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Mecanismos de Bioquímica · Enzymes

Catálise enzimática e cinética

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O que você vai aprender

  • Explain how general acid–base, covalent and metal-ion catalysis lower the activation barrier without changing the equilibrium constant.
  • Draw the arrow-pushing mechanisms of serine, cysteine and aspartic proteases, lysozyme, ribonuclease A and carbonic anhydrase with the correct proton donors and acceptors.
  • Calculate rates, kcat, kcat/Km and apparent Km values from the Michaelis–Menten equation and inhibition data.
  • Classify reversible inhibitors as competitive, uncompetitive or noncompetitive from kinetic data and distinguish them from irreversible inactivators.

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Enzymes lower the barrier, not the equilibrium

An enzyme binds the transition state more tightly than the substrate, so ΔG‡ falls while ΔG° and the equilibrium constant stay the same; the forward and reverse reactions speed up by the same factor. At 25 °C every 5.7 kJ/mol of ΔG‡ removed (2.303RT) makes the reaction ten times faster. Stable molecules that copy the geometry of the transition state are transition-state analogues and bind very tightly. Aspartic proteases add water to a peptide C=O through a tetrahedral gem-diol; replacing the scissile C(=O)–NH by CH(OH)–CH₂ keeps a tetrahedral carbinol carbon in that position but leaves no bond to cut. A carbinol carbon in place of the gem-diol carbon is the design behind pepstatin (its statine unit) and many HIV-1 protease inhibitors (drawn: the gem-diol from N-methylacetamide and its CH(OH)–CH₂ mimic). Binding also holds reacting groups close together and correctly aligned. The effective molarity of a neighbouring group, k_intra/k_inter, can be hundreds of mol/L, far more than any reachable concentration.

General acid and general base catalysis

A general base removes a proton in the same step as a nucleophile attacks; a general acid gives a proton to a leaving group as it departs. Histidine is the most common choice because its imidazole side chain has a pKa near 6–7, so at pH 7 both the neutral imidazole (base) and the imidazolium ion (acid) are present. Carboxylates of Asp and Glu (pKa about 4) usually act as bases, or as acids when a nonpolar pocket raises their pKa. A pH–rate profile shows which states are needed: a limb that rises with pH reports a group that must be deprotonated, a limb that falls reports a group that must stay protonated, and a bell shape means both are required.

Covalent catalysis: serine and cysteine proteases

In chymotrypsin the Asp102–His57–Ser195 triad turns Ser195 into a strong nucleophile: His57 takes the hydroxyl proton as the oxygen attacks the peptide carbonyl. The tetrahedral oxyanion is held by two backbone N–H groups, the oxyanion hole. His57, now protonated, gives its proton to the leaving nitrogen, so a neutral amine, not Ser195, leaves and an acyl-enzyme ester forms. Water then attacks the ester with His57 as the base, and the enzyme is regenerated. Acyl donors with better leaving groups react faster (amide < alkyl ester < aryl ester < anhydride): with p-nitrophenyl acetate, acylation is fast and deacylation slow, so one yellow p-nitrophenolate per active site appears in a burst before the slow steady state, and the burst size counts active sites. Cysteine proteases such as papain use a Cys25 thiolate–His159 imidazolium ion pair and form a thioester acyl-enzyme instead. The S1 pocket sets specificity: chymotrypsin cleaves after Phe, Tyr and Trp, trypsin after Lys and Arg (Asp189 at the bottom of the pocket), elastase after small residues.

Two carboxyl groups: aspartic proteases and lysozyme

Aspartic proteases (pepsin, HIV-1 protease) make no covalent intermediate. One aspartate deprotonates a water molecule as it attacks the carbonyl, while the other aspartic acid protonates the carbonyl oxygen, giving a neutral gem-diol; the roles then swap to expel the amine. Lysozyme cuts a β-glycosidic bond with Glu35 (protonated, in a nonpolar pocket) as the general acid and Asp52 (ionized) as the nucleophile that forms a covalent glycosyl-enzyme. Water, deprotonated by Glu35, then displaces Asp52. Two inversions give overall retention of the β configuration.

Ribonuclease A and carbonic anhydrase

Ribonuclease A uses two histidines. His12, as a base, deprotonates the 2′-OH, which attacks phosphorus; His119, as an acid, protonates the 5′-oxygen of the leaving nucleotide. The product is a 2′,3′-cyclic phosphate, a five-membered ring, which the same two histidines then hydrolyse with their roles reversed. DNA has no 2′-OH and is not cleaved. Carbonic anhydrase binds Zn²⁺ to three histidines and one water. The metal lowers the pKa of the bound water to about 7, so a zinc-bound hydroxide attacks CO₂ at neutral pH; water displaces the bicarbonate, and His64 shuttles a proton away to regenerate Zn–OH.

