1 Enzymes have a high affinity for the transition state structures progress of reaction  G ‡  G transition states E+S ESEP E+P “I think that enzymes are molecules that are complementary in structure to the activated complexes of the reactions that they catalyzed, that is, the molecular configuration is intermediate between the reacting substances and the products of the reaction” Linus Pauling, 1948

2 Mechanisms for Stabilizing Transition States and Accelerating Rates

3 Bringing Two Substrates into Close Proximity at the Active Site of an Enzyme: effective concentration is increased and precise relative orientation. Rate Acceleration by Proximity

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5 Catalysis by Proximity In binding their substrate(s), enzymes freeze out the relative rotational and translational motions of the substrate(s) and reacting group(s). This can result in significant rate enhancement (up to ~ 10 7 ) There is, however, a significant entropic cost associated with this loss of translational and rotational freedom. It is paid for by the very favorable enthalpy associated with substrate binding.

6 Proximity Fix the substrate at the active site both tightly and in precisely the correct position to increase the probability of the reaction with small loss of entropy Strain The enzyme may destabilize the substrate at its active site such that it reacts faster. Induced fit A specific substrate may change the enzyme conformation to convert it to a catalytically active form. Binding interactions are used to increase the rate

7 Lysozyme Chair conformation

8 OH O O O O Glu 35 O O O O O O O O Asp 52 O O O O D-ring O O O O E-ring + C-ring Transition state H2O H HO + E-ring Chair Half-chair Mechanism of lysozyme action: substrate strain SubstrateStrained Substrate

9 OH O O O O Glu 35 O O O O O O O O Asp 52 O O O O D-ring O O O O E-ring + C-ring Transition state H2O H HO + E-ring Chair Half-chair SubstrateStrained Substrate O O C-ring Binds 3600x better Mechanism of lysozyme action: substrate strain

10 Mechanism for bringing about catalysis Functional groups of enzymes that can act as general acid or base include: -COO- of asp and glu (pKa ~ 4.5) imidazole of histidine (pKa~7) -SH of cysteine (pKa~8-9) protonated amino groups of lysine (pKa~10-11) N-terminal amino group of peptide (pKa~8) General acid-base catalysis

11 General acid-base catalysis The uncatalyzed hydrolysis of an acetal leads to a transition state in which positive and negative charges develop across the C—O bond. This charge separation is quite unfavorable and leads to a very slow rate of reaction.

12 General acid-base catalysis The general acid catalyzed hydrolysis of an acetal stabilizes the developing negative charge on the oxygen of the acetal by transferring a proton from the general acid catalyst. Partial proton transfer from a general acid catalyst lowers the free energy of activation by stabilizing the developing negative charge in the transition state.

13 General acid-base catalysis The uncatalyzed attack of water on an ester leads to a transition state in which positive charge develops on the attacking water molecule and negative charge develops on the carbonyl oxygen. These developing charges are unfavorable in the transition state.

14 General acid-base catalysis The general base catalyzed attack of water on an ester allows the developing positive charge on the water oxygen to be stabilized by the transfer of its proton to the general base catalyst. Partial proton transfer to a general base catalyst lowers the free energy of activation by stabilizing the developing positive charge in the transition state.

15 General acid-base catalysis Acid-base catalysis is termed “general” to distinguish it from specific acid-base catalysis. In specific acid-base catalysis, the catalyst is the proton or hydroxide ion itself.

16 Example: Enolase phosphoenolpyruvate2-phosphoglycerate general acid catalyst general base catalyst ene-diolate intermediate

17 Covalent catalysis - Nucleophilic catalysis Common nucleophlic groups on enzymes & example enzymes: serine hydroxylSerine proteases Cholinesterases Esterases Cysteine thiolThiol proteases G3P dehydrogenase Lysine amino groupPLP-dependent enzymes acetoacetate decarboxylase Histidine imidazolephosphoglycerate mutase succinyl-CoA synthetase

18 Chymotrypsin Tetrahedral intermediate covalent intermediate nucleophile

19 Common Characteristics all contain a catalytic triad - serine, histidine, and aspartate all share an oxyanion hole

20 This arrangement of Asp, His, and Ser residues in chymotrypsin has become known as the charge-transfer relay system or catalytic triad nucleophile

21 Michaelis ComplexTetrahedral Intermediate Enzyme binds the transition state of the reaction it catalyzes with far greater affinity than it binds either the substrates or the products.

