*2.10. Elemental Analysis*

The C, H, and N contents of organosolv lignins were determined in triplicate by elemental analysis in a Flash EA1112 (ThermoFinnigan). The oxygen content was calculated from the difference between the sample weight and the C, H, N and S contents.


**4. Field investigations**

Field investigations have revealed the existence of about 22 dormant volcanoes on the Jos Plateau region alone (**Table 1**) and are generally aligned in series of NNW–SSE trend [6–8] (**Figure 2**). None of these volcanoes have record of any activity in recent past [8, 9]. They are composed mainly of basaltic scoria and pyroclastic materials.

**Tables 1** and **2** present the inventory of the dormant volcanoes on the Jos Plateau and the Biu Plateau, respectively. From the NNW end are the Ganawuri volcanic line, Hoss volcanic line, Panyam (Sura) volcanic line and Gu (Jiblik) volcanic line (**Figure 2**). The Ganawuri line comprises from the north to south of the Bum, Jal, and Kwakwi volcanoes. The Hoss volcanic line consists of two volcanoes; Miango in the north and Hoss volcano in the south. The Miango line consists of five volcanoes from the north to the south viz.: Rukuba, Miango north, Miango south, Vom and Kassa volcanoes. The Southern-most end members are namely the Panyam and Gu volcanic lines. The Panyam volcanic line consists of seven volcanoes aligned in a NNE–SSW trending directions along a hypothetical fracture line [6, 10]; Dai volcano (referred to as Wushik volcano), Amshel volcano (referred to as Kugol volcano), Dutsin volcano, Kerang volcano, Tingyaras volcano, Ampang volcano (referred to as Mufil volcano), Pidong Crater Lake.

The Kerang twin volcanoes are located at Kerang town and its environs in the present Mangu Local Government Area, about 120 km from Jos, Plateau State (**Figure 1**). The Kerang I (Dustin) volcano has a peak of 1456 m above sea level and a crater diameter of 300 m. The volcanic pile consists of ash, lapilli, scoria, pumices, *Is a Volcanic Eruption Possible in Nigeria? DOI: http://dx.doi.org/10.5772/intechopen.84253*

Netherlands, Geological Survey Laboratory. For quality control, a duplicate geochemical analysis on the same basaltic rocks was carried out at the University of Cardiff, Wales using the Inductively Coupled Plasma Optical Emission Spectrome-

A constant monitoring of the Pidong Crater Lake through continuous water sampling 24–36 calendar months was done. The following physical parameters were recorded in the field using MT 806/pH/EC/TDS/Temp portable meter (pH, Temperature, Electrical Conductivity (EC), Total Dissolved Solids (TDS)). The water samples were collected in 100 ml polyethylene plastic bottles for cations and anion analysis. The sample for cations analysis was acidified with 0.1 M Nitric acid to prevent precipitating and bacterial growth. The following cations: Mg, Ca, Na, K, Cr, Ni, Co, Sc, V, Cu, Pb, Zn, Bi, Cd, Sn, W, Ma, As, Sb, Rb, Cs, Ba, Sr., Ga, Li, Ta, Nb, Hf, Zr, Y, Th, U, B, Fe & REEs were analyzed using ICP-MS method at Bureau Veritas Minerals Laboratory Limited, Canada while the anions: SO4, Cl, HCO3, NO3, F, Br and PO4 were carried out using colometry method at Maxxam Laboratory,

H), and (∂3

of the Pidong Crater Lake, Bwonpe Volcanic Spring and rainfall were analyzed at Activation Laboratory Ontario, Canada using cavity Ring down spectroscopy (CRDS) model L11 02-1 California, USA with V-SMOW standards with typical standards

Field investigations have revealed the existence of about 22 dormant volcanoes on the Jos Plateau region alone (**Table 1**) and are generally aligned in series of NNW–SSE trend [6–8] (**Figure 2**). None of these volcanoes have record of any activity in recent past [8, 9]. They are composed mainly of basaltic scoria and

**Tables 1** and **2** present the inventory of the dormant volcanoes on the Jos Plateau and the Biu Plateau, respectively. From the NNW end are the Ganawuri volcanic line, Hoss volcanic line, Panyam (Sura) volcanic line and Gu (Jiblik) volcanic line (**Figure 2**). The Ganawuri line comprises from the north to south of the Bum, Jal, and Kwakwi volcanoes. The Hoss volcanic line consists of two volcanoes; Miango in the north and Hoss volcano in the south. The Miango line consists of five volcanoes from the north to the south viz.: Rukuba, Miango north, Miango south, Vom and Kassa volcanoes. The Southern-most end members are namely the Panyam and Gu volcanic lines. The Panyam volcanic line consists of seven volcanoes aligned in a NNE–SSW trending directions along a hypothetical fracture line [6, 10]; Dai volcano (referred to as Wushik volcano), Amshel volcano (referred to as Kugol volcano), Dutsin volcano, Kerang volcano, Tingyaras volcano, Ampang

The Kerang twin volcanoes are located at Kerang town and its environs in the present Mangu Local Government Area, about 120 km from Jos, Plateau State (**Figure 1**). The Kerang I (Dustin) volcano has a peak of 1456 m above sea level and a crater diameter of 300 m. The volcanic pile consists of ash, lapilli, scoria, pumices,

H) and Carbon-14 (14C) isotopes

try (ICP-OES).

*Forecasting Volcanic Eruptions*

**3.4 Isotope study**

**4. Field investigations**

pyroclastic materials.

**8**

**3.3 Hydrogeochemical monitoring study**

Vancouver, Canada (subsidiary of Bureau Veritas Ltd).

deviation for 18O 0.1% and 1% for Tritium unit (TU).

volcano (referred to as Mufil volcano), Pidong Crater Lake.

