Kinetics - NC State: WWW4 Serverfranzen/public_html/CH433/lecture/Enzymes_Catalysi… · Ziegler-Natta catalyst for politi fthllymerization of ethylene Ziegler-Natta catalysts are

KineticsKineticsCatalysisyEnzymes

Catalysis involves lowering of the energy barrierthe energy barrier

ΔH‡

ΔH‡

A catalyst provides an alternative reaction pathwayA catalyst provides an alternative reaction pathwaywith a lower activation energy or activation enthalpy.

Types of catalysis yp y

Homogeneous catalysis - the catalyst is in the sameHomogeneous catalysis - the catalyst is in the samephase as the reactants.Example: acid or base catalysisp y

Heterogeneous catalysis - the catalyst is in adifferent phase from the reactants.Example: metal complexes, surfaces, zeolites

Enzymatic catalysis - the catalyst is a protein thathas a substrate binding site and controlled reactionhas a substrate binding site and controlled reactionpath

Zeolites:i t t l f t l tan important class of catalysts

Database of zeolite structures:http://www.iza-structure.org/databases/

Example: search for ZSM-5

Unit cell parameters:a = 20.090Å b = 19.738Å c = 13.142 Å alpha 90 0° beta 90 0° gamma 90 0°alpha = 90.0° beta = 90.0° gamma = 90.0°volume = 5211.28 Å3

Basis for heterogeneous t l i i litcatalysis in zeolites

Zeolites are crystalline solids made up of SiO4 building blocks. These tetrahedral units join together to form several different i d t t Th h t i ti th t tring and cage structures. The characteristic that separates

zeolites from all-silica minerals is the substitution of aluminum into the crystalline framework. The substitution of aluminumygenerates a charge imbalance, which is compensated by aproton. The acid site formed behaves as a classic Brønstedacid or proton donating acid site The highly acidic sitesacid 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 i d t i l t l tindustrial catalyst.

Z lit h l ti t l iZeolites: 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. Classical industrial processesClassical industrial processes are based on "olid phosphoric acid" catalysts, with problems of handling safety corrosionof handling, safety, corrosion and waste disposal. These can be avoided by using zeolite catalysts.


The medium poresize zeolite ERB 1size zeolite ERB-1has greater reactivity forreactivity for cumene formation than larger pore size catalysts.


Calculated energyf fsurface for

cumene in BEA.

Diffusion of cumene in zeoliteBEA.

Ziegler-Natta catalyst for l i ti f th lpolymerization 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 ofcontaining 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 polymerizationby 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 baseddeveloped further variations of the Ziegler catalyst based on his findings on the mechanism of the polymerization reaction.


TiCl3 can arrange itself into a number of crystal structures. The one that we're interested in is called α-TiCl3. It looks something like this:

TiCl Cl

Cl

TiCl Cl

Cl

TiCl

Cl

Cl ClCl

ClTi

Cl

ClTi

Cl

Cl

Cl Cl ClCl

ClTi

Cl

ClCl ClCl

ClTi

ClCl

ClTi

ClCl

ClClTi

ClCl

As we can see, each titanium atom is coordinated to six chlorine atoms, with octahedral geometry.


At the surface of the crystal a titanium atom is surrounded on one side by five chlorine atoms, but on th th id b t Thi l tit ithe other side by empty space. This leaves titanium a chlorine short. Titanium, as one of the transition metals, has six empty orbitals (resulting

Clp y ( g

from one 4s and five 3d-orbitals) in the outermost electron shells. The surface Ti atom has an Cl

TiCl

Cl

Cl

The surface Ti atom has an empty orbital, shown as an empty square in the picture.

Cl ClCl

ClTi

Cl

ClCl ClCl


Titanium wants to fill its orbitals. But first, Al(C2H5)2Cl enters the picture It donates one of its ethyl groups toenters 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.

CH3Al

Cl

H CH C

Cl

ClTi

ClAl

Cl

CH2CH3H3CH2C

+ Cl

ClTi

C

CH3AlH3CH2C

CCl

3C 2ClCl


The the aluminum is coordinated, though not covalently bonded, to the CH2 carbon atom of the ethyl group it just donated to the titanium and to one of the chlorinejust donated to the titanium and to one of the chlorine atoms adjacent to the titanium.

