Chapter 14. Enzyme Kinetics

Transcription

1 Chapter 4. Enzyme inetics

2 Chemical kinetics Elementary reactions A P (Oerall stoichiometry) (ntermediates) Rate equations aa bb zz P Rate k[a] a [B] b [Z] z k: rate constant The order of the reaction (ab z): olecularity of the reaction Unimolecular (first order) reactions: A P Bimolecular (second order) reactions: A P or A B P Termolecular (third order) reactions

3 Rates of reactions A P (First-order reaction) d[p] d[a] - k[a] dt dt A P (Second-order reaction) d[p] dt d[a] - k[a] dt A B P (Second-order reaction) d[p] dt d[a] d[b] - - k[a][b] dt dt

4 Rate constant for the first-order reaction d[a] k[a] dt d[a] kdt [A] [A] [A] d[a] [A] k ln[a] ln[a] ln[a] ln[a] [A] [A] e kt t kt kt dt The reactant concentration decreases exponentially with time (t)

5 Half-life is constant for a first-order reaction ln[a] ln[a] t / ln [A] [A] kt kt ln kt / ln.693 k k For the first-order reaction, half-life is independent of the initial reactant concentration

6 Second-order reaction with one reactant A P d[a] k[a] dt d[a] kdt [A] [A] [A] d[a] [A] [A] k [A] t kt dt [A] [A] Slope k kt / [A] t / [A] k[a] [A] Time (t) Half-life is dependent on the initial reactant concentration

7 Pseudo first-order reactions k[a][b] When [B] >> [A], k [A] where k k[b] e.g. B is water (55.5): k' 55.5k

8 Arrhenius equation k Ae -E a/rt Actiation energy (E a )

9 ultistep reactions hae rate-determining steps k > k k < k k k Rate-determining step: the slow step ( the higher actiation energy)

10 Catalysts reduce the actiation energy ΔE a (the reduction in E a by the catalyst) Rate enhancement k cat /k uncat e ΔE a/rt e.g. When ΔE a 5.7 kj/mol, the reaction rate increases fold When ΔE a 34 kj/mol, the reaction rate increases 6 fold

11 ichaelis-enten equation V the initial rate V the imum rate the ichaelis constant the substrate concentration

12 Steady state approximation E S ES P E k k - k

13 Deriatization of ichaelis-enten equation E S ES P E k k - k d k k dt ( k k ( The initial elocity The imum elocity ( V d[ P] k dt k k ( T ) ( k k k k k ) k T T ) T T k k k k where k T k ) occurs at high substrate concentration when the enzyme is entirely in the form : V T V (Steady state approximation) k ) k k k T

14 ichaelis constant at which V / f an enzyme has a small alue of, it achiees imal catalytic efficiency at low substrate concentrations easure of the enzyme s binding affinity for the substrate (The lower, the higher affinity)

15 Lineweaer-Burke plot V V V V

16 k cat / is a measure of catalytic efficiency Catalytic constant or turnoer number of k cat V T an enzyme: ery little ES is formed and consequently V When V k >> cat T, k cat T

17 Catalytic perfection kcat k k k k k The ratio is imal when k k cat k >> k, (Diffusion-controlled limit: 8 to 9 - s - )

18 nhibitors Substances that reduce an enzyme s actiity Study of enzymatic mechanism Therapeutic agents Reersible or irreersible inhibitors O CO - O CO - H N HN O N N N H N H N H CO - H N N NH N N N N CH 3 N H CO - Dihydrofolate (Dihydrofolate reductase substrate) ethotrexate (Dihydrofolate reductase inhibitor, anticancer drug )

19 odes of the reersible inhibition Competitie inhibitors Binds to the substrate binding site Uncompetitie inhibitors Binds to enzymesubstrate complex Non-competitie inhibitors Binds to a site different from the substrate binding site ixed inhibitors Binds to the substratebinding site and the enzyme-substrate

20 Competitie inhibition T T T T T [] where, Since [] [] [] [] [] [] (Steady state approximation) [] V k V k k k k k k k k dt d

21 Competitie inhibitors affect ; V V regardless of

22 Determination of of the competitie inhibitor V V

23 Uncompetitie inhibition ' [] ' where ' ' ', Since ' [] ' [] ' [] ' [] ' [] [] ' T T T T T V V k V k k

24 Uncompetitie inhibitors decrease both V and V ' ' V ; ' V >> ; (Effects of an uncompetitie inhibitor become negligible) V V no inhibitor (') ncreasing [] V / V / ' [] '