Oxygen-18 (∂18O) and deuterium (∂2

#### **Table 1.**

*Inventory of the volcanoes of the Jos Plateau, Nigeria.*

breccias, basalts, boulders, and pyroclastic materials of various sizes. The Kerang II (Kerang) volcano has three craters with a peak height of 1510 m above sea level with a crater diameter ranging from 600 m to 1 km (**Table 1**). This volcano (Kerang II) is the second largest volcano on the Jos Plateau compared to the Jiblik volcano which has a peak height of 1670 m above sea level. The volcanic pile of the Kerang II volcano is composed of ash, lapilli, scoria, breccias, bombs, basaltic boulders and pyroclastic materials (lapilli, granitic and lava flows).

The Pidong volcano (Maar) has a series of three craters and aligned along the general North-South trend of the Panyam Volcanic Line [10]. The Pidong Maar consists of a sequence of pyroclastic materials (mixture of large fragments of basement rocks/pyroclastics, scoria and ash) and indicative of violent eruption [9]. The Gu volcanic line consist of five volcanoes from NW to SW namely Jiblik, Kagu, Katul and Lagdak volcanoes. The volcanic cones are composed essentially of volcanic ash, lapilli, bombs, tuff agglomerates, basalts and scoria. Most of them occur as single cinder cones (like at Miango, Wushik, Kerang Swan junction, etc.) but rarely as clusters of two or more volcanoes (for example Jiblik, Kassa, Kerang twin volcanoes, Pidong, etc.)

Also, the relatively large sizes of some of these volcanoes (Miango, Kassa, Jiblik, Kerang, etc.) suggest that quite a large volume of ejecta materials were spewed out covering quite a large landmass (valleys and low-lying plains) as lava flows. Lava flows apparently from the Jiblik volcanic can be traces to several kilometers south of the Jos Plateau escarpment. If any of these volcanoes erupt today with the same intensity and volume presumed, a large expanse of land would be buried and about 2 million people living around these volcanoes are potentially at risk.

altitude above sea level relative to those of the Jos Plateau, which extruded the

*Geological map of the 22 dormant volcanoes of the Jos Plateau showing sample locations. M = Miango*

by a large volume of volcanic ash and pyroclastic materials (for example, at Gwamya, Tilla Crater Lake, Gadam, Batadeka, Buratai, Katla volcanoes, etc.) (**Table 2**), suggesting that there was a tremendous spewing of ejecta materials (ashes and gases) into the atmosphere prior to the violent eruptions and/or in-

Also, unlike the volcanoes of the Jos Plateau, those of Biu Plateau are constituted

The major and trace elements geochemical compositions of the basaltic rock samples collected from the various volcanic cones in the Jos Plateau volcanic

already high-level Younger Granite bodies.

*Is a Volcanic Eruption Possible in Nigeria? DOI: http://dx.doi.org/10.5772/intechopen.84253*

*volcanoes, K = Kassa volcanoes, S = Sura volcanoes, and G = Gu volcanoes.*

**5. Geochemical results and interpretations**

between the eruptions.

**Figure 2.**

**11**

The volcanoes of the Biu Plateau (**Table 2**) present similar physical and petrographic characteristics as those of the Jos Plateau region. The volcanoes also form near linear alignments from the north to the south and extend right through the low-lying Basement complex into the sedimentary formations of the Benue valley (Garkida-Gombi-Song areas in Adamawa State). The volcanoes are simple and never in clusters, but with very large craters of greater than 1 km, (Caldera). The volcanoes extruded directly the basement rocks and therefore are of lower

#### **Figure 2.**

breccias, basalts, boulders, and pyroclastic materials of various sizes. The Kerang II (Kerang) volcano has three craters with a peak height of 1510 m above sea level with a crater diameter ranging from 600 m to 1 km (**Table 1**). This volcano (Kerang II) is the second largest volcano on the Jos Plateau compared to the Jiblik volcano which has a peak height of 1670 m above sea level. The volcanic pile of the Kerang II volcano is composed of ash, lapilli, scoria, breccias, bombs, basaltic

20 Lakdak 7000 cone Scoraceous

The Pidong volcano (Maar) has a series of three craters and aligned along the general North-South trend of the Panyam Volcanic Line [10]. The Pidong Maar consists of a sequence of pyroclastic materials (mixture of large fragments of basement rocks/pyroclastics, scoria and ash) and indicative of violent eruption [9]. The Gu volcanic line consist of five volcanoes from NW to SW namely Jiblik, Kagu, Katul and Lagdak volcanoes. The volcanic cones are composed essentially of volcanic ash, lapilli, bombs, tuff agglomerates, basalts and scoria. Most of them occur as single cinder cones (like at Miango, Wushik, Kerang Swan junction, etc.) but rarely as clusters of two or more volcanoes (for example Jiblik, Kassa, Kerang twin volca-

Also, the relatively large sizes of some of these volcanoes (Miango, Kassa, Jiblik, Kerang, etc.) suggest that quite a large volume of ejecta materials were spewed out covering quite a large landmass (valleys and low-lying plains) as lava flows. Lava flows apparently from the Jiblik volcanic can be traces to several kilometers south of the Jos Plateau escarpment. If any of these volcanoes erupt today with the same intensity and volume presumed, a large expanse of land would be buried and about

The volcanoes of the Biu Plateau (**Table 2**) present similar physical and petrographic characteristics as those of the Jos Plateau region. The volcanoes also form near linear alignments from the north to the south and extend right through the low-lying Basement complex into the sedimentary formations of the Benue valley (Garkida-Gombi-Song areas in Adamawa State). The volcanoes are simple and never in clusters, but with very large craters of greater than 1 km, (Caldera). The volcanoes extruded directly the basement rocks and therefore are of lower

boulders and pyroclastic materials (lapilli, granitic and lava flows).

2 million people living around these volcanoes are potentially at risk.

noes, Pidong, etc.)

