Enzymes: Basic Concepts and Kinetics

1. Enzymes: Basic Concepts and Kinetics 1. Enzymes are specific catalysts 2. ΔG is useful for understanding enzymes 3. Enzymes accelerate reactions by facilitating the formation of the transition state 4. Michaelis – Menten model describes Kinetic properties of many enzymes 5. Enzymes can be inhibited

2. Enzymes accelerate Reactions Carbonic anhydrase: an enzyme in the blood hydrating CO2 Transfer of CO2 from the tissue -> blood -> release into air -> one of the fastest enzymes -> hydrates 106 molecules/sec

3. Enzymes are highly specific -> in reactions -> in substrate Proteases: A -> Trypsin B -> Thrombin Some proteases can also be more unspecific in terms of: -> substrate (different peptides) -> reaction (cleave also esters) DNA polymerase is highly specific: -> 1 mistake in less than 1000 bps

4. Enzymes require Cofactors Apo enzyme + cofactor -> Holo enzyme

5. Enzymes may transform Energy ATPase: Oxidation and ATP synthesis are coupled by transmembrane H+ fluxes

6. The enzyme classification(EC number)

7. ΔG (Free energy) provides information about reaction positive 0 negative ΔG: Equilibrium Reaction cannot occurs spontaneously Reaction occurs spontaneously ΔG -> depend on: G (product ) – G (reactants) -> independent of path or mechanism -> no information about rate of reaction (rate depends on ΔG activation )

8. ΔGO (Standard Free energy) related to Equilibrium Konstant K´eq A + B C + D • -> ΔG= ΔG° + RT ln [C][D] / [A][B] • ΔG° is ΔG under standard conditions: • [C]=[D]=[A]=[B]= 1M

9. ΔGO (Standard Free energy) related to Equilibrium Konstant K´eq • Equilibrium constant: K’eq= [C][D] / [A][B] • At Eq. ΔG=0 => 0=ΔG° + RT ln K’eq =>ΔG°= - RT ln K’eq => ΔG°= -2.303 RT Log K’eq => K’eq = 10 - ΔG° / 2.303 RT • ΔG° for biochemical reactions: pH=7.0, T= 298K

10. The ration of [GAP] to [DHAP] at equilibrium. K’eq = 0.0475 (pH 7.0, 25°C) => ΔG°’= + 1.80 kcal mol-1 (not spontaneous) -> at equilibrium not spontaneous !!! -> at different initial concentrations: [DHAP]=2 10-4 M ; [GAP]=3 10-6 M ΔG= ΔG° + RT ln [GAP]/[DHAP] ΔG= 1.80 – 2.49 -> ΔG= - 0.69 kcal mol-1 (spontaneous) Only spontaneous by adjusting concentrations !!! Example: conversion of DHAP into GAP

11. Enzymes do not alter equilibrium Enzymes -> alter reation rate -> alter NOT equilibrium -> equilibrium is faster reached with enzyme !!!!

12. Enzymes accelerates reaction by lowering the activation energy (ΔG‡) • ΔG‡ = GX‡ - GS • Enzymes facilitate formation of transition states

13. Reaction speed vs Subst. Conc. : Indirect evidence for ES complexes A  B Non-catalyzed reaction A  B Enz.-catalyzed reaction -> Enzym catalyzed reaction have saturation effect -> maximum velocity !!! -> evidence for ES complex !!!

14. X-ray crystallography to ”see” ES complexes Cytochrome P450

15. Active site: 3D cleft with residues far apart in sequence Small proportion in volume Cleft or crevice with non-polar residues, little water (unique microenvironment) Substrate binding by several weak attractions (e.g. H-bonds) Binding specificity governed by 3D arrangement of atoms Active sites in enzymes: a number of common features Lysozyme

16. Hydrogen bonding between substrate and active site Ribonuclease: Forms H-bonds with uridine component of substrate

17. Binding specificity governed by 3D arrangement of atoms Lock and Key model (E. Fisher, 1890) Induced-Fit model(D.E. Koshland, 1958) Active site complementary to shape of substrate Active site forms a complementary shape of substrate after binding substrate

18. Example of induced-fit: interfacial activation in lipasesDatabase of Macromolecular Movements (www.molmovdb.org) A lipid

19. Michaelis-Menten Equation describes kinetic of many enzymes rate = D[A] D[B] rate = - Dt Dt Thermodynamics – does a reaction take place? Kinetics – how fast does a reaction proceed? Reaction rate is the change in the concentration of a reactant or a product with time (M/s). A B D[A] = change in concentration of A over time period Dt D[B] = change in concentration of B over time period Dt Because [A] decreases with time, D[A] is negative.