22 Acid-base and Covalent Catalysis General acid: donates proton General base: accepts proton General base Serine forms a covalent bond with the substrate

23 General acid Covalent intermediate General base

24 General acid

25 Metal ion catalysis Two classes: metalloenzymes (Fe 2+, Fe 3+, Cu 2+, Zn 2+, Mg 2+, Mn 2+, or Co 3+ ) and metal-activated enzymes (Na +, K +, Mg 2+, or Ca 2+ ) Participate in reactions: –By binding substrates –By mediating oxidation-reduction reactions –By electrostatically stabilizing or shielding negative charges

26 Can make a reaction center more susceptible to receiving electrons because it can stabilize a developing negative charge on a transition state. (electrophilic catalyst) Metal ion catalysis

27 Can stabilize developing negative charge on a leaving group, making it a better leaving group. (electrophilic catalyst) Metal ion catalysis

28 Metal ion catalysis Can increase the rate of a hydrolysis reaction by forming a complex with water, thereby increasing water’s acidity.

29 Example:  -lactamase (B. cereus)

30 Enzymes decrease the activation energy in many ways: Entropy effect Substrate strain Acid-base catalysis Covalent catalysis

31 Enzyme Kinetics Kinetics is the study of the rates of chemical reactions. Unlike Thermodynamics which tells us if a reaction can occur, kinetics provides information on the rate and mechanism of the reaction. Enzyme kinetics deals with the factors that affect the rate of enzyme-catalyzed reactions. Factors: temperature, substrate concentration, inhibitor concentration, pH, ionic strength, enzyme concentration.

32 Why do we study enzyme kinetics? Kie enzyme’s substrate preference and cofactor requirements identify potent inhibitors of potential therapeutic value. enzyme inhibition can provide insight into the mechanism of catalysis or the order of ligand binding. Advanced kinetic techniques identify an enzyme’s catalytic mechanism or to assist in the identification of key catalytic residues.

33 Chemical Kinetics The rate of a reaction is proportional to the frequency with which the reacting molecules simultaneously come together.

34 General Chemical Reactions Enzyme generally catalyze 1 st and 2 nd order reactions. 3 rd order reactions are quite rare and 4 th and higher order reactions are not observed.

35 Kinetics of a 1 st Order Reaction Lets examine a simple 1 st order reaction. Radioactive decay is a typical example of a 1 st order reaction Rate = v = d[P]/dt = -d[A]/dt v = d[P]/dt = -d[A]/dt = k 1. [A] -d[A]/dt = k 1. [A]

36 Kinetics of a 1 st Order Reaction ln[A] - ln[A o ] = -k 1 t ln[A]/[A o ] = -k 1 t 1st order kinetics are characterized by a half-lifeln(0.5) = 0.69 = -kt 1/2 A 1st order rate constant has units of 1/time e.g sec -1

37 Second Order Reaction Kinetics V = -d[A]/dt = k 1 [A] 2 1/[A] – 1/[A o ] = k 1 tor1/[A] = 1/[ A o ] + k 1 t The second order rate constant has units of 1/molar concentration and 1/time; e.g. M -1 s -1. Plot of 1/[A] vs. time yields a line with slope k 1. Evaluation of enzyme kinetic data requires an understanding of these two simple reaction rate equations.

38 A + BP E + A + B E.A.BE.P E + P Enzyme-substrate complex

39 Enzyme Kinetics A minimal mechanism for an enzyme-catalyzed reaction Where: E is enzyme, S is substrate, P is product, ES is enzyme- substrate complex and EP is enzyme-product complex. This pathway can be simplified only the initial stage of the reaction is considered (little product formed).

40 Enzyme Kinetics A minimal mechanism for an enzyme-catalyzed reaction The rate constant k 1 is for the formation of ES (the enzyme substrate complex) k -1 is the rate constant for dissociation of ES and k 2 is the rate constant for product formation.

