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Read "Biochemical Engineering and Biotechnology" by Ghasem Najafpour available from Rakuten Kobo. Sign up today and get $5 off your first purchase. Biochemical Engineering James M. Lee eBook Version Click to go to: • Table of Contents • General Guide: • • Navigation Printing Helps Biochemical. Purchase Biochemical Engineering and Biotechnology - 2nd Edition. Print Book & E-Book. eBook ISBN: Hardcover ISBN.

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Introduction to Biochemical Engineering. Front Cover · D. G. Rao. Tata McGraw- Hill Education, - Biochemical engineering - pages. 5 Reviews. Biochemical Engineering - Kindle edition by Fabian E. Dumont, Jerry Mander. Download it once and read it on your Kindle device, PC, phones or tablets. eBook features: Highlight, take notes, and search in the book; In this edition, page numbers are just like the physical edition; Length: pages; Format: Print .

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Ed , Krull, R. Ed , Gu, M. Ed , Ouyang, P. Ed , Chen, J. Ed , Eibl, D. Ed Over the past five years, the immense financial pressure on the development and manufacturing of biopharmaceuticals has resulted in the increasing use and acce- ance of … Available Formats: Softcover Hardcover eBook Book Optical Sensor Systems in Biotechnology Rao, G.

Ed Of all things natural, light is the most sublime. Therefore, like any other catalysts, they increase the rate of reaction without themselves undergoing permanent chemical changes. The catalytic ability of enzymes is due to its particular protein structure. A specific chemical reaction is catalyzed at a small portion of the surface of an enzyme, which is known as the active site.

Some physical and chemical interactions occur at this site to catalyze a certain chemical reaction for a certain enzyme. Enzyme reactions are different from chemical reactions, as follows: An enzyme catalyst is highly specific, and catalyzes only one or a small number of chemical reactions. A great variety of enzymes exist, which can catalyze a very wide range of reactions.

Only a small amount of enzyme is required to produce a desired effect. The reaction conditions temperature, pressure, pH, and so on for the enzyme reactions are very mild. Nomenclature of Enzymes Originally enzymes were given nondescriptive names such as: The new system categorizes all enzymes into six major classes depending on the general type of chemical reaction which they catalyze.

Each main class contains subclasses, subsubclasses, and subsubsubclasses. Therefore, each enzyme can be designated by a numerical code system.

As an example, alcohol dehydrogenase is assigned as 1. Bohinski, Commercial Applications of Enzymes Enzymes have been used since early human history without knowledge of what they were or how they worked. They were used for such things as making sweets from starch, clotting milk to make cheese, and brewing soy sauce.

Enzymes have been utilized commercially since the s, when fungal cell extracts were first added to brewing vats to facilitate the breakdown of starch into sugars Eveleigh, The fungal amylase takadiastase was employed as a digestive aid in the United States as early as Enzyme Kinetics Table 2.

Oxidoreductases 1. Specific substrate is ethyl alcohol 2. Transferases 2.

Transfer of methyl groups 2. Transfer of glycosyl groups 3. Hydrolases 4. Lyases 5. Isomerases 6.

Ligases Example Reaction: Trivial Name: Enzymes are usually made by microorganisms grown in a pure culture or obtained directly from plants and animals. The enzymes produced commercially can be classified into three major categories Crueger and Crueger, Industrial enzymes, such as amylases, proteases, glucose isomerase, lipase, catalases, and penicillin acylases 2.

Analytical enzymes, such as glucose oxidase, galactose oxidase, alcohol dehydrogenase, hexokinase, muramidase, and cholesterol oxidase 3. Alkaline protease is added to laundry detergents as a cleaning aid, and widely used in Western Europe. Proteins often precipitate on soiled clothes or make dirt adhere to the textile fibers. Such stains can be dissolved easily by addition of protease to the detergent.

Protease is also used for meat tenderizer and cheese making. The scale of application of analytical and medical enzymes is in the range of milligrams to grams while that of industrial enzymes is in tons. Analytical and medical enzymes are usually required to be in their pure forms; therefore, their production costs are high. Simple Enzyme Kinetics Enzyme kinetics deals with the rate of enzyme reaction and how it is affected by various chemical and physical conditions.

Kinetic studies of enzymatic reactions provide information about the basic mechanism of the enzyme reaction and other parameters that characterize the properties of the enzyme. The rate equations developed from the kinetic studies can be applied in calculating reaction time, yields, and optimum economic condition, which are important in the design of an effective bioreactor.

In order to understand the effectiveness and characteristics of an enzyme reaction, it is important to know how the reaction rate is influenced by reaction conditions such as substrate, product, and enzyme concentrations. If we measure the initial reaction rate at different levels of substrate and enzyme concentrations, we obtain a series of curves like the one shown in Figure 2.