20. The Rate Law The rate law expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to some powers. reaction is xth order in A xA + yB cC + dD reaction is yth order in B Rate = k [A]x[B]y reaction is (x +y)th order overall Temp dependent A products rate = k [A] Unimolecular reaction A + B products rate = k [A][B] Bimolecular reaction 2nd order reaction (A +B) can appear as 1st order if -> [B] in excess + [A] is low -> 1st order for [A] -> rate independend on [B] -> Pseudo 1st order reaction !!

21. The Rate Law Given a basic reaction k1 A + B C we assume that the rate of forward reaction is linearly proportional to the concentrations of A and B, and the back reaction is linearly proportional to the concentration of C. k-1 Equilibrium is reached when the net rate of reaction is zero. Thus or This equilibrium constant tells us the extent of the reaction, NOT its speed.

22. Michaelis and Menten In 1913, Michaelis and Menten proposed the following mechanism for a saturating reaction rate k1 k2 S + E ES P + E k-1 Complex. no back reaction -> no k-2 product

23. Enzyme-catalyzed reaction progression curves V0 -> initial velocity -> product formed /sec at the beginning of the reaction (t=0) -> V0 changes with [S] -> V0 rises when [S] rises -> until saturation (Max. Velocity)

24. Vmax: maximal velocity when all sites occupied Km: Michaelis constant, when [S] gives Vmax/2 k1 k2 E + S ES E + P k-1 k-2 Velocity vs Substrate Concentration:The Michaelis-Menten model

25. k1 k2 E + S ES E + P k-1 k-2 Basic assumptions in the Michaelis-Menten model The velocity equation is too complex to be directly evaluated, so assumptions must be made. • Formation of ES complex is necessary intermediate in catalysis • Reversion of Product to Substrate is negligible in initial stage of reaction ([P] << [S]): v = k-2[E][P] (Rate Law)

26. k1 k2 E + S ES E + P k-1 Another basic assumption: the Steady State (Briggs & Haldane, 1925) Rapidly, ES complex reaches a constant concentration If [S] >> [E], [ES] remains constant because the large excess of S molecules rapidly fill all enzyme active sites: d[ES]/dt = 0. This holds true until all of S is used up

27. Michaelis-Menten Kinetics • When [S] << KM, the reaction velocity increases linearly with [S]; I.e. vo = (Vmax / KM ) [S] -> pseudo 1st order reaction, Very little [ES] is formed • When [S] = KM, vo = Vmax /2 (half maximal velocity); this is a definition of KM: the concentration of substrate which gives ½ of Vmax. This means that low values of KM imply the enzyme achieves maximal catalytic efficiency at low [S]. • When [S] >> Km, vo = Vmax • -> pseudo 0 order reaction

28. Michaelis-Menten Kinetics When the enzyme is saturated with substrate, the reaction is progressing at its maximal velocity, Vmax. At saturation [E]T = [ES], and the equation for reaction velocity simplies to Vmax = k2 [E]T Combing the steady-state assumption (d[ES]/dt=0) with the conservation condition ([E]T=[E] + [ES]) vo leads to the Michaelis-Menten Equation of enzyme kinetics: where Km is KM= (k-1 + k2)/k1

29. Michaelis-Menten Kinetics How do determine experimentally KM and Vmax ? (y= d + k x) Lineweaver-Burk plot Eadie-Hofstee plot

30. Michaelis-Menten Kinetics What is KM ? • The concentration of substrate which gives ½ of Vmax. This means that low values of KM imply the enzyme achieves maximal catalytic efficiency at low [S]. • KM gives an idea of the range of [S] at which a reaction will occur. When k-1>>k2, Km=k-1/k1 (ES complex dissociates faster than product is formed -> no strong binding affinity) and KES=[E][S]/[ES]=k-1/k1 thus Km= KES (dissociaton constant) -> indicates binding strength (substrate affinity) • The larger the KM, the WEAKER the binding affinity of enzyme for substrate.