**10**

**S. No.**

**Name/ locality**

*Forecasting Volcanic Eruptions*

16 Pidong volcano

17 Jiblik volcano

18 Kagu volcano

19 Katul volcano

**Table 1.**

**Coordinates Estimated**

N09° 170 650″;E009° 120 312″

N09° 160 591″;E009° 160 890″

N09° 130 901″; 008° 160 383″

N09° 110 264″;E009° 150 795″

*Inventory of the volcanoes of the Jos Plateau, Nigeria.*

**population of people at risk**

100,000 Cinder

**Type of volcano**

Cone

**Diameter of crater**

50,000 Crater Lake 700 m 1378 m Scoria/

50,000 Cone 1 km 1060 m Scoraceous

5000 Cone 700 m 976 m Scoraceous

**Elevation (ASL)**

1 km 1228 m Scoraceous

**Materials deposited**

pyroclastics

basalt +garnet/ pyroclastics

> basalt/ pyroclastics

> basalt/ pyroclastics

> basalt/ pyroclastics

*Geological map of the 22 dormant volcanoes of the Jos Plateau showing sample locations. M = Miango volcanoes, K = Kassa volcanoes, S = Sura volcanoes, and G = Gu volcanoes.*

altitude above sea level relative to those of the Jos Plateau, which extruded the already high-level Younger Granite bodies.

Also, unlike the volcanoes of the Jos Plateau, those of Biu Plateau are constituted by a large volume of volcanic ash and pyroclastic materials (for example, at Gwamya, Tilla Crater Lake, Gadam, Batadeka, Buratai, Katla volcanoes, etc.) (**Table 2**), suggesting that there was a tremendous spewing of ejecta materials (ashes and gases) into the atmosphere prior to the violent eruptions and/or inbetween the eruptions.

### **5. Geochemical results and interpretations**

The major and trace elements geochemical compositions of the basaltic rock samples collected from the various volcanic cones in the Jos Plateau volcanic

**S/ No.**

**Name/ locality**

*Is a Volcanic Eruption Possible in Nigeria?  DOI: http://dx.doi.org/10.5772/intechopen.84253*

**S/ No.**

**Name/ locality**

*Forecasting Volcanic Eruptions*

1 Tasha Village

2 After Tasha Village

3 Tagwaye (twin) volcanoes (In Kwaya Kusar LGA of Borno State)

4 Gadam Volcano (Kwayar Kusar LGA, Borno State)

5 Location 5 N10°

6 Location 6 N10° 300

7 TUM N10° 360

8 Wakama (a) (BCG Village)

9 Wakama (b)

10 Gwamya Volcano

11 Tilla Volcanic Hill

12 Tilla Crater Lake

**12**

**Coordinates Estimated**

388″ E011° 240 406″

N10°170

N10° 160 .661″ E011° 270 .143″

N10° 300 .530″ E011° 300 .402″

N10° 310 .951″ E011° 530 .485″

320 .876″ E011° 570 .751″

. 279″ E011° 500 726″

. 2540 E012° 060 564″

N10° 360 .4720 E012° 070 126″

N10° 370

N10° 330 .496″ E012° 060 .

341″

N10° 320 .549″ E012° 080 .477″

N10° 320 .336″

.2110 E012° 080 886″

**population of people at risk**

**Type of volcano**

5000 Cluster of 3 volcanic cones.

 The volcanic cones situated at the northern end of the volcanic line here referred to as the north-western group are represented by Miango (M1 & M2) and Kassa (K1–5), while the south-eastern end group are represented by Jiblik (G1 &G2), Tingyaras (S1), Ampang (S2), Pidong (S3), Wulshik (S4), Kugol (S5) and Kerang (S6).

The rocks display similar SiO2 wt% contents (44.84–50.06 wt%) for the northwestern group of volcanoes (M1&2 and K1–5) and 45.26–46.25 wt% for S1–6 and 49.69 wt% for the Jiblik volcano (G1). However, the sample G2 from Jiblik with high SiO2 content of 64.21 wt% is exceptionally acidic and does not seem to be a basalt. Many of the rocks from the Kassa volcanoes (K1, K3, K4, and K5) display the highest SiO2 content (46.99–50.06 wt%) as opposed to those from Miango volcanoes (M1 &M2) and the southern volcanoes (S1–6) whose SiO2 contents are typical of a normal basalt (45.26–46.25 wt%).The Miango and the Kassa volcanoes display higher Fe2O3 contents (12.33–12.61 and 10.42–11.35 wt% respectively). The southern group (G1 & S1–6) displays lower Fe2O3 content; 9.83 wt% for the Jiblik volcano (G1); and a relatively higher but similar concentrations of between 11.25 and 11.92 wt% for the Panyam Volcanic line members (S1–6).

In general, the Al2O3 contents of all the basalts from the different volcanic cones are significantly high but vary narrowly inter/intra the volcanic cones (13.87–18.07 wt % for the north-western group and 12.41–18.07 wt% for the southern group (G1 & S1–6)). In terms of the MgO content, the southern group (S1–6) presents relatively higher values of between 10.71 and 12.58 wt% as against an average of 8.00 wt% for the northern group (M1–2 & K1–5). The CaO, Na2O, K2O and TiO2 contents for all the volcanoes vary narrowly; averagely 8; 3; 1.5 and 2 wt%, respectively.

Their Al2O3/TiO2 ratios vary narrowly and could be on that basis be subdivided into two groups; those with ratios between 5.53 and 5.69 and then those between 6.39 and 6.62 for the entire volcanic line (N-S) (**Figure 3**).  DOI: http://dx.doi.org/10.5772/intechopen.84253*

