Enzymes are Proteins with Defined 3D Structures

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Ribonuclease A

2,3-dihydroxybiphenyl 1,2-dioxygenase (BphC)

-chymotrypsin

Active site:

uncatalysed reaction

acid-catalysed reaction

Freeenergy

Reaction co-ordinate

Eact(uncat)

Eact(cat)

ΔG

transition states

uncatalysed reaction

ESEPenzyme-catalysed

reaction

Freeenergy

Reaction co-ordinate

Eact(uncat)

Eact(cat)

ΔG

transition state

E.Int

A.

B.

S

P

SH+PH+

S

P

Enzyme Catalysis: What Enzymes Can & Can’t DoAcid-catalysed reaction

Enzyme-catalysed reaction

ESE + S

1. Direct UVP (UV active at 394 nm)

+ ENZ

time

slope v

S* P*2. Radiochemical

separate P*

scintillation counting

time

P*(counts perminute)

3. Indirect UV

ENZ ENZ

ENZ

UV active at 340 nm

+ ENZ

time

slope v

4. Coupled UV assay

ENZ ENZ 2

excess of coupling enzyme

monitor decrease in absorbance at 340 nm

S

A394

S P

NAD+NADH

A340

S P Q

NAD+NADH

Types of Enzyme Assay

1 Unit = activity required to convert 1 µmole S to P per minute

O

OUDPNHAc

HOHO

HN

ONH

O

HN

MurG

N-dansyl lipid I

O

NHAc

OO

OH

O

HN

O

NH-O2C

O

HN

O P

O

O-

O P

O-

O

O

O

NHAcHO

HO

OHN

NHO

NH

HN

O

NH

O

HN

CO2

O2C

S OO

NMe2

heptaprenyl

Ex 290 nm

340 nm

Em 500 nm

Fluorescence Resonance Energy Transfer Assay for MurG

0.2 M Tris pH 7.5, 10 mM MgCl2, 0.2% CHAPS2.7 µM Fl UDPGlcNAc, 3.0 µM dansyl lipid I+ 3.0 µg E. coli MurG

J.J. Li and T.D.H. Bugg,Chem. Commun., 182-183 (2004).

lyse cells at high pressure

extractcelldebris

high speedcentrifugation

Obtain or grow cellscontaining enzyme

enzymes

cell wall

Preparation of Cell Extract

Volume Enzyme activity Protein concentration Specific activity Purification

(ml) (units/ml) (mg/ml) (units/mg) (-fold)

Crude extract 14 13.1 62.0 0.212 1.0

DEAE sephadex pool 19 11.6 17.0 0.684 3.2

Phenyl agarose pool 11 11.8 0.085 140 662

MonoQ anion exchange pool 6.0 29.2 0.037 787 3710

Purification Table

Enzyme Purification

SDS-PAGE gel

k2

k-1

k1E + PESE + S

Michaelis-Menten Model for Enzyme Kinetics

Kinetic Model

= kcat [E]o [S]

Km + [S]+ [S]

k1

k2 [E]o [S]

k-1 + k2

Rate of production of P = k2 [ES] =

vmax

Km + [S]

vmax [S]=Observed rate v

where vmax = kcat [E0]

v

vmax/2

Km[S]

1/[S]

1/v

Lineweaver-Burk Plot:

1

vmax

Km= +

vmax

1

v

1

slope Km/vmax

1/vmax

Eadie-Hofstee Plot:

v = vmax - Km v

v

v/[S]

vmax

slope -Km

[S] [S]

Graphical Determination of Km & kcat

ES

E + S

[S] >> Km

v = kcat [Eo] Enzyme saturated with substrate

ESE + S

[S] = Km

v = kcat [Eo] Enzyme 50% saturated with substrate

2

ES

E + S

[S] << Km

v = kcat [Eo][S] Free enzyme + substrate

Km

What do Km & kcat really mean?

kcat - turnover number1st order rate constant (units s-1) for turnoverat high [S]

Km - Michaelis constantMeasure of affinity ofSubstrate bindingBUT not the same as Kd!

kcat/Km - catalytic efficiency2nd order rate constant(units M-1 s-1) for turnoverat low [S]

A) Competitive Inhibition

E + S ES E + P

EI

Ki + I

1/vmax

1/[S]

1/vinc. [I]

unchanged

Km(app) = Km 1 + [I]

Ki

B) Noncompetitive Inhibition

-1/Km

1/[S]

1/v

+ IKi

EI + S

E + PESE + S

EIS

Ki + I

inc. [I]

unchanged

Ki

vmax(app) = vmax 1 + [I]

Enzyme Inhibition - Reversible

OO

O OH

A

tRNA

O

NH3

NH2

OO

O OH

A

tRNA

O

NH3

O

NH3

L-Lys

D-Ala

γ-D-Glu

D-Ala

L-Ala

MurNAc

C55-OPP

NH

L-Lys

D-Ala

γ-D-Glu

D-Ala

L-Ala

MurNAc

C55-OPP

NH

L-Lys

D-Ala

γ-D-Glu

D-Ala

L-Ala

MurNAc

C55-OPP

GlcNAc GlcNAc GlcNAc

HOO

O R

N

PO

NH3

-O

N

N

N

NH2

R = OH, H

OO

O OH

tRNA

O

NH3

NH

L-Lys

D-Ala

γ-D-Glu

D-Ala

L-Ala

MurNAc

C55-OPP

GlcNAc N

N

N

N

NH2

Transition State Analogues for Ligase MurM

Inhibitor design: mimic tetrahedral transition state:

