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Enzyme Kinetics
Enzyme Catalysis
Outline: Enzyme catalysis
- enzymes and non-bonding interactions (review)
- catalysis (review - see section 9.2 of A&D)
- general principles of catalysis
- differential binding
- types of catalysis
- approximation
- electrostatic
- covalent
- acid-base catalysis
- strain and distortion
- enzyme catalysis and energy diagrams 2
Enzymes
- proteins that play functional biological roles
- responsible for the catalysis of nearly all chemical reactions that take place in living organisms - acceleration of reactions by factors of 10^6 to 10^17
- biological catalysts that bind and catalyse the transformation of substrates
- the three-dimensional structures of many enzymes have been solved (through X-ray crystallography) 3
Reminder: Amino acid structures
- as proteins, enzymes are polymers of amino acids whose side chains interact with bound ligands (substrates) 4 R CO 2 H H 2 N H
Coenzymes
- organic molecules, very often vitamins
- e.g.: nicotinic acid gives NAD; pantothenic acid gives CoA
- intermediates in the transport of functional groups
- e.g. H (NAD), acyl (CoA), CO 2 (biotin), etc
- also known as prosthetic groups 7
Protein-ligand interactions
- covalent bonds
- ionic bonds
- ion-dipole and dipole-dipole interactions
- hydrogen bonds
- charge transfer complexes
- hydrophobic interactions
- van der Waals interactions 8
Covalent bond
- the formation of a covalent bond can represent a stabilisation of 40 to 110 kcal/mol e.g.: N R H activé O R H 2 N 9 activated
Ionic bonds
- Coulombic attraction between full positive and negative charges
- ~5 kcal/mol of stabilisation NH 2 H OH (^) O 2 C
O 2 C
O
O
δ+^ N δ− 10
Charge transfer complex
- special type of dipole-dipole interaction
- involves π electrons, often in aromatic rings (Phe, Tyr, Trp, His)
- stabilisation : < 3 kcal/mol 13
Hydrophobic interactions
- stabilisation largely due to desolvatation (entropy increase)
- stabilisation : ~0.5 kcal/mol CH 2 CH 2 H O H H O H H O H H O H H O H H surface + O (^) H hydrophobe H H^ O 6 (désolvatation) CH 2 CH 2 H O H H (^) O H H (^) O H H O H 14 hydrophobic surface (desolvation)
van der Waals interactions
- special type of dipole-dipole interaction
- movement of electrons in electron cloud of alkyl chains induces the formation of temporary dipoles
- very important over short distances
- stabilisation : ~0.5 kcal/mol (per interaction) 15
Outline: General principles of catalysis
- see section 9.1 of A&D
- principles of catalysis
- differential bonding 16
Catalysis and free energy
- catalysis accelerates a reaction by stabilising a TS relative to the ground state - free energy of activation, ΔG‡, decreases - rate constant, k , increases
- catalysis does not affect the end point of an equilibrium, but only accelerates how quickly equilibrium is attained - free energy of the reaction, ΔG°, remains unchanged - equilibrium constant, K eq, remains unchanged 19
Energy profile of catalysis
20 Free energy Reaction coordinate Δ G‡uncat Δ G‡cat A Δ Gºrxn P unchanged uncatalysed A • cat P • cat catalysed
Transition state binding
- interaction between a catalyst and reactant or activated complex can stabilise one or the other
- if the activated complex is bound more strongly than the substrate, the activation barrier will be decreased
- HOWEVER, the activated complex is not a molecule – so the catalysts must first of all interact with the substrate, and then release the product at the end of the reaction : A + cat A•cat P•cat (^) P + cat 21
Differential binding
- consider 4 scenarios : Energy Rxn. coord. Δ G‡non-cat Energy Rxn. coord. Δ G‡non-cat Energy Rxn. coord. Δ G‡non-cat Energy Rxn. coord. Δ G‡non-cat Δ G‡cat binding binding Δ G‡cat binding Δ G‡cat binding binding Δ G‡cat binding 22
Catalysis by approximation
