Experiment 6 KINETICS, MICHAELIS CONSTANT AND INHIBITION

Transcription

1 Experiment KINETICS, MICHAELIS CONSTANT AND INHIBITION This experiment involves three parts, a determination of the kinetics of reactions at two different [A], a determination of K M and V max and a determination of the nature of an inhibitor and its K I. Fig. - shows the effect of [A] on the rates of an enzyme-catalyzed reaction. The rate at any given [A] is expressed by Eqn. -l V = V max[a] K M + [A] = k cat[e] T [A] K M + [A]. where V o is the initial observed velocity (rate), V max is the maximum velocity attainable, [A] is the initial substrate concentration where [A] >> [E] T, K m is the substrate concentration at which V o =. V max, k cat = V max /[E] T and [E] T is the enzyme concentration. At [A]!. K M the [A] term in the denominator of Eqn. - can be ignored and V o = V max [A] /K M, which is the differential equation for a firstorder reaction with respect to substrate concentration. Under these conditions a plot of product concentration versus time gives a curvilinear line (line B of Fig. -) while a plot of log([a] /[A]) versus time gives a straight line relationship (Figure - insert). [A] is the concentration of substrate left at a given time in the reaction. At [A] " K M the K M term in the denominator of Eqn. - can be ignored and thus V o = V max which is the differential equation for a zero-order reaction with respect to substrate concentration. Under these conditions a plot of product concentration versus time is a straight line (line A of Fig. -). At [A] >. K M < K m the order of the reaction is a mixture of first and zero order with respect to [A]. In order to determine K M most precisely, the [A] should range from approximately. K m to K m. An idea of the range of [A] needed to meet this requirement is obtained by the kinetics part of this experiment.

2 K M and V max are best obtained from the experimental data by a linear transformation of Eqn. -. Taking the reciprocal of both sides of Eqn. - as suggested by Lineweaver and Burk in 9 is one such transformation as shown in Eqn. -. V = K M V max [A] + V max. Therefore, a plot of /V o versus /[A] gives a linear relationship with the y intercept being /V max and the slope K m /V max as shown in Figs. - and -. Product concentration B A Log [Ao]/[A] B T i m e T im e Figure -. Product formed as a function of time. Relation of product concentration versus time in line A is linear indicating a zero-order reaction with respect to substrate concentration. Relation of product concentration versus time in line B is non-linear and the line curves downward indicating that the order of reaction is higher than zero. A replot of the data of line B as log[a] /[A] versus time as shown in the insert is linear indicating the reaction is first order with respect to substrate concentration. When another compound, in addition to substrate, is added to an enzyme catalyzed reaction the compound may activate, inhibit or have no effect on rate of the reaction. In this experiment using alkaline phosphatase we want to evaluate the effect of adding a fixed amount of inorganic phosphate on the rate of the reaction and to determine whether inorganic phosphate is an activator or inhibitor. If it is an inhibitor we want to determine whether it is a competitive, non-competitive or uncompetitive inhibitor of alkaline

3 phosphatase. This can best be done by adding a fixed amount of the inhibitor to reactions done at various substrate concentrations, by plotting the data as /V o versus /[A] and by observing the effect relative to that of a control reaction in which no inhibitor is added. Fig. - shows that for a competitive inhibitor the slopes but not the y-intercepts change. Fig. - shows that for a non-competitive inhibitor both the slopes and y-intercepts change. Fig. - shows that for an uncompetitive inhibitor the y-intercepts but not the slope change. When there is a change in the slope and/or y-intercept it is by the constant term + [I]/K I. Thus, not only the nature of the inhibition but also K I can be determined by the plots of data shown. 8 slope=(+[i]/ki)(km/vmax) /Vo [I] [I] [I]= -/Km slope=km/vmax /Vmax - - / [ S o ] Figure -. Effect of a competitive inhibitor on the rates of an enzyme catalyzed reaction.