**(%)**

**(%)**

**(%)**

**(%)**

**(%)**

**(%)**

**(%)**

**(%)**

**(%)**

**(%)**

**(%)**

**TiO2**

**TiO2**

**CaO**

**unit**

M1 M2 G1 G2

S1 S2 S3 K1 K2 K3 K4 K5 S4 S5 S6 **Table 3.** *Major element*

*compositions*

 *(in weight percentage)*

 *of volcanic rocks from the Jos Plateau Volcanic Province.*

#### *Is a Volcanic Eruption Possible in Nigeria? DOI: http://dx.doi.org/10.5772/intechopen.84253*

**Table 3.**

*Major element compositions (in weight percentage) of volcanic rocks from the Jos Plateau Volcanic Province.*

province are presented in **Tables 3** and

*Inventory of the volcanoes of the Biu Plateau, Nigeria.*

The rocks display similar SiO

2 content (46.99

3 contents (12.33

2 O

% for the north-western group and 12.41

highest SiO

**S/ No.**

**Name/ locality**

*Forecasting Volcanic Eruptions*

26 Kurara Volcanic Hill (Garkida junction Adamawa State)

27 Song (Song-Gombi Road)

28 Song (Hawul Mountains)

**Table 2.**

25 Kukuwa II N11° 06

**Coordinates Estimated**

0 . 443 ″ E011° 53 0 . 534 ″

N10° 22 0 .460 ″ E012° 34 0 .284 ″

N9° 51 0 .036 ″ E012° 36 0 .383 ″

N9° 49 0 .504 ″ E012° 370 .155 ″

**population of people at risk**

**Type of volcano**

Plugs

5000 Several

**Diameter of crater**

50,000 Cone 1 km 661 m asl Weathered

50,000 Cone 700 m 477 m Weathered

250 m each

**Elevation (asl)**

200 m 435 m asl Columnar

**Materials deposited**

basalt

scoriaceous basalt/ pyroclastics

scoriaceous basalt/ pyroclastics

Weathered scoriaceous basalt/ pyroclastics

higher Fe

S1

**14**

of a normal basalt (45.26

In general, the Al

the northern group (M1

Their Al 2 O 3/TiO

2 O

represented by Miango (M1 & M2) and Kassa (K1

(S3), Wulshik (S4), Kugol (S5) and Kerang (S6).

**4**. The volcanic cones situated at the

–50.06 wt%) as opposed to those from Miango volca-

–46.25 wt%).The Miango and the Kassa volcanoes display

3 contents of all the basalts from the different volcanic cones

2O, K

2 ratios vary narrowly and could be on that basis be subdivided

–5), while the south-eastern end

420-1000 m asl

–11.35 wt% respectively). The south-

–6).

–18.07 wt% for the southern group (G1 &

2O and TiO

–50.06 wt%) for the north-

–6) presents relatively

2 contents for all

northern end of the volcanic line here referred to as the north-western group are

10,000 4

different cones aligned N-S

group are represented by Jiblik (G1 &G2), Tingyaras (S1), Ampang (S2), Pidong

western group of volcanoes (M1&2 and K1–5) and 45.26–46.25 wt% for S1–6 and 49.69 wt% for the Jiblik volcano (G1). However, the sample G2 from Jiblik with high SiO2 content of 64.21 wt% is exceptionally acidic and does not seem to be a basalt. Many of the rocks from the Kassa volcanoes (K1, K3, K4, and K5) display the

noes (M1 &M2) and the southern volcanoes (S1–6) whose SiO2 contents are typical

are significantly high but vary narrowly inter/intra the volcanic cones (13.87–18.07 wt

higher values of between 10.71 and 12.58 wt% as against an average of 8.00 wt% for

–5). The CaO, Na

into two groups; those with ratios between 5.53 and 5.69 and then those between 6.39 and 6.62 for the entire volcanic line (N-S) (**Figure 3**). This is further a

the volcanoes vary narrowly; averagely 8; 3; 1.5 and 2 wt%, respectively.

–12.61 and 10.42

and 11.92 wt% for the Panyam Volcanic line members (S1

–6)). In terms of the MgO content, the southern group (S1

–2 & K1

ern group (G1 & S1–6) displays lower Fe2O3 content; 9.83 wt% for the Jiblik volcano (G1); and a relatively higher but similar concentrations of between 11.25

2 wt% contents (44.84

*Southeastern volcanoes: G1—basalt of Jiblik volcano; S1—basalt of Timjagha'as volcano; S2—basalt of Ampang volcano; S3—basalt of Pidong volcano; S4—basalt of Wushik volcano; S5—basalt of Kogul volcano; S6—basalt of Kerang volcano. Northwestern volcanoes: M1—basalt of Miango North volcano; M2—basalt of Miango South volcano; K1—basalt of Kassa volcano; K2—basalt of Kassa volcano; K3—basalt of Kassa volcano; K4—basalt of Kassa volcano; K5—basalt of Kassa volcano.*

#### **Table 4.**

*Trace elements compositions (in ppm) of the basaltic rocks from the Jos Plateau Volcanic Province.*

reflection of the variations in Al2O3 contents of the basalts since TiO2 contents remain relatively constant. Similarly, their CaO/TiO2 and Al2O3/CaO ratios vary from 2.6 to 4.31 and 1.34–1.60 respectively. Such narrow difference in these ratios is expected from a low degree of magmatic differentiation of the same parent material by partial melting process (**Figures 3** and **4**).

Similarly, the rocks present subtle variations in incompatible element ratios Ba/Sr. and Zr/Y (0.73–0.90 and 8.77–9.35, respectively); all supportive of their subjection to low degree of magmatic differentiation and/or similar source.

#### **5.1 Silica versus major oxides correlation plots**

In the SiO2 versus MgO wt% plot, the southern volcanoes overwhelmingly display higher MgO contents as opposed to the lower values for the northern group of volcanoes (**Figure 5c**). It is expected that the Kassa volcanoes (K1–5) which are more differentiated (by their higher SiO2 contents) than the others to present lower MgO contents but instead display similar MgO contents. This scenario is true of their Fe2O3 contents. However, there is a weak negative correlation between Fe2O3, MgO, TiO2 and MnO versus silica indicating a progressive decrease of these oxides with differentiation (Miango-Southern group-Kassa) corresponding to compositional variations related to the removal of different proportions of olivine/pyroxenes from the melt as it becomes more felsic (**Figure 6a–d**).