From these curves we can conclude the following: The reaction rate is proportional to the substrate concentration that is, first-order reaction when the substrate concentration is in the low range. The reaction rate does not depend on the substrate concentration when the substrate concentration is high, since the reaction rate changes gradually from first order to zero order as the substrate concentration is increased.

The maximum reaction rate rmax is proportional to the enzyme concentration within the range of the enzyme tested. The rate is proportional to CS first order for low values of CS, but with higher values of CS, the rate becomes constant zero order and equal to rmax. Since Eq. Brown proposed that an enzyme forms a complex with its substrate. The complex then breaks down to the products and regenerates the free enzyme. The main concept of this hypothesis is that there is a topographical, structural compatibility between an enzyme and a substrate which optimally favors the recognition of the substrate as shown in Figure 2.

The reaction rate equation can be derived from the preceding mechanism based on the following assumptions: Enzyme Kinetics 1.

The amount of an enzyme is very small compared to the amount of substrate. The product concentration is so low that product inhibition may be considered negligible. In addition to the preceding assumptions, there are three different approaches to derive the rate equation: Michaelis-Menten approach Michaelis and Menten, It is assumed that the product-releasing step, Eq.

This is an assumption which is often employed in heterogeneous catalytic reactions in chemical kinetics. Therefore, enzymes can be analogous to solid catalysts in chemical reactions. Furthermore, the first step for an enzyme reaction also involves the formation of an enzyme-substrate complex, which is based on a very weak interaction.

Therefore, it is reasonable to assume that the enzyme-substrate complex formation step is much faster than the product releasing step which involves chemical changes. Briggs-Haldane approach Briggs and Haldane, This is also known as the pseudosteady-state or quasi-steady-state assumption in chemical kinetics and is often used in developing rate expressions in homogeneous catalytic reactions. Practically, it is also our best interests to use as little enzymes as possible because of their costs.

Since the first step involves only weak physical or chemical interaction, its speed is much quicker than that of the second step, which requires complicated chemical interaction. This phenomena is fairly analogous to enzyme reactions. Numerical solution: Solution of the simultaneous differential equations developed from Eqs.

Michaelis-Menten Approach If the slower reaction, Eq.

The concentration of the enzyme-substrate complex CES in Eq. Since the rate of reaction is determined by the second slower reaction, Eq. Enzyme Kinetics the initial enzyme concentration. By substituting Eq.

KM in Eq. Therefore, the value of KM is equal to the substrate concentration when the reaction rate is half of the maximum rate rmax see Figure 2. KM is an important kinetic parameter because it characterizes the interaction of an enzyme with a given substrate. Another kinetic parameter in Eq. The main reason for combining two constants k3 and CE0 into one lumped parameter rmax is due to the difficulty of expressing the enzyme concentration in molar unit.

To express the enzyme concentration in molar unit, we need to know the molecular weight of enzyme and the exact amount of pure enzyme added, both of which are very difficult to determine. Since we often use enzymes which are not in pure form, the actual amount of enzyme is not known. Enzyme concentration may be expressed in mass unit instead of molar unit. However, the amount of enzyme is not well quantified in mass unit because actual contents of an enzyme can differ widely depending on its purity.

Therefore, it is common to express enzyme concentration as an arbitrarily defined unit based on its catalytic ability. Care should be taken for the consistency of unit when enzyme concentration is not expressed in molar unit. Briggs-Haldane Approach Again, from the mechanism described by Eqs. This is true with many enzyme reactions. Since the formation of the complex involves only weak interactions, it is likely that the rate of dissociation of the complex will be rapid.

The breakdown of the complex to yield products will involve the making and breaking of chemical bonds, which is much slower than the enzyme-substrate complex dissociation step. Explain when the rate equation derived by the Briggs-Haldane approach can be simplified to that derived by the MichaelisMenten approach. Then, dCES 2. Therefore, in Eq. Numerical Solution From the mechanism described by Eqs.

Since the analytical solution of the preceding simultaneous differential equations are not possible, we need to solve them numerically by using a computer. Among many software packages that solve simultaneous differential equations, Advanced Continuous Simulation Language ACSL, is very powerful and easy to use. For example, Eq. You can also use Mathematica Wolfram Research, Inc. It should be noted that this solution procedure requires the knowledge of elementary rate constants, k1, k2, and k3.

The elementary rate constants can be measured by the experimental techniques such as pre-steady-state kinetics and relaxation methods Bailey and Ollis, pp. Furthermore, the initial molar concentration of an enzyme should be known, which is also difficult to measure as explained earlier. However, a numerical Enzyme Kinetics solution with the elementary rate constants can provide a more precise picture of what is occurring during the enzyme reaction, as illustrated in the following example problem.

