life’s fastest engines: diffusion- controlled enzymes how does catalysis approach the diffusion...
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Life’s fastest engines: Diffusion-controlled enzymes
How does catalysis approach the diffusion limit?
Michael Daily
Program in Molecular Biophysics
Carbonic anhydrase Triosephosphate isomerase Acetylcholinesterase
Enzyme power: remarkable rate enhancement
• Some biological reactions are “geologically slow” (hundreds – 1 billion years half time)
• All catalyzed reactions operate at millions per second
• Transition state affinities as high as 1024 M
Wolfenden & Snider (2001). Acc. Chem. Res. 34, 938-45Ornithine decarboxylase:
t1/2 = 78 million years at 25 C.
Crystal structure: Almrud, J.J. et. al. (2000). JMB 295, 7.
Some major enzyme problems
• Bond rearrangement
• Stabilization of high-energy intermediates, transition state
• Orientation of reactive groups
• Proton shuttling at neutral pH
Enzyme catalysis: mathematics
kcat/KM = knon*KA‡
E + S
ES
E + Sts
ES‡
E + P
knon
KM
kcat
KA‡
Enzymes exert remarkable control over kcat/KM relative to the variation of knon
Radzicka, A. and Wolfenden, G. (1995). Science 267 (5194), 90-93.
-16
-14
-12
-10
-8
-6
-4
-2
0
2
4
6
8
ODC
SNase
AMPas
eADA
CDAAch
eCPA
PTETIM
CMU
CYCPCAII
kcat/KM: 102.5 variation
knon: 1014 variation
Diffusion-controlled enzymes
Molecular encounter limits kcat/KM if k2 is high
If
;
]E/[
P E ES S E
112
21
21
1
21
2totmax
211
kK
k,kk
kk
kk
K
k
k
kkK
kVk
M
cat-
M
catM
cat
k/kk -
What is the limit of the molecular encounter rate?
1
2
3
Alberty, R.A. and Hammes, G.G. (1958). J. Phys Chem 62, 154-59
1) According to Smolouchowski equation, E-S collision rate is limited to ~109/s
2) Orientational constraints limit the reactive encounter rate to ~106/s
3) Electrostatic attraction or guidance of S to E can raise the diffusion limit to 108-109/s.
Electrostatics cause large differences in barnase-barstar association rates
Wild type (top) and barnase mutants
~1000x variation in k1 at 0.1M ionic strengthBasal k1 ~
105 M-1s-1
Schreiber, G. and Fersht, A.R. (1996). Nat. Struct. Biol. 3 (5), 427-431.
Summary: enzymes overcome two physical problems
• Chemical efficiency – Geometry (entropic problem)– High-energy intermediates (enthalpic
problem)– Enzyme rate does not appear to be limited by
knon
• Molecular encounter– Coulomb’s law (enthalpic effect)– Steering (entropic effect)
Three diffusion-controlled enzymes
enzyme knon kcat kcat/KM kcat/knon
catalytic proficiency
Carbonic Anhydrase
1.30E-01 1.00E+06 1.20E+08 7.69E+06 9.23E+08
TriosePhosphateIsomerase
4.30E-06 4300 2.40E+08 1.00E+09 5.58E+13
Acetyl-cholinesterase
1.40E-09 14000 1.60E+08 1.00E+13 1.14E+17
Carbonic Anhydrase II – an introductory case
• CO2 control – very important metabolically
• Ubiquitous, independently evolved 3 times
• Very fast uncatalyzed reaction (t1/2 = 5s)
• Rapid, efficient proton shuttling
Crystal structure: Hakansson, K. et. al. (1992). J. Mol. Biol. 227, 1192.
The CA II reaction has two major steps
CO2 hydration
CO2 + OH- <-> HCO3-
Rate-limiting nucleophile regeneration
Zn-H2O <-> Zn-OH + H+
Silverman, D.N. and Lindskog,S. (1988). Acc. Chem. Res. 21, 30-36.
Tu, C. et al. (1989). Biochemistry 28, 7913-18.