Cl There is still a

CHCH3Al

Cl

H3CH2C

There is still a vacant site where polymerizationCl

ClTi

Cl

CH2 polymerizationcan occur.

Cl ClCl


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 commonlythat make up the complex), so we have what is commonly termed a heterogeneous catalyst (also known as a solid solution).

Cl H

CHCH3Al

Cl

H3CH2C CCH3H

Cl

ClTi

Cl

CHC

HHCl ClCl


Upon binding ethylene forms bonds with the Ti atom and the carbon of the ethylene ligand.and the carbon of the ethylene ligand.

Cl H

CCH3Al

Cl

H3CH2C CCH3H

Cl

ClTi

Cl

CH2 C

HHCl ClCl


CH3

The growing polymer chainis initiated.

H2CCH3

Cl HAl

Cl

H3CH2C CCH3H

Cl

ClTi

Cl

CHHCl Cl

Cl


H2CCH3The vacant site is

available for thet th l

Cl CCH3H

next ethylenemolecule tobind.

Al

Cl

H3CH2C C

Cl

ClTi

Cl

HH

Cl ClCl

Enzymatic CatalysisEnzymatic Catalysis

Michaelis-Menton KineticsAlcohol Dehydrogenasey g

Serine Proteases

Mi h li M t ki tiMichaelis-Menton kineticsThe rate of an enzyme catalyzed reaction in whichThe rate of an enzyme catalyzed reaction in whichsubstrate S is converted into products P depends on the concentration of the enzyme E even though thethe concentration of the enzyme E even though theenzyme does not undergo any net change.

ka k b

E + S ↔ ES → P + EE + S ↔ ES → P + Ek ′k a

Michaelis-Menton rate tiequations

ka k bka k b

E + S ↔ ES → P + Ek a′

d[S ]dt = – k a[E][S ] + k a′[ES ]

d[ES ]dt = k a[E][S ] – k a′[ES ] – k b[ES ]

d[P]d[P]dt = k b[ES ]

Steps in the Michaelis-Menton mechanism

Step 1. Bimolecular formation of the enzyme E andand substrate S:E S ES t f f ti f ES k [E][S]E + S ES rate of formation of ES = ka[E][S]

Step 2. Unimolecular decomposition of the complex:ES E + S rate of decomposition of ES = -k [ES]ES E + S rate of decomposition of ES = ka’ [ES]Step 3. Formation of products and release from the enzyme:yES P + E rate of formation of P = kb[ES]

h l f h f f hThe rate law of interest is the formation of the product in terms of E and S.

The enzyme substrate complexb li i t dcan be eliminated

The enzyme substrate complex is formed transiently and can be approximated using thetransiently and can be approximated using the steady state approximation.

d [ES ]d[ES ]dt = k a[E][S ] – k a′[ES ] – k b[ES ] ≈ 0

The result of this approximation is

[ES ] k a[E][S ][ES ] = a[ ][ ]k a′ + k b

Pseudo-first order Michaelis-Menton kinetics

In an experiment we know the total enzyme concentration [E]0 and not the unbound enzyme [E].[ ] y [ ]The total concentration of enzyme [E]0 = [E] + [ES].

k [E] [ES ] [S ]

which rearranges to

[ES ] =k a [E]0 – [ES ] [S ]

k a′ + k bwhich rearranges to

[ES ] = k a[E]0[S ][ES ]k a′ + k b + k a[S ]

Mi h li M t tMichaelis-Menton parameters

The rate of formation of product can be written

d[P]dt =k b[E]0 where k = k b[S ]

K M + [S ]where KM is the Michaelis constant and kb is themaximum turnover number. The Michaelis

M [ ]

constant is:

K = k a′ + k bK m =k a

Limiting conditions of ti itenzyme reactivity

• Maximal rateMaximal rate: If there is excess substrate present the rate is limited by the rate at which the ES complex f ll t Th t f f ti f d t ifalls apart. The rate of formation of products is a maximum and Vmax = kb[E]0 is called the maximum velocity.

