Kinetics Catalysis y Enzymes

Transcription

1 Kinetics Catalysis Enzymes

2 Catalysis involves lowering of the energy barrier ΔH ΔH A catalyst provides an alternative reaction pathway A catalyst provides an alternative reaction pathway with a lower activation energy or activation enthalpy.

3 Types of catalysis Homogeneous catalysis - the catalyst is in the same phase as the reactants. Example: acid or base catalysis Heterogeneous catalysis - the catalyst is in a different phase from the reactants. Example: metal complexes, surfaces, zeolites Enzymatic catalysis - the catalyst is a protein that has a substrate binding site and controlled reaction path

4 Zeolites: an important t class of catalysts t Database of zeolite structures: Example: search for ZSM-5 Unit cell parameters: a = Å b = Å c = Å alpha = beta = gamma = volume = Å 3

5 Basis for heterogeneous catalysis in zeolites Zeolites are crystalline solids made up of SiO 4 building blocks. These tetrahedral units join together to form several different ring and cage structures. t The characteristic ti that t separates zeolites from all-silica minerals is the substitution of aluminum into the crystalline framework. The substitution of aluminum generates a charge imbalance, which is compensated by a proton. The acid site formed behaves as a classic Brønsted acid or proton donating acid site. The highly acidic sites combined with the high selectivity arising from shape selectivity and large internal surface area makes the zeolite an ideal industrial i catalyst. t

6 Zeolites: shape selective catalysis The alkylation of benzene with propylene is an important petrochemical process because the product (cumene) is a chemical intermediate used to synthesize phenol and acetone. assical industrial processes are based on "olid phosphoric acid" catalysts, with problems of handling, safety, corrosion and waste disposal. These can be avoided by using zeolite catalysts.

7 Zeolites: shape selective catalysis The medium pore size zeolite ERB-1 has greater reactivity for cumene formation than larger pore size catalysts.

8 Zeolites: shape selective catalysis Calculated energy surface for cumene in BEA. Diffusion of cumene in zeolite BEA.

9 Ziegler-Natta catalyst for polymerization of ethylene Ziegler-Natta catalysts are an important class of mixtures of chemical compounds remarkable for their ability to effect the polymerization of olefins (hydrocarbons containing a double carbon-carbon bond) to polymers of high molecular weights and highly ordered (stereoregular) structures. These catalysts were originated in the 1950s by the German chemist Karl Ziegler for the polymerization of ethylene at atmospheric pressure. Ziegler employed a catalyst consisting of a mixture of titanium tetrachloride and an alkyl derivative of aluminum. Giulio Natta, an Italian chemist, extended the method to other olefins and developed further variations of the Ziegler catalyst based on his findings on the mechanism of the polymerization reaction.

10 Ziegler-Natta catalyst for polymerization of ethylene Ti 3 can arrange itself into a number of crystal structures. The one that we're interested in is called α-ti 3. It looks something like this: Ti Ti Ti Ti Ti Ti Ti Ti Ti As we can see, each titanium atom is coordinated to six chlorine atoms, with octahedral geometry.

11 Ziegler-Natta catalyst for polymerization of ethylene At the surface of the crystal a titanium atom is surrounded on one side by five chlorine atoms, but on the other side by empty space. This leaves titanium i a chlorine short. Titanium, as one of the transition metals, has six empty py orbitals (resulting from one 4s and five 3d-orbitals) in the outermost electron shells. Ti The surface Ti atom has an empty orbital, shown as an empty square in the picture. Ti

12 Ziegler-Natta catalyst for polymerization of ethylene Titanium wants to fill its orbitals. But first, Al(C 2 H 5 ) 2 enters the picture. It donates one of its ethyl groups to the impoverished titanium, but kicks out one of the chlorines in the process. We still have an empty orbital. Ti H Al 3 CH 2 C + Al H3 3CH 2 C CH 2 CH 3 CH 3 CH Ti C l

13 Ziegler-Natta catalyst for polymerization of ethylene The the aluminum is coordinated, though not covalently bonded, to the CH 2 carbon atom of the ethyl group it just donated to the titanium and to one of the chlorine atoms adjacent to the titanium. There is still a vacant site Al CH H 3 3 CH 2 C where CH 2 polymerization can occur. Ti

14 Ziegler-Natta catalyst for polymerization of ethylene This process forms the active polymerization catalyst, which happens to be insoluble (unlike the 2 components that make up the complex), so we have what is commonly termed a heterogeneous catalyst (also known as a solid solution). H CH 3 H 3 CH 2 C Al CH 3 C CH C Ti H H

15 Ziegler-Natta catalyst for polymerization of ethylene Upon binding ethylene forms bonds with the Ti atom and the carbon of the ethylene ligand. H 3 CH 2 C Al C H 2 Ti H CH 3 H C C H CH 3

