Enzyme Kinetics Chapter 7 Biochem 4511 Figures Essentials of Biochemistry 3rd Ed OSU Custom Edition Principles of Biochemistry 5th Ed Moran et al Lehninger Principles of Biochemistry 5th Ed Nelson Cox Fundamentals of Biochemistry 2nd Ed Voet Voet Pratt Reaction Rates Kinetics is the study of reaction rates For the simplest of reactions S P S reactant P product The reaction rate or velocity v is equal to the disappearance of A and the formation of P over time t v S t P t Enzyme Catalyzed Reactions the Enzyme Substrate Complex Uncatalyzed S P Enzyme catalyzed E S ES P E k1 k 1 k1 k 1 k2 k 2 k2 P E Simplified E S ES With high S reaction is zero order with respect to S In other words enzyme is saturated with S to form ES Most enzymes can be described by formation of ES and breakdown to product Adrian Brown 1902 Michaelis Menten Kinetics In 1913 Leonor Michaelis and Maud Menten proposed a simplified model of enzyme kinetics refined by Briggs Haldane in 1925 where vo k2 ES to describe EP E S ES k2 P E k1 k 1 Michaelis Menten Kinetics In 1913 Leonor Michaelis and Maud Menten proposed a simplified model of enzyme kinetics refined by Briggs Haldane in 1925 where vo k2 ES k2 is rate limiting Assumption 1 Because product formation takes time first step ES formation follows rules for equilibria Assumption 2 If we consider only initial velocity v0 there will be no significant change in S or P and we can ignore reversion of P to ES simplified model Steady State Assumption These add together to make the steady state assumption ES is constant over the reaction as long as S E T E S ES k2 P E k1 k 1 EP Initial Velocity Initial velocity v0 product formation in P time Substrate is consumed as reaction proceeds so changes in S with time lead to a change in observed velocity When only initial velocity is considered changes in S do not matter Steady State Assumption Steady state assumption Formation and breakdown of the ES complex occurs at the same rate so the ES is constant over time In the case of S E T formation of the ES complex is maximized and ES does not change over time Under these conditions the reaction is at steady state Note E T is total enzyme E is free enzyme E T E ES Michaelis Menten Kinetics E S ES P E k2 k1 k 1 Under Michaelis Menten conditions S E 1 k2 is the rate limiting step and v0 k2 ES Problem We cannot measure ES 2 The steady state assumption is in effect ES t 0 3 At maximum reaction velocity vmax E Tot ES Using these assumptions p 192 194 of your textbook derives v0 vmax S S KM This is the Michaelis Menten Equation Michaelis Menten Kinetics v0 vmax S S KM E S ES P E k2 k1 k 1 v0 initial velocity S on x axis KM Michaelis Constant vmax maximal possible reaction rate for an enzyme v0 for infinite S such that when ES E T How to derive Michaelis Menten Equation E S E S E P k2 k1 k 1 1 Steady State Assumption S0 E0 Briggs and Haldane d E S dt 0 d E S dt k1 E S k2 E S k 1 E S 2 Mass balance E E0 E S 3 Substitution d E S dt 4 Velocity k1 E0 E S S k2 E S k 1 E S 0 E S E0 S S k2 k 1 k1 v0 k2 E S k2 E0 S S k2 k 1 k1 S S KM v0 vmax kcat k2 KM k2 k 1 k1 k2 k1 Kd kcat KM k2 KM k2 k2 k1 Kd k2 Kd Meaning of the Michaelis Constant Km E S ES P E k2 k1 k 1 v0 vmax S S KM KM k 1 k2 E S k1 ES KM is the substrate concentration where v0 Vmax When k2 k 1 as is the case when product formation is rate limiting fundamental assumption KM k 1 k1 E S ES In other words under these conditions KM is the dissociation constant for the ES complex Similar to KD a large KM represents weak binding and a smaller KM represents stronger binding Michaelis Menten Kinetics v0 vmax S S KM KM is the substrate concentration S at which v0 vmax 2 KM is characteristic for each enzyme substrate pair Michaelis Menten Kinetics Graph v0 vmax S S Km Based on the equation above when S Km v0 vmax 2 It is difficult to determine Km and vmax numbers directly from this plot since vmax is an asymptote Specialized software or Lineweaver Burk Plots Also referred to as Double Reciprocal Plots It is difficult to determine vmax directly from the curves we have discussed We transform the Michaelis Menten equation into a form that can be plotted as a line y mx b Michaelis Menten Lineweaver Burk v0 vmax S S Km 1 Km 1 1 v0 vmax S vmax y m x b Lineweaver Burk Plots 1 Km 1 1 v0 vmax S vmax Determine v0 at multiple S plot 1 v0 as y vs 1 S as x x intercept 1 KM y intercept 1 Vmax Slope KM Vmax Enzyme Turnover We need a property to describe the reaction efficiency for an enzyme independent of substrate binding the rate constant when the enzyme is saturated We define this as the kcat or catalytic constant also called the turnover number This is the rate constant when the enzyme is saturated Note that under Michaelis Menten conditions kcat k2 kcat vmax E Tot When S Km ES is low and E Tot E v0 k2 ES combines with ES to give E Tot S Km kcat Km v0 E S S Km E Tot E v0 vmax S S Km Specificity Constant kcat Km The specificity constant kcat Km is a good measure of catalytic activity because it takes into account the rate of catalysis kcat and the enzyme substrate interaction Km kcat Km can be used to compare enzyme preferences for different substrates For the specificity constant kcat Km a larger number means the compound is a better substrate for the enzyme Note Non Michaelis Menten reactions Michaelis Menten works only for a subset of enzymes Many enzymes require have more complex characteristics for example multisubstrate enzymes like transferases Note Ping Pong mechanism of transketolase below Note Non Michaelis Menten reactions Michaelis Menten works only for a subset of enzymes that follow the stated characteristics Many enzymes have more complex characteristics Note non hyperbolic curve typical of allosteric or cooperative behavior in an oligomeric enzyme Enzyme Inhibition Enzymes can be treated with a molecule that prevents These can be irreversible enzyme cannot recover These can be reversible enzyme can recover These can be nonspecific or specific targeted activity Example of irreversible targeted inhibition Serine proteases Chymotrypsin Irreversible covalent modification can be combined with substrate recognition to generate a specific …