Zinc hydroxide nucleophile: A well-understood problem
T199 orients Zn-bound OH- to attack CO2
T199A mutant has ~0.01x the kcat/KM of wt
E106 anchors T199
E106A,E106Q mutants have ~0.1x the kcat/KM of wt
Catalytic residues (E106,T199,H64)
Zn ion and ligands
2bcc.pdb
Xue et. al. (1993). Proteins 17 (1), 93-106.
Krebs et. al. (1993). J. Biol. Chem. 268 (36), 27458-66.
Liang et. al (1993). Eur. J. Biochem. 211 (3), 821-7.
Nucleophile regeneration: problems and solutions
• Proton transfer from Zn(OH2) to solution OH- is limited to 103/s– Concentrated solution buffers deprotonate
Zn(OH2) at as high as 106/s (Jonsson et. al 1976)
• Solution buffer cannot efficiently penetrate to the buried Zn(OH2) active center– Active site waters and H64 efficiently shuttle
protons from the active center to the surface (Tu et al. 1989, Silverman 1995, Jackman et. al 1996, Skolnick et. al 1996).
His 64-water network nucleophile regeneration mechanism
Four water molecules transfer protons from catalytic site to his 64
Proton shuttle
H64
Catalytic residues
Catalytic water
Bulk solvent
Unsolved problems of CA II
• CO2 hydration-
– Position of CO2 (weak binding)
• Proton transfer– Effect of moving the proton shuttle– Which waters are involved in proton transfer?
• Quantum mechanical mechanistic details– Beyond structural biology
CA II is a well-understood enzyme (from a structural biology viewpoint)• Catalytic groups identified• Function, importance of catalytic groups
known• Exact details of proton transfer still being
researched• Quantum mechanical mechanism still
being researched• Mechanism is probably understood at the
design level
Triosephosphate Isomerase (TIM)An intermediate case
• Ubiquitous (glycolytic enzyme)
• Large rate enhancement (~1013)
• Two difficult proton transfers
• Paradoxical E-S electrostatic attraction
Catalytic residues (H95, E165, K12)
Substrate (DHAP)
TIM mechanism involves two difficult proton transfers
DHAP enediolate
GAP
C1 deprotonation (rate limiting)
O1-O2 proton transfer
DHAP
GAPKnowles, J.R. (1991).
Nature 350, 121-124.
TIM catalysis solves three problems
• Difficult C1 deprotonation (pKa ~ 20)
• Unstable negatively charged enediolate intermediate
• Proton transfer from O1 to O2 (pKa ~ 14)
The crucial C1 deprotonation step is well-understood
Unusually close E165-C1 contact prepares for C1 deprotonation
H95 and K12 polarize C2 carbonyl, lowering C1 pKa from ~20 to ~14
Nickbarg et al (1988),
Lodi & Knowles (1991)
1.2A Crystal structure: Jogl et. al (2003). PNAS 100 (1), 50-55
A multi-pronged positive field stabilizes negative enediolate
O1, O2 hbond with H95
K12+ stabilizes O2-
positive end of helix dipole
O1-O2 proton transfer: two pathways
Neutral H95 moves proton from O1 (OH) to O2-
Low-barrier hbond (LBHB): between H950 and enediolate (both pKa ~14) facilitates H95-O2 proton transfer
E165 is known to participate in O1-O2 transfer some fraction of the time.
Harris et. al. (1998), Cui and Karplus (2001).
Electrostatics: paradox of E-S attraction in TIM
Oxygen atoms
Nitrogen atoms
Substrate (DHAP)
1NEY.pdb (yeast TIM)
Yeast TIM has net charge of -6 at pH 7.
