Bioreactor Engineering Laboratory

Transcription

1 Bioreactor Engineering Laboratory Determination of kinetics parameters of enzymatic hydrolysis of lactose catalyzed by β-galactosidase. Supervisor: Karolina Labus, PhD 1. THEROETICAL PART Enzymes are macromolecular, in most protein catalysts, which accelerate specific chemical reactions by lowering their activation energy. Most of enzymatic reactions proceed millions of times faster than their non-enzymatically catalyzed counterparts. Like all catalysts, also enzymes are not consumed during reaction, and do not affect their equilibrium. Nevertheless, they significantly differ from the usual chemical catalysts. They are commonly characterized by high specificity with regard to catalyzed reaction as well as converted substrate (so called substrate specificity). The shape of enzyme molecule is responsible for its high specificity both in terms of geometric fitting to the substrate as well as hydrophobic-hydrophilic and electrostatic interactions. Enzymes also exhibit high levels of stereospecificity, regioselectivity and chemoselectivity. Since many years, there is a continuous increase of interest in the efficient use of enzymatic reactions, both in the food, chemical, pharmaceutical industry, as well as in medicine and environmental protection. Among others from main advantages of biocatalysis, as an alternative to the conventional chemical processes, could be listed: multiple increase in the rate of reactions catalyzed by enzymes, their high substrate, regio- and stereospecificity, as well as ability to perform such processes in a wide range of reactants concentrations and under mild ph and temperature conditions. In biotransformation reactions most commonly used are enzyme preparations, which are the mixture of different proteins and other ballast substances. Isolation of the enzyme as homogeneous (pure) solution from biological material is associated with high workload and costs. Therefore, the amount of enzyme in such preparations is usually determined by the rate of catalyzed reaction, rather than through its weight. Under certain conditions, this rate is proportional to the enzyme concentration, and can be presented in units defined as the amount of enzyme which cause specified reaction rate (usually determined by loss of the substrate or the appearance of the product). 1

2 The Michaelis-Menten Model of Enzyme Catalysis There are several mathematical models for enzymatic reactions. One of the simplest and most useful is that developed by Michaelis and Menten. Consider the following set of reactions for an enzyme-catalyzed process: (1) Where: E is the free enzyme; S is the free substrate, the substance for which the enzyme serves as a reaction catalyst; ES is the enzyme-substrate complex; P is the product of the reaction; kn s are the individual forward and backward rate constants. Note that the equilibrium constant for the first step in the reaction is Keq = k 1 /k -1. Usually the reaction is studied only in its early stages so that there is no significant buildup of the product P. Therefore, very little of the back reaction represented by k -2 occurs. In this case, Equation (1) can be simplified to: (2) Where k cat is the catalytic rate constant for the conversion of the enzyme-substrate complex ES to the product P and regenerating the free enzyme E, which is then able to react with another substrate molecule. Under these conditions, the reaction rate or reaction velocity v is linearly proportional to the enzyme concentration [E], assuming it remains at a low, catalytic level. However, a plot of v as a function of [S] shows a linear dependence and first-order kinetics only during the initial stages of the reaction, about the first 10% or so, before the rate of the back reaction becomes significant. The plot then becomes curvilinear downward and approaches an asymptomatic value of V. 2

3 Without going into the details of its derivation, the Michaelis-Menten equation was developed to explain the observed kinetic behavior: (3) Where: V is the velocity of the reaction, V max is the maximum (theoretical) velocity, K m is the Michaelis constant, (k -1 + k cat )/k 1. The maximum theoretical velocity, Vmax, is the velocity when the substrate binds to all of the active sites on all the enzymes, when it is totally saturated. This is impossible because there will always be some free E available; the reaction to produce product and free E is always going on. The Michaelis constant K m turns out to be numerically equal to the substrate concentration [S] that produces a velocity V = V max /2. Vmax can be roughly estimated from plots of v vs. [S], and then Km can be obtained from the value of [S] at V max /2 on the plot (Fig.1). Figure 1. The Michaelis-Menten plot 3

4 The Michaelis-Menten equation (3) can be linearized to give Lineweaver-Burk equation: (4) The Lineweaver Burk plot is the useful graphical method for determination of kinetics parameters V max and K m (Fig.2). Figure 2. The Lineweaver Burk plot K m and V max provide very important information about an enzymatic reaction, and are among the very first things that scientists try to determine or verify for an enzyme they are using. One of the reasons that K m is important is that it provides an idea of the affinity, the binding strength, of the enzyme for the substrate. With Vmax and the actual molar concentration of the enzyme, k cat can be calculated. This is also called the turnover number, the number of substrate molecules transformed to product per unit time by a single enzyme molecule under maximal conditions. This provides a good measure of the speed and efficiency of an enzyme. To write short test at the beginning of the classes it is necessary to get familiar with material inserted in the instruction (both theoretical and practical part). 4

