Enzyme catalysis
Catalytic power of enzymes Enzymatic reactions are involved in most biological processes. There is a major practical and fundamental interest in finding out what makes enzymes so efficient to design enzymes for practical applications. Many crucial pieces of this puzzle were provided by biochemical and structural studies Actual reason for the catalytic power of enzymes is not widely understood. It is clearly not explained by the statement that the enzyme binds the transition state stronger than the ground state because the real question is how the differential binding can be accomplished. Similarly, it is not true that evolution can use any factor to accelerate reactions.
Basic concept Chemical reactions rely on acids, bases and nucleophiles as catalyst. Enzymes use the same chemistry, but greatly enhance and fine-tune it by binding the ground state substrate, transition state, and products in subtle ways Transition state theory : - The processes by which the reagents collide are ignored: the only physical entities considered are the ground state substrate, transition state substrates which are the most unstable species on the reaction pathway. - Occurs at the peak in the reaction coordinate diagram, in which the energy of the reagents is plotted as the reaction proceeds. - Chemical bonds are in the process of being made and broken - Intermediate: bonds are fully formed, occupying the troughs - Transition state and ground state are in thermodynamic equilibrium - A simple way of deriving the rate of the reaction Overall reaction rate : [concentration of the transition state] X [rate constant of its decomposition]
Analysis for a unimolecular reaction Difference in Gibbs free energy between the transition state, X*, and the ground state, X, which are in thermodynamic equilibrium : ΔGǂ [x*] = [x] exp(- ΔGǂ/ RT) from ΔGǂ= - RT ln K The frequency at which the transition state decomposes is the same as the vibrational frequency of the bond that is breaking - This frequency is obtained from the equivalence of the energies of an excited oscillator calculated from quantum theory ( E= h υ ) and classical physics (E= kt) Thus, v = kt / h where k is the Boltzmann constant and h is the Planck constant At 25 o C, v= 6.212 X 10 12 /sec Rate of decomposition of X is given by - d [x] / dt = υ [X*] = [X] (k T/h ) exp (- ΔGǂ/ RT )
The first-order rate constant for the decomposition of X is given by k 1 = (kt/h) exp (- ΔGǂ/ RT ) Gibbs free energy of activation, ΔGǂ, may be separated into enthalpic and entropic terms ΔGǂ = ΔHǂ T Δ Sǂ Rate constant becomes k 1 = (k T/h) exp (ΔSǂ/ R) exp (-ΔHǂ/ RT)
Significance and application of transition state theory Importance of TS theory: it relates the reaction rate to the difference in Gibbs free energy between the transition state and the ground state - Comparison of the relative reactivities of different substrates Analysis of the relation between the substrate structure and reaction rate - Rates of a given reaction under different sets of conditions Mechanisms to facilitate enzyme catalysis vs. non-catalyzed reaction - Acid-base catalysis - Entropic advantages - Orbital steering : orientation - Electrostatic catalysis : desolvation electrostatic interactions - Metal ion catalysis : electrophilic catalysis - Covalent catalysis - Nucleophilic catalysis
General-base catalysis - Stabilization of unfavorable positive charge developed in the transition state General-acid catalysis - Stabilization of unfavorable negative charge Specific acid or base catalysis: proton or hydroxide ion Nucelophilic catalysis : stabilization of the transition state without changing the mechanism - For nucleophilic catalysis to be efficient, the nucleophile must be more nucleophilic than the one it replaces, and the intermediate must be more reactive than the parent compound Covalent catalysis : substrate is transiently modified by formation of a covalent bond with the catalyst to give a reactive intermediate -PLP-dependent enzymes