The initial substrate and enzyme concentrations are 0. The values of the reaction constants are: Table 2. To determine how the concentrations of the substrate, product, and enzyme-substrate complex are changing with time, we can solve Eqs. Each block when present must be terminated with an END statement. The Adams-Moulton and Gear's Stiff are both variable-step, variable-order integration routines.

For the detailed description of these algorithms, please refer to numerical analysis textbooks, such Enzyme Kinetics interval integration step size is equal to the comunication interval CINT divided by the number of steps NSTP. The run-time control program is shown in Table 2. Figure 2. Evaluation of Kinetic Parameters In order to estimate the values of the kinetic parameters, we need to make a series of batch runs with different levels of substrate concentration. Then the initial reaction rate can be calculated as a function of initial substrate concentrations.

The results can be plotted graphically so that the validity of the kinetic model can be tested and the values of the kinetic parameters can be estimated. The most straightforward way is to plot r against CS as shown in Figure 2. However, this is an unsatisfactory plot in estimating rmax and KM because it is difficult to estimate asymptotes accurately and also difficult to test the validity of the kinetic model. Therefore, the Michaelis-Menten equation is usually rearranged so that the results can be plotted as a straight line.

Some of the better known methods are presented here. The Michaelis-Menten equation, Eq. This can be achieved in three ways: The intercept will be K M rmax , as shown in Figure 2.

This plot is known as Lineweaver-Burk plot Lineweaver and Burk, This plot is known as the Eadie-Hofstee plot Eadie, ; Hofstee, The Lineweaver-Burk plot is more often employed than the other two plots because it shows the relationship between the independent variable CS and the dependent variable r. This is illustrated in Figure 2. The points on the line in the figure represent seven equally spaced substrate concentrations.

The space between the points in Figure 2. On the other hand, the Eadie-Hofstee plot gives slightly better weighting of the data than the Lineweaver-Burk plot see Figure 2. A disadvantage of this plot is that the rate of reaction r appears in both coordinates while it is usually regarded as a dependent variable. The values of kinetic parameters can be estimated by drawing a least-squares line roughly after plotting the data in a suitable format.

The linear regression can be also carried out accurately by using a calculator with statistical functions, spreadsheet programs such as Excel Microsoft. However, it is important to examine the plot visually to ensure the validity of the parameters values obtained when these numerical techniques are used. The advantages of this technique are that: In conclusion, the values of the Michaelis-Menten kinetic parameters, rmax and KM, can be estimated, as follows: Make a series of batch runs with different levels of substrate concentration at a constant initial enzyme concentration and measure the change of product or substrate concentration with respect to time.

Estimate the initial rate of reaction from the CS or CP versus time curves for different initial substrate concentrations. Estimate the kinetic parameters by plotting one of the three plots explained in this section or a nonlinear regression technique. It is important to examine the data points so that you may not include the points which deviate systematically from the kinetic model as illustrated in the following problem.

Evaluate the Michaelis-Menten kinetic parameters by employing the Langmuir plot, the Lineweaver-Burk plot, the Eadie-Hofstee plot, and nonlinear regression technique. In evaluating the kinetic parameters, do not include data points which deviate systematically from the MichaelisMenten model and explain the reason for the deviation. Compare the predictions from each method by plotting r versus CS curves with the data points, and discuss the strengths and weaknesses of each method.

Repeat part a by using all data. Examination of the data reveals that as the substrate concentration increased up to 10mM, the rate increased.

However, the further increases in the substrate concentration to 15mM decreased the initial reaction rate. This behavior may be due to substrate or product inhibition.

The two data points which were not included for the linear regression were noted as closed circles. You can choose one of the four iterative methods: The Gauss-Newton iterative methods regress the residuals onto the partial derivatives of the model with respect to the parameters until the iterations converge.

You also have to specify the model and starting values of the parameters to be estimated. It is optional to provide the partial derivatives of the model with respect to each parameter. However, the rate predicted from the Lineweaver-Burk plot fits the data accurately when the substrate concentration is the lowest and deviates as the concentration increases.

This is because the Lineweaver-Burk plot gives undue weight for the low substrate concentration as shown in Figure 2. The rate predicted from the Eadie-Hofstee plot shows the similar tendency as that from the Lineweaver-Burk plot, but in a lesser degree. The rates predicted from the Langmuir plot and nonlinear regression technique are almost the same which give the best line fit because of the even weighting of the data.

Enzyme Kinetics 80 8 0. In that case, all data points have to be included in the parameter estimation. By adding two data points for the high substrate concentration, the parameter values changes significantly.

In the case of the Langmuir plot, the change of the parameter estimation was so large that the KM value is even negative, indicating that the Michaelis-Menten model cannot be employed.

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The nonlinear regression techniques are the best way to estimate the parameter values in both cases. Enzyme Reactor with Simple Kinetics A bioreactor is a device within which biochemical transformations are caused by the action of enzymes or living cells. The bioreactor is frequently called a fermenter6 whether the transformation is carried out by living cells or in vivo7 cellular components that is, enzymes.