• Second order regimeSecond order regime: If [S] << KM then the rate of formation of products is d[P]/dt = kb/KM [E]o[S]. The rate dependson [S] as well as [E]on [S] as well as [E]o.

• A plot of 1/k yields kb and KM but not the rate constantsk d k ’ Th l tt t t t b bt i dka and ka’. The latter rate constants can be obtained from stopped-flow experiments.

C t l ti t t t kCatalytic rate constant kcat

• Catalytic rateCatalytic rate: The rate constant kb is also called the catalyticrate constant or kcat. Since this is an intrinsic rate constant,it i t b bl H it b l l t d fit is not an observable. However, it can be calculated fromobservables kcat = Vmax/[E]0.

• Turnover numberTurnover number: When the enzyme is saturated, i.e.when [S] >> KM, then kcat is also called the turnover number.

Integrated form of the Michaelis-Menten equation

KMln [S][S]0

+ [S] – [S]0 = – Vmaxt

or

KMln [S]0

[S] + [S]0 – [S]t =

M [S] [ ]0 [ ]

Vmax

K ln 2 + [S]0

τ1/2 =KMln 2 + [ ]0

2Vmax

The half-time τ1/2 is the time at which half of the original substrate is consumed.

General expression for reaction velocity

Based on the previous analysis the velocity at anarbitrary substrate concentration is:

[S ]vv = [S ]vmax

K M + [S ]

Li B k Pl tLineweaver-Burke Plots

• The Michaelis-Menton expression is non-linear.• The Lineweaver-Burke plot is linearized plot of data.

1v =

K M + [S ][S ]v

= 1v

+ K M

v1

[S ]

• This expression has the form of an equation for a line:

v [S ]vmax vmax vmax [S ]

• This expression has the form of an equation for a line:y = intercept + slope x

• Such plots are not necessary today with common non-linearfitting programs.

Lineweaver-Burke Plots

vmax 1 + K Mmax

v = 1 + M

[S ]

Transition State StabilizationTransition State Stabilization

Th i i l id f th h i iThe original idea of the enzyme having maximum complementarity to the TS was put forward by Linus Pauling in 1946. It wasn't until the early 70's gthat the idea was put on a more solid grounding. As put forward by Lienhard and Wolfenden the idea is as follows:is as follows:

Kn‡ kn

E + S E + S‡ E + P

Ks KtKc

‡ kcc cES ES‡ E + P

b lTransition State Stabilization Defining the equilibrium constants as association constants:Defining the equilibrium constants as association constants:Kn

‡ = [S‡]/[S] , Kt = [ES‡]/[E][S‡]from TS theory: ΔG‡ = -RT ln K‡ and kobs = (kBT/h)e-ΔG‡/RTTh k (k T/h)K ‡ d k (k T/h)K ‡Thus, kn = (kBT/h)Kn‡ and kc = (kBT/h)Kc‡where c means catalyzed and n means uncatalyzed.

From the scheme you can see that Ks Kc‡ = Kn‡ Kthence Kt/Ks = Kc‡/Kn‡ however, kc/kn = Kc‡/Kn‡Therefore the observed rate enhancementTherefore the observed rate enhancementkc/kn = Kt/Ks >> 1Therefore the transition state geometry S‡ must bind

ti htl th th b t t S i it ilib i t !more tightly than the substrate S in its equilibrium geometry!

T iti St t A lTransition State AnalogsThe transition state stabilization hypothesis was tested by yp ydesigning so-called transition state analogs, molecules which mimick the real TS as closely as possible. One of the first enzymes examined was proline racemase:first enzymes examined was proline racemase:

COO- H

N COO-

H

N

H

N

H

HCOO

COO-H

The compound on the right is a planar TS state analog. This molecule was found to be a good inhibitor with Ki some

HHH

This molecule was found to be a good inhibitor, with Ki some two orders of magnitude smaller than Km.

Th R l f E tThe 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 come from the intrinsic u gy ou d o obinding energy. The entropy loss arises from the loss of translational and rotational degrees of freedom when the substrate is bound The configurational entropy is:substrate is bound. The configurational entropy is: S = kB lnWwhere W is the number of degrees of freedom available toa molecule.

