# Mathematical Modeling Thermal Stability Activity Inulinase Enzyme Reaction Biology Essay

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Fructose and fructooligosaccharides are emerging fast as important ingredients in the food and pharmaceutical industry. Both fructose and fructooligosaccharides can be produced from inulin, which consists of a linear β-2, 1-linked polyfructan chain, terminated by a glucose residue. The inulinases are classified among the hydrolases and target on the β-2, 1 linkage of inulin and hydrolyze it into fructose and glucose. Thus the use of inulinases has been proposed as the most promising approach to obtain fructose syrups from inulin. The thermal stability of inulinases is a very important parameter in enzyme reactor designs, as it was determined the limits for use and reuse of the enzyme, and therefore process costs of production of fructose and fructooligosaccharides. The mathematical modeling of the thermal stability and activity of the enzyme was developed using thermodynamic concepts and experimental data of inulinases from Kluyveromyces marxianus, which were used as examples. The model was designed to predict the enzyme activity with respect to the temperature and time course of the enzymatic process, as well as its half-life, in a broad temperature range. The knowledge and information provided by the model could be used to design the operational temperature conditions, leading to higher enzyme activities, while preserving acceptable stability levels, which represent the link between higher productivity and lower process costs. In this study, it was found that the working temperature is not necessarily the same as the maximum reaction rate temperature, but preferably a lower temperature where the enzyme is much more stable.

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LIST OF TABLES ii

LIST OF FIGURES iii

INTRODUCTION 1

OBJECTIVE 2

LITERATURE REVIEW 3

MATERIALS AND METHODS 9

Materials 9

Methods 13

RESULTS AND DISCUSSIONS 12

CONCLUSION 19

LITERATURE CITED 20

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iiiLIST OF FIGURES

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Mechanism of inulinase

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## INTRODUCTION

Inulin is hydrolyzed by two of inulinases: exo-inulinase (β-D-fructan fructanohydrolase) and endo-inulinase (2,1-β-D-fructan fructanohydrolase), both of which are producing fructooligosaccharide and only fructose, respectively (Skowronek and Firedurek, 2004; Vandamme and Derycke, 1983; Santos et al., 2007). Thus the use of inulinases has been proposed as the most promising approach to obtain pure fructose syrups from inulin. In enzyme reactor designs, the temperature and pH is very important parameter. It's defines the limits to use and reuse of the enzyme. The mathematic model could be used to design the operational temperature conditions, leading to higher enzyme activities, while preserving acceptable stability levels. The simple and reliable method, such as the one described in this work, leading not only to knowledge of the effect of temperature on enzyme activity and stability, but also to the most convenient working temperature, has not yet been reported (Santos et al., 2007).

Inulinases are produced by many microorganisms. Microorganisms are the best source for commercial production of inulinases because of their easy cultivation and high yields of the enzyme. It has been found that the microorganisms which can produce high level of inulinases include Kluyveromyces spp., Pichia spp., Sporotrichum spp., Candida spp., Aspergillus spp., Penicilium spp., Arthrobacter spp., Bacillus spp., Clostridium spp., Pseudomonas spp., Arthrobacter spp. and Staphylococcus spp., (Chi et al., 2009). Kluyveromyces marxianus can be produced a high activities of inulinases. In this study, inuilnases from Kluyveromyces marxianus was used as a model enzyme to develop the methodology for enzyme reactor design.

OBJECTIVE

To study, the mathematical modeling of the thermal stability and activity of inulinases and was developed using thermodynamic concepts and experiment from free and immobilized inulinases.

LITERATURE REVIEW

## Inulin

Inulin is present as a reserve carbohydrate in the root and tuber of many members of the Compositae such as Helianthus tuberosus (Jerusalem artichoke), Cichorium intybus (chicory) and Taraxacum officinalis (dandelion). The yields of root and tubers are very high as dried materials of the tubers contain over 70% inulin (Chi et al., 2009; Van Loo et al., 1995). Inulin consists of linear chains of β-2,1-linked polyfructose displaying a terminal glucose unit (Vandamme and Derycke, 1983). The fructose units in this mixture of linear fructose polymers and oligomers are each linked by β-2,1 bonds. A glucose molecule typically resides at the end of each fructose chain and is linked by an α-1,2 bond, as in sucrose (Molina et al., 2005).