However, in this text, we call the bioreactor employing enzymes an enzyme reactor to distinguish it from the bioreactor which employs living cells, the fermenter. A batch enzyme reactor is normally equipped with an agitator to mix the reactant, and the pH of the reactant is maintained by employing either a buffer solution or a pH controller.

An ideal batch reactor is assumed to be well mixed so that the contents are uniform in composition at all times. Therefore, the fermenter was also limited to a vessel in which anaerobic fermentations are being carried out. However, modern industrial fermentation has a different meaning, which includes both aerobic and anaerobic large-scale culture of organisms, so the meaning of fermenter was changed accordingly.

This equation shows how CS is changing with respect to time. With known values of rmax and KM, the change of CS with time in a batch reactor can be predicted from this equation. In a plug-flow enzyme reactor or tubular-flow enzyme reactor , the substrate enters one end of a cylindrical tube which is packed with immobilized enzyme and the product stream leaves at the other end. The long tube and lack of stirring device prevents complete mixing of the fluid in the tube.

Therefore, the properties of the flowing stream will vary in both longitudinal and radial directions. Since the variation in the radial direction is small compared to that in the longitudinal direction, it is called a plug-flow reactor.

If a plug-flow reactor is operated at steady state, the properties will be constant with respect to time. The ideal plug-flow enzyme reactor can approximate the long tube, packed-bed, and hollow fiber, or multistaged reactor. However, the time t in Eq. Rearranging Eq. V, CS F CS Figure 2.

Continuous Stirred-Tank Reactor A continuous stirred-tank reactor CSTR is an ideal reactor which is based on the assumption that the reactor contents are well mixed. Therefore, the concentrations of the various components of the outlet stream are assumed to be the same as the concentrations of these components in the reactor. Continuous operation of the enzyme reactor can increase the productivity of the reactor significantly by eliminating the downtime. It is also easy to automate in order to reduce labor costs.

As can be seen in Eq. For the steady-state CSTR, the substrate concentration of the reactor should be constant. If the MichaelisMenten equation can be used for the rate of substrate consumption rS , Eq. Another approach is to use the Langmuir plot CS r vs CS after calculating the reaction rate at different flow rates. The reaction rate can be calculated from the relationship: However, the initial rate approach described in Section 2.

Inhibition of Enzyme Reactions A modulator or effector is a substance which can combine with enzymes to alter their catalytic activities. An inhibitor is a modulator which decreases enzyme activity. It can decrease the rate of reaction either competitively, noncompetitively, or partially competitively. Competitive Inhibition Since a competitive inhibitor has a strong structural resemblance to the substrate, both the inhibitor and substrate compete for the active site of an enzyme.

The formation of an enzyme-inhibitor complex reduces the amount of enzyme available for interaction with the substrate and, as a result, the rate of reaction decreases. A competitive inhibitor normally combines reversibly with enzyme. Therefore, the effect of the inhibitor can be minimized by increasing the substrate concentration, unless the substrate concentration is greater than the concentration at which the substrate itself inhibits the reaction.

The mechanism of competitive inhibition can be expressed as follows: In this book, both terminologies are used. It is interesting to note that the maximum reaction rate is not affected by the presence of a competitive inhibitor.

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However, a larger amount of substrate is required to reach the maximum rate. The graphical consequences of competitive inhibition are shown in Figure 2. Noncompetitive Inhibition Noncompetitive inhibitors interact with enzymes in many different ways. They can bind to the enzymes reversibly or irreversibly at the active site or at some other region.

In any case the resultant complex is inactive. The mechanism of noncompetitive inhibition can be expressed as follows: The graphical consequences of noncompetitive inhibition are shown in Figure 2. Note that making these plots enables us to distinguish between competitive and noncompetitive inhibition. Several variations of the mechanism for noncompetitive inhibition are possible. One case is when the enzyme-inhibitor-substrate complex can be decomposed to produce a product and the enzyme-inhibitor complex.

This mechanism can be described by adding the following slow reaction to Eq. The derivation of the rate equation is left as an exercise problem. Other Influences on Enzyme Activity The rate of an enzyme reaction is influenced by various chemical and physical conditions. Some of the important factors are the concentration of various components substrate, product, enzyme, cofactor, and so on , pH, temperature, and shear.

The effect of the various concentrations has been discussed earlier. In this section, the effect of pH, temperature, and shear are discussed. The optimum pH is different for each enzyme. For example, pepsin from the stomach has an optimum pH between 2 and 3.

Chymotrypsin, from the pancreas, has an optimum pH in the mildly alkaline region between 7 and 8. The reason that the rate of enzyme reaction is influenced by pH can be explained as follows: Enzyme is a protein which consists of amino acid residues that is, amino acids minus water.