Transition state Phosphonate analogue

0.0 0.2 0.4 0.6 0.8 1.00

20

40

60

80

100

MurM activity (%)

Inhibitor Conc (mM)

Inhibition by 2’-deoxyadenosine analogue

IC50 = 100 µM

HOO

O

N

PO

NH3

-O

N

N

N

NH2

+ IKi

EI

E + PESE + S

kiE-I

Act

time

vi

1/vi

1/[I]

1/ki

slope Ki/ki

HN N

His57

O

Ser195

H

P

O

F

Enzyme Inhibition - Irreversible Inhibition

e.g. serine protease inhibitor DFP

Data SimulationData Simulation Single Exponential ModeSingle Exponential Mode

A = AA = A00 + +AA11 exp (- exp (-kk11t)t)

Double Exponential ModeDouble Exponential Mode

A= AA= A00 + + AA11 exp (- exp (-kk11t) + t) + AA22 exp (-exp (-kk22t)t)

Triple Exponential ModeTriple Exponential Mode

A= AA= A00 + + AA11 exp (- exp (-kk11t) + t) + AA22 exp (-exp (-kk22t) + t) +

AA33 exp (-exp (-kk33t) t)

Data SimulationData Simulation Single Exponential ModeSingle Exponential Mode

A = AA = A00 + +AA11 exp (- exp (-kk11t)t)

Double Exponential ModeDouble Exponential Mode

A= AA= A00 + + AA11 exp (- exp (-kk11t) + t) + AA22 exp (-exp (-kk22t)t)

Triple Exponential ModeTriple Exponential Mode

A= AA= A00 + + AA11 exp (- exp (-kk11t) + t) + AA22 exp (-exp (-kk22t) + t) +

AA33 exp (-exp (-kk33t) t)

Pre-Steady State Kinetics —— Application to C-C Hydrolase MhpC

CO2

O

O2C OH

CO2

O

O2C O

O2C OH CO2

CO2

-

-

-

-

+

Low pH A317 High pH A394

MhpC

-+

-

-

A270

0

1

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4Association Time (s) -2? 10

Position (Arc s)

? 10-2

-4

-3

-2

-1

0

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4Association Time (s) -2? 10

Error (Arc s)

? 10-1

0

1

2

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4Association Time (s) -2? 10

Position (Arc s)

? 10-2

-5

-2.5

0

2.5

5

0 0.2 0.4 0.6 0.8 1 1.2 1.4Association Time (s) -2? 10

Error (Arc s)

Fit with single exponential (1 step) Fit with double exponential (2 step)

0.037-55.40.223-146H263A

18-117144-131Wild type.270nm(dienol P)

0.04078.5 0.34 96.6H263A

153.2145.6Wild type.317nm(dienol S)

kk2 2 (s(s-1-1))AA22 (×10 (×1033))kk1 1 (s(s-1-1))AA11 (×10 (×1033))pH=7.0

E + RFP E.RFP E.RFP E.succ E + succinate150s 18 s-1 -1

k

0.34s-1 0.04s-1

H263 is involved in both ketonization and C-C cleavage !H263 is involved in both ketonization and C-C cleavage !H263 is involved in both ketonization and C-C cleavage !H263 is involved in both ketonization and C-C cleavage !

Analysis of His263Ala Mutant

pH=8.0 KKMM (μM) (μM) kkcatcat (s (s-1-1)) kkcatcat/ K/ KM M (M(M

-1-1ss-1-1))

WT 6.8 28 4.1 x 106

H263A 5.5 0.0029 5.3 x 102

Kinetic ParametersKinetic Parameters Kinetic ParametersKinetic Parameters

Pre-steady state Kinetic ParametersPre-steady state Kinetic Parameters Pre-steady state Kinetic ParametersPre-steady state Kinetic Parameters

20ms 317nm20ms 317nm20ms 317nm20ms 317nm 200ms 317nm200ms 317nm200ms 317nm200ms 317nm 200s 317nm200s 317nm200s 317nm200s 317nm

Analysis of Ser110Ala Mutant

pH=8.0 KKMM (μM) (μM) kkcatcat (s (s-1-1)) kkcatcat/ K/ KM M (M(M

-1-1ss-1-1))

WT 6.8 28 4.1 x 106

S110A 18.5 0.0054 2.9 x 102

Kinetic ParametersKinetic Parameters Kinetic ParametersKinetic Parameters

Pre-steady state KineticPre-steady state Kinetic Pre-steady state KineticPre-steady state Kinetic

E + RFP E.RFP E.RFP E.succ E + succinate150s 18 s

-1 -1k

E.RFP*

140s-1 0.02s-1

3.1s-1