25 Determination of of the uncompetitie inhibitor V V '

26 ixed inhibition ' [] ' and [] where ', Since ' ' ' ' ' ' [] [] ' [] [] [] ' [] T T T T T T T V k V k k

27 Lineweaer-Burk plot of a mixed inhibition V V '

28 Noncompetitie inhibition A special mixed inhibition when V ' [] where and When V ( ', ' ) V ' [] '

29 Noncompetitie inhibitors affect not but V V ; [] where V V V no inhibitor () ncreasing [] V / V / []

30 Determination of of the noncompetitie inhibitor V V / ncreasing [].5 (no inhibitor) /V Slope /V [] /

31 Effects of inhibitors on V and of the ichaelis-enten equation V app app

32 Effects of ph Binding of substrate to enzyme Catalytic actiity of enzyme onization of substrate Variation of protein structure (only at extreme phs) V ' V f f / f [H [H V and where E ES ' ' ' ] [H ] [H E ES ] ] ( f / f ) E - ES - E H H ES k k EH S ESH P EH E H k - ES H EH ESH

33 Approximate identity of catalytic amino acid residues p a ~4 Catalytic Asp or Glu residue p a ~6 Catalytic His residue p a ~ Catalytic Lys residue Caution should be taken because p a of amino acid residues are enironmentally sensitie

34 Bisubstrate reactions 6% of biochemical reactions inole two substrates and two products Transfer reactions and oxidation-reduction reactions

35 Cleland s nomenclature system for the enzymatic reactions Substrates: A, B, C, D in the order that they add to the enzyme Products: P, Q, R, S in the order that they leae the enzyme nhibitors:, J,, L Stable enzyme complexes: E, F, G, H with E being the free enzyme Numbers of reactants and products: Uni (one), Bi (two), Ter (three), and Quad (four) e.g. Bi Bi reaction: a reaction that requires two substrates and yields two products

36 Types of Bi Bi Reactions Sequential reactions (single displacement reactions): all substrates bind before chemical eent Ordered mechanism Random mechanism Ping pong reactions (double displacement reactions): chemistry occurs prior to binding of all substrates

37 Differentiating bisubstrate mechanisms easure rates Change concentration of substrates and products Lineweaer-Burk plot ntercept (/V ): the elocity at saturated substrate concentration t changes when the substrate A binds to a different enzyme form with the substrate B Slope ( /V ): the rate at low substrate concentration t changes when both A and B reersibly bind to an enzyme form

38 Ping Pong Bi Bi echanism ntercept changes because A and B bind to the different enzyme forms E and F, respectiely Slope remains same because the binding of A and B is irreersible due to the release of the product (P)

39 Sequential Bi Bi echanism or Ordered Random ntercept changes because A and B binds to the different enzyme forms (E or EB) and (EA or E), respectiely Slope changes because the binding of A and B is reersible

40 Differentiating Bi Bi mechanisms by product inhibition Competitie inhibition Substrate and inhibitor competitiely bind to the same site of the enzyme Ping Pong A s Q: Competitie B s P: Competitie A s P: Noncompetitie B s Q: Noncompetitie Ordered sequential A s Q: Competitie B s P: Noncompetitie A s P: Noncompetitie B s Q: Noncompetitie Random sequential Under assumption of dead-end complex formation (A is similar with Q and B is similar with P) A s Q: Competitie B s P: Competitie A s P: Noncompetitie B s Q: Noncompetitie

41 Dead-end complexes A B E Q P Q B Dead-end complex (no chemistry) A P no chemistry competitie ATP Creatine ADP Creatine-phosphate competitie

42 Differentiating Bi Bi mechanisms by isotope exchange Ping Pong echanism A* P isotope exchange is possible without B B* Q isotope exchange is possible without A or Sequential echanism Two substrates are required for the isotope exchange

43 sotope exchanges in a ping pong mechanism Sucrose phosphorylase (Sucrose) Glucose-fructose phosphate E Glucose--phosphate fructose sotope exchange experiments E Glucose-fructose fructose* Glucose--phosphate phosphate* Glucose-fructose* fructose E Glucose--phosphate* phosphate Glucose-fructose E Glucose-E phosphate E E Fructose Glucose-E Glucose--phosphate E Ping Pong echanism (Double displacement)

44 sotope exchanges in a sequential mechanism altose phosphorylase (altose) Glucose-glucose phosphate E Glucose--phosphate glucose sotope exchange experiments E Glucose-glucose glucose* Glucose--phosphate phosphate* E Glucose-glucose phosphate* E Glucose--phosphate glucose* No isotope exchange E No isotope exchange Glucose--phosphate* glucose Glucose-glucose phosphate Sequential echanism (Single displacement)