelling the substrate, which is tracked for the transition of substrate through intermediate state to the product during the reaction progress [92]. The crystallographic structures of separated intermediate complexes and the various states of enzymes during the reaction progress reveal most of the mechanistic aspect of the reaction. With the advent of instrumentation technology, the product can be separated or analysed by thin-layer chromatography, separation techniques such as high-performance liquid chromatography, electrophoresis and gel filtration. The high-performance liquid chromatography is the most applied system as it gives the separation and quantification of substrate as well as product in real time. Recent studies showed that the mass spectrometric (MS) techniques are applied to study the conversion of substrate into product and their behaviour in the presence of modulators. Matrix-assisted laser desorption ionization-time of flight-mass spectroscopy (MALDI-TOF-MS) is proved as more effective technique when compared to other mass spectrometric techniques, such as electronspray ionization MS, as it showed negligible interference due to the presence of buffers and reagents. MALDI-TOF-MS can quantify the ratio of substrate to product form. Greis et al. studied the phosphorylation catalysed by kinases using this technique for accurate prediction of the kinetics of reaction [93]. This technique has been used in combination with various chromatographic techniques such as capillary isoelectric focusing, frontal affinity chromatography and size exclusion chromatography to analyse the inhibition of the enzyme in direct or indirect manner [93–96]. This method is free of laborious work of labelling or derivatization and can be done in short period of time.

To estimate the enzyme inhibition and relative kinetic parameters, the stepwise process has to follow with the aim of minimum human error, which is discussed in the following sections.