31. Michaelis-Menten Kinetics

32. Michaelis-Menten Kinetics What is Vmax? • Vmax gives an idea of how fast the reaction can occur under ideal circumstances. • If [Etot] is known, Vmax indicates TURN-OVER Number Vmax=k2[Etot] or k2=Vmax/[Etot] k2 is also called kcat or TURN-OVER Number

33. Michaelis-Menten Kinetics

34. The kcat/Km criterion: a measure for catalytic efficiency • When [S]>>Km (enzyme saturated – steady state conditions) -> V=Vmax, function of kcat (turn over number) • Under physiological conditions most enzymes are NOT saturated -> 0.01 Km<[S]< Km , V<< kcat (most sites are unoccopied) -> Combining V0=k2[ES] with [ES]=[E][S]/Km gives V0=(kcat/Km) [S][E] -> When [S]<< Km then [E]free=[Etot] -> kcat/Km is the rate constant for E and S interaction is measure for catalytic efficiency !!! -> ratio kcat/Km considers: -> rate of catalysis (kcat) and -> strength of enzyme/substrate interaction

35. The kcat/Km criterion: to probe chymotrypsin ”specificity” Highest kcat/Km -> best substrate -> highest efficiency for that substrate!

36. Enzymes at ”kinetic perfection” • Ultimative limit on kcat/Km is set by k1, rate of formation of ES • This rate cannot be faster than diffusion-controlled encounter between Enzyme and Product (108 to 109 s-1 M-1)

37. Multiple-substrate reactions A + B  P + Q • Sequencial displacement: All substrates must bind to enzyme before product is released -> ordered (substrates bind in defined sequence) or random A + B + E  EAB  E + P + Q Ordered:

38. Multiple-substrate reactions A + B  P + Q • Double displacement (Ping-Pong) One or more products are released before all substrates bind -> a substituted enzyme intermediate exists A + B + E  EA + B  E + P + B  EB  E + Q

39. Allosteric enzymes DO NOT follow Michaelis-Menten kinetics -> often show sigmoidal behaviour -> consists of multiple subunits with multiple active sites -> binding of substrate to one site alters properties for other sites in the same enzyme -> binding of substrate is cooperative -> activity altered by regulatory molecules that bind reversible to other sites than active site -> Example: Hemoglobin 4 subunits -> 4 active sites

40. Enzyme Inhibition -> Reversible Inhibitor binds to active site -> prevents substrate from binding -> structural analog Inhibitor binds only to ES complex Inhibitor does NOT prevent substrate from binding -> both can bind at the same time -> decreases turnover number

41. Inhibition overcome by increase in substrate concentration Km altered: apparent Km value increased Competitive inhibition affects Km

42. Non-Competitive inhibition affects Vmax • -> Inhibition cannot be overcome by increase in substrate concentration • -> Vmax altered: apparent Vmax value decreased

43. Un-Competitive inhibition affects Vmax and Km • -> Inhibition cannot be overcome by increase in substrate concentration • -> Vmax altered: apparent Vmax value decreased • -> Km altered: apparent Km value decreased

44. Enzyme Inhibition -> Irreversible • Group-specific reagents -> e.g. SN –Reaction Esterfication • Substrate analogs

45. Enzyme Inhibition -> Irreversible • Suicide inhibitors -> modified substrate that is catalytically modified by enzyme -> reactive intermediate -> inactivates enzyme Deprenyl -> inhibits monoamine oxidase -> MAO deaminates neurotransmitter such as dopamine and serotonin -> lowering their levels in the brain Parkinson: low level of dopamine Depression: low level of serotonin

46. Transition-state analogs: the case of proline racemase Pyrrole 2-carboxylic acid binds 160 times more tightly than L-proline