Michaelis–Menten kinetics

For E + S ⇌ ES → E + P, the initial rate is v = Vmax[S]/(Km + [S]). Km is the substrate concentration that gives half of Vmax; it equals (k−1 + k2)/k1, so it matches the dissociation constant k−1/k1 only when k2 is much smaller than k−1. kcat = Vmax/[E]T is the turnover number, and kcat/Km, the specificity constant, compares substrates competing for the same enzyme; its upper limit is diffusion, about 10⁸–10⁹ M⁻¹ s⁻¹.

Inhibition

A competitive inhibitor binds the free enzyme at the active site: Vmax is unchanged and the apparent Km rises to Km(1 + [I]/Ki), so high substrate overcomes it. An uncompetitive inhibitor binds only ES and lowers Vmax and Km by the same factor, giving parallel Lineweaver–Burk lines. A pure noncompetitive inhibitor binds E and ES equally, lowering Vmax with Km unchanged; mixed inhibitors change both. Irreversible inactivators, such as the laboratory reagent PMSF (phenylmethylsulfonyl fluoride) on the active-site serine, remove active enzyme covalently and are not described by Ki. The molecules they leave unmodified are normal, so irreversible inactivation also lowers Vmax without changing Km. Test reversibility directly: reversible inhibition usually takes effect at once and disappears on large dilution or dialysis, while irreversible inactivation grows with preincubation time and survives both. Class-specific reagents also identify a protease: PMSF for serine, iodoacetamide for cysteine, pepstatin for aspartic, and metal chelators such as EDTA for metalloproteases.

How the drawings model an active site

The mechanisms draw only the reacting part of each residue: methanol for the Ser side chain, methanethiolate for Cys, imidazole for His, acetate or acetic acid for Asp and Glu, and a bare zinc ion for the Zn(His)₃ centre. Short substrates such as N-methylacetamide stand in for a peptide. The electron flow is the same as in the enzyme; binding, the oxyanion hole and the surrounding protein are described in words.

What to carry forward

Enzymes speed reactions by binding the transition state and by placing acids, bases, nucleophiles and metal ions exactly where the electrons need them. Follow every proton: the residue that removes a proton in one step usually gives it back in the next, so the catalyst ends unchanged. Kinetics then measure how well this works: kcat for turnover, Km for substrate concentration at half-saturation, kcat/Km for specificity, and the change in Vmax or Km for the type of inhibition.

Problemas de prática (40)

Praticar é grátis com uma conta.

Desenhe o mecanismo 15

Serine and cysteine proteases

  • Acetylcholinesterase acetylates its active-site serineDraw how the catalytic serine of acetylcholinesterase is acetylated by acetylcholine, with histidine as general base and then general acid so that neutral choline leaves.
  • Chymotrypsin and p-nitrophenyl acetate: the burstDraw the fast acylation of Ser195 by p-nitrophenyl acetate and the resonance that makes the released p-nitrophenolate a good leaving group and a yellow chromophore.
  • Papain acylation: a thiolate forms a thioester acyl-enzymeDraw how the Cys25 thiolate of a cysteine protease attacks a peptide carbonyl and how His159 protonates the leaving amine to form the thioester acyl-enzyme.
  • Papain deacylation regenerates the thiolate–imidazolium pairDraw how water, activated by His159, hydrolyses the thioester acyl-enzyme of a cysteine protease and restores the Cys25 thiolate.
  • Iodoacetamide alkylates the active-site cysteineDraw the SN2 alkylation of the active-site cysteine thiolate of papain by iodoacetamide.
  • Chymotrypsin acylation: the catalytic triad forms the acyl-enzymeDraw how His57 activates Ser195 to attack the peptide carbonyl, how the tetrahedral oxyanion collapses, and how His57 protonates the leaving amine to give the acyl-enzyme.
  • Chymotrypsin deacylation: water hydrolyses the acyl-enzymeDraw how His57 activates water to attack the acyl-enzyme ester and then protonates Ser195 as it leaves, regenerating the free enzyme.
  • Trypsin acylation: His57 makes the amine the leaving groupDraw how trypsin's Ser195 adds to a lysine amide and how His57, now acting as a general acid, makes the tetrahedral intermediate expel the amine rather than Ser195.