Fructooligosaccharides (FOS) have been accepted as functional sweeteners similar to other microbial oligosaccharides. Recent interest in the process development for the production of fructooligosaccharides has concentrated on high content commercial products. Inulin, being a polyfructan, has been widely investigated as a useful source for production of ultra- high fructose syrup. However, the effort to utilize inulin for the production of functional sweeteners is a more recent approach (Cho et al., 2001).

## Inulinases

Inulin is hydrolyzed by enzyme known as inulinases. The inulinases are classified among the hydrolyzes and target on the β-2,1-linked of inulin and hydrolyze it into fructose and glucose. They can be divided into exoinulinases and endoinulinases. The exoinulinases catalyze removal of the terminal fructose residues from the non-reducing end of the inulin molecule while the endoinulinases hydrolyze the internal linkages in inulin to yield inulotriose, inulotetraose, and inulopentaose.

Type of inulinases

Endo-inulinases

Endo-inulinases are specific for inulin. They hydrolyze inulin by breaking bonds between fructose units that are located away from the ends of the polymer network, to produce oligosaccharides.

Exo-inulinase

Exo-inulinases split terminal fructose units in sucrose, rafffinose and inulin to liberate the fructose.

Figure 1 Mechanism of inulinase.

Source: Worawuthiyanun (2005)

Characterization of the inulinases

Effect of pH

The enzyme have ionic group. These ionic groups must be in a suitable form, as acid or base to function. The pH of the medium results in changes in the ionic form of the active site and the activity of enzyme and the reaction rate. Changes in pH may also three-dimensional shape of the enzyme. For these reason, enzyme are only act certain pH range. The pH of the medium may affect the maximum reaction rate and the stability of the enzyme. Thus, the pH optimum and stability for an enzyme is usually determined experimentally (Shuler and Kargi, 1992). The optimal pH of the purified inulinases from fungi and yeasts are in the range of 4.5-6.0 (Chi et al, 2009). The optimal pH of purified inulinase from Kluyveromyces marxianus var. bulgaricus for sucrose was 4.75 (Kushi et al., 2000). In addition to the inuA1 gene encoding an exoinulinase from Aspergillus niger AF10 was expressed in Pichia pastoris. The determination of the optimum pH for inulinase activity expressed by inuA1was at a pH 4.5 (Zhang et al., 2004). Chen et al. (2009) reported five inulinases were purified from the culture of Aspergillus ficuum JNSP5-06. These are stable at a wide range pH 4-8 with optimum pH for exo- and endo-inulinase at 4.5 and 5. These suggest that the optimal and stability of pH from yeast and fungi are also almost the same as range and stability range around pH 4-8.

Effect of temperature

The effect of temperature of inulinases from yeasts has been primarily characterized in Kluyveromyces fragilis and Kluyveromyces marxianus. The partially purified inulinase reported in Kluyveromyces fragilis was optimal temperature at 45oC. However, the purified inulinase from Candida aureus G7a was optimum temperature at 50&deg;C and the inulinase activity produced by Pichia guilliermondii strain 1 is the highest at 60&deg;C (Singh and Gill, 2006; Sheng et al., 2008; Gong et al., 2008). From this reports, the inulinases seemed to have considerable thermophilic enzyme. In contrast, the stability of inulinases from Kluyveromyces marxianus var. bulgaricus was stable for 3 h. at 50oC and rapid loss of activity at 55-60oC (Singh and Gill, 2006). Chen et al. (2009) reported that the optimum temperature of purified inulinase from Aspergillus ficuum JNSP5-06 was range 45-55 oC. It was only 40% relative activity when observed after 1 h at 60 oC. From the results, the inulinase of yeast is optimum at high temperature but it's not stable at high temperature.

