Purpose of Protein engineering
• Dissection of the structure and activity of existing proteins through systematic alterations of the
amino acids at specific sites and investigation of the changes in their phenotypes
• Generation of novel proteins for use in industry and medicine
• Approaches
- de novo protein design: still difficult
- Change the amino acid residue by site-directed mutagenesis: Minor alteration of existing proteins
- Grafting the segments: Cut and paste segments from one protein to another
ex) humanized antibody: grafting of the antigen-binding loops from a mouse monoclonal
antibody onto a human framework with hardly any loss of binding activity
Requirements for systematic site-directed mutagenesis studies
Accurate structure-activity study : absolute values of rate constants
•
Active-site titration
- Variation in the enzyme activity from batch to batch owing to contamination with
the denatured products
- Isolated enzymes are not 100% pure
- Portion of the active enzyme  generate absolute values of rate constants
• Pre-steady state kinetics
- Measure the individual rate constants for the formation or decay of enzyme-bound
intermediates
- First-order rates of change  exponential curves : enzyme undergoes a single turnover
- Kcat : 1~ 10 7 /s  measurement of a time range : 1 ~ 10 -7 s
- Initial burst of product formation
- The rate constants for first-order exponential time courses are independent of enzyme
concentration and unaffected by the presence of denatured enzyme
- Steady-state rates are directly proportional to the concentration of the enzyme
Rapid mixing and sampling techniques
• Continuous-flow method
- Constant flow rate in the tube: elapsed time (Length / flow rate)
- Dead time: shortest time after mixing at which the reaction can be
observed  low as 10 us  used for studying protein folding
- Data are collected over the whole length by a CCD camera that resolves
the time-course into 1035 points
• Stopped-flow method
- Solutions are forced from syringes into a mixing chamber.
After a very short period of flow (a few ms), the flow is stopped
when the observation cell is filled by an opposing piston
that is linked to a sensing switch that triggers the measuring device
like CD and fluorescence detector
• Rapid quenching techniques
- Solution is quenched to stop the reactions using trichloacetic acid
 Reaction products are directed analyzed
• Flash photolysis
- Minimize the dead time of flow techniques
- Use of pre-mixed solution of reagents
 initiate the reaction by perturbing the solution by flash photolysis or pulse of light
- ex) derivative of ATP termed caged ATP may be photo-dissociated by a flash at 347 nm
with a half-time of ms to generate ATP
- Caged ATP is unreactive, useful for studying ATP-utilizing reactions
Analysis of pre-steady state kinetics
• Detection and analysis of transient enzyme-bound species as they arise and decay during the early
phase of reaction
- Enzyme undergoes a
single turnover in contrast to the multiple recycling of the steady state
• Simple exponentials
- Irreversible reactions
A B, Kf = rate constant
d[B]/dt = kf [A], d[A]/dt = -kf [A]
[A]t = [A]o exp(- kft)
Half-life of the reaction : t ½, where [A]= [B] = [A]o/2
t ½ = 0.6931/k f = 0.6931 τ
-τ
= relaxation time = 1/Kf ; characteristic time required for a system to reach an equilibrium condition
after perturbation
- 1/τ = rate constant for the approach to equilibrium
• Initial rate method
vo= kf [A]o , kf = vo /∆[A] o
For irreversible reaction, ∆[A] o = [A] o
• Quasi-reversible reaction
E  ES’ +P1  E + P2, first-step rate constant k1 [S] if [S] >> [E]o,
second-step rate constant= k 2
ex) serine protease ; chymotrypsin
[ES’] ss= k 1 [S] [E]o/ ( k2 + k1 [S])
Applying the initial-rate treatment yields
1/ τ = Vo / [ES’] ss = k2 + k1 [S]
- The intermediate is formed with a rate constant that is greater that the rate constant
for the transformation of the preceding intermediate (K2)
- Analytical solution for the rate is
[S] = [E]o ( k1’/k1’+ k2) x (k1’/k1’+K2{ 1- exp[1-(k1’+k2)t]} + k2t), where k1’= k1 [S]
Initial exponential phase, which disappears after t is about 5 times greater than τ.
