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.