Enzyme Kinetics 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 Biochemistry 3rd Ed Voet Voet 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 S and the formation of P over time t v S t P t Enzyme Substrate Complex Uncatalyzed S P Enzyme catalyzed E S ES complex EP complex E P With high S reaction is zero order with respect to S S high and constant E varies E is constant S varies Michaelis Menten Kinetics In 1913 Leonor Michaelis and Maud Menten proposed a simplified model of enzyme kinetics Simplification 1 Michaelis and Menten did not consider ES and EP to be independent species E S k1 ES k2 P E k 2 k 1 Simplification 2 If you consider only initial velocity v0 there will be no conversion of product back to substrate so k 2 disappears E S k1 k 1 ES k2 P E Initial Velocity Initial velocity v0 moles second product formation at reaction initiation Substrate is consumed as reaction proceeds so S changes with time leading to an observed change in velocity Initial velocity v0 is linear Michaelis Menten Kinetics E S k1 ES k2 P E k 1 Simplification 3 The formation of ES is at equilibrium k 1 k2 If the above is true then k2 is the rate limiting step and v0 k2 ES This simplification is commonly referred to as the Steady State Assumption 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 Michaelis Menten Constant Km E S k1 ES k2 P E k 1 In steady state the formation and breakdown of ES occurs at same rate so k1 E S k 1 k2 ES This can rearrange to E S k 1 k2 ES k1 We can define an equilibrium constant Km the Michaelis constant that has units of concentration and is equal to terms above E S k 1 k2 Km ES k1 Meaning of Km E S k 1 k2 Km ES k1 When and only when k2 k 1 as is the case when product formation is rate limiting Simplification 3 Km k 1 k1 E S ES Kd In other words under these conditions Km is the dissociation constant for the ES complex As we discussed for Kd values a large Km represents weak binding and a smaller Km represents stronger binding Michaelis Menten Kinetics derivation is given at the end of the lecture E S k1 ES k2 P E k 1 Under Michaelis Menten conditions when S E 1 The steady state assumption is in effect ES t 0 2 k2 is the rate limiting step and v0 k2 ES 3 At saturation ES E Tot and maximum reaction velocity vmax k2 E Tot Under these conditions This is the S Michaelis Menten v0 vmax S K Equation m have to know 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 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 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 S S Km Michaelis Menten v0 vmax Lineweaver Burk 1 1 Km 1 v0 vmax S vmax y m x b Lineweaver Burk Plots 1 Km 1 1 v0 vmax S vmax x x x x You must determine the v0 at multiple substrate concentrations to generate a Lineweaver Burk Plot Enzyme Turnover We can define a catalytic constant for any enzyme kcat The catalytic constant kcat is the turnover number or the number of reaction processes catalyzed per unit time kcat vmax E Tot Note that under Michaelis Menten conditions kcat k2 Assumes total saturation of the enzyme and does not take into account affinity of the enzyme for its substrate 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 The specificity constant kcat Km better represents the overall ability of an enzyme to convert substrate into product Note Non Michaelis Menten reactions Michaelis Menten works only for a subset of enzymes Many enzymes have more complex characteristics for example multisubstrate enzymes like transferases Note Ping Pong mechanism of transketolase below Non Michaelis Menten reactions ACD toxin of Vibrio Cholerae ACD covalently crosslinks actin into non functional species ACD binds to one molecule of ATP and two molecules of actin Actin 1 Actin 2 ACD Actin Crosslinking Domain Non Michaelis Menten reactions ACD toxin of Vibrio Cholerae Neutrophil chasing Staphylococcus aureus by David Rogers Vanderbilt University 1950s Non Michaelis Menten reactions ACD toxin of Vibrio Cholerae Kudryashova et al 2012 PloS One Excess of actin variable ATP Excess of ATP variable ATP Actin dimers Actin dimers Actin monomer Actin monomer Typical Michaelis Menten kinetics for ATP as a substrate Non Michaelis Menten kinetics for actin as a substrate bimolecular Note Non Michaelis Menten reactions Michaelis Menten works only for a subset of enzymes that follow the stated characteristics Many enzymes require have more complex characteristics Note non hyperbolic curve typical of allosteric or cooperative behavior in an oligomeric enzyme Enzyme Inhibition Irreversible covalently modify the active site of the enzyme Reversible Competitive binds to the active site Noncompetitive binds to an allosteric site does not affect affinity for a substrate Uncompetitive binds only after the substrate is bound Mixed binds to an allosteric site affects affinity for a substrate Why inhibition 1 Allosteric regulation metabolism signaling etc 2 Drugs e g antibiotics anti cancer drugs etc Irreversible Enzyme Inhibition An efficient way to inhibit an enzyme is to irreversibly modify a catalytically important active site residue Consider an enzyme with a Cys residue at the active site Note Iodoacetamide will react with all accessible Cys side