5 2. PRACTICAL PART 2.1. The measurements of enzyme catalytic activity using indirect spectrophotometric method In measurements of the enzyme activity (β-galactosidase) will be used the analytical test for glucose, which is one of the products of reactions catalyzed by this enzyme (Fig. 1). galactose glucose Figure1. Hydrolysis of lactose to glucose and galactose catalyzed by β-galactosidase. The principle of this analysis method is as follows: glucose during the first process catalyzed by glucose oxidase is converted to gluconic acid and simultaneously one molecule of hydrogen peroxide is generated (Reaction 1). Then hydrogen peroxide reacts (in the presence of peroxidase) with hydroxybenzoic acid (HBA) and 4- aminoantipyrine (AAP) to form a red dye quinoneimine (Reaction 2). Intensity of obtained color is directly proportional to the glucose concentration in the sample. REAGENT I: (active ingredients: glucose oxidase, peroxidase, AAP, HBA, phosphate buffer). The method of making analytical tests for glucose content: From the properly diluted sample take 10 µl and place into 1 mł of REAGENT I (Glucose OXY DST, Alpha Diagnostics), incubate of 5 min at 37 C, and after this time measure the absorbance of obtained solutions on a UV-Vis spectrophotometer at 500 nm. Before measurement the apparatus must be reset (zero base) on 1 ml of Reagent I. 5

6 The steps of the experiment: I determination of glucose standard curve Prepare solutions with the desired concentration of glucose (0.05, 0.1, 0.25, 0.5, 0.75, 1.0, 1.5, 2.0, 3.0 i 4.0 g/l) in 0,1M phosphate buffer ph 7.5 For all prepared glucose solutions in duplicate perform the analytical test for glucose in accordance to the following procedure: to 1 ml of Reagent I add 10 µl of sample with known glucose concentration Incubate exactly 5 min in 37 C After this time measure the absorbance at 500 nm On the basis of obtained results plot the graph C GLUCOSE =f(abs500) with consideration of (0,0) point. II measuring the catalytic activity of the enzyme (β-galactosidase) using different concentrations of lactose in 0,1M phosphate buffer ph 7.5 prepare solution of the substrate (lactose) with following concentrations: 1, 2, 5, 10, 20, 30, 50, 75, 100 g/l Then, in thermostate bath (40 C) place the test tube with 5 ml of substrate and incubate for about 10 min. In the meantime, prepare rack of 7 test tubes and add to each 1 ml Reagent I (pink). After this time, to the substrate add 0.5 ml of enzyme solution with given concentration (prepared by the supervisor) and start the timer. For about 10 min after each 2 minutes take the sample from the test tube (10 µl), which should be immediately be placed in 1 ml of Reagent I (pink) and put exactly for 5 minutes in a water bath (37 C), and after that measure the absorbance at 500 nm on a spectrophotometer. Before measurements, the apparatus must be reset (zero base) on 1 ml of Reagent I. 6

7 2.2. Presentation of obtained results On the basis of the absorbance results for different glucose concentrations plot a graph of C GLUCOSE = f(abs500). Determine the equation of the calibration curve (considering [0,0] point), which further will be used for determining the amount of glucose formed in enzymatic reaction Absorbance results (500 nm), obtained for the samples taken from the reactor during the enzymatic reaction, calculated from the calibration curve for glucose [g/l], and then plot a graph C GLUCOSE = f(t). On its basis, determine the rate of glucose formation in the reaction time [mg GLUCOSE /min] Plot a Michaelis-Menten graph (V=f(C LACTOSE )) then plot the Lineweavera-Burk graph (1/V = f(1/c LACTOSE ) and determine the kinetics parameters (K M and V MAX ) Calculate the k cat constant using equation V max = k kat x C ENZYME Comment obtained results LITERATURE 1. Stryer L. Biochemistry (Enzymatic Kinetics Chapter) 2. Runge S.W. et al., A Simple Classroom Teaching Technique To Help Students Understand Michaelis-Menten Kinetics, CBE Life Sciences Education 5 (2006),