InhibitionInhibitionAn inhibitor is any compound that causes a decrease in thecatalytic rate. We will consider non-covalent ligands thatcan bind to the enzyme. The general scheme is shown below:

S kc I = inhibitorc b oE ES E + P Inhibition occurs if

ki[EIS] < kc[ES]I II I

S kiEI EIS EI + P

C titi I hibitiCompetitive Inhibition

Competitive inhibition results from the direct competition between the I and S for the substrate binding site. Thereis an additional equilibrium constant:

EI E + I K = [E][I ]

The velocity under these conditions turns out to be:

EI E + I K I =[EI ]

The velocity under these conditions turns out to be:

v = [S ]vmax α = 1 + [I ]vαK M + [S ] α = 1 + K I

Non-competitive InhibitionNon competitive InhibitionNon-competitive inhibition arises when I can bind at site th t i t th th b t t bi di it Ththat is not the same as the substrate binding site. Thereis an additional equilibrium constant:

[E][I ]

Here the complex IE indicates that the inhibitor does not

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:

[S ]v = [S ]vmax

α K M + [S ] α = 1 + [I ]K IM [ ] I

Distinguishing competitive and non-competitive inhibition

The tradition method is to use Lineweaver-Burke analysis.On a L-B plot competitive inhibition will give rise tolines of varying slope, but with the same intercept. On theother hand, non-competitive inhibition will give rise to lines with different intercepts.d pNon-competitive:

1 =α K M + [S ]

= αK M + α

Competitive:

1v =

[S ]vmax

= M

[S ]vmax

+ αvmax

1 αK + [S ] αK 11v = αK M + [S ]

[S ]vmax

= αK M

[S ]vmax

+ 1vmax

Plots of competitive and non-titi i hibiticompetitive inhibition

vmax

v = α 1 + K M

[S ]vmax

v = 1 +αK M

[S ]

Non-competitive Competitive

Enzymatic catalysis:Al h l d h dAlcohol dehydrogenase

The enzyme alcohol dehydrogenase (EC 1 1 1 1 ) isThe enzyme alcohol dehydrogenase (EC. 1.1.1.1.) 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,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 theoccurs during the glycolysis pathway in the mitochondria of animal cells. Cofactors include zinc or iron that act on primary and secondary alcohols or hemiacetals.

Enzymatic catalysis:Al h l d h dAlcohol dehydrogenase

Zinc functions as a Lewis acid it deprotonates theZinc 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.

Binding site of NADObli t i id idObligatory amino acid residues

Ser-48His-51Lys-228NAD

S b t t bi di itSubstrate binding site

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

Application of Michaelis-Menten Kinetics

In the presence of excess NAD+ the rate for the reaction:

CH CH OH + NAD+ → CH CHO+ NADH + H+

Can be determined as a function of ethanol. [CH CH OH] Rate

CH3CH2OH + NAD → CH3CHO+ NADH + H

[CH3CH2OH] Ratemol/L M-1s-1

0.007 0.060 015 0 110.015 0.110.031 0.160.068 0.210.1 0.230.2 0.280 3 0 290.3 0.290.4 0.28

Bendinskas, et al. J. Chem. Ed. 82, 1068 (2005).

Application of Michaelis-Menten Kinetics

In the presence of excess NAD+ the rate for the reaction:

CH CH OH + NAD+ → CH CHO+ NADH + H+

Can be determined as a function of ethanol. [CH CH OH] Rate

CH3CH2OH + NAD → CH3CHO+ NADH + H

[CH3CH2OH] Ratemol/L M-1s-1

0.007 0.060 015 0 110.015 0.110.031 0.160.068 0.21 Vmax = 0.3 M-1 s-1

K 0 03 M0.1 0.230.2 0.280 3 0 29

KM = 0.03 M

0.3 0.290.4 0.28

A Lineweaver-Burke plot is a double reciprocal plotdouble reciprocal plot

1/[CH3CH2OH] 1/Rate3 2mol/L M-1s-1

142.8 16.6766 7 9 1066.7 9.1032.3 6.2514.7 4.7710 0 4 3510.0 4.355.0 3.573.3 3.45 Vmax = 0.3 s-1