New proposal Electrostatic effects : Provide the most important contributions to enzyme catalysis : - Pre-organized polar environment of the enzyme active site QM/MM (quantum mechanics/molecular mechanics) method: - Introduced by A. Warshel and M. Levitt in 1976 (JMB, 103 (2): 227 49. - Molecular simulation method that combines the strengths of the QM (accuracy) and MM (speed) approaches - Allows the study of chemical processes in solution and in proteins (in particular, enzyme active site) - Nobel prize in Chemistry with Martin Karplus in 2013
Basic equations of enzyme kinetics Steady-state kinetics 1. Experimental basis: The Michaelis-Menten equation - Enzyme concentration is very low compared to the substrate - Initial reaction rate : v - Experimental findings: - v is directly proportional to the enzyme concentration - v generally follows saturation kinetics with respect to the substrate concentration - At sufficiently low [S], v increases linearly with [S] But, as [S] is increased, this relationship begins to break down, and v increases less rapidly and reaches a limiting value, termed V max 2. Michaelis-Menten equation : Expression of experimental observation quantitatively - Basic equation of enzyme kinetics
v= Vmax [S] / (K M + [S]) where V max = kcat [E]o The substrate concentration at which v= ½ Vmax is termed K M, the Michaelis constant. At low [S], where [S]<< K M v= kcat /K M [E]o [S] 3. Interpretation of the kinetic phenomena for single-substrate reactions: The Michaelis-Menten mechanism - Michaelis and Menten developed the theory of earlier workers and proposed the reaction scheme in 1913.
The catalytic reaction is divided into two processes - The enzyme and the substrate first combine to give an enzyme- substrate complex, ES. - This step is assumed to be rapid and reversible with no chemical changes taking place - The enzyme and substrate are held together by non-covalent interactions - Next, the chemical processes occur in a second step with a first-order rate constant, kcat (turnover number) Concept of enzyme-substrate complex: E + S < ES E + P - Foundation stone of enzyme kinetics and understanding of the mechanism of enzyme catalysis
Enzyme-substrate complex is in thermodynamic equilibrium Ks = [E] [S] / [ES] = k -1 /k 1 v= k cat [ES] The relationship in the free and bound enzyme is [E]o = [E] + [ES] Thus, v= k cat [E] o [S]/ (Ks + [S]) - Briggs-Helden kinetics: Extension of M-M mechanism, when k 2 is comparable to k -1 Steady-state approximation for ES complex v= k 2 [E] o [S]/ (K M + [S]), K M = Ks + k 2 /k 1. If k -1 >>k 2, K M =K s
Meaning of k cat : Catalytic constant -Turnover number: maximum No of substrate molecules converted to products per active site per unit time K M : Apparent dissociation constant - [E] [S]/ [ES] K cat /K M : Measure of catalytic efficiency, apparent second-order rate constant - If [S] is low, v= (k cat /K M )[E] o [S]: enzyme is largely unbound, and [E] ~ [E]o - Relates the reaction rate to the concentration of free enzyme rather than total enzyme - Measure of the catalytic efficiency of mutant enzymes For two mutant enzymes, E 1 and E 2, for the same substrate, V 1 /V 2 = (k cat /K M ) 1 [E 1 ]/ (k cat /K M ) 2 [E 2 ] - Measure of substrate specificity: determine the specificity for competing substrate toward the same enzyme For two substrates A and B, V A = (k cat /K M ) A [E] [A], V B = (kat/k M ) B [E] [B], thus, V A /V B = (k cat /K M ) A [A] / (k cat /K M ) B [B]
Magnitude of rate constants for enzymatic reactions Upper limits on rate constants - Reaction rate constants for chemical reactions: collision theory Rate constant for a bimolecular reaction : A + B product k 2 = Z p exp ( - E act /RT) Z: frequency of collision p: Steric factor to allow for the fraction of the molecules that are in correct orientation E act : Activation energy to allow for the fraction of molecules that are sufficiently thermally activated to react - Maximum bimolecular rate constant: activation energy is zero and steric factor is 1 diffusion controlled, and rate constant is equal to the encounter frequency of molecules - General second order rate constants: ~ 10 9 s -1 M -1