16 Ziegler-Natta catalyst for polymerization of ethylene The growing polymer chain is initiated. H 3 CH 2 C Al Ti CH 3 H 2 C H CH 3 C C H H

17 Ziegler-Natta catalyst for polymerization of ethylene The vacant site is available for the next ethylene molecule to bind. CH 3 H 2 C H CH 3 C H 3 CH 2 C Al H C H Ti

18 Enzymatic Catalysis Michaelis-Menton Kinetics Alcohol Dehydrogenase Serine Proteases

19 Michaelis-Menton M kinetics The rate of an enzyme catalyzed reaction in which substrate S is converted into products P depends on the concentration of the enzyme E even though the enzyme does not undergo any net change. k a k b E + S ES P + E k a

20 Michaelis-Menton rate equations k a k b E + S ES P + E k a d [S ] = k dt a [E][S ]+k a [ES ] d [ES ] = k dt a [E][S ] k a [ES ] k b [ES ] d [P] = k dt b [ES ]

21 Steps in the Michaelis-Menton mechanism Step 1. Bimolecular formation of the enzyme E and and substrate S: E + S ES rate of formation of ES = k a [E][S] Step 2. Unimolecular decomposition of the complex: ES E + S rate of decomposition of ES = -k a [ES] Step 3. Formation of products and release from the enzyme: ES P + E rate of formation of P = k b [ES] h l f h f f h The rate law of interest is the formation of the product in terms of E and S.

22 The enzyme substrate complex can be eliminated i The enzyme substrate complex is formed transiently and can be approximated using the steady state approximation. d [ES ] dt = k a [E][S ] k a [ES ] k b [ES ] 0 The result of this approximation is k [E][S ] [ES ] = a k a + k b

23 Pseudo-first order Michaelis-Menton kinetics In an experiment we know the total enzyme concentration [E]0 and not the unbound enzyme [E]. The total concentration of enzyme [E]0 = [E] + [ES]. which rearranges to [ES ]= k a [E] 0 [ES ] [S ] k a + k b [ES ] = k a [E] 0 [S ] k a + k b + k a [S ]

24 Michaelis-Menton M parameters The rate of formation of product can be written d [P] dt =k b [E] where k 0 = k b[s ] K + [S M [ ] where K M is the Michaelis constant and k b is the maximum turnover number. The Michaelis constant is: k a + k K b m = k a

25 Limiting conditions of enzyme reactivity it Maximal rate: If there is excess substrate present the rate is limited by the rate at which the ES complex falls apart. The rate of formation of products is a maximum and V max = k b [E] 0 is called the maximum velocity. Second order regime: If [S] << K M then the rate of formation of products is d[p]/dt = k b /K M [E] o [S]. The rate depends on [S] as well as [E] o. A plot of 1/k yields k b and K M but not the rate constants k a and dk a. The latter rate constants t can be obtained from stopped-flow experiments.

26 Catalytic ti rate constant t k cat Catalytic rate: The rate constant k b is also called the catalytic rate constant or k cat. Since this is an intrinsic rate constant, it is not an observable. bl However, it can be calculated l from observables k cat = V max /[E] 0. Turnover number Turnover number: When the enzyme is saturated, i.e. when [S] >> K M, then k cat is also called the turnover number.

27 Integrated form of the Michaelis-Menten equation K M ln or [S] [S] 0 +[S] [S] 0 = V max t t = K ln [S] 0 M + [S] [S] [S] 0 V max [S] τ 1/2 = K Mln V max The half-time τ 1/2 is the time at which half of the original substrate is consumed.

28 General expression for reaction velocity Based on the previous analysis the velocity at an arbitrary substrate concentration is: v = [S ]v max K M +[S ]

29 Lineweaver-Burke Plots The Michaelis-Menton expression is non-linear. The Lineweaver-Burke plot is linearized plot of data. 1 = K M +[S ] = 1 + K M 1 v [S ]v v v [S max max max ] This expression has the form of an equation for a line: y = intercept + slope x Such plots are not necessary today with common non-linear fitting programs.

30 Lineweaver-Burke Plots v max K v = 1 + M [S ]

31 Transition State Stabilization The original i idea of the enzyme having maximum complementarity to the TS was put forward by Linus Pauling in It wasn't until the early 70's that the idea was put on a more solid grounding. As put forward by Lienhard and Wolfenden the idea is as follows: K n E + S E + S k n E + P Ks K t K c ES ES k c E + P

32 Transition State Stabilization bl Defining the equilibrium constants as association constants: K n = [S ]/[S], Kt = [ES ]/[E][S ] from TS theory: ΔG = -RT ln K and kobs = (k B T/h)e-ΔG /RT Thus, kn = (k B T/h)K n and kc = (k B T/h)K c where c means catalyzed and n means uncatalyzed. From the scheme you can see that K s K c = K n K t hence K t /K s = K c /K n however, k c /k n = K c /K n Therefore the observed rate enhancement k c /k n = K t /K s >> 1 Therefore the transition state geometry S must bind more tightly than the substrate t S in its equilibrium i geometry!