4 /Vo Intercept= ((+ [I]/Ki))/Vmax [I] slope= (Km(+[I]/Ki))/Vmax [I] [I]= -/Km slope=km/vmax /Vmax - - / [ S o ] Figure -. Effect of a non-competitive inhibitor on the rates of an enzyme-catalyzed reaction. [I] intercept= (+[I]/Ki)/Vmax [I] /Vo [I]= /Vmax slope=km/vmax / [ S o ] Figure -. Effect of an uncompetitive inhibitor on the rate of an enzyme-catalyzed reaction.

5 REAGENTS: Bovine intestine alkaline phosphatase (Sigma 7, units/mg) Buffer.. M glycine, ph gm glycine dissolved in approximately ml water and N NaOH added until the ph is 9.7. Make to ml. Substrate.. and. M disodium p-nitrophenyl phosphate (Sigma -) in water.. N NaOH Potassium phosphate solution.. x - M in. M glycine buffer, ph 9.7. p-nitrophenol.. x - M. Prepare fresh daily by dilution of a stock solution containing.9 gm p-nitrophenol in ml which is. M (molecular weight of p-nitrophenol is 9.). Disodium p-nitrophenyl phosphate will be used as the substrate and the reaction will be followed in a Shimadzu spectrophotometer by the rate of increase in absorbance at nm due to formation of nitrophenol (see below). O N O P O O - O - (colorless) + H O O N OH + HPO = pk a 7. O N O - O N O (yellow) PROCEDURE: Kinetics. Pipette. ml of. x - M substrate into a cuvette, add.7 ml deionized water and. ml of. M glycine buffer, ph 9.7. Equilibrate at 7 C for a minimum of min. Remove tube, add. ml enzyme, mix and rapidly return tube to

6 the spectrophotometer. Record absorbance at nm for min. at -second intervals. Repeat the experiment using. ml of x - M substrate,.8 ml water,. ml of. M glycine buffer, ph 9.7 and. ml enzyme.. Michaelis constant. Into five test tubes each containing ml of. M glycine buffer, ph 9.7, pipette.,.,.7,. or. ml of. x - M disodium p-nitrophenyl phosphate solution. Add water to bring the volume in each tube to.8 ml. In turn, equilibrate each tube at 7 C for at least min., add. ml enzyme, mix and place in a spectrophotometer. Record absorbance at nm for min at -second intervals. Inhibition. Repeat the experiment on Michaelis constant exactly as above except substitute. ml of. x - M phosphate in. M glycine buffer, ph 9.7, for the buffer. (In other words, use buffer containing the inhibitor.) NOTE. In a more complete experiment at least two other concentrations of orthophosphate would be included to determine whether inhibition is linear or not. Standard curve. In order to relate absorbance at nm to concentration of p- nitrophenol produced it is necessary to have a standard curve relating these two parameters. To prepare the standard curve, mix water, x - M p-nitrophenol and. M NaOH in the amounts given. Tube No. p-nitrophenol ( x - M) (ml) Water (ml). M NaOH (ml) Mix thoroughly and transfer to a cuvette. Read in the spectrophotometer (see Appendix F for operation) at nm using tube no. as blank.

7 EXPERIMENT KINETICS, MICHAELIS CONSTANT AND INHIBITION Laboratory Report Name: Date: A. Kinetics. Submit a graph in which p-nitrophenol concentration (molar) produced (y-axis) is plotted versus time for each substrate concentration. Your absorbances are converted to concentrations using the standard curve. (Please include your standard curve.). Replot data, if necessary, to give a linear relationship with time.. Report the order and rate constant for each of the reactions. B. Michaelis constant. Submit a graph in which absorbance readings (y-axis) are plotted against time for each of the five substrate concentrations.. For each of the five reactions, determine the initial velocity (expressed as moles/liter/min) and record in a table along with [A], /V o and /[A].. Submit a graph in which /v o versus /[A] is plotted.. Report the values of K m and V max C. Inhibition. Submit a graph in which absorbance readings (y-axis) are plotted against time for each of the five substrate concentrations in the presence of orthophosphate. 7

8 . For each of the five reactions, determine the initial velocity (expressed in moles/liter/min) and record in a table along with [A], /v o and /[A].. On the same graph as used for Michaelis constant data plot /v o versus /[A] in the presence of inhibitor.. Report the value of K i and the type of inhibition found. 8