recrystallization of clinopyroxenes in the early stages of crystallization. In general, there is a positive correlation depicting a progressive increase of CaO with differentiation from Miango to the southern group to Kassa (**Figure 5a–f**). This increase is not visible at the level of one volcano but several of them put together. The high Fe2O3, MgO and CaO could be as a result of the bulk crystallization of olivine, pyroxene and plagioclase during the early stages of differentiation. The progressive increase in the contents of Al2O3 corresponds with the increase in the alkaline metals content (Na2O+K2O) suggesting the crystallization of plagioclase with increased degree of differentiation. The alkaline oxides (Na2O+K2O) are correspondingly highest in the most differentiated rocks (K1–5) (**Figure 6d**). In a silica versus total alkali diagram (**Figure 7**), the rocks fall within the alkaline field and are therefore classified as predominantly alkaline basalts. Only a few rocks fall in the

**Figure 4.**

**17**

**Figure 3.**

*Plot of SiO2 versus Al2O3/TiO2 ratios.*

*Is a Volcanic Eruption Possible in Nigeria? DOI: http://dx.doi.org/10.5772/intechopen.84253*

*Plot of SiO2 versus Al2O3/CaO ratios.*

The Kassa volcanoes in the northern group and those of the southern group exhibit higher CaO contents compared to lower CaO values at Miango (M1&M2) and also of the northern group. The observed high CaO content suggest the

*Is a Volcanic Eruption Possible in Nigeria? DOI: http://dx.doi.org/10.5772/intechopen.84253*

**Figure 3.** *Plot of SiO2 versus Al2O3/TiO2 ratios.*

recrystallization of clinopyroxenes in the early stages of crystallization. In general, there is a positive correlation depicting a progressive increase of CaO with differentiation from Miango to the southern group to Kassa (**Figure 5a–f**). This increase is not visible at the level of one volcano but several of them put together. The high Fe2O3, MgO and CaO could be as a result of the bulk crystallization of olivine, pyroxene and plagioclase during the early stages of differentiation. The progressive increase in the contents of Al2O3 corresponds with the increase in the alkaline metals content (Na2O+K2O) suggesting the crystallization of plagioclase with increased degree of differentiation. The alkaline oxides (Na2O+K2O) are correspondingly highest in the most differentiated rocks (K1–5) (**Figure 6d**). In a silica versus total alkali diagram (**Figure 7**), the rocks fall within the alkaline field and are therefore classified as predominantly alkaline basalts. Only a few rocks fall in the

reflection of the variations in Al2O3 contents of the basalts since TiO2 contents remain relatively constant. Similarly, their CaO/TiO2 and Al2O3/CaO ratios vary from 2.6 to 4.31 and 1.34–1.60 respectively. Such narrow difference in these ratios is expected from a low degree of magmatic differentiation of the same parent material

*Trace elements compositions (in ppm) of the basaltic rocks from the Jos Plateau Volcanic Province.*

Similarly, the rocks present subtle variations in incompatible element ratios Ba/Sr. and Zr/Y (0.73–0.90 and 8.77–9.35, respectively); all supportive of their subjection to

**Ba ppm SR ppm Y ppm Sc ppm Zr ppm Be ppm V ppm Ba/Sr Zr/Y**

M1 619 840 25 19 234 2 161 0.74 9.36 M2 865 799 26 19 239 2 153 1.08 9.19 G1 518 637 18 15 205 2 122 0.81 11.39 G2 1215 723 26 12 328 3 121 1.68 12.62 S1 530 654 22 23 193 2 185 0.81 8.77 S2 554 646 21 22 190 2 178 0.86 9.05 S3 794 1098 24 15 228 2 174 0.72 12.00 K1 571 782 25 18 177 2 161 0.73 7.08 K2 551 460 43 20 155 2 171 1.20 3.06 K3 820 983 26 7 258 3 155 0.83 9.92 K4 672 758 38 19 176 2 164 0.89 4.63 K5 523 1095 24 18 177 2 157 0.48 7.36 S4 569 748 23 21 212 2 178 0.76 9.22 S5 585 697 23 23 204 2 180 0.84 8.84 S6 688 766 23 20 215 2 172 0.90 9.35 *Southeastern volcanoes: G1—basalt of Jiblik volcano; S1—basalt of Timjagha'as volcano; S2—basalt of Ampang volcano; S3—basalt of Pidong volcano; S4—basalt of Wushik volcano; S5—basalt of Kogul volcano; S6—basalt of Kerang volcano. Northwestern volcanoes: M1—basalt of Miango North volcano; M2—basalt of Miango South volcano; K1—basalt of Kassa volcano; K2—basalt of Kassa volcano; K3—basalt of Kassa volcano; K4—basalt of Kassa volcano; K5—basalt*

In the SiO2 versus MgO wt% plot, the southern volcanoes overwhelmingly display higher MgO contents as opposed to the lower values for the northern group of volcanoes (**Figure 5c**). It is expected that the Kassa volcanoes (K1–5) which are more differentiated (by their higher SiO2 contents) than the others to present lower MgO contents but instead display similar MgO contents. This scenario is true of their Fe2O3 contents. However, there is a weak negative correlation between Fe2O3, MgO, TiO2 and MnO versus silica indicating a progressive decrease of these oxides with differentiation (Miango-Southern group-Kassa) corresponding to compositional variations related to the removal of different proportions of olivine/pyrox-

The Kassa volcanoes in the northern group and those of the southern group exhibit higher CaO contents compared to lower CaO values at Miango (M1&M2) and also of the northern group. The observed high CaO content suggest the

by partial melting process (**Figures 3** and **4**).

**Analyte symbol unit**

*Forecasting Volcanic Eruptions*

*of Kassa volcano.*

**Table 4.**

**16**

**5.1 Silica versus major oxides correlation plots**

low degree of magmatic differentiation and/or similar source.

enes from the melt as it becomes more felsic (**Figure 6a–d**).

**Figure 5.** *(a–f) Plots of SiO2 versus major oxides of the volcanic rocks of the Jos Plateau Volcanic Province.province.*

sub-alkaline field which could be of tholeiitic character (high silica and Fe Contents). Furthermore, in a log (Zr/TiO2) versus SiO2 diagram (**Figure 8**), the bulk of the rocks fall in the alkaline field reaffirming their alkaline nature (**Figure 9**).