Rate constants for the association of proteins with one another and with other molecules - Influenced by the geometry of the interaction and electrostatic factors - Only small part of protein is involved in the interaction: bad steric factor on the reaction - Association rate constants : 10 4 s -1 M -1 - Fast association : > 5 x 10 9 s -1 M -1 at low ionic strength for proteins that have complementary charged surface Association of enzyme and substrate - Diffusion-controlled encounter frequency: 10 6 ~ 10 8 s -1 M -1 - K cat /K m : catalytic efficiency of enzyme reaction :~ 10 8 s -1 M -1 diffusion-controlled encounter If Km >> [S], V = k cat / k m [E] o [S]. Thus, K cat /K m is a second-order rate constant for the reaction between free enzyme and free substrate Dissociation rate constants for enzyme-substrate and enzyme-product complexes : much lower than the diffusion-controlled limit - Product release is rate-limiting
Case study of protein engineering practice: Tyrosyl-tRNA synthetase First enzyme to be studied by protein engineering Understanding the catalytic mechanism: - Interaction energy between the enzyme and substrate throughout the whole course of the reaction - How binding energy is used to lower activation energies, optimize equilibrium constants, and determine specificity Enzyme-transition state complementarity Catalytic mechanism for the activation of tyrosine Fine-tuning of the activity Basic feature - Symmetrical dimer : Mr = 2 x 47316 - Catalyze the amino-acylation of trna tyr in a two-step reaction E + Tyr + ATP E-Tyr-AMP + Ppi: enzyme-bound tyrosyl adenylate complex E-Tyr-AMP + trna Tyr-tRNA +E + AMP
Mechanism of Tyrosyl-tRNA synthetase First step: Adenosine triphosphate - Activation: Nucleophilic attack of the carboxylate of Tyr on the α-phosphate of ATP to generate either 5-coordinate transition state or a high energy intermediate Second step: Transfer of Tyr to 3 -end of trna
Crystal structures of the complex: Starting points Enzyme-bound tyrosyl adenylate complex
Residues of the tyrosyl-trna synthetase that form hydrogen bonds with tyrosyl adenylate based on the complex crystal structure Dissection of the activity, catalytic mechanism, and use of binding energy
Choice of mutation for mechanistic study Ideal mutation: non-disruptive deletion that simply removes an interaction without causing a reorganization or distortion of the structure of the enzyme, either locally or globally - Reorganization or distortion of structure: Unknown energy change complicate the changes arising from the direct interaction of the target side chain - Enzyme or enzyme complex tolerates a cavity within it because there is just the loss of the noncovalent interaction energies General rules - Choose a mutation that deletes a part of a side chain to an isosteric change Deletions are preferred to mutations that increase the size of the side chain Any increase in volume of the side chain induces the distortion of the structure - Avoid creating buried unpaired charge: Solvation energies of ions are high that charged groups must be solvated - Delete the minimal number of interactions : avoid the deletions of multiple interactions where possible - Do not add new functional groups to side chains : can cause local reorganization of structure
Preferred mutations Probe of hydrophobic interactions : Ile Val, Ala Gly, Thr Ser - Creation of a tiny cavity Probe of hydrogen bonds: Ser Ala, Tyr Phe, Cys Ala, His Asn, His Gln Large energy loss: Ile Ala, Val Ala, Leu Ala - Greater movement of surrounding side chains into the cavity or the ingress of solvent Isosteric substitution of one polar residue for another: Asp Asn, Glu Gln - Acceptable on the surface of a protein Mutate to Ala or Gly when in doubt : - General deletion mutation - Wider freedom of conformations
