1. Write the Michaelis-Menten equation (define all terms). Explain why this equation is valid only if the initial rates (vi) of an enzyme-catalyzed reaction are measured.
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- 1). The initial velocity of an enzyme-catalyzed reaction has been determined at several substrate concentrations with and without an inhibitor I. The total enzyme concentration [E]ot present in each experiment is 1.20 x 10 M. [1] = 5.00 x10 M. (Note: v initial rate or velocity.) [S], M 1.25E-3 2.50E-3 5.00E-3 10.0E-3 v, M/min, no inhibitor 0.480E-3 0.660E-3 0.810E-3 0.920E-3 v, M/min, 5.00x10 M 9.43E-5 1.41E-4 1.70E-4 2.10E-4 b). What kind of inhibition occurred. c). Calculate the value of Ki = a). Use the Lineweaver-Burk plot to determine the values of Vmax and KM at [1] = 0.00 mM, and the values of Vmax and KM at 0.500 mM of I. it in 'How many molecules of3. (a) The beakers below represent different conditions for measuring the initial velocity (vo) of an enzyme-catalyzed reaction under the steady-state approximation. The gray "donut-shaped" struc- tures represent the enzyme. The blue, filled circles represent free substrate molecules. The red cir- cles represent substrate molecules bound in the active site of the enzyme forming the Michaelis (ES) complex. Indicate in the diagram of the double reciprocal plot which kinetic parameters or variables each of the three "beaker conditions" represent either alone or in combination with another. A B 455 C V₁™¹ [So]-¹1. A Lineweaver-Burk Plot is shown below. 30 25 Curve A y = 3.1207x + 2.4978 20 15 Curve B y = 1.0003x + 2.3602 10 5 -3 1 5 7 11 1/[Catechol] (mM1) With these curves, determine the following enzyme parameters. Show all pertinent solutions. a. Km of Curve A and Curve B b. Vmax of Curve A and Curve B c. Assuming that one of these curves corresponds to the kinetics of one enzyme and one substrate, which curve represents the effect of an inhibitor? Why do you say so? d. What type of inhibition is exhibited by your answer in question c? Why do you say so? 1/V, (units of activity 1)
- 1. For enzyme catalyzed reaction: ki S + E=X (fast) k2 X -2> P + E (slow) derive the rate law and answer the following: a) What is meant by Michaelis-Menten constant km? (b) Prove that order of reaction in substrate changes from unity to zero at higher [S]. (c) What is the rate and value of km, if k2 >> k1. (d) Draw the potential energy diagram for enzyme catalyzed reaction.1. You are studying the enzyme catalyzed reaction below, and you find the KM is 3.3x10-4 M,. You also find that k1 is 4.3x106 M-'s-1. What is the dissociation constant (KD) for the enzyme/substrate complex? k1 k2 E+S ES E+P k.17., For the enzyme reaction mechanism with an inhibitor that produces product from both ES and EIS, E+S1→ ES -2➜ E+ P E+1+3 → El El +S4→ EIS -5→ El + P with reaction rate constants of k₁ and k-1 (and so on) for each of the reactions: A. Write the enzyme balance B. Write each of the equations that result from applying the quasi steady state assumption. C. Write each of the equations that result from applying the rapid equilibrium assumption. D. Based on the mechanism, what type of inhibitor is this? (competitive, uncompetitive or non-competitive) Why?
- 1. Consider an enzyme-catalyzed reaction giving the following results at a fixed enzyme concentration of 1 x 10-6 M in the presence or absence of 5 mM or 10 mM concentrations of an inhibitor I [S] (mol/L) 0.0010 0.0025 0.0050 0.0100 0.0500 0.1000 a) Control 0.00167 0.00333 0.00500 0.00667 0.00909 0.00952 v (m/s) [I] = 5 mM 0.00090 0.00200 - 0.00333 0.00500 0.00833 0.00909 [I] = 10 mM 0.00062 0.00142 0.00250 0.00400 0.00769 0.00869 Estimate Vmax and KM for all cases. What type inhibitor is [I]? Estimate K₁ and/or Kı' depending on the type inhibitor. Estimate Kcat. Estimate Kcat/KM.24. Researcher X did a series of experiments and determined the following about Enzyme A and its substrate (S). KM - 4 mM Vmax 100 mM/s axis. (. a) Draw the Michealis-Menton plot with all the above information shown. Be sure to label Vmax Rate of neation (mm) rate of react in mm. supstratiate concentration MM/S b) Convert the Michealis-Menton plot into a Lineweaver-Burk plot below, Label the axis. Vmax Rate of reaction (MM) 8 100 90 Go 100 80 - tmax 30 201 c) Using a dotted line, add in how á uncompetitive inhibitor how the rate would look with (S) (MM/S) x 1|S an uncompetitive inhibitor added. 100 KOMI Ke Vmax Vmar Sun competiti 6 • substante (MMIS)2. The initlal velocity for an enzyme-catalyzed reaction has been determined at a number of different substrate concentrations. Data are given below: [S (mM) Va ( umoles product/min) 5 22 10 39 20 65 50 102 100 120 200 135 500 147 Use the data above to create a Michaelis-Menten plot in Excel, plotting ye vs [S]. Include a copy of your plot, with axes labeled appropriately. Estimate Vmax and KM from this graph. 3. From the data given in problem #2 above, determine the value of the dissociation constant (Ko) for the ES complex. What is the value of the affinity or association constant (KA)?
- 1. Provided in the Table below kinetic data for an enzymatic reaction that was carried out in the presence (last two columns) and absence (second column = reaction at a concentration of 2 mM. The enzyme concentration was similar in all and was approximately 0.001 control) of enzyme inhibitor. Both inhibitors were added in each ИМ. Calculate both Vmax and KM for the control using Lineweaver-Burk curve. b. Provide the type of inhibition for both? Find, KI, for the inhibitor binding to the enzyme, for experiments (2) and (3). d. Calculate the reaction Kcat for the Control in experiment (1). Draw a velocity versus [S] showing Michaelis-Menten curve for the Control. Clearly show Vmax and KM for the enzyme. a. c. e. [S] (mM) (1) V. [(umol/(ml.s)] (2) V. [(umol/(ml.s)] (3) V. [(umol/(ml.s)] 7.6 4.4 6.6 4 14.6 8.6 11.4 26.6 16.4 17.8 16 45.8 29.8 24.6 24 60 40.8 28.241 The following data describe an enzyme-catalyzed reaction (hydrolysis of carbobenzoxyglycyl-L-tryptophan) Plot these results using the Lineweaver-Burk method, and determine values for KM and Vmax Velocity (mM.sec-) 0 024 0 036 0 053 0 060 0 061 0 062 Substrate Concentration (mM) 25 50 10 0 15 0 200 25 0 42 If the KM of an enzyme for its substrate remains constant as the concentration of the inhibitor increases, what can be said about the mode of inhibition and why? 43 Calculate the turnover number for an enzyme, assumıng Vmax IS 05 M sec1 and the concentration of the enzyme used is 0 002 M Why is it useful to know this? 44 Dıscuss the mechanism of the Bohr effect that occurs during the interactions of Hb with oxygen under physiological conditions in the lungs and tissues Make use of relevant graphs and diagrams to explain your answer12. Suppose an enzyme is known to obey Michaelis-Menten kinetics, but the parameters V and K are not known. Since two parameter values are missing, we might be able to find them by two independent measurements. So, suppose that two data points ( 51, Ri) (2 μΜ, 0.5 μΜ/s) and (82, R2) = (5 µM, 1 µM/s) are measured. By substituting the data points into the Michaelis-Menten law, find values of K and V that fit the data.