Chapter 14. Enzyme Characteristics. Enzyme Terminology. BCH 4053 Summer 2001 Chapter 14 Lecture Notes. Slide 1

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1 BCH 4053 Suer 200 Chapter 4 Lecture Notes Chapter 4 Enzye Kinetics 2 Enzye Characteristics Catalytic ower Rate enhanceents as uch as 0 4 Specificity Enzyes can distinguish between closely related cheical species D and L isoers cis and trans isoers Diastereoers (glucose and galactose) Regulation Ability to activate or inhibit enzyes can control which reactions occur and when. An exaple of specificity is illustrated by the enzye fuarase which catalyzes addition of water to the double bond of fuaric acid to for L-alic acid. The cis isoer of fuarate, aleic acid, does not wor. Neither does D-alic acid, the enantioer of L-alic acid. 3 Enzye Terinology Substrates Substances whose reaction is being catalyzed roducts End products of the catalyzed reaction For reversible reaction, designation depends on point of view. A + B + Q A, B products,, Q reactants, or vice versa An enzye is a catalyst, and as such does not influence the equilibriu position of the reaction only its rate. So one can start with A and B and get and Q fored, but one can also start with and Q and get A and B fored. Chapter 4, page

2 4 Enzye Noenclature Soe naes are historical coon naes Trypsin, chyotrypsin, Soe have coon naes related to the substrate(s), usually ending in ase. urease, protease, ribonuclease, ATase, glucose-6-phosphatase All enzyes have a systeatic nae based on international agreeent 5 Systeatic Classification of Enzyes. Oxidoreductases 2. Transferases 3. Hydrolases 4. Lyases 5. Isoerases 6. Ligases 6 Oxidoreductases Catalyze transfer of electrons between species (i.e., oxidation and reduction) Soe are called dehydrogenases in their coon nae. Soe are called oxidases or reductases. Often coenzyes such as NAD, NAD, FAD, or a etal ion is involved in the reaction. Chapter 4, page 2

3 7 Transferases Catalyze transfer of a functional group fro one olecule to another e.g., phosphate groups, ethyl groups, acyl groups, glycosyl groups, etc. Enzyes catalyzing transfer of a phosphate fro AT to another acceptor are coonly referred to as inases. 8 Hydrolases and Lyases Hydrolases catalyze hydrolysis of a cheical bond Includes proteases, esterases, phosphatases, etc. Lyases catalyze reversible addition of groups to a double bond. Usually H 2 O or NH 3 added Interconversion of fuaric acid and L-alic acid which we alluded to earlier. 9 Isoerases and Ligases Isoerases catalyze Conversion of one isoer to another. The only enzye class in which a single substrate and product is involved. Ligases catalyze the foration of a cheical bond at the expense of hydrolysis of AT. We will encounter a nuber of exaples of ligases later. Learn the general classification groups. As we study new enzyes, be able to fit an enzye into one of these groups, but you won t be held for nowing the specific systeatic nae. We will usually refer to ore coon naes and soeties there is ore than one! Chapter 4, page 3

4 0 Coenzyes Coenzyes are non-protein substances required for activity, soeties called cofactors. (See Table 4.2) Metal ions Soe etal ion cofactors are directly involved in the catalytic echanis. Others are required siply for stabilization of protein structure. Organic cofactors Non-aino acid copounds required for catalytic activity Organic Coenzyes Two classes of organic coenzyes Coenzye cosubstrates Transfored in the reaction, regenerated in another reaction Loosely bound to the enzye, dissociates during course of reaction Coenzye prosthetic groups articipates in the reaction, but original structure regenerated during catalytic cycle Tightly bound, soeties covalently, does not dissociate during course of reaction. Your textboo does not ae this distinction clear between these two classes of coenzyes, yet eeping their differences straight is iportant in understanding soe etabolic processes. As we study new enzyes involving coenzyes, be prepared to classify the type of coenzye involved. An enzye lacing its prosthetic group is called an apoenzye. When its prosthetic group is present, it is called a holoenzye. 2 Enzye Kinetics Cheical inetics refers to the rate of cheical reactions, and things which influence that rate. Enzyes as catalysts accelerate the rate, but not the equilibriu position. A cheical rate law describes the effect of variables, such as reactant concentration, on the rate of the reaction. Chapter 4, page 4

