Enzyme Kinetics of Inhibition - Lab Report Example

Lab report: Enzyme kinetics of inhibition al affiliation Background information: Enzyme catalyze reactions in the humanbody by converting substrates into products. They increase the reaction rate by lowering the activation energy thereforereaching the steady state more rapidly. Enzyme activity is affected by temperature, pH and substrate concentration. Inhibitors also affect working of enzyme by competitively, non-competitively and mixed reaction. Method: a calibration graph that had been previously prepared was used. A Line-weaver Burk was plotted with reciprocal of substrate plotted against reciprocal of reaction rate was made to determine Vmax and Km values of three sets of reactions. The three sets of reactions were prepared by adding varying amounts of 0.25M sucrose and distilled water. In one set, 0.2 ml of 75mM of magnesium chloride was added, and in another set, an equal amount of 4M Urea was added as inhibitors to the reaction. Results: Calibration curve and Line-weaver Burk plotted to determine the Km and Vmax values of substrate with the different inhibitors. Conclusion: The inhibitors reduced the rate of enzymatic reaction. However, it was difficult to determine what mode of inhibition magnesium chloride and urea exhibited. Aim: To determine the kinetics of inhibition of invertase. Hypothesis: Urea and magnesium chloride are competitive inhibitors of invertase in a sucrose substrate. Introduction Reactions in living organisms are slow, enzymes speed up the reactions so as to maintain life. The enzymes control the reactions by ensuring that every reaction is catalyzed by a specific enzyme and at a particular point in a cell. They have a tertiary structure and are folded in a conformation that many intramolecular interactions of amino acids that make up the molecule. They are not used up in the reactions therefore can be used in several reactions. They are substrate specific that is they fold in a shape assisted by chaperone proteins that will determine which substrate the enzyme will act upon. Coenzymes and cofactors aid enzymes in their functions. Enzymes can be denatured by extremes in temperature and pH. Competitive inhibitors, noncompetitive inhibitors and allosteric inhibitors regulate enzyme activity. The enzymes do not change the reactions’ equilibrium since the free energies of the reactants or products are not changed. Enzymes are catalysts that are protein in nature that increase the rate of a chemical reaction by providing an alternative reaction pathway with a lower free energy of activation. The reaction is usually expressed as E + S ↔ ES → E + P In enzyme kinetics, the Michaelis Menten reaction relates the reaction rate (ν) to [S] which is the concentration of a substrate. The Km and the Vmax of an enzyme can be determined from determination of the initial rates of the enzyme catalyzed reactions over the concentration of the substrate. The maximum rate achieved is Vmax while Km is the Michaelis constant, is the substrate concentration at which the reaction rate is half of Vmax. Km varies from one enzyme to another but is constant for one particular enzyme. A low Km means that there is a high affinity between the enzymes for its substrate, the substrate molecules reacting readily with the enzyme molecules. A high Km means that there is a relatively low affinity between the enzyme and substrate, therefore the substrate molecules react readily with the enzyme molecules (Tzafriri 2003, p. 1120). Sucrose is the only naturally occurring sugar that is hydrolysed by pure invertase to give equal parts of glucose and fructose which are more stable. The use of yeast enzyme is more popular due to the need to produce colorless invert syrup. Sucrose is α-D-glucopyranosyl (1→2)-β-D-fructofuranoside and can be hydrolised by both α-glucosidases and β-fructofuranosidases. Invertase is β-fructofuranosidases that hydrolyses sucrose in addition to other β-fructans such as raffinose. Materials and methods An invertase extract in buffer solution, DNS reagent and solutions of a mixture of 1.67mM glucose and 1.67mM fructose were provided in addition to a solution of sucrose as a substrate and solutions of two inhibitors. DNS assay procedure A calibration curve was prepared by taking blank, 1. 