In respect to their Mg#, it varies very narrowly within the individual volcano signifying a subtle degree of differentiation (partial melting) and thus reflecting a low degree of magmatic differentiation and the consequent subtle compositional variations observed. However, for the entire volcanoes put together, the Mg# vary significantly from 27 to 56 suggesting formation of the rocks by fractional crystallization at larger scale. The southern volcanoes (S1–6) have the highest Mg# relative to those of the northern group (K1–5 and M1 & M2) (**Figure 10a–d**). When the rocks are plotted in Mg# versus Fe2O3 diagram (**Figure 10b**), a positive correlation is obtained indicating a progressive decrease in Fe2O3 with increasing degree of magmatic differentiation. The relatively similar Ba/Sr. and Zr/Y ratios for these rocks but with progressive decrease in Mg# lends credence to their derivation from

the same magma reservoir by differentiation. It appears that the rocks with the highest Mg# (samples S1–6) present compositions that are close to that of the parent materials since the magma did not suffer high degree of differentiation giving rise to a variety of rocks. The subtle variation of Mg# and the incompatible

*Silica versus Total Alkali diagram [11] of the volcanic rocks of the Jos Plateau (Alk = alkaline and*

*(a–d) Plots of SiO2 versus major oxides of the volcanic rocks of the Jos Plateau Volcanic Province.*

**Figure 6.**

*Is a Volcanic Eruption Possible in Nigeria? DOI: http://dx.doi.org/10.5772/intechopen.84253*

**Figure 7.**

**19**

*Subalk = subalkaline).*

*Is a Volcanic Eruption Possible in Nigeria? DOI: http://dx.doi.org/10.5772/intechopen.84253*

**Figure 7.**

sub-alkaline field which could be of tholeiitic character (high silica and Fe Contents). Furthermore, in a log (Zr/TiO2) versus SiO2 diagram (**Figure 8**), the bulk of the rocks fall in the alkaline field reaffirming their alkaline nature (**Figure 9**). In respect to their Mg#, it varies very narrowly within the individual volcano signifying a subtle degree of differentiation (partial melting) and thus reflecting a low degree of magmatic differentiation and the consequent subtle compositional variations observed. However, for the entire volcanoes put together, the Mg# vary significantly from 27 to 56 suggesting formation of the rocks by fractional crystallization at larger scale. The southern volcanoes (S1–6) have the highest Mg# relative to those of the northern group (K1–5 and M1 & M2) (**Figure 10a–d**). When the rocks are plotted in Mg# versus Fe2O3 diagram (**Figure 10b**), a positive correlation is obtained indicating a progressive decrease in Fe2O3 with increasing degree of magmatic differentiation. The relatively similar Ba/Sr. and Zr/Y ratios for these rocks but with progressive decrease in Mg# lends credence to their derivation from

*(a–f) Plots of SiO2 versus major oxides of the volcanic rocks of the Jos Plateau Volcanic Province.province.*

**Figure 5.**

*Forecasting Volcanic Eruptions*

**18**

*Silica versus Total Alkali diagram [11] of the volcanic rocks of the Jos Plateau (Alk = alkaline and Subalk = subalkaline).*

the same magma reservoir by differentiation. It appears that the rocks with the highest Mg# (samples S1–6) present compositions that are close to that of the parent materials since the magma did not suffer high degree of differentiation giving rise to a variety of rocks. The subtle variation of Mg# and the incompatible

*Plot of Log (Zr/TiO2) ratio versus SiO2 [12] of the volcanic rocks of Jos Plateau Volcanic province (Sub-AB = subalkaline basalts, AB = alkaline basalts).*

element ratios highlighted above are supportive of the derivation of these basalts by

*(a–d) Plot of some selected major oxides versus Mg# for the volcanic rocks of the Jos Plateau volcanic province.*

The geochemical data plotted in the ternary diagram of Ti/100-Zr-Y\*3 [12] show clearly that they were majorly emplaced within the continental crust (**Figures 11** and **12**). This fact distinct these basalts from those of the Island arc and the Mid Oceanic Ridge.

The incompatible elements when plotted in a spidergraph normalized to Chondrites in comparison with OIB (**Figure 13**) display a relatively similar pattern with slight enrichment in their incompatible elements. These characteristic features are typical of most alkali basaltic suites derived from a deeper mantle source akin to that

A sample by sample result is presented in **Table 5**. The Ar/Ar ages span between 1.3 and 2.5 Ma, confirm the earlier K-Ar ages of 2.1 and 1.9 0.31 Ma reported by [1] on dolerites on the Jos Plateau. The short interval in the radiometric ages suggests volcanic eruptions occurred at discrete times, separated by short periods of

non-activity at a mean age average of 0.55 Ma (CN3 = 2.500 0.318 Ma and CN5 = 1.970 0.173 Ma). This long period must have been dominated by profound erosion. The considerable long-time difference from the oldest to the youngest eruption suggests that there was relatively steady magma source overtime.

partial melting process of a magma from the same source.

**5.2 Tectonic environment of emplacement**

*Is a Volcanic Eruption Possible in Nigeria? DOI: http://dx.doi.org/10.5772/intechopen.84253*

**5.3 Incompatible elements spidergraph**

of the OIB [12, 14, 16–19].

**5.4 Ar40-Ar39 dating**

**21**

**Figure 10.**

**Figure 9.** *SiO2 versus Na2O+K2O classification diagram of basalts of the Jos Plateau volcanoes [13].*

*Is a Volcanic Eruption Possible in Nigeria? DOI: http://dx.doi.org/10.5772/intechopen.84253*

**Figure 10.** *(a–d) Plot of some selected major oxides versus Mg# for the volcanic rocks of the Jos Plateau volcanic province.*

element ratios highlighted above are supportive of the derivation of these basalts by partial melting process of a magma from the same source.

#### **5.2 Tectonic environment of emplacement**

The geochemical data plotted in the ternary diagram of Ti/100-Zr-Y\*3 [12] show clearly that they were majorly emplaced within the continental crust (**Figures 11** and **12**). This fact distinct these basalts from those of the Island arc and the Mid Oceanic Ridge.