TIM-GAP attraction is dominated by potential in active site vicinity
• TIMs of varying charge (-12 to +12) have rate enhancements from 100-1000
• Attractive field is calculated near the active site and within 10A of the enzyme
• Biological application: TIM can function at diffusion limit in different pH environments
(Wade et. al 1998, Proteins 31:406-416)
TIM: answered questions
• Catalysts: E165 and H65
• Rate-limiting step: C=O polarization stimulates α-C deprotonation
• Enediolate stabilization: multi-pronged positive field
• E-S encounter mechanism – Active site region is crucial in attracting S
TIM: unresolved problems
• O1-O2 proton transfer– E165 and H95 are both involved, but at what
ratio: probably a random element
• Role of low-barrier H-bond (LBHB)– Does this explain how a neutral H95 can
protonate the enediolate?– Highly controversial concept
Acetylcholinesterase – diffusion control and amazing catalytic power
• Remarkable catalytic proficiency (~1017)
• Difficult nucleophilic step, unstable intermediate
• Electrostatic E-S attraction and guidance
Catalytic triad (S200, H440, E327)
Harel et. al. (2000)
Sussman et. al (1991). Science 253, 872-879.
Ache catalytic mechanism: nucleophilic carbonyl hydrolysis
acetyl-choline
Oxyanion 1
choline
acetate
Oxyanion 2
acetylcholine acetatecholine
Ache facilitates a difficult hydrolysis and stabilizes buried substrate charges
• S200 nucleophile polarization and deprotonation: the rate-limiting step
• Oxyanion intermediate stabilization: a negative charge in a buried active site
• Quaternary ammonium stabilization: a positive charge in a buried active site
Ache catalytic triad facilitates a difficult nucleophilic attack
S200: the nucleophile
H440 polarizes and deprotonates S200-OH nucleophile
Transition state analog:
TMTFA
E327: short, strong H-bond stabilizes H440+
(Massiah et. al 2001)
Crystal structure:
Harel et. al (1996). JACS 118, 2340-6.
Ache oxyanion hole stabilizes high-energy tetrahedral intermediate
acetylcholine
oxyanionOrdentlich et. al (1998). JBC 273 (31), 19509-17
Mechanism could be H-bond, dipole, or concerted proton transfer to O-
Ache catalytic center:A serine protease … sort of
Mirror image catalytic triads
Two-pronged oxyanion hole
Three-pronged oxyanion hole
Chymotrypsin AChE
Pdb: Yennawar et. al (1994). Pdb: Harel et. al (2000).Ref: Sussman et. al 1991.
TMA binding pocket: dealing with a buried positive charge
S200 nucleophile
Cation-π interactions
Coulombic interaction
H-bonds to waters
Harel et. Al (1993). PNAS 90(19),9031-5.
E-S attraction: Coulombic attraction and aromatic guidance
Negative charges on surface (red) attract positive acetylcholine
Aromatic residues in gorge make cation-π interactions with acetylcholine
Electrostatic potential gradient guides acetylcholine into the active site
Figure 8
Felder et al (1997). J. Mol. Graph. Model. 15, 318-327.
Also see Radic et. al (1997), Ripoll et. al (1993).
Acetylcholinesterase is a well-understood enzyme
• Catalytic triad facilitates difficult proton transfers
• Oxyanion stabilization
• TMA binding
• E-S attraction: Coulomb’s law and guidance (Felder).
Some “minor details” are still being worked out
• How much do short, strong hydrogen bonds (SSHBs) in the active site facilitate proton transfer?
• What is the precise mechanism of the oxyanion hole?
• What exact matrix of interactions gives rise to acetylcholine – AChE attraction?
Superoxide dismutase – designed to be super-perfect
• Converts O2- to H2O2,
Cu and Zn-dependent• Asymmetric potential
distribution -> E- attracts S- (Getzoff et. Al 1983, Klapper et. Al 1986)
• By reducing negative charge near active center, ke can be raised to 2*109s-1. (Getzoff et. Al 1992, Nature 358,
347-351).Structure: Tainer et. al. (1982). JMB 160, 181.
Enzyme catalytic mechanisms: qualitatively understood, quantitatively imprecise
• Proton transfers – pKa lowering, proton shuttling, networking, low-barrier H-bond
• Bond polarization – activate nucleophile, increase electrophilicity, lower pKa
• Intermediate stabilization – often electrostatic
• Perfect geometry – easy to observe, difficult to recreate (Knowles 1991).