Strategy Mutate the side chains that interact with the substrate and measure the changes in activity - Radical drop in activity: critical to activity Change the side chains that simply bind to the substrate and are not obviously catalytic Measure the small change in activity : simple steady-state kinetics, k cat /K M Fully developed strategy: measure the complete free energy profiles for wild-type and mutants For the tyrosyl-trna synthetase, K T K A k 3 K P E E.Tyr E.Tyr.ATP E.Tyr.AMP.PP i E.Tyr.AMP + Pp i k -3 The constants to be measured: K T : dissociation constant (equilibrium constant) of E.Tyr complex ( by equilibrium dialysis or kinetics) K A : dissociation constant of ATP from the ternary complex, E.Tyr.ATP ( from kinetics) k 3 : rate constant for the chemical step (from pre-steady state kinetics using stopped-flow and the mixing of E.Tyr with ATP) k -3 : rate constant pyrophosphorolysis of E.Tyr.AMP to E.Tyr.ATP ( from pre-steady state kinetics using stopped-flow and the mixing of E.Tyr.AMP with Ppi Kp: dissociation constant of Ppi from E.Tyr.AMP.Ppi complex ( from the kinetics)
Free energy profile Calculated for wild-type and mutant using equilibrium thermodynamics with equilibrium constants and transition state theory with the rate constant Difference energy diagram for wild-type and mutant - Difference in energy : Apparent binding energy of a group : G app when mutation deletes an interaction G app = G mutant - G wild ǂ Superposition of free energy profile for wild-type and mutant
Difference energy diagram Enzyme-transition state complementarity - Difference energy diagrams for the mutation of Thr-40 to Ala no effect on the binding energies of Tyr and ATP to the enzyme - But, a significant raising of the energy in the transition state by 20 kj/mol - Negligible effect on the binding of Tyr-AMP So, Thr-40 binds to Tyr and ATP in the transition state of the reaction first direct experimental explanation for the enzyme-transition state complementarity - Mutation of His- 45 to Ala, Asn, and Gln: similar result to Thr-40. [E.Tyr] [E.Tyr.ATP] [E.Tyr.AMP]ǂ [E.Tyr.AMP.Pp] [E.T.A]
Thr-40 and His-45 form a part of a binding site for γ-phosphate of ATP in the penta-covalent transition state or intermediate - No contribution to the binding energy with ATP before the reaction takes place - The enzyme catalyze the reaction through the subtle change in bond angles at the α-phosphate during the reaction Model of transition state for tyrosyl adenylate formation
Enzyme-intermediate complementarity Mutagenesis of the residues Cys-35 and His-48 that bind to the ribose ring in E.Tyr.ATP complex to Gly no or little contribution to interaction energy with ATP in the ground state complex But, significant contribution to stabilization of ATP in the transition state Contribute to catalysis because their binding energy is used to lower the energy difference between the ground state and the transition state : Enzyme-intermediate complementarity Advantages of enzyme-intermediate complementarity a) Enzyme-product complementarity changes the equilibrium constant for highly unfavorable reactions Tyr + ATP Tyr-AMP + PP i Equilibrium constant K D ( [Tyr-AMP] [PP i ]/ [Tyr] [ATP]) = ~ 3.5 x 10-7 -Internal equilibrium constant for the enzyme-bound reaction, namely, [E.Tyr.AMP.Ppi ]/[E.Tyr.ATP] : 2.3 10 7 -fold increase : enzyme binds to Tyr-AMP far more tightly than Tyr + ATP necessary for catalysis because the rate-limiting step in vivo is the attack of trna Tyr on the E.Tyr.AMP complex
b) Increase in the yield of reaction by minimizing side reactions and sequestering the highly reactive intermediate - The enzyme minimizes the dissociation rate constant by enzyme-aminoacyl adenylate complementarity - Reactive intermediate: aminoacyl adenylates rapid hydrolysis in aqueous solution within a few minutes protection against hydrolysis by groups on the enzyme that interfere with the attack of water or hydroxide ion Detection of an induced-fit mechanism - Lys-230 and Lys-233 on a loop ( the KMSK loop) : too far away to interact with the model-built transition state - Analysis of temperature factor ( B-values) : measure of either motional freedom or random disorder Loop is very mobile and able to wrap around the transition state as the reaction proceeds - Induced-fit mechanism: If the loop in the enzyme were in the orientation optimal for binding to the transition state, it would block the access of substrate to the active site: the loop undergoes conformational change to have interaction - Flexibility and induced fit mechanism: compromise between enzyme-transition state complementarity and open access of substrate to the active site