#### **5.3 Incompatible elements spidergraph**

The incompatible elements when plotted in a spidergraph normalized to Chondrites in comparison with OIB (**Figure 13**) display a relatively similar pattern with slight enrichment in their incompatible elements. These characteristic features are typical of most alkali basaltic suites derived from a deeper mantle source akin to that of the OIB [12, 14, 16–19].


**1. Introduction**

The mast cell, part of the innate immune system, generally resides in tissues such as the lung and the skin to protect against pathogens like bacteria and parasites. Mast cells have also been described to participate in diseases such as asthma, allergies, and rheumatoid arthritis. Over the last decades, the mast cell has been implicated in cardiovascular diseases as well, for example in atherosclerosis [1,2], the underlying pathology of acute cardiovascular diseases including peripheral artery disease (PAD) [3,4]. Interestingly, mast cell numbers in advanced human atherosclerotic plaques obtained after endarterectomy surgery were seen to be of predictive value for the incidence of a secondary cardiovascular event [5]. In those plaques, mast cell density associated with the number of CD31+ microvessels [5]. Mast cells have also been associated with arteriogenesis and collateral formation [6]. Mast cells can secrete growth factors and pro-inflammatory cytokines that can recruit immune cells such as neutrophils and monocytes to the site of inflammation, thus further enhancing a

pro-inflammatory response [6–8]. Patients with systemic mastocytosis, a disease that is characterized by the excessive accumulation of mast cells in tissue or organs, experienced an increased prevalence of cardiovascular disease events, such as myocardial infarction, stroke, and importantly, peripheral artery disease, which is actually caused by the development of atherosclerosis in the arteries that supply oxygen to the extremities [9]. These associative data suggest that the mast cell may actively contribute to these underlying pathologies, and preclinical studies have been performed to elucidate underlying mast cell pathways that are causally related to vascular remodeling and the related disease outcome.

We speculate that mast cells may a ffect atherosclerotic plaque progression and PAD by increasing angiogenesis. Plaque angiogenesis has been shown to be related to atherosclerotic plaque progression and also, during tumor development, mast cells have been implicated in angiogenesis [10]. Mast cells have been shown to induce tumor endothelial proliferation by the release of Vascular Endothelial Growth Factor (VEGF) in response to the hypoxic environment in the tumor [10], which may be translatable to muscles in PAD patients, in which hypoxia occurs as well [11,12]. Although induction of neovascularization, in particular angiogenesis, maybe unfavorable for atherosclerosis progression, in PAD, the induction of neovascularization by mast cells, more precisely by inducing collateral formation and angiogenesis, may act as a repair pathway to resupply the ischemic limb tissue with oxygen. This neovascularization process requires a pro-inflammatory response, which is thus, on one hand, beneficial to resolve ischemia, but may on the other hand lead to enhanced progression of atherosclerosis. This two-faced process is also known as the Janus phenomenon [13]. Recently, the contribution of mast cells to arteriogenesis and collateral formation in a shear-stress induced mouse model of hind limb ischemia (HLI) has been described by Chillo and colleagues [6]. In that study, mast cells were systemically activated with the mast cell activator compound 48/80 upon ligation of the femoral artery, which resulted in increased hind limb perfusion. Treatment with the mast cell stabilizer cromolyn prevented the mast cell-induced e ffects on arteriogenesis and the investigators identified the neutrophil as a prominent e ffector cell involved in the mechanism behind mast cell-induced arteriogenesis. However, in that study, mast cell activation-dependent e ffects on angiogenesis in the ischemic muscles were not reported.

In this study, we aimed to investigate whether local induction of mast cell activation can stimulate blood flow recovery in a mouse hind limb ischemia model by inducing angiogenesis as well as arteriogenesis.

First, we analyzed the number and activation status of mast cells in human ischemic tissue, obtained after limb amputation. Next, we induced hind limb ischemia in mice by ligation of the femoral artery and at time of ligation, we activated mast cells in the hind limb by a skin sensitization/challenge protocol using a pluronic gel to apply the hapten DNP locally at the ligation site as described before [7,14], after which blood perfusion was measured using laser Doppler imaging. Mast cell activation increased reperfusion of the hind limb by not only increasing arteriogenesis, but also angiogenesis, which is at least partly induced by increasing the pro-inflammatory monocyte response.

#### **2. Materials and Methods**

#### *2.1. Tissue Collection from Patients with End-Stage Peripheral Artery Disease*

Sample collection of tissues from patients with end-stage peripheral artery disease undergoing limb amputation was approved by the Medical Ethics Committee of the Leiden University Medical Center (Protocol No. P12.265). Written informed consent was obtained from the participants. Inclusion criteria were a minimum age of 18 years and lower limb amputation, excluding ankle, foot, or toe amputations. Exclusion criteria were suspected or confirmed malignancy and inability to give informed consent. Gastrocnemius and soleus muscle samples obtained from 15 patients were formalin fixed, processed, para ffin embedded sectioned, and stained for mast cells. From these patients, *n* = 1 had type I diabetes and *n* = 7 su ffered from type II diabetes.

#### *2.2. Hind Limb Ischemia Model*

This study was performed in accordance with the Directive 2010/63/EU of the European Parliament and Dutch government guidelines. All experiments were approved (reference number 14185) by the Leiden University and Leiden University Medical Center committee on animal welfare (Leiden, the Netherlands). Wild-type C57Bl/6J mice were bred in our in-house breeding facility. Male mice aged 8 to 12 weeks were housed in groups with free access to water and regular chow.

Before the unilateral hind limb ischemia, mice were anesthetized by i.p. injection of midazolam (8 mg/kg, Roche Diagnostics, Basel, Switzerland), medetomidine (0.4 mg/kg, Orion, Espoo, Finland), and fentanyl (0.08 mg/kg, Janssen Pharmaceuticals, Beerse, Belgium). Hind limb ischemia was induced by electrocoagulation on two locations of the left femoral artery; the first ligation proximal to the superficial epigastric artery and the second proximal to the bifurcation of the popliteal and saphenous artery [15,16]. After surgery, anesthesia was antagonized with with atipamezol (2.5 mg/kg, Orion, Espoo, Finland) and flumazenil (0.5 mg/kg, Fresenius Kabi, Bad Homburg vor der Höhe, Germany).and buprenorphine (0.1 mg/kg, MSD Animal Health, Keniworth, NJ, USA) was provided as a painkiller. For the time course, 5 mice per time point were used, whereas for both the long-term (t28) and short-term (t9) HLI experiments, 8–9 mice per group were used.