K 0 03 M2.5 3.57 KM = 0.03 M

A Lineweaver-Burke plot is a double reciprocal plotdouble reciprocal plot

1/[CH3CH2OH] 1/Rate3 2mol/L M-1s-1

142.8 16.6766 7 9 10

1/Vmax = 3.3 MsKM/Vmax = 0.09 M66.7 9.10

32.3 6.2514.7 4.7710 0 4 3510.0 4.355.0 3.573.3 3.45

Vmax ~ 0.3 M-1 s-1

KM ~ 0.03 M

2.5 3.57

Serine ProteasesTrypsin is one of the three principal digestive proteinases, the other two being pepsin and chymotrypsin. Trypsin and chymotrypsin are both

i t th t it i il Th h t l ti t i d fserine proteases that are quite similar. They have a catalytic 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 activitypromotes its maximal enzymatic activity.

Trypsin hydrolyzes peptides containing arginine and lysine.Chymotrypsin hydrolyzes peptides containing tyrosine, y yp y y p p g y ,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.

Structural classification:i tserine proteases

Class: All beta proteinsClass: All beta proteins Fold: Trypsin-like serine proteases

barrel, closed; n=6, S=8; greek-key duplication: consists of two domains of the same foldduplication: consists of two domains of the same fold

Superfamily: Trypsin-like serine proteases

Families:Prokaryotic proteases (9) Eukaryotic proteases (41)Eukaryotic proteases (41) Viral proteases (4)

beta sheet in the first domain is opened rather than forms a barrelopened rather than forms a barrel

Viral cysteine protease of trypsin fold (3)

Zymogens: protease precursorsM h i d i i i fMost proteases are synthesized in an inactive form. This form is known as the zymogen. A protein cleaveage step is required to active the proteasecleaveage step is required to active the protease. This type of control is important for the transport of enzymes capable of protein degradation.e y es capab e o p ote deg adat o

Chymotrypsin Chymotrypsinogen with inhibitor

Prokaryotic structural examplesTrypsin from Streptomyces griseus

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-102

5. 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)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 tothe imidazole activating water by general base catalysis so as to facilitate its nucleophilic attack on the carbonyl.

Serine protease mechanism

Substrate binding to chymotrypsin

The oxyanion hole i i tin serine proteases

The catalytic triadThe key experiment that elucidates the role of aspartate in the Asp-His-Ser catalytic triad is the p p ymutation of aspartate 102 to asparagine. Since the aspartate residue is essential there has been a

d l f i i d di h hgreat deal of interest in understanding the charge relay hypothesis.

A ti A id I id l M th lAcetic Acid Imidazole Methanol(Asp) (His) (Ser)

Using Density Functional Theory to model the catalytic triad

The role of the aspartate can be modeled by determiningthe charge on oxygen and the potential energy for removal of hydrogen in from the serine oxygen by calculationof hydrogen in from the serine oxygen by calculation.

PES = Potential Energy Surface

Charge on Og

Systematically change thisSystematically change thisgroup to H2O, -OH, etc.

Calculated potential energy surfacesfor deprotonation of the serine hydroxylfor deprotonation of the serine hydroxyl

Modified Michaelis-Menten scheme for serine proteases

The appropriate reaction scheme for a serine proteaseThe 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↓

To distinguish between rates k and k one uses esters

k –1 ↓P1

To distinguish between rates k2 and k3 one uses estersthat form a stable 4-coordinate intermediate. For thesek3 < k2.

See Ferscht “Enzyme Kinetics” Chapter 5

Key pointsKey points1. The Arrhenius expression for the rate constant k Ae E /RTk = Ae-Ea/RT

2. The assumption of transition state theory TST(activated complex is in equilibrium with reactants)( p q )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 productsalternative reaction pathway, but does not alter the products.5. Homogeneous vs. Heterogeneous catalysis6. Examples:

Z lit h l ti t l ia. Zeolites: shape selective catalysisb. Ziegler-Natta: polymerization catalystc. Alcohol dehydrogenasey gd. Serine protease

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Kinetics - NC State: WWW4 Serverfranzen/public_html/CH433/lecture/Enzymes_Catalysi… · Ziegler-Natta catalyst for politi fthllymerization of ethylene Ziegler-Natta catalysts are