The amino acid residues possess basic, neutral, or acid side groups which can be positively or negatively charged at any given pH. As an example Wiseman and Gould, , let's consider one acidic amino acid, glutamic acid, which is acidic in the lower pH range. On the other hand, an amino acid, lysine, is basic in the range of higher pH value.

An enzyme is catalytically active when the amino acid residues at the active site each possess a particular charge. Therefore, the fraction of the catalytically active enzyme depends on the pH. Let's suppose that one residue of each of these two amino acids, glutamic acid and lysine, is present at the active site of an enzyme molecule and that, for example, the charged form of both amino acids must be present if that enzyme molecule is to function.

Effect of Temperature The rate of a chemical reaction depends on the temperature according to Arrhenius equation as 2. The temperature dependence of many enzyme-catalyzed reactions can be described by the Arrhenius equation.

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An increase in the temperature increases the rate of reaction, since the atoms in the enzyme molecule have greater energies and a greater tendency to move. However, the temperature is limited to the usual biological range. As the temperature rises, denaturation processes progressively destroy the activity of enzyme molecules.

This is due to the unfolding of the protein chain after the breakage of weak for example, hydrogen bonds, so that the overall reaction velocity drops. Some enzymes are very resistant to denaturation by high temperature, especially the enzymes isolated from thermophilic organisms found in certain hot environments. Effect of Shear Enzymes had been believed to be susceptible to mechanical force, which disturbs the elaborate shape of an enzyme molecule to such a degree that denaturation occurs.

The mechanical force that an enzyme solution normally encounters is fluid shear, generated either by flowing fluid, the shaking of a vessel, or stirring with an agitator. The effect of shear on the stability of an enzyme is important for the consideration of enzyme reactor design, because the contents of the reactor need to be agitated or shook in order to minimize mass-transfer resistance.

However, conflicting results have been reported concerning the effect of shear on the activity of enzymes. Charm and Wong showed that the enzymes catalase, rennet, and carboxypeptidase were partially inactivated when subjected to shear in a coaxial cylinder viscometer. The remaining activity could be correlated with a dimensionless group gammatheta, where gamma and theta are the shear rate and the time of exposure to shear, Enzyme Kinetics respectively.

However, Thomas and Dunnill studied the effect of shear on catalase and urease activities by using a coaxial cylindrical viscometer that was sealed to prevent any air-liquid contact. They found that there was no significant loss of enzyme activity due to shear force alone at shear rates up to sec They reasoned that the deactivation observed by Charm and Wong was the result of a combination of shear, air-liquid interface, and some other effects which are not fully understood.

Charm and Wong did not seal their shear apparatus. This was further confirmed, as cellulase deactivation due to the interfacial effect combined with the shear effect was found to be far more severe and extensive than that due to the shear effect alone Jones and Lee, Enzyme Kinetics Objectives: The objectives of this experiment are: To give students an experience with enzyme reactions and assay procedures 2.

To determine the Michaelis-Menten kinetic parameters based on initial-rate reactions in a series of batch runs 3. To simulate batch and continuous runs based on the kinetic parameters obtained Materials: Spectrophotometer 2. Glucose assay kit No. Cellobiose 5. Water bath to control the temperature of the jacketed vessel Calibration Curve for Glucose Assay: Prepare glucose solutions of 0, 0.

Using these standards as samples, follow the assay procedure described in the brochure provided by Sigma Chemical Co. Plot the resulting absorbances versus their corresponding glucose concentrations and draw a smooth curve through the points.

Experiment Procedures: Prepare a 0. Dilute the cellobiase-enzyme solution so that it contains approximately 20 units of enzyme per mL of solution. Initiate the enzyme reaction by adding 1 mL of cellobiase solution to the reaction mixture and start to time. Take a 1 mL sample from the reactor after 5- and minutes and measure the glucose concentration in the sample.

Data Analysis: Calculate the initial rate of reaction based on the 5 and 10 minute data. Determine the Michaelis-Menten kinetic parameters as described in this chapter. Simulate the change of the substrate and product concentrations for batch and continuous reactors based on the kinetic parameters obtained.

Compare one batch run with the simulated results. For this run, take samples every 5 to 10 minutes for 1 to 2 hours. Problems 2. The reaction was initiated by adding 1 mL of enzyme beta-glucosidase solution which contained 0. At 1, 5, 10, 15, and 30 minutes, 0.

The results were as follows: A unit is defined as the enzyme activity which can produce 1mumol of product per minute. What is the initial rate of reaction? Derive the rate equation by making the Michaelis-Menten assumption. If the concentration of S1 is much higher than that of S2, how can the rate equation be simplified? Please note that the rate constants of the second equilibrium reaction are the same as those of the third reaction.