33 Transition State t Analogs The transition state stabilization hypothesis was tested by designing so-called transition state analogs, molecules which mimick the real TS as closely as possible. One of the first enzymes examined was proline racemase: N COO - H N H COO - N COO - H H H The compound on the right is a planar TS state analog. This molecule was found to be a good inhibitor, with Ki some two orders of magnitude smaller than Km.

34 The Role of Entropy In a seminal paper Page and Jencks showed that the loss in entropy in going from a bimolecular to a unimolecular reaction, i.e. E + S <=> ES, could account for as much as 108 of the observed rate enhancement. In other words, this much free energy would oud come from the intrinsic binding energy. The entropy loss arises from the loss of translational and rotational degrees of freedom when the substrate is bound. The configurational entropy is: S = k B lnw where W is the number of degrees of freedom available to a molecule.

35 Inhibition An inhibitor is any compound that causes a decrease in the catalytic rate. We will consider non-covalent ligands that can bind to the enzyme. The general scheme is shown below: S k c I = inhibitor E ES E + P Inhibition occurs if k i [EIS] < k c [ES] I I S k i EI EIS EI + P

36 Competitive Inhibition Competitive inhibition results from the direct competition between the I and S for the substrate binding site. There is an additional equilibrium constant: EI E + I K [E][I ] I = [EI ] The velocity under these conditions turns out to be: v = [S ]v max α = 1 + [I ] αk M +[S ] K I

37 Non-competitive Inhibition Non-competitive inhibition arises when I can bind at site that t is not the same as the substrate t binding site. There is an additional equilibrium constant: EI E + I K I = [E][I ] [EI ] Here the complex IE indicates that the inhibitor does not bind in the same site as the substrate. The velocity under these conditions is: v = [S ]v max α =1+ [I ] α K + [S K M [ ] I

38 Distinguishing competitive and noncompetitive inhibition The tradition method is to use Lineweaver-Burke analysis. On a L-B plot competitive inhibition will give rise to lines of varying slope, but with the same intercept. On the other hand, non-competitive inhibition will give rise to lines with different intercepts. Non-competitive: Competitive: 1 α K M +[S ] αk M v = = + α [S ]v max [S ]v max 1 v = αk M + [S ] = αk M + 1 [S ]v max [S ]v max v max v max

39 Plots of competitive and non- competitive inhibition v max v = α 1+ K M [S ] Non-competitive v max v = 1+αK M [S ] Competitive

40 Enzymatic catalysis: Alcohol l dehydrogenase d The enzyme alcohol dehydrogenase (EC ) 111)is also known as aldehyde reductase. This enzyme belongs to the oxidoreductase class of enzymes. Alcohol dehydrogenase catalyzes the oxidation of ethanol to acetaldehyde with the reduction of NAD to NADH. The alcohol can be in the form of a primary, secondary, cyclic secondary, or a hemiacetal to produce these products; aldehyde, ketone, and NADH. This reaction occurs during the glycolysis pathway in the mitochondria of animal cells. Cofactors include zinc or iron that act on primary and secondary alcohols or hemiacetals.

41 Enzymatic catalysis: Alcohol l dehydrogenase d Zinc functions as a Lewis acid it deprotonates the Zinc functions as a Lewis acid, it deprotonates the alcohol substrate in order to facilitate hydride transfer. The hydride is transferred through space from the OH group of the substrate to the C4 position of the nicotinamide ring.

42 Binding site of NAD Obligatory amino acid residues Ser-48 His-51 Lys-228 NAD

43 Substrate t binding site The hydrophobic pocket: Leu-57, Phe-93, Leu-116, Phe-110, Phe-140, Leu-141, Val-294, Pro-295, Ile-318. Zinc (orange), Cys-174 (purple), Cys-46 (yellow) His-67 (green) Cyclohexylformamide (blue) oxygen involved in the dehydrogenation reaction shown in white.

44 Application of Michaelis-Menten Kinetics In the presence of excess NAD+ the rate for the reaction: CH CH 2 OH + NAD CH 3 CHO+ NADH + H Can be determined as a function of ethanol. [CH 3 CH 2 OH] Rate mol/l M -1 s Bendinskas, et al. J. Chem. Ed. 82, 1068 (2005).