0, 2.0, and 3.0 aliquots of an aqueous solution containing both 1.67mM D-glucose and 1.67mM D-fructose. Every sample was made up to 3.0 ml by addition of distilled water where necessary. 1 ml of DNS was added in each tube, stoppers wer put in place and placed in in a bath of boiling water for exactly 5 minutes then allowed to cool at rom temperature. 3ml of distilled water was added to each tube and the absorbance of each determined by a spectrophotometer at 540nm. A calibration graph was prepared whereby the absorbance of each the relative to the blank at 540nm was found. Reaction samples should be assayed (Taking 3.0ml samples) the reaction being stopped on the addition of DNS reagent. Kinetic determinations Three sets of tubes should be labeled as follows: 1, 2, 3, 4, 5, 1U, 2U, 3U, 4U, 5U, 1M, 2M, 3M, 4M, 5M. 0, 0.25, 0.5, 1.0, and 1.5 of 0.25M sucrose were added respectively in each set of tubes. In the first set, 2.0, 1.75, 1.5, 1.0, and 0.5 ml of distilled water were added respectively in the tubes. In the other two sets, 1.8, 1.55, 1.3, 0.8, and 0.3 ml of distilled water were added correspondingly. In the sets labeled M, 0.2 ml of 75mM of magnesium chloride was added. 0.2 ml of 0.4M Urea was added in the tubes labeled U. The solutions were then warmed to 37 o C and incubations were ready to be timed. 1 ml of invertase extract containing 0.05M sodium acetate pH 4.7 was added quickly at intervals of 5 seconds to each tube. The tubes were then incubated for exactly 10 minutes at 37 o C. The reaction was stopped by the addition of 1.0 ml of the DNS reagent and assay as before and each tube covered and placed in a bath of boiling water for exactly 5 minutes followed by cooling at room temperature. 3ml of water was added to each tube.The absorbance of each tube should be determined relative to the blank at 540nm by spectrophotometer. Results Table 1 Glucose & Fructose (ml) Concentration Absorbance 0 0 0 1 0.557 0.69 2 1.113 1.44 3 1.60 2.15 Table 2: The table below shows concentration values using the absorbance values using the three reaction sets Sample Absorbance Concentrations Samples with no inhibitors 1 0 0 2 0.06 0.0412 3 0.118 0.0809 4 0.191 0.1310 5 0.192 0.1317 Sample with urea 1U 0 0 2U 0.047 0.0322 3U 0.317 0.2174 4U 0.430 0.2949 5U 0.438 0.3004 Sample with magnesium chloride 1M 0 0 2M 0.120 0.0823 3M 0.149 0.1022 4M 0.247 0.1694 5M 0.252 0.1728 Graph 1: Standard Curve Table 3 Reactions with no inhibitor Volume of sucrose Concentration of sucrose (mM) 1/substrate concentration (mM) Absorbance Concentration of products(mM) Rate –Vo (mmol/min) 1/Vo 0 0 0 0 0 0 0 0.25 20.83 0.048008 0.06 0.0412 0.1356 7.375 0.5 41.6 0.24038 0.118 0.0809 0.1194 5.015 1.0 83.3 0.012005 0.191 0.1310 0.2990 3.344 1.5 125 0.008 0.192 0.1317 0.3007 3.325 Reaction with urea 0 0 0 0 0 0 0 0.25 20.83 0.048008 0.047 0.0322 0.2288 4.370 0.5 41.6 0.24038 0.317 0.2174 0.2578 3.786 1.0 83.3 0.012005 0.430 0.2949 0.430 2.325 1.5 125 0.008 0.438 0.3004 0.4380 2.283 Reaction with magnesium chloride 0 0 0 0 0 0 0 0.25 20.83 0.048008 0.120 0.0823 0.41152 2.430 0.5 41.6 0.24038 0.149 0.1022 0.469 2.132 1.0 83.3 0.012005 0.247 0.1694 0.5358 1.866 1.5 125 0.008 0.252 0.1728 0.5534 1.807 The Lineweaver-Burk plot is produced by taking reciprocal of both sides of the Michaelis-Menten equation that is The Graph 2 above was plotted from the inverse substrate concentration and rates obtained from Table 3 so as to determine Km, Vmax and Ki of Urea and MgCl2. The Km is the reciprocal of x intercept, while vmax is the reciprocal of the y intercept. Calculation Without inhibitor y = 11.43x + 3.2 y = 0, x = 0.27997 = -1/km = -3.571 x = 0, y = 3.2 vmax = 0.3125 With urea y = 8.636x + 1.9 y = 0, x = 0.22= -1/km= -4.5453 x = 0, y = 1.9 vmax = 0.5263 With magnesium chloride y = 0, x = 0.360 = -1/km = -2.778 x =0, 1/ vmax x = 0, y= 1.4, vmax = 0.714 The table 4 below shows km, Vmax and Ki values estimated from the experiment using the Line-weaver Burk plot. Vmax Km Ki Without inhibitor 0.1325 -3.571 N/A With Urea 0.5263 -4.5453 N/A With magnesium chloride 0.714 -2.778 N/A Discussion The purpose of this experiment is to determine the kinetic properties of sucrose invertase and inhibition mode of inhibitors such as urea and magnesium chloride. Vo which is the initial rate of enzyme reaction at different substrate concentration was determined in Table 3 so as to determine Km and Vmax of enzyme. Urea and magnesium chloride used as inhibitors and their mode of