State your assumptions. The Michaelis-Menten kinetic parameters were found to be as follows: Assume that you obtained the CS versus t curve you calculated in part a experimentally. Is this approach reliable? Chemostat continuously stirred-tank reactor runs with various flow rates were carried out. The reactor volume is cm3. Assume that the enzyme concentration in the reactor is constant so that the same kinetic parameters can be used. To measure the maximum reaction rate catalyzed by the enzyme, you measured the initial rate of the reaction and found that 10 percent of the initial substrate was consumed in 5 minutes.

The initial substrate concentration is 3. Assume that the reaction can be expressed by the Michaelis-Menten kinetics.

What is the maximum reaction rate? Enzyme Kinetics b.

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What is the concentration of the substrate after 15 minutes? Assume that the Michaelis-Menten kinetic parameters for this enzyme reaction are: What should be the size of the reactor if you employ a plug-flow reactor instead of the CSTR in part a?

The flow rate is 0. Is the two-reactor system more efficient than one reactor whose volume is equal to the sum of the two reactors? Explain how you can estimate the parameters of the rate equation in part c experimentally.

Derive the rate equation for the production of galactose by using Briggs-Haldane approach. Does galactose inhibit noncompetitively? In this mechanism, glucose is released from the enzymesubstrate complex first, leaving the enzyme-galactose complex, which subsequently releases the galactose molecules. How is the rate equation developed by this model simplified to that by Scott et al.

Is prostigmine competitive or noncompetitive inhibitor? Evaluate the Michaelis-Menten kinetic parameters in the presence of inhibitor by employing the Langmuir plot.

The following table shows the amount of sugar inverted in the first 10 minutes of reaction for various initial substrate concentrations. The amount of invertase was set constant. Substrate Sugar Con. To take into account the substrate inhibition effect, the following reaction mechanism was suggested: Derive the rate equation using the Michaelis-Menten approach.

Determine the three kinetic parameters of the equation derived in part a using the preceding experimental data. What is the reaction rate in the reactor?

You measured the steady-state outlet substrate concentration as a function of the inlet flow rate and found the following results. Estimate Michaelis kinetic parameters by using the best plotting technique for the equal weight of all data points. Flow rate Outlet Substrate Conc. Calculate the Michaelis-Menten constants of the above reaction. When the inhibitor was added, the initial reaction rate was decreased as follows: Justify your answer by showing the effect of the inhibitor graphically.

The obtained Michelis-Menten kinetic parameters are as follows: Write the kinetic model for this enzyme reaction. Derive the rate equation. State your assumptions for any simplification of the rate equation.

Estimate the value of inhibition kinetic parameter. It has been found Frantz and Stephenson, J. The course of the reaction is followed by adding tyrosine decarboxylase which evolves CO2.

References Advanced Continuous Simulation Language: Concord, MA: Mitchell and Gauthier, Assoc. Bailey, J. Ollis, Biochemical Engineering Fundamentals.

New York, NY: McGraw-Hill Book Co. Bohinski, R. C, Modern Concepts in Biochemistry, p. Boston, MA: Allyn and Bacon, Inc.

Briggs, G. Brown, A. Burden, R. Faires, Numerical Analysis. Carberry, J.

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Carnahan, B. Luther, and J. Wilkes, Applied Numerical Methods. Chapra, S. Canale, Numerical Methods for Engineers. Charm, S. Crueger, W. Crueger, Biotechnology: A Textbook of Industrial Microbiology, pp. Madison, WI: Science Tech, Inc. Eadie, G. Eveleigh, D. Hofstee, B. Wheatley, Applied Numerical Analysis. Reading, MA: Addison-Wesley Pub.

Jones, E. Levenspiel, O. Corvalis, OR: Oregon State University, Lineweaver, H. Michaelis, L. SAS User's Guide: Statistic 5th ed. Cary, NC: SAS Institute, Inc. Scott, T. Hill, and C. Thomas, C. Wiseman, A. Gould, Enzymes, Their Nature and Role, pp. London, UK: Hutchinson Educational Ltd. Yang, S. Immobilized Enzyme 3. Immobilization Techniques Effect of Mass-Transfer Resistance Chapter 3. Immobilized Enzyme Since most enzymes are globular protein, they are soluble in water.

Therefore, it is very difficult or impractical to separate the enzyme for reuse in a batch pr ocess. Enzymes can be immobilized on the surface of or inside of an insoluble matrix either by chemical or physical methods. They can be also immobilized in their soluble forms by retaining them with a semipermeable membrane. A main advantage of immobilized enzyme is that it can be reused since it can be easily separated from the reaction solution and can be easily retained in a continuous-flow reactor.

Furthermore, immobilized enzyme may show selectively altered chemical or physical properties and it may simulate the realistic natural environment where the enzyme came from, the cell. Immobilization Techniques Immobilization techniques can be classified by basically two methods, the chemical and the physical method. The former is covalent bond formation dependent and the latter is noncovalent bond formation dependent.