Mechanism of transfer step - No acidic or basic groups suitably placed to catalyze the attack of the ribose OH of 3 -end of trna on the C=O of Tyr-AMP - Tyr-AMP: extremely activated substrate with a t 1/2 for hydrolysis in solution of one minute - Intramolecular attack of the OH in the ternary complex is very rapid + AMP
Apparent binding energy Relative energies of two different enzymes that bind to the same substrate Ex) relative energies of two enzymes (wild-type and a mutant) binding to a native substrate or a transition state - Measure of the specificity of binding - Not equal to the true incremental binding energy of a group that is deleted - Vary according to the mutation types Ex) Mutation of Tyr-34 to Phe: removal of hydrogen bond donor to the substrate Different types of cavities - If no accompanying rearrangement of structure and no access of water to the cavity that is formed at the site of mutation: decrease in the defined binding energy between the enzyme and substrate - Open access of water to the cavity : apparent binding energy represents the difference in energy between the substrate making a hydrogen bond with tyrosine and the substrate making a bond with water (solvation energy) - Mutation that induces a different interaction, apparent binding energy reflects the difference between the interactions in wild-type and a mutant Apparent binding energy do not necessarily equal the true binding energy But, changes in the apparent binding energy : equal to the changes in true binding energy Most valid in cavity-inducing mutations in which interaction is removed from the wild-type complex Crucial for interpretation of the mutational effects on mutants
Utilization of enzyme-substrate binding energy in catalysis The use of extra binding energy when [S] >K M v = k cat [E] o because enzyme is saturated with substrate Three extreme cases - Stabilization of both ES and ESǂ : uniform binding energy effect Decrease in K M, but no change in Kcat: No catalytic advantage by extra binding - Stabilization of only ES: differential binding energy effect Increase in activation energy of Kcat decreased reaction rate - Stabilization of only ESǂ : differential binding energy Extra binding energy is used for transition state stabilization Decrease in activation of Kcat increase in the reaction rate catalytic advantage
Differential and uniform binding changes : probing evolution Differential binding change: Residues contribute different binding energies with the substrate, transition state, and product Ex) Thr-40 and His-45 of trna synthetase - No binding to substrate or intermediate - Great stabilization of the transition state Lower the transition state energy with respect to ground state increase in K cat increased rate Uniform binding changes: ex) OH of Tyr-169 with NH3 + of substrate Tyr; Coo- of Glu-173 with NH3+ of Tyr - Uniform increase in binding energies, ES and ES*, lowers the energies of each of the state equally i) When [S] >> K M, the rate is given by v=k cat [E] o. No increase in the rate because they do not increase K cat ii) When [S] << K M, the rate is given by v= (k cat /K M )[E] o [S], and leads to an increase in K cat /K M and reaction rate because of an decrease in Km, even though kcat remains almost constant Only differential binding increases the reaction rate when [S] >> K M Evolution of enzymes with differential binding changes : efficient catalysis Guidelines for rational design of enzymes with high catalytic efficiency