inhibition. A Line weaver Burk plot where the reciprocal of substrate concentration is plotted against the reciprocal of the reaction rate so as to obtain the Vmax. The x intercept gives the -1/Km and 1/Vmax as the intercept of the y axis. The Michaelis Menten equation analyses initial velocity measurements and full time course data to the integrated form of equations such as inhibition of product, and derived single constant to represent all information (Johnson & Goody 2011). It was difficult to determine whether urea and magnesium chloride are competitive or non-competitive inhibitors. A Line weaver Burk plot is useful in determining between the competitive and non-competitive inhibitors. In absence of an inhibitor, the intercept on the y axis plot is usually unchanged same as in competitive inhibition where the intercept on y axis is the same in presence of an inhibitor. In determination of initial velocities of enzyme catalyzed reactions there are chances of experimental error therefore it is advisable to decide on the best weighting scheme by examining the variability of deviations from the plotted graph (Storer, Darlison & Cornish Bowden 1975, p. 365). It is necessary to choose appropriate pH, temperature and appropriate buffer even if the dependence studies are being made. An appropriate design should also involve choosing and appropriate substrate and effector concentrations (Cornish-Bowden 214, p. 123). Distinction between competitive and non-competitive inhibitors is done by the Line-weaver Burk plot. In competitive inhibition, the intercept on the y axis of the plot of 1/ Vo versus 1/ [S] is the same in the presence and in the absence of an inhibitor though the slope is increased. Vmax is not altered in competitive inhibitor therefore the intercept is unchanged. The strength of competitive inhibitor binding of competitive inhibitor is indicated by the increase in in the slope of 1/Vo versus 1/[S] plot since at a high concentration that is sufficient, all the active sites are filled by the substrate. The inhibitor can combine with either the enzyme or the enzyme-substrate complex in non-competitive inhibition. In pure non-competitive inhibition, the values of the dissociation constants of the inhibitor and the enzyme-substrate complex are equal. The value of the Vmax is increased and the new slope is larger by the same factor. However, non-competitive inhibition does not affect Km. Deviations form the linear rate equation at high substrate concentration. For instance, liver alcohol dehydrogenase and lactic dehydrogenase show substrate inhibition with high concentration of alcohol and pyruvate (Nesakumar, Sethuraman, Krishnan & Rayapan 2014, p. 2590). Conclusion Enzyme inhibition is mainly used to control enzyme activity. In competitive inhibition the reaction is stopped when inhibitor is bound to the active site. In uncompetitive inhibition, inhibitor directly interacts with the enzyme-substrate complex but not with the free enzyme, inhibitor interacts with both the enzyme and the enzyme substrate complex therefore km and vmax. Reference Bowski, L., Saini, R., Ryu, D. Y., Vieth, W. R. 2006. ‘Kinetic modelling of the hydrolysis of sucrose by invertase’. Biotechnology and Bioengineering. Vol. 13, no. 5, pp. 641-656 Cornish-Bowden, A. 2014. ‘Analysis and interpretation of enzyme kinetic data’. Perspectives in Science. Vol. 1, no. 6, pp. 121-125 Ewing G.W. 1975. “Instrumental methods of chemical analysis” Fourth edition, McGraw-Hill, Tokyo, Japan. Johnson, K. A., Goody, S. R. 2011. The Original Michaelis Constant: Translation of the 1913 Michaelis-Menten Paper, Biochemistry. vol. 50, no. 39, pp 826-8269. Nesakumar, N., Sethuraman, S., Krishnan, U. M., Rayappan, J. B. 2014. “Estimation of Michaelis-Menten Constant and Maximum Rate of Reaction: A Non-linear Approach”. Journal of Computational and Theoretical Nanoscience, vol. 11, no. 12, pp. 2588-2595. Roberts, M., Reiss, M. J., & Monger, G. 2000. Advanced biology. Walton-on-Thames, Nelson. Storer, A. C., Darlison, M. G., Cornish-Bowden. 1975. The nature of experimental error in enzyme kinetic measurements. Biochem Journals. vol 151, no.2, pp. 361-367. Trevor P. 1991 “Understanding Enzymes” Third edition, Ellis Horwood Lim., Tzafiri, A. R. 2003. ‘Michaelis-Menten kinetics at high enzyme concentrations’ Bulletin of mathematical biology, vol 65, no. 6, pp 1111-1129 Read More