Chemical Method Covalent Attachment: The covalent attachment of enzyme molecules via nonessential amino acid residues that is, amino acids minus water to waterinsoluble, functionalized supports are the most widely used method for immobilizing enzymes. It is called a functional group. Already active polymers such as maleic anhydride copolymers will be simply mixed with enzymes to produce immobilized enzymes. Normally, natural or synthetic polymers need to be activated by treating them with reagents before adding the enzyme.

The activation involves the chemical conversion of a functional group of the polymer. The enzyme's active site should not be involved in the attachment, in which case the enzyme would lose its activity upon immobilization.

The following experiment illustrates the immobilization of glucose oxidase in agarose Gutcho, Activation of agarose: Eliminate excess water from the water-swollen, ball-shaped agarose particles Sepharose 2B by subjecting them to suction on a glass filter.

Add 3. Wash the activated product on a glass filter with 1 L of ice water. Finally wash the particles rapidly with 0. Binding with glucose oxidase: React the activated polymer for 10 hours with mild stirring with 24 mg of glucose oxidase dissolved in 1 mL of 0. Immobilized Enzyme a b c Figure 3. Cross-linking Using Multifunctional Reagents: Water-insoluble enzymes can be prepared by using multifunctional agents that are all bifunctional in nature and have low molecular weight, such as glutaraldehyde.

Enzymes can be reacted with multifunctional reagent alone so that they are cross-linked intermolecularly by the reagent to form a water-insoluble derivative. Another method is to adsorb enzymes on a water-insoluble, surface-active support followed by intermolecular cross-linking with multifunctional reagents to strengthen the attachment.

Multifunctional reagents can be also used to introduce functional groups into water-insoluble polymers, which then react covalently with water-soluble enzymes. Physical Method Adsorption: This method is the simplest way to immobilize enzymes. Enzymes can be adsorbed physically on a surface-active adsorbent by contacting an aqueous solution of enzyme with an adsorbent. Commonly employed adsorbents are Zaborsky, The advantages of adsorption techniques are as follows: The procedure of immobilization is simple.

It is possible to separate and purify the enzymes while being immobilized. The enzymes are not usually deactivated by adsorption.

The adsorption is a reversible process. However, adsorption techniques also have several disadvantages: The bonding strength is weak. The state of immobilization is very sensitive to solution pH, ionic strength, and temperature. The amount of enzymes loaded on a unit amount of support is usually low. Enzymes can be entrapped within cross-linked polymers by forming a highly cross-linked network of polymer in the presence of an enzyme.

This method has a major advantage in the fact that there is no chemical modification of the enzyme, therefore, the intrinsic properties of an enzyme are not altered.

However, the enzyme may be deactivated during the gel formation. Enzyme leakage is also a problem. The most commonly employed cross-linked polymer is the polyacrylamide gel system. This has been used to immobilize alcohol dehydrogenase, glucose oxidase, amino acid oxidase, hexokinase, glucose isomerase, urease, and many other enzymes.

Enzymes can be immobilized within semipermeable membrane microcapsules. This can be done by the interfacial polymerization technique. Organic solvent containing one component of copolymer with surfactant is agitated in a vessel and aqueous enzyme solution is introduced.

The polymer membrane is formed at the liquid-liquid interface while the aqueous phase is dispersed as small droplets. One example of this process is the polyamide nylon system, in which 1,6-diaminohexane is the water-soluble diamine and 1,decanoyl chloride is the organic-soluble diacid halide.

The organic solvent for this system is a chloroform-cyclohexane mixture 1: The immobilized enzyme produced by this technique provides an extremely large surface area. Effect of Mass-Transfer Resistance The immobilization of enzymes may introduce a new problem which is absent in free soluble enzymes.

It is the mass-transfer resistance due to the large particle size of immobilized enzyme or due to the inclusion of enzymes in Immobilized Enzyme Bulk liquid 1 2 3 Immobilized enzyme CSb CS Figure 3. If we follow the hypothetical path of a substrate from the liquid to the reaction site in an immobilized enzyme, it can be divided into several steps Figure 3.

Steps 1 and 2 are the external mass-transfer resistance. Step 3 is the intraparticle masstransfer resistance. External Mass-Transfer Resistance If an enzyme is immobilized on the surface of an insoluble particle, the path is only composed of the first and second steps, external mass-transfer resistance.

During the enzymatic reaction of an immobilized enzyme, the rate of substrate transfer is equal to that of substrate consumption. This equation shows the relationship between the substrate concentration in the Immobilized Enzyme bulk of the solution and that at the surface of an immobilized enzyme. Depending upon the magnitude of NDa, Eq. If NDa! The rate that would be obtained with no mass-transfer resistance at the interface is the same as Eq. Internal Mass-Transfer Resistance If enzymes are immobilized by copolymerization or microencapsulation, the intraparticle mass-transfer resistance can affect the rate of enzyme reaction.