5 3 Enzye Kinetics--Applications What can inetics tell us? Kinetic studies can help us understand how etabolic pathways are controlled, and the conditions under which an enzye is active. Kinetic studies can yield inforation about the echanis of an enzyatic reaction. However, inetic studies can only rule out echanistic odels that do not fit the data. They cannot prove a echanis. 4 5 Reaction Rate The rate of a reaction is the slope of a progress curve. (See Figure 4.4) For the siple reaction: A Æ d[] d[a] rate = or - dt dt Reaction Rate Theory: The Transition State For cheical bond breaage and foration to occur, the reactants ust go through an interediate transition state. The free energy of the transition state is higher than that of either the reactants or the products. (See Figure 4.) Only a sall fraction of the reactants have sufficient energy to achieve this activation energy, referred to as G. Note that the slope of the progress curve changes with tie. Most studies in enzye inetics try to deal with the initial rate of a reaction, that is the slope of the curve where t = 0. Many things can influence the catalytic ability of an enzye, including the accuulation of products as well as denaturation of the protein itself. It is only at the initiation of the reaction that one is sure of the aount of active enzye present and the other conditions of substrate and product concentration. Chapter 4, page 5

6 6 Reaction Rate Theory: Effect of Teperature Increasing the teperature increases the fraction of reactants which have enough energy to achieve the transition state. This relationship is expressed in the Arrhenius Equation: G RT = Ae where G is the activation energy (see Figure 4.5a) 7 Reaction Rate Theory: Effect of a catalyst A catalyst accelerates the rate of a reaction by lowering the activation energy of the reaction. (See Figure 4.5b) 8 Rate Law Expresses relationship between rate and concentration of reactants. e.g. v = [A], v = [A] 2, v = [A][B] is the rate constant (a proportionality constant between rate and the concentration ters). Effect of teperature on reaction rate is an effect on. Chapter 4, page 6

7 9 Reaction Order The order of a reaction is given by the exponents of the reactant concentrations in the rate law. v = [A] n n=0, zero order (no dependence on [A] n=, first order n=2, second order v = [A] 2 [B] second order in A, first order in B, third order overall 20 Reaction Order, con t. Experiental reaction rate order Deterined by experiental easureents. Need not be whole nubers Theoretical reaction rate order Interpreted as the olecularity of eleentary steps in the reaction. The reaction A + B Æ + Q Would have a olecularity of 2, and a theoretical rate law: v = [A][B] 2 Effect of Enzye Concentration on Rate First establish the effect of Enzye concentration on reaction rate. Try to wor only in region where v = [E t ] First order in [E] E v tie [E] Chapter 4, page 7

8 Effect of Substrate Concentration on Rate For any enzyatic reactions, the experiental rate law is given by the equation for a rectangular hyperbola. as v = b + S 23 Michaelis Menten Rate Law a = 00 (asyptote of curve) V a/2 = 50 v=as/(b+s), where a = 00, b = 20 b = S 24 Mixed Order Nature of the Experiental Rate Law At high S (S >>> b) v = a zero order in S At low S (S <<<b) v = (a/b)s first order in S Chapter 4, page 8

9 25 Michaelis Menten Model to Explain Experiental Rate Law Terinology of M.M. equation a is called V, the axiu velocity This is the asyptote of the saturation curve, the axiu velocity that can be achieved at a very high S concentration. It has the units of v. b is called K, the Michaelis constant This is the substrate concentration at which v is onehalf of V. It has the units of S. 26 Michaelis Menten Model Michaelis and Menten proposed an enzye echanis (a odel) to explain the rate law behavior. Features of their odel give soe insight into what is happening, nevertheless their odel was overly siplistic. Deriving the rate law fro their odel shows it is consistent with the data, but does not prove the odel. 27 ostulates (Assuptions) of the M.M. Model. Enzye and substrate cobine to for an ES coplex, which breas down to for product. Note the odel assues only one substrate. This is actually true only for isoerases. 2 E+ S ES E+ Chapter 4, page 9

10 28 ostulates (Assuptions) of the M.M. Model, con t. 2. [S]>>[E], so [S t ] = [S free ] And [ES] can be ignored 3. Last step is irreversible either -2 = 0, or [] = ,<<< -, the rapid equilibriu assuption (The binding of S to E is rapid copared to the breadown of the ES coplex.) 29 Derivations fro the M.M. ostulates [E][S] (a) K [ES] = = 2 (c) [E ] = [E] + [ES] t (b) v = [ES] where [E] is the free enzye Algebraically eliinate [E] and [ES] fro these equations to give an equation with v as a function of [S] 30 Derivations fro the M.M. ostulates, con t. Divide (b) by (c), and substitute (a) v [ES] 2 = [E ] [E] + [ES] t v [ES] 2 = [E K[ES] t ] + [ES] [S] [E 2 t][s] V[S] v = = K + [S] K + [S] where V = [E] 2 t and K = Chapter 4, page 0