- the catalyst brings together the reactants, increasing their effective concentrations , and orients them with respect to the reactive groups Jencks :
- the loss of entropy associated with the restriction of rotation and translation of substrate must be compensated by the intrinsic energy of binding (favourable non-bonding interactions) Bruice / Kirby :
- the magnitude of this effect is given by the effective concentration , determined by comparison if the rate constants of the bimolecular and intramolecular reactions 25
Intramolecular approximation
- an intramolecular reaction implies a smaller decrease in entropy (and therefore a decrease in the free energy of activation) Coordonnée de réaction Énergie libre ΔG réactifs A + B A B ΔG = ΔH - TΔS intermolecular intramolecular Reaction co-ordinate reactants Free energy (^) note trade-off between enthalpy (in bond formation) and entropy 26
Example of catalysis by approximation
- the catalyst brings together the reactants, increasing their effective concentrations , and orients them with respect to the reactive groups k (^1) obs k 2 obs = 5000 M = la^ concentration effective O 2 N O O CH 3
- O 2 N^ O- O CH 3 (H 3 C) 3 +N
(H 3 C) 2 NCH 3 k obs 2 = 4,3 M-1s- O 2 N O O CH 2 CH 2 (H 3 C) 2 NCH 2 O 2 N (^) O- O CH 2 (H 3 C) 2 +N
k obs 1 = 21 500 s- 27 effective concentration , or effective molarity (EM)
Example: Ester hydrolysis
Réaction Constante de vitesse relative ( k rel) Concentration effective (M) O OAr
CH 3 CO 2 - 1 M-^1 s-^1 - O OAr O- O 220 s-^1 220 M O OAr O- O 5.1 × 104 s-^1 5.1 × 104 M O OAr O- O 2.3 × 106 s-^1 2.3 × 106 M O O OAr O O-^ 1.2^ ×^107 s-^1 1.2^ ×^107 M decreasing entropy of rotation and translation parent reaction
Reaction k rel
Effective concentration (M) 28
Electrostatic catalysis
- e.g.: oxyanion hole of subtilisin: J. Mol. Biol. 1991 , 221 , 309-325. (^) 31
Electrostatic catalysis
- can be very important :
- consider the triple mutant of subtilisin where each residue of its catalytic triad is replaced (S221A-H64A-D32A) - catalyses proteolysis 10^6 -fold less than the native enzyme - BUT the reaction with the mutant is still 10^3 -fold faster than the uncatalysed reaction!! - an important part of catalysis is due to the electrostatic environment 32
Metal catalysis
- electrostatic charges developed at the TS can also be stabilised by metal ions
- coordination of a ligand by a metal (as a Lewis acid) can also lead to polarisation of a ligand - e.g. p K a of metal-bound H 2 O is 7.2, making it easier to deprotonate, therby generating – OH as a nucleophile - for example, zinc-bound water in carbonic anhydrase, a highly efficient metalloenzyme as well as certain enzyme models 33
Covalent catalysis
- catalyst forms a covalent intermediate that reacts faster than uncatalysed reaction : A + B P vs intermédiare A + B + C AC^ + B^ P + C more reactive intermediate 34
Nucleophilic catalysis
- catalyst attacks substrate to form intermediate that is even more susceptible to nucleophilic attack, by a second reactant - e.g. reaction of acid chlorides with alcohols, catalysed by addition of a tertiary amine: R Cl O (^) R'OH R O O (lente)^ R' R N O Et Et Et R'OH (rapide) NEt (^3) NEt 3 Energy Rxn. coord. Δ G‡uncat Δ G‡cat 37
Acid-base catalysis
- the catalyst (namely an acid or a base) accelerates the reaction through protonation or deprotonation 38
Specific acid-base catalysis
- catalysis by H+^ or – OH, controlled only by pH, where a fast equilibrium precedes the rls : - e.g.: 39 O O O O H O O H H^ O^ H^ O O H H^ O^ H OH O H HO
OH O
Rate laws of specific acid-base catalysis
- when a substrate must be protonated before its reaction in the rls, this appears as a pH dependence in the rate law: - e.g.: v = k [R]×[H+]/ K a,RH
- when a substrate must be deprotonated before its reaction in the rls, this appears as a pH dependence in the rate law: - e.g.: v = k [RH]× K a,RH /[H+] 40