E-S encounter: a simple but important problem
• Principal mechanism: Create an attractive electrostatic field near the active site, even if E and S are Coulombically repulsed
• Some E-S have been designed to have super-perfect (~109/s) encounter rates (e.g. SOD/superoxide, barnase/barstar)
• Precise details still being elucidated, but
To understand an enzyme: Progress and future directions
Identify enzyme
Identify catalytic residues
Precise structural
details (crystal structure)
Qualitative understanding
Quantitative (QM) understanding)
Enzyme Design
Predictions for the future
• Enzyme design / engineering – definitely possible, but can naturally high rates be attained?
• Can any protein fold be an enzyme, or are some protein folds more suited than others?
• Quantum level understanding – may help in optimizing enzymes, but not a critical part of basic understanding
Acknowledgements
• Dr. Jim Stivers
• Dr. Marc Ostermeier
• Dr. Jeff Gray and Gray lab members
• Practice talk attendees
ReferencesGeneral:Schreiber, G. and Fersht, A.R. (1996). Rapid, electrostatically assisted
association of proteins. Nat. Struct. Biol. 3 (5), 427-431.Radzicka, A. and Wolfenden, R. (1995). A proficient enzyme. Science 267
(5194), 90-93.Hiromi, K. (1979). Kinetics of Fast Enzyme Reactions. Kodansha Ltd., Tokyo.Alberty, R.A. and Hammes, G.G. (1958). Application of the theory of diffusion-
controlled reactions to enzyme kinetics. J. Phys. Chem. 62, 154-159.
Carbonic Anhydrase:Lindskog, S. (1997). Structure and mechanism of carbonic anhydrase.
Pharmacol. Ther. 74(1), 1-20.Jackman, J.E., Merz K.M. Jr., Fierke, C.A. (1996). Disruption of the active site
solvent network in carbonic anhydrase II decreases the efficiency of proton transfer. Biochemistry 35 (51): 16421-8.
Krebs, J.F., Ippolito, J.A., Christianson, D.W., Fierke, C.A. (1993). Structural and functional importance of a conserved hydrogen bond network in human carbonic anhydrase II.
Xue, Y., Liljas, A., Jonsson, B.H., and Lindskog, S. (1993). Structural analysis of the zinc hydroxide-Thr199-Glu106 hydrogen bond network in human carbonic anhydrase II. Proteins 17(1), 93-106.
Tu, C., Silverman, D.N., Forsman, C., Jonsson, B.H., and Lindskog, S. (1989). Role of histidine 64 in carbonic anhydrase II studied with a Site-Specific Mutant. Biochemistry 28, 7913-7918.
Triose Phosphate Isomerase:
Jogl, G., Rozovsky, S., McDermott, A.E., Tong, L. (2003). Optimal alignment for enzymatic proton transfer: structure of the Michaelis complex of triosephosphate isomerase at 1.2A resolution. PNAS 100(1), 50-55.
Kursula, I. and Wierenga, R.K. (2003). Crystal structure of triosephosphate isomerase complexed with 2-phosphoglycolate at 0.83A resolution. J. Biol. Chem. 278 (11), 9544-51.
Cui, Q. and Karplus, M. (2001). Triosephosphate isomerase: a theoretical comparison of alternative pathways. JACS 123 (10), 2284-90.
Wade, R.C., Gabdoulline, R.R., Luty, B.A. (1998). Species dependence of enzyme-substrate encounter rates for triose phosphate isomerase. Proteins 31, 406-416.
Harris, T.K., Abeygunawardana, C., Mildivan, A.S. (1997). NMR studies of the role of hydrogen bonding in the mechanism of triosephosphate isomerase. Biochemistry 36 (48), 14661-75.
Komives, E.A., Chang, L.C., Lolis, E., Tilton, R.F., Petsko, G.A., Knowles, J.R. Electrophilic catalysis in triosephosphate isomerase: the role of histidine 95. Biochemistry 30 (12), 3011-9.
Lodi, P.J. and Knowles, J.R. (1991). Neutral imidazole is the electrophile in the reaction catalyzed by triosephosphate isomerase: structural origins and catalytic applications. Biochemistry 30 (28), 6948-56.