11 3 Briggs-Haldane Refineent: The Steady State Assuption Assue that [ES] does not change over the course of the reaction. i.e., it is being broen down as rapidly as it is being ade. (See Figure 4.8) d[es] = 0= [E][S] [ES] [ES] 2 dt [E][S] 2 [E][S] = ( + )[ES] = + = K 2 [ES] Note the ey difference between the results of the rapid equilibriu assuption and the steady state assuption is the interpretation of K. In the first case, it is the dissociation constant of the ES coplex. In the second it is a ore coplicated assebly of rate constants. 32 Michaelis-Menten Equation as a Theoretical Rate Law: Suary V[S] v = K + [S] Based on echanis: 2 E+ S ES E+ where V = [E ] and 2 t K = (rapid + 2 = equilibriu assuption) or K (steady state assuption) 33 Enzye Units Quantity of an enzye often easured in ters of its catalytic activity. International Unit aount that catalyzes foration of one icroole of product in one inute. atal--aount that catalyzes conversion of one ole of substrate to product in one second turnover nuber substrate olecules converted per enzye olecule per unit tie. International units and atals can be expressed even in a crude ixture where the purity of the enzye or the actual quantity of enzye protein present are not nown. Turnover nuber, on the other hand, requires that one now the nuber of oles of enzye present in the reaction. Chapter 4, page

12 34 Turnover Nuber, con t. Called cat Equivalent to 2 in the M.M. equation provided V ax and [E t ] are in the sae olar units. For exaple, V ax in ol-sec - -l - and [E t ] in ol-l - Varies over a wide range (See Table 4.4) 35 Catalytic Efficiency cat easures inetic efficiency, and K is inversely related to the binding affinity cat /K easures the catalytic efficiency of an enzye how well it has evolved to do its job. It is the first order rate constant at low substrate concentration: v cat = [S] [E ] K t 36 Catalytic Efficiency, con t. Using the M.M. odel and the steady state assuption: cat 2 2 = = K ( + ) 2 ( + ) 2 when >>> cat 2 = = K 2 2 and the reaction is Diffusion Controlled The reaction can never proceed faster than the tie it taes the substrate to bind to the enzye in the first place. In the extree where every substrate binding event leads to product, the reaction is said to be diffusion controlled. Theoretically, the axiu rate for these collisions is about 0 8 sec - M -. See Table 4.5 for soe enzyes that see to have achieved this perfection. Chapter 4, page 2

13 37 Validity of M.M. Model Assuptions. (a) Enzye and substrate cobine to for an ES coplex, which breas down to for product. This basic assuption ust be true in any odel. (b) One substrate, one product: Seldo true; approxiation if everything else is held constant. 2 E+ S ES E+ 38 Validity of M.M. Model Assuptions, con t. 2. [S]>>[E], so [S t ] = [S free ] And [ES] can be ignored Usually true in the test tube, not always in the cell. 3. Last step is irreversible either -2 = 0, or [] = 0 Usually only artificially when [] = 0 4) Rapid equilibriu, or steady state assuption. Steady state assuption is ore general 39 Expanding the M.M. Model Assuptions Adding additional steps in the echanis Maing the last step reversible More than one substrate or product Chapter 4, page 3

14 40 Additional Steps in the Mechanis Suppose there is a rearrangeent step added to the echanis E S ES 2 E 3 + E + 2 The rate law becoes: [E ][S] 2 3 t v= S ( + + ) You can derive this equation if you wish. Just note there are now three fors of the enzye (E + ES + E), and there are two steady state assuption stateents: d[es]/dt = 0 = [E][S] + -2 [E] ( )[ES] and d[e]/dt = 0 = 2 [ES]-( )[E]. And v = 3 [E]. 4 Additional Steps in the Mechanis, con t. This equation still has the sae for as the M.M. equation, but the interpretation of V ax and K are different: 2 3 V = [E t] K + + = ( + + ) Therefore steady state inetics cannot distinguish between echaniss that just involve different nubers of rearrangeent steps. The ore coplicated the echanis, the ore coplicated the interpretation of K in ters of the paraeters of the odel. 42 Maing the Last Step Reversible 2 3 E+ S ES E E+ 2 3 the rate law taes the for a[s] b[] v = c + d[s] + e[] where a, b, c, d, and e are asseblies of rate constant ore coplicated, but not ipossible, to analyze Chapter 4, page 4

15 43 More Than One Substrate or roduct Even siplest echanis is uch ore coplex. Several pathways are possible: B A E EA E' B B A EB EAB E'B Q Q A Q E" E"A E 44 Ordered Sequence Mechaniss Ordered, Single-Displaceent. Substrates add in a definite order. E A B EA EAB E'B E Q 45 Ordered Sequence Mechaniss Ordered. Double-Displaceent (ing-ong) First substrate is converted to product before second substrate adds. Requires two fors of free enzye. A E EA E' B E'B E Q Chapter 4, page 5