Acid–base and metal-ion catalysis

  • Aspartic protease: the gem-diol breaks downDraw how the two aspartates swap roles to collapse the gem-diol intermediate into a carboxylic acid and an amine, restoring the starting enzyme.
  • Aspartic protease: two aspartates add water to the peptide bondDraw how an aspartate general base and an aspartic acid general acid act together to add water to a peptide carbonyl, forming the neutral gem-diol intermediate.
  • Carbonic anhydrase: zinc hydroxide hydrates CO₂Draw how zinc-bound hydroxide adds to CO₂, how water displaces the bicarbonate from zinc, and how His64 regenerates the zinc hydroxide.
  • Lysozyme: Asp52 forms the glycosyl-enzymeDraw how Glu35 protonates the leaving sugar oxygen while Asp52 displaces it at the anomeric carbon to form the covalent glycosyl-enzyme.
  • Lysozyme: water releases the sugar with retentionDraw how Glu35 activates water to attack the anomeric carbon of the glycosyl-enzyme, releasing the sugar hemiacetal and regenerating Asp52.
  • Ribonuclease A: hydrolysis of the 2′,3′-cyclic phosphateDraw how His119 and His12 swap roles to hydrolyse the 2′,3′-cyclic phosphate to the 3′-phosphate, regenerating the enzyme.
  • Ribonuclease A: the 2′-OH forms a 2′,3′-cyclic phosphateDraw how His12 and His119 act as general base and general acid while the 2′-OH of RNA attacks phosphorus to give a 2′,3′-cyclic phosphate.

Preveja o produto 3

Michaelis–Menten kinetics and inhibition

  • Choose a competitive inhibitorPredict which substrate look-alike acts as a competitive inhibitor of succinate dehydrogenase.

Acid–base and metal-ion catalysis

  • Which anomer does a retaining glycosidase release?Predict the anomeric configuration of the first-formed product of a retaining, double-displacement glycosidase.

Serine and cysteine proteases

  • Where does trypsin cut?Predict the P1 residue preferred by trypsin from the charge in its S1 pocket.

Classificar 5

Michaelis–Menten kinetics and inhibition

  • Classify an inhibitor from Vmax and KmClassify a reversible inhibitor as competitive from an unchanged Vmax and an increased apparent Km.

Catalytic strategies

  • Which enzyme uses covalent catalysis?Identify the enzyme that forms a covalent enzyme–substrate intermediate.
  • Name the role of His57Classify the role of His57 in Ser195 attack as general base catalysis.
  • Which side chain can be either acid or base?Choose the side-chain model whose pKa lets it act as either general acid or general base near pH 7.

Acid–base and metal-ion catalysis

  • Classify a protease from its inhibitorsAssign a protease to its catalytic class from its response to class-specific inhibitors.

Comparar 2

Serine and cysteine proteases

  • Rank acyl donors toward Ser195Order four acetyl donors by how readily they acylate an active-site serine, using leaving-group pKa values.

Michaelis–Menten kinetics and inhibition

  • Rank substrates by specificity constantRank competing substrates by kcat/Km rather than by kcat or Km alone.

Calcular 8

Serine and cysteine proteases

  • Count active sites from the burstCalculate the concentration of active enzyme from the amplitude of a pre-steady-state burst.

Michaelis–Menten kinetics and inhibition

  • Apparent Km with a competitive inhibitorCalculate the apparent Km in the presence of a competitive inhibitor from Ki and the inhibitor concentration.
  • Km is not always the dissociation constantCalculate Km from the individual rate constants of the Michaelis–Menten scheme and compare it with Kd.
  • Initial rate from the Michaelis–Menten equationCalculate an initial rate from Vmax, Km and the substrate concentration.
  • Turnover number from VmaxCalculate kcat from Vmax and the total enzyme concentration with consistent units.

Catalytic strategies

  • Effective molarity of a neighbouring groupCalculate an effective molarity from intramolecular and intermolecular rate constants and relate it to proximity and orientation.
  • Barrier lowering for a 10⁶-fold rate increaseCalculate how much an enzyme must lower ΔG‡ to give a stated rate enhancement.

Acid–base and metal-ion catalysis

  • How much zinc hydroxide at pH 7.5?Calculate the fraction of carbonic anhydrase in the active zinc-hydroxide form from the pKa of zinc-bound water.

Encontre o erro 1

  • Reversible or irreversible?Diagnose a misclassified inhibitor from its time dependence and its failure to wash out on dilution and dialysis.

Interprete as evidências 3

Catalytic strategies

  • Read a pH–rate profileAssign the acidic limb of the chymotrypsin pH–rate profile to the residue that must be deprotonated.

Acid–base and metal-ion catalysis

  • Why is RNase A activity bell-shaped?Explain a bell-shaped pH–rate profile from the opposite protonation states needed by two catalytic histidines.

Michaelis–Menten kinetics and inhibition

  • Parallel double-reciprocal linesIdentify uncompetitive inhibition from parallel Lineweaver–Burk lines.

Trabalhe de trás para frente 1

  • Which substrate made this acyl-enzyme?Work back from an acyl-enzyme to the peptide substrate and the bond that chymotrypsin cut.

Planeje uma síntese 1

  • Design a transition-state analogueChoose the stable isostere that best mimics the tetrahedral gem-diol intermediate of aspartic-protease amide hydrolysis.

Explique por quê 1

  • What does an enzyme change?Explain why an enzyme speeds a reaction without changing its equilibrium constant.

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