A linear term eventually predominates
• If first step is fast and second step is negligible slow, the release is P1 is easily measured and related to
the concentration of enzyme
• If the second step is not negligible, there is an initial burst of formation of P1 followed by a progressive
increase as the intermediate turns over
• Linear portion extrapolates back to a burst, π,
π = [E]o { k1’/(k1’ + k2)} 2
(P1)
If the ratio k1’ : k2 is high, the squared term is close to 1, so the burst is equal to the enzyme concentration
Slope = [E]o k1’ k2/ (k1’ + k2)
1/ τ = k2 + k1’
• Lower limit to 1/ τ : 1/ τ cannot be less than k2, setting a limit on the measurement of these rate
constants
• A good stopped-flow spectrophotometer can detect the rate constants of 1000 s -1.
• Many enzyme-substrate dissociation constants are faster than 1,000 s -1
• Dissociation rate constant of tyrosin from its complex with tyrosyl-tRNA synthetase is low: 1.5 ~ 53
• Association and dissociation rate constants can be measured by stopped-flow method
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
k2 = Z p exp ( - Eact/RT)
Z: frequency of collision
p: Steric factor to allow for the fraction of the molecules that are in correct orientation
Eact: 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 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
- Kcat /Km : catalytic efficiency of enzyme reaction :~ 10 8 s -1 M -1  diffusion-controlled encounter
V = kcat / km [E]o [S], if Km >> [S], second-order rate constant for the reaction of 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
Steady-state enzyme kinetics
• Basic Michaelis-Menten equation: experimental basis
v= kcat [E]o [S]/ (KM + [S])
• Michaelis-Menten mechanism : Interpretation of the kinetic phenomena
E + S <--> ES  E +P
- Concept of enzyme-substrate complex: Foundation stone of enzyme kinetics and understanding of
the mechanism of enzyme catalysis
- Enzyme-substrate complex is in thermodynamic equilibrium
v= kcat [E]o [S]/ (Ks + [S])
- Briggs-Helden kinetics: Extension of M-M mechanism, when k2 is comparable to k-1
- Steady-state approximation for ES complex
v= k2[E]o [S]/ (KM + [S]), KM= Ks + k2/k1. If k-1 >>k2, KM=Ks
• Meaning of kcat: Catalytic constant
-Turnover number: maximum No of substrate molecules converted to products per active site per unit time
• KM: Apparent dissociation constant
- [E] [S]/ [ES]
• Kcat /KM: Measure of catalytic efficiency, apparent second-order rate constant
- If [S] is low, v= (kcat/KM)[E]o [S]: enzyme is largely unbound, and [E] ~ [E]o
- Relates the reaction rate related to the concentration of free enzyme rather than total enzyme
- Measure of the catalytic efficiency of the mutant enzymes
For two mutant enzymes, E1 and E2, for the same substrate,
V1/V2 = (kcat/KM) 1 [E1]/ (kcat/KM) 2 [E2]
- Measure of substrate specificity: determine the specificity for competing substrate toward the same enzyme
For two substrates A and B, VA = (kcat/KM) A [E] [A], VB= (kat/KM) B [E] [B],
so VA/VB= (kcat/KM)A [A] / (kcat/KM) B [B]
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 tRNAtyr 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
Adenosine triphosphate
• First step:
-Activation: Nucleophilic attack of the carboxylate of Tyr on the a-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, kcat/K M
• Fully developed strategy: measure the complete free energy profiles for wild-type and mutants
• For the tyrosyl-tRNA synthetase,
KT
KA’
k3
KP
E  E.Tyr  E.Tyr.ATP  E.Tyr.AMP.PPi  E.Tyr.AMP + Ppi
k-3
The constants to be measures:
KT: dissociation of E.Tyr complex( by equilibrium dialysis or kinetics)
KA’: dissociation constant of ATP from the ternary complex, E.Tyr.ATP( from kinetics)
k3: 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
- Difference in energy : Apparent binding energy of a group : ∆ ∆G app when mutation deletes an interaction
∆∆G app = ∆G mutant -∆G wild
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 complemnentarity
- Mutation of His- 45 to Ala, Hly, Asn, and Gln: similar result ro Thr-40.