The previous study, the thermal stability of inulinases has below 50oC. It's not application for production of fructooligosaccharide and fructose. Thus, the industrial processes are finding a woking temperature that give high enzyme activity with good stability represents a compromise between lower process costs and higher productivities (Santos et al., 2007).

## Production of high-fructose syrup from inulin

Inulinases are an important class of enzyme for the production of fructose syrup. Fructose syrup has beneficial effects in diabetic patients, increases the iron absorption in children, and has high sweetening capacity. Also, it can be used in the diet of obese persons, stimulates calcium absorption in postmenopausal women, stimulates growth of bifidobacteria in large and small intestines and prevents colon cancer (Rocha et al., 2006). Fructose is also widely used in many foods, pharmaceuticals, and beverages instead of sucrose. It can be produced from inulin, which consists of a linear β-2, 1-linked polyfructant chain, terminated by glucose residue. Inulin was found in various plant materials, such as dahlias, chicory, and Jerusalem artichokes, there have been reported as effective raw materials for high fructose production (Gill et al., 2006).

The best procedure involves the use of microbial inulinases, which, after one-step enzymatic hydrolysis of inulin, yields 95% pure fructose. Therefore, the exoinulinases from different microorganisms are used for production of ultra-high- fructose syrup from inulin and inulin containing materials. The hydrolysis of inulin was studied using a combination of the concentrated crude inulinase (from Cryptococcus aureus G7a) and inulin. The concentrated of crude enzyme was added to 900 μl of 2.0% (w/v) inulin in acetate buffer (0.1 M, pH 5.0). The mixtures were incubated at 50 &deg;C for 16 h. The results showed that a large amount of monosaccharides and oligosaccharides with different molecular size were the inulin hydrolysis by the crude inulinase (Sheng et al., 2007). Sirisansaneeyakul et al. (2008) found that Aspergillus niger TISTR 3570 inulinases containing endoinulinase and exoinulinase produced the concentration 37.5 g/l of fructose in 20 h at 40&deg;C while the yeast inulinase (exoinulinase) afforded 35.3 g/l of fructose in 25 h at initial inulin concentration of ∼100 g/l and the enzyme concentration of 0.2 U/g of substrate. Moreover, they studied the mixed inulinases of mold and yeast at ratio of 5:1 which proved superior to individual crude inulinase in hydrolyzing inulin to fructose.

## The model formulation

Enzymatic activity, or reaction rate, can be expressed by Equation (1).

(1)

Where K is the kinetic constant (min-1)

E is the active enzyme concentration (µmol/ml)

In addition, K varies with temperature, Thus it can be expressed by an Arrhenius type equation (Eq. (2)):

(2)

Where K0 is constant (min-1).

Ea is activation energy constant (Kcal/mol).

R is gas constant (1.982) (cal/mol K).

T is absolute temperature (K-1).

At high temperatures, the enzymatic denaturation becomes an important factor, so an additional term must be included in the equation, which will predict enzyme decay. Assuming that inulinase denaturation is a first order process, enzyme decay can be expressed by the following equations (3) and (4):

(3)

(4)

Where E0 is active enzyme concentration at the starting point, usually zero time

(Kcal/mol).

As the denaturation constant (Kd), it can be expresses by Arrhenius type equation.

(5)

Where Kd is denaturation constant (min-1).

Kd0 is constant (min-1).

Ed is activation enery constant for enzyme denaturation (Kcal/mol).

The final model representing enzyme activity as a function of temperature and reaction time can be expresses by the set of relationships represented in the following equations( (1)-(5)):

The final model representing enzyme activity as a function of temperature and reaction time can be combined in the equation (6)

(6)

This equation represents, thus, two major of enzyme reaction process: by the first part of equation (the right hand site) is the K part, which is significant at the lowest temperature and the second part is the inactivation process as the E part which is significant at the highest temperature. Since K0 and E0 constant

The thermal enzyme stability is another important parameter in enzyme reactor design which can be expressed by its half-life as shown in Eq. (7), which is obtained from Eq. (4) by substituting E by E0/2 and Kd by its respective expression from Eq. (5).

(7)