45 Application of Michaelis-Menten Kinetics In the presence of excess NAD+ the rate for the reaction: CH CH 2 OH + NAD CH 3 CHO+ NADH + H Can be determined as a function of ethanol. [CH 3 CH 2 OH] Rate mol/l M -1 s V max = 0.3 M -1 s -1 K 003M M =

46 A Lineweaver-Burke plot is a double reciprocal plot 1/[CH 3CH 2OH] 1/Rate mol/l M -1 s V max = 0.3 s -1 K M = 003M 0.03

47 A Lineweaver-Burke plot is a double reciprocal plot 1/[CH 3CH 2OH] 1/Rate mol/l M -1 s /V max = 3.3 Ms K M /V max = 0.09 M V max ~ 0.3 M -1 s -1 K M ~ 0.03 M

48 Serine Proteases Trypsin is one of the three principal digestive proteinases, the other two being pepsin and chymotrypsin. Trypsin and chymotrypsin are both serine proteases that t are quite similar. il They have a catalytic ti triad of Asp-His-Ser. Trypsin continues the process of digestion (begun in the stomach) in the small intestine where a slightly alkaline environment (about ph 8) promotes its maximal enzymatic activity. Trypsin hydrolyzes peptides containing arginine and lysine. Chymotrypsin yp hydrolyzes y peptides p containing tyrosine, phenylalanine, tryptophan, methionine, and leucine. Trypsin is the most discriminating of all the proteolytic enzymes in terms of the restricted number of chemical bonds that it will attack. Chemists use trypsin widely as a reagent for the orderly and unambiguous cleavage of such molecules.

49 Structural classification: serine proteases ass: All beta proteins Fold: Trypsin-like serine proteases barrel, closed; n=6, S=8; greek-key duplication: consists of two domains of the same fold Superfamily: Trypsin-like serine proteases Families: Prokaryotic proteases (9) Eukaryotic proteases (41) Viral proteases (4) beta sheet in the first domain is opened rather than forms a barrel Viral cysteine protease of trypsin fold (3)

50 Zymogens: protease precursors Most proteases are synthesized in an inactive i form. This form is known as the zymogen. A protein cleaveage step is required to active the protease. This type of control is important for the transport of enzymes es capable of protein degradation. Chymotrypsin Chymotrypsinogen with inhibitor

51 Prokaryotic structural examples Trypsin from Streptomyces griseus

52 Mechanistic overview 1. Substrate binding 2. General base catalysis by imidazole to activate the Ser-OH 3. Nucleophilic catalysis by Ser-OH to form a tetrahedral adduct 4. Stabilization of the tetrahedral transition state by hydrogen bonding to the "oxyanion hole" and by the electrostatic environment, provided in part by Asp General acid catalysis of the departure of the leaving group to form the acyl-enzyme (covalent) intermediate and departure of the P1 leaving group (amine or alcohol) 6. Reverse of the above to hydrolyze the acyl-enzyme. Beginning with the imidazole activating water by general base catalysis so as to facilitate its nucleophilic attack on the carbonyl.

53 Serine protease mechanism

54 Substrate binding to chymotrypsin

55 The oxyanion hole in serine proteases

56 The catalytic triad The key experiment that elucidates the role of aspartate in the Asp-His-Ser catalytic triad is the mutation of aspartate 102 to asparagine. Since the aspartate residue is essential there has been a great deal of interest in understanding di the charge relay hypothesis. A ti A id I id l M th l Acetic Acid Imidazole Methanol (Asp) (His) (Ser)

57 Using Density Functional Theory to model the catalytic triad The role of the aspartate can be modeled by determining the charge on oxygen and the potential energy for removal of hydrogen in from the serine oxygen by calculation. PES = Potential Energy Surface Charge on O Systematically change this Systematically change this group to H 2 O, - OH, etc.

58 Calculated potential energy surfaces for deprotonation of the serine hydroxyl

59 Modified Michaelis-Menten scheme for serine proteases The appropriate reaction scheme for a serine protease involves the release of two intermediates (i.e. the N- and C-terminus of the cleaved peptide). k 1 k 2 k 3 E + S ES EA E + P k 1 To distinguish between rates k 2 and k 3 one uses esters that form a stable 4-coordinate intermediate. For these k 3 < k 2. P 1 See Ferscht Enzyme Kinetics Chapter 5

60 Key points 1. The Arrhenius expression for the rate constant k = A e-e a/rt 2. The assumption of transition state theory TST (activated complex is in equilibrium with reactants) 3. Relationship of TST rate constant and Arrhenius rate const. 4. A catalyst lowers the barrier for a reaction. It provides an alternative reaction pathway, but does not alter the products. 5. Homogeneous vs. Heterogeneous catalysis 6. Examples: a. Zeolites: shape selective catalysis b. Ziegler-Natta: polymerization catalyst c. Alcohol dehydrogenase d. Serine protease