#### *2.3. Local Mast Cell Activation with DPN treatment*

Mice were skin-sensitized on the shaved abdomen and paws for 2 consecutive days with a dinitrofluorobenzene (DNFB (D1529) solution (0.5% *v*/*v* in acetone:olive oil (4:1), Sigma-Aldrich, St. Louis, MO, USA) as described previously to sensitize the mice for the hapten DNP [7,14]. In the control mice, a vehicle solution of acetone:olive oil (4:1) was applied. At the end of the hind limb ischemia procedure, which was scheduled one week after the skin-sensitization procedure, 50 μg dinitrophenyl hapten (DNP (D198501), Sigma-Aldrich, St. Louis, MO, USA) in a pluronic gel (25% *w*/*v*, Sigma-Aldrich, St. Louis, MO, USA) was applied around the ligated areas of the left hind limb to locally activate the mast cells. Empty pluronic gel was applied in the control mice. This model has been previously applied [7,14,17,18] and has been shown to specifically induce mast cells activation upon local hapten application.

#### *2.4. Laser Doppler Perfusion Measurements*

Before and directly after surgery and at 3, 7,10, 14, 21, and 28 days after surgery, blood flow recovery to the ligated hind limb and the unligated control paw were measured using Laser Doppler Perfusion Imaging (LDPI) (Moor Instruments, Axminster, UK). Before the LDPI measurements, mice were anesthetized by i.p. injection of midazolam (8 mg/kg) and medetomidine (0.4 mg/kg,). Next, mice were placed in a double glazed pot, perfused with water at 37 ◦C for 5 min [19]. After LDPI, anesthesia was antagonized by subcutaneous injection of flumazenil (0.7 mg/kg). LDPI measurements in the ligated paw were normalized to measurements of the unligated paw, as an internal control. At sacrifice, after the last LDPI measurement, analgesic fentanyl (0.08 mg/kg) was administered, blood was drawn, and mice were sacrificed via cervical dislocation. The adductor and soleus muscles were harvested and fixed in 4% formaldehyde. For a second short experiment, animals were sacrificed at day 9, where blood was collected by orbital bleeding and the inguinal lymph nodes were isolated for further analyses. Again, the adductor and soleus muscles were harvested and fixed in 4% formaldehyde for histology analysis.


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 k2 >> k�1, ES complex breakdown occurs as rapidly as it is produced to form product and thus steady state can never be achieved. When k2 << 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, Km = 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�

½S� ¼ ½ES� ½ET�

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

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

½ES� ¼ k�1 þ k2

Wherein, Km = 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

k2 ¼ v

k2 ¼ Vmax

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

¼ ½ES�

v Vmax

½S� ¼ v Vmax k1

k1ð½ET��½ES�Þ½S�¼ðk�1 þ k2Þ½ES� (12)

½S�½ET��½S�½ES� ¼ Km½ES� (14)

½S�½ET�¼ðKm þ ½S�Þ½ES� (15)

ðKm þ ½S�Þ (16)

v ¼ k2½ES� (17)

Vmax ¼ k2½ET� (18)

½ES� (19)

½ET� (20)

½ET� (21)

ðKm 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 k2 >> 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 k2 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/Km cannot be greater than k2 i.e. decomposition of ES complex to E and P. The most efficient catalyst has values of kcat/km near the controlled diffusion limits of 10�8 –10�9 m�1 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/Km for second order in which Km is the value of the concentration of substrate. When v ¼ 1 2 Vmax, kcat/Km measures total activity of the enzyme, which includes the ability of enzyme to bind with a particular substrate.

x. When Km = [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 Km and Initial velocity decreases with increase in Km 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 k2 is denoted as kcat at saturation levels and gives the value of turnover number. It ranges from 1 to 104

greater than k2 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 ¼ Vmax

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 ¼ kcat Km

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/Km for second order in which

dt ¼ Vmax ¼ k2½ES� ¼ k2½ET� (27)

. Upper limit to the value of kcat/Km cannot be

–10�9 m�1 s

½ET� (28)

½E�½S� (29)

�1

. These enzymes

(30)

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

dP

values of kcat/km near the controlled diffusion limits of 10�8

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 Km 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 –Km 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 Km 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

km þ ½S�

v ¼ Vmax � Km

Plotting v against v/[S] gives Vmax from the ordinate intercept and –Km 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

½S� (33)

½S� Þ ¼ Vmax (34)

þ v ¼ Vmax (35)

(36)

1 v ¼ 1 Vmax þ Km 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/Km is quantified from the intercept and Vmax/Km 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/v0 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.

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 v ¼ VAB

Rapid equilibrium ordered sequential mechanism v ¼ VAB

Double-displacement mechanism v ¼ VAB

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

Mechanism Rate equation Double reciprocal plots

Steady state ordered sequential mechanism v ¼ VAB ðKiaKbþKbAþKaBþABÞ Intersecting lines Theorell-Chance mechanism v ¼ VAB ðKiaKbþKbAþKaBþABÞ Intersecting lines

ðKiaþKbAþKaBþABÞ Intersecting lines

ðKiaKbþKbAþABÞ Intersecting lines

ðKaBþKbAþABÞ 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].

v ¼ Vmax½A�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

ðKiaKmbð1 þ ð½B�=KibÞÞ þ Kmb½A� þ Kma½B�ð1 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. v0 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

ðKiaKmbð1 þ ð½B�=KibÞÞ þ Kmb½A� þ Kma½B�ð1 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.

v ¼ Vmax½A�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 Km and Vmax (Figure 12).

In this case, Km 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