•
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 + PPi
Equilibrium constant KD ( [Tyr-AMP] [PPi]/ [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 tRNATyr 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) : 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 the transition state, it would block the a
ccess of substrate
to the active site
- 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 t1/2 for hydrolysis in solution of one minute
- Intramolecular attack of the OH in the ternary complex is very rapid
Apparent binding energy
• Relative energies of two different enzymes that bind the same substrate
Ex) relative energies of two mutants binding a native substrate and 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 to Phe: removal of hydrogen bond donor to the substrate
- No accompanying rearrangement of structure and no access of water to the cavity that is formed at the site
of mutation: change 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 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
• Crucial for interpretation of the mutational effects for mutants
Differential and uniform binding changes : probing evolution
• Differential binding changes: 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 energy of the transition with respect to ground state  increase in K cat
• Uniform binding changes: ex)Tyr-169 and Glu-173
- Uniform increase in binding energies , ES and ES*, lowers the energies of each of the state equally
- No change in kcat: Neutral effect
- When [S] << KM, the rate is given by v= (kcat/KM)[E]o [S], and leads to an Increase in Kcat/KM and reaction rate
- When [S] >> KM, the rate is given by v=kcat [E]o. Uniform binding changes do not increase the rate at saturating
concentrations of substrate because they do not increase Kcat
Only differential binding increases the reaction rate
• 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: binding energy is used for increasing kcat/KM
- kcat : 0.17  2.8, KM: 32~25, kcat/KM: 5 440
• Elastase
-Increased length of the polypeptide chain of substrate: increase in kcat/KM
- kcat: 0.09 2.8, KM: 4.2~ 43, kcat/KM: 21  2200
• Pepsin
- Additional binding energy by larger substrate is used to increase Kcat rather than lower the KM
 Higher kcat/KM for the larger substrates
kcat: 0.5 112, KM: 0.3~0.06, kcat/KM: 1700 ~ 2x10 6
• Binding energy of the additional groups does not lower KM: binding energy is not used to bind to
the substrate but increase Kcat
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 that of the substrate
• Lysozyme and glucosidase
- Hydrolysis of the polysaccharide component of plant cell walls and synthetic polymers of β(14)-linked
units of N-acetylglucosamins(NAG)
- Transition state analogues with a lactone ring that mimics the carbonium ion-like transition state
Binds tightly to lysozyme: Kd=~ 8 x 10 -8 M : electrostatic interaction of the negatively charged Asp32 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 the substrate
• Enzyme-transition state complementarity maximizes kcat/KM.
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/KM = 10 6 M-1 s-1 , [S] = 10 -3 M, Overall reaction rate : (kcat/KM) x [S]
KM (M)
10-6
10-5
10-4
10-3
10-2
10-1
1
kcat (s-1)
Rate (s-1)
1
10
102
103
104
105
106
1
9
99
500
909
990
999
• Maximization of the rate : high value of KM evolution of enzymes to bind weakly to the substrate
Principle for maximizing the KM at constant k cat/KM
• Strong binding of the substrate to the enzyme: Low ES Low KM high activation energy ∆ G$T
• Evolution of an enzyme to give maximum reaction rate
V= kcat/KM [E][S]
- Maximum value of kcat/KM through the enzyme complementary to the transition state of the substrate
- Free enzyme portion [E] is maximized by high KM  as much of the enzyme as possible in the free state
ex) At KM= [S], half of the enzyme is free  the rate is 50 % of the maximum possible
At KM= 5[S], 5/6 of the enzyme is unbound  the rate is 83 % of the maximum
• Exception to the principle of high KM: Control enzyme
- Metabolic pathways are regulated by a key enzyme: the activity of a control enzyme is controlled by
variations in the KM for critical substrate via allosteric effects : KM of control enzymes evolved for the purpose
of regulations, and not necessarily subject to the rate enhancement
- Low KM : advantageous for the first enzyme on a metabolic pathway control the rate of entry to the
pathway
ex) Hexokinase: first enzyme in glycolysis, KM for glucose( 0.1 mM). Glucose concentration in the human
erythrocyte : ~ 5 mM
 Ten-fold increase or decrease in the glucose level : negligible effect on the glycolysis rate
• Substrate concentrations and KM in glycolysis
- KM in the range of 1 to 10 and 10 to 100 times the substrate concentrations
• Perfectly evolved enzyme for maximum rate
-State of evolution: maximum rate
- Kcat/KM: 10 8 ~ 10 9 M-1s -1 KM : greater than [S]