16 46 Rando Addition Mechaniss A and B can add in any order, and Q can be released in any order. B E A EA B A EB EAB E'B E"A Q E Q 47 Kinetic Consequences of Multisubstrate Mechaniss Hold one substrate constant, and vary the other one: M.M. inetics (rectangular hyperbola) shown only for: Ordered sequence echaniss Rando echaniss if the rapid equilibriu assuption holds. Only si the textboo analysis of two-substrate reactions. Their treatent is incoplete, and an adequate treatent would tae ore tie than we have available. 48 Linear Transforations of the M.M. Equation Before the days of coputers, linear plots of the M.M. equation were used to calculate values for the inetic constants V ax and K Linear plots are still useful in visualizing the data. Three coon linear plots: Lineweaver-Bur plot Haynes -Woolf plot Eadie-Hofstee plot Mechaniss which give true rectangular hyperbola give straight lines in these plots. Such echaniss are referred to as linear echaniss. Hence ordered sequence echaniss are linear, while only rapid equilibriu rando echaniss are linear. In all cases, the assuption that the reverse reaction is insignificant ust be correct for the results to be linear. Chapter 4, page 6

17 49 Lineweaver-Bur lot Tae the reciprocal of the M.M. equation, and rearrange it: plot /v versus /[S] K + [S] K = or = + x v V[S] v V V [S] y = x + b slope = ; intercept = see Figure 4.9 K V V 50 Hanes-Woolf lot Multiply Lineweaver-Bur equation through by [S]: plot [S]/v versus [S] [S] K = [S] + v V V See Figure Eadie-Hofstee lot Multiply Lineweaver-Bur equation through by v and V : plot v versus v/[s] V = v+ K v [S] v or v= V K [S] v y intercept = V slope = -K v/[s] Chapter 4, page 7

18 52 Enzye Inhibition Two general classes of inhibitors Reversible inhibitors can dissociate and be reoved through dilution or dialysis Irreversible inhibitors for a covalent alteration of the enzye v no inhibitor irreversible inhibitor reversible inhibitor Reversible inhibition is usually iediate, whereas irreversible inhibition ay vary with tie of incubation of the enzye with the inhibitor. Soe irreversible inhibitors are called suicide inhibitors, in that the enzye converts the inhibitor into soething which covalently binds to it and destroys its activity. enicillin is an exaple. See Figure 4.7. [E] 53 Classes of Inhibition Based on reversible inhibition. Based on siple M.M. one-substrate odel Four types: (Your text only describes three) ) Copetitive 2) Uncopetitive 3) ure noncopetitive 4) Mixed noncopetitive (2, 3, and 4 also called not-copetitive ) 54 Copetitive Inhibition Assues that the inhibitor binds only to the free enzye. 2 E+ S ES E+ i [E][I] E+ I EI; K I = i [EI] gives the following rate law: K [I] = + ( + ) v V V K [S] I Chapter 4, page 8

19 55 Copetitive Inhibition, con t. Effect is only on slope and not the intercept of the Lineweaver-Bur plot. See Figure 4.3 Interpretation is that the inhibitor binds at the sae site as the substrate. Both cannot bind to the free enzye. Exaple is succinate dehydrogenase, inhibited by alonate. 56 Uncopetitive Inhibition Assues that the inhibitor binds only to the ES coplex. 2 E+ S ES E+ i [ES][I] ES+ I ESI; K' I = i [ESI] gives the following rate law: [I] K = ( + ) + v V K' V [S] I 57 Uncopetitive Inhibition, con t. Effect is on intercept and not slope of the Lineweaver-Bur plot. Gives parallel lines. Interpretation is that inhibitor can only bind after substrate has bound incre asi ng I /v no I / [S] Chapter 4, page 9

20 58 Noncopetitive Inhibition Assues inhibitor binds to either the free enzye, or the ES copex. 2 E+ S ES E+ E+ I EI; ES+I ESI i ' i i ' -i [E][I] [ES][I] K I = ; K' I = [EI] [ESI] 59 Noncopetitive Inhibition, con t. Gives the following rate law: [I] K [I] = v V K' V K [S] ( ) ( ) I I Both intercept and slope of Lineweaver-Bur plot are affected. ure Noncopetitive, when K I = K I Lines cross at x axis. (See Figure 4.5) Mixed Noncopetitive, when K I ¹ K I Lines do not cross at x axis. (See Figure 4.6) 60 Ribozyes Several cases are now nown where RNA has catalytic activity lie an enzye. RNase, involved in splicing out a piece of trna, has an RNA coponent. Self-splicing RNA fro several sources. eptidyl transferase of protein synthesis is an RNA coponent of the ribosoe. Chapter 4, page 20

21 6 Abzyes Enzyes wor by lowering the energy of the transition state. They bind the transition state better than the substrate. Antibodies raised by using transition state analogues as antigens show catalytic activity. So far the reaction types are liited and catalytic enhanceent is low. Chapter 4, page 2