41 Michaelis-Menten Enzyme Kinetics with Briggs-Haldane refinement Assumption 1: The Steady state assumption. The concentration of ES remains constant throughout the reaction. Assumption 2: Rate of product formation is proportional to [ES]: v = k 2 [ES] (i.e. k 2 is rate limiting)

42 Michaelis-Menten Enzyme Kinetics with Briggs-Haldane refinement d[ES]/dt = k 1 [E][S] – k -1 [ES] – k 2 [ES] = 0; at steady state Rearranging yields: [E][S]/[ES] = (k -1 + k 2 )/k 1 Lets define: K M = (k -1 + k 2 )/k 1 (the Michaelis Constant) K M = [E][S]/[ES]or[ES] = [E][S]/ K M eq.1 [E] T = [E] + [ES]or[E] = [E] T – [ES]eq.2 Substituting into eq. 1 yields[ES] = ([E] T – [ES])[S]/ K M

43 Michaelis-Menten Enzyme Kinetics with Briggs-Haldane refinement Rearranging [ES] K M = ([E] T – [ES])[S]yields Solving for [ES] [ES] K M + [ES][S] = [E] T [S] [ES] = [E] T [S]/ (K M + [S]) Remembering that v = k 2 [ES] yields:

44 Michaelis-Menten Enzyme Kinetics with Briggs-Haldane refinement The maximum possible rate of the reaction is: V max = k 2 [E] T ; Substituting this in gives: Michaelis-Menton Equation

45 Michaelis-Menten Kinetics K m is the substrate concentration at which the rate of the reaction is half the maximum rate (V max )

46 Lineweaver-Burke Plot A method for linearizing the hyperbolic [S] vs. velocity plot and help derive K m and V max Slope = K m /[S

47 The meaning of K m Substitution of =V max /2 into the Briggs-Haldane equation shows that: The value of K m does NOT necessarily give a measure of the affinity of the enzyme for the substrate. When k 2 is small relative to k -1, K m approximates to the dissociation constant of the ES complex, K S. Since K S is a true dissociation constant, only K S gives a true measure of the enzyme-substrate binding affinity.  K m ≥ K S

48 k cat (s -1 ) is the catalytic constant, also called the “turnover number”. It is a pseudo-first order rate constant and is independent of the total enzyme concentration. The meaning of V max, k cat, and Specific Activity V max (Ms -1 ) is the maximal velocity of an enzyme-catalyzed reaction. The maximal velocity is reached when the substrate is saturating. V max is dependent on [E] t. (k cat [E] t ) = V max Specific Activity (U/mg total protein) is often used to characterize enzyme activity when the enzyme solution is impure. It is, most always, a quick but less accurate means of kinetically characterizing an enzyme. 1 International Unit (1 U) is the amount of enzyme which catalyzes the formation of 1  mole of product per minute under defined conditions. i.e. 1 U = 1  mole/min

49 The kinetic significance of k cat k cat, a pseudo-first order rate constant, includes the individual rate constants for all steps leading from the ES complex to product release. For example, in a more complex kinetic scheme such as: k1k1 k -1 k2k2 k -2 k3k3 E + SESEPE + P k cat It can be shown that k cat is comprised of all the individual rate constants between ES and E + P (k 2, k -2 and k 3 ): (If you’re feeling particularly ambitious or if you have some trust issues, feel free to derive the initial velocity expression for the above scheme using the steady state approximation. It gets a little messy but it’s done exactly as shown earlier for the simple scheme) k cat = k2 k3k2 k3 (k 2 + k -2 + k 3 ) ESE + P

50 The kinetic significance of k cat /K m k cat /K m (catalytic efficiency) is a second-order rate constant that describes the conversion of free E and free S into E + P. The rate at low [S] is directly proportional to the rate of enzyme-substrate encounter. When the substrate concentration is very low ([S] << K m ): v i = (V max /K m )[S] Recall that V max = k cat [E] t So, v i = (k cat /K m )[S][E] t Also, when [S] is very low, very little of the total enzyme species will be tied up in the ES complex (or any other intermediate complex). [E] t = [E] + [ES] But at low substrate concentrations, [E] t ≈ [E] (because [ES] ≈ 0) thus, v i = (k cat /K m )[S][E] when [S] << K m

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