In order to derive an equation that shows how the mass-transfer resistance affects the effectiveness of an immobilized enzyme, let's make a series of assumptions as follows: The reaction occurs at every position within the immobilized enzyme, and the kinetics of the reaction are of the same form as observed for free enzyme.

Mass transfer through the immobilized enzyme occurs via molecular diffusion. There is no mass-transfer limitation at the outside surface of the immobilized enzyme. The immobilized enzyme is spherical.

The model developed by these assumptions is known as the distributed model. First we derive a differential equation which describes the relationship between the substrate concentration and the radial distance in an immobilized enzyme. The material balance for the spherical shell with thickness dr as shown in Figure 3. After opening up the brackets and simplifying by eliminating all terms containing dr2 or dr3, we obtain the second order differential equation: Let's solve the equation first for the simple cases of zero-order and first-order reactions, and for the Michaelis-Menten equation.

Zero-order Kinetics: Figure 3. Therefore, the substrate diffuses into the core of the particle, which results in a fairly flat concentration distribution throughout the radial location of a particle.

The actual reaction rate with the diffusion limitation would be equal to the rate of mass transfer at the surface of an immobilized enzyme, while the rate if not slowed down by pore diffusion is kCSb. Therefore, differentiating Eq. It can be solved by various numerical techniques. We repeat this process until the solution of the initial value problem satisfies the boundary conditions. When guessing the values of Rc and xS0 , we can think of two different cases: This is the case when the rate of enzyme reaction is slow compared to that of mass transfer which is represented by the low value of phi.

As a result, the substrate reaches the center of sphere. Therefore, assume the value of Rc. As a result, the substrate is consumed before it reaches the center of sphere. Table 3. If it is not, a new value of xS is estimated using the equation: Immobilized Enzyme First Solution: X 3rd column: Effective Diffusivities in Biological Gels The analysis of intraparticle mass-transfer resistance requires the knowledge of the effective diffusivity DS of a substrate in an immobilized matrix, such as agarose, agar, or gelatin.

Gels are porous semisolid materials, which are composed of macromolecules and water. The gel structure increases the path length for diffusion, and as a result decreases the diffusion rate. Various techniques are available for determining the effective diffusivity of solute in gel Itamunoala, One of the most reliable techniques is the thin-disk method which uses a diffusion cell with two compartments divided by a thin gel.

Each compartment contains a well-stirred solution with different solute concentrations. Effective diffusivity can be calculated from the mass flux verses time measurement Hannoun and Stephanopoulos, A few typical values of effective diffusivities are listed in Table 3. Derive the equation for the effectiveness of an immobilized enzyme for this diffusion limited case by employing the same assumptions as for the distributed model.

The rate of substrate consumption can be expressed by the Michaelis-Menten equation. Since all substrate is consumed in the thin layer, we can assume that the layer has a flat geometry. Consider a control volume defined by the element at r with thickness dr, as shown in Figure 3.

However, in this problem we do not need to solve this equation. Problems 3. Assume that the external mass-transfer resistance for substrate is not negligible and that the Michaelis-Menten equation describes the intrinsic kinetics of enzyme reaction. Derive an expression which shows the relationship between the substrate concentration at the surface and that in the bulk solution.

If they are different, what will be the meaning of rmax and K Mapp? You can pack the immobilized enzyme in a cylindrical column pass through substrate solution, which is known as a packed-column immobilized reactor. What will be the effect of the substrate flow rate on K Mapp for the packed-column reactor? Can you determine the intrinsic kinetic parameters rmax and KM for free enzyme by using the packed-column immobilized reactor?

The Immobilized Enzyme effectiveness of the immobilized enzyme was found to be 70 percent of the free enzyme when the concentration of the substrate was 0. The reaction was carried out in a stirred reactor with an agitation speed of 50 rpm. The rate of substrate consumption can be expressed as a first-order reaction.

Initial concentration of substrate is 0. It has been found that both external and internal mass-transfer resistance are significant for this immobilized enzyme. The mass-transfer coefficient at the stagnant film around the particle is about 0. Immobilized Enzyme a. If the internal mass transfer resistance is negligible, what is the concentration of the substrate at the surface of the particle?

What is the effectiveness factor for this immobilized enzyme?

If the internal mass-transfer resistance can be described as the distributed model and the external mass transfer resistance is not negligible, what is the concentration of the substrate at the surface of the particle? What is the overall effectiveness factor considering both internal and external mass-transfer resistance?Type of Bioreactor 6. Membrane Technology. Unavailable for purchase. Processes and Technologies Derks, Mark S.

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