Experimental evidence for the utilization of binding energy in catalysis and enzyme-transition state complementarity Serine protease - A series of subsites for binding the amino acid residues of the polypeptide substrates Chymotrypsine - larger groups occupy the leaving group site in the enzyme : binding energy is used for increasing k cat /K M - Depending on substrate sequences, k cat (s -1 ) : 0.17 ~ 7.5 ; K M (mm) : 15~32 ; k cat /K M (s -1 M -1 ) : 2 ~ 440 Elastase -Increased length of the polypeptide chain of substrate: increase in k cat /K M - k cat : 0.02 ~ 8.5, K M : 3.9 ~ 43, k cat /K M : 21 ~ 2200 Pepsin - Additional binding energy by larger substrate is used to increase K cat rather than lower the K M Higher k cat /K M for the larger substrates k cat : 0.002 ~ 409, K M : 0.03~0.6, k cat /K M : 1700 ~ 2x10 6 Binding energy of the additional groups does not lower K M : binding energy is not used to bind to the substrate, but increase Kcat
Probes of complementarity: Transition state analogues Direct evidence for enzyme-transition state complementarity: Binding of transition state analogues - Synthesis of transition state mimics and their binding to the enzyme compared with original substrate Lysozyme and glucosidase - Hydrolysis of the polysaccharide component of plant cell walls and synthetic polymers of β(1 4)-linked units of N-acetylglucosamin (NAG) - Transition state analogues with a lactone ring that mimics the carbonium ion-like transition state binds tightly to lysozyme: K d =~ 8 x 10-8 M : 100-fold tighter binding of the transition state analogue: electrostatic interaction of the negatively charged Asp52 with the partial positive charge on the carbonyl carbon of the lactone - Dissociation constant of (NAG) 4 : ~ 10-5 M
Evolution of the maximum rate Strong binding of the transition state and weak binding of substrate Enzyme-transition state complementarity maximizes kcat/k M - Not a sufficient criterion for maximizing the overall reaction rate - Maximum reaction rate is dependent on the individual values of kcat and K M ex) kcat/k M = 10 6 M -1 s -1, [S] = 10-3 M, Overall reaction rate : (kcat/k M ) x [S] K M (M) kcat (s -1 ) Rate (s -1 ) 10-6 1 1 10-5 10 9 10-4 10 2 99 10-3 10 3 500 10-2 10 4 909 10-1 10 5 990 1 10 6 999 Maximization of the rate : high value of K M evolution of enzymes to bind weakly to substrate
Principle of maximization of K M at constant k cat /K M Strong binding of substrate to an enzyme: Low ES Low K M high activation energy G $ T Evolution of an enzyme to give maximum reaction rate The M-M equation can be simplified to V= kcat/k M [E][S] to relate the reaction rate to the free enzyme conc. - To maximize the reaction rate, i) kcat/k M is maximized through the enzyme complementary to the transition state of substrate ii) Free enzyme portion [E] is maximized by high K M as much of enzyme as possible in free state ex) At K M = [S], half of the enzyme is free rate is 50 % of the maximum possible At K M = 5[S], 5/6 of the enzyme is unbound rate is 83 % of the maximum Exception to the principle of high K M : Control enzyme - High K M is necessary for maximization of the reaction rate - Metabolic pathways are characterized by their regulation, which is regulated by a key enzyme activity of a control enzyme is controlled by variations in K M for critical substrate via allosteric effects : - K M of control enzymes evolved for the purpose of regulations, and not necessarily subject to the rate enhancement
- Low K M : advantageous for the first enzyme on a metabolic pathway control the rate of entry to the pathway and prevent it from being overloaded and accumulating reactive intermediates ex) Hexokinase: first enzyme in glycolysis - K M for glucose: 0.1 mm. Glucose concentration in the human erythrocyte : ~ 5 mm Even ten-fold increase or decrease in the glucose level has a negligible effect on the glycolysis rate Experimental observations of KM values - Non-regulatory glycolytic enzymes: K M in the range of 1 to 10, and 10 to 100 times the substrate concentrations ex) triosephosphate isomerase: Evolutionarily perfect enzyme K M /[S] for G3P and DHAP : ~ 153 and 17 in muscle Perfectly evolved enzyme for maximum rate -State of evolution: maximum rate : diffusion-controled encounter of the enzyme and substrate - K cat /K M : 10 8 ~ 10 9 M -1 s -1 K M >> [S] ex) Carbonic anhydrase and triosephosphate isomerase