1

The control of enzyme activity

Enzyme Engineering

Two ways to control enzyme activity

1. Controlling concentration of enzyme : Regulation of transcription and translation →Long-term

2. Controlling activities of enzyme → Rapid responses

6.2 Control of the activities of single enzymes

1. By covalent bonds

2. By reversible binding of ‘regulator’

3. Inhibitor, [S], product inhibition, etc…

2

6.2 Control of the activities

1. Control by covalent bondIrreversible, mostly intracellular regulation

Example: phosphorylation, ubiquitination, …

1.1 Irreversible changes in covalent bond (Proteolysis)

(mostly for extracellular regulation)

6.2.1.1 Control by irreversible changes in covalent bond

Signal amplification mechanism of proteolysis

1) Pancreatic proteases

2) Blood coagulation Fibrinogen

prothrombin → thrombin →

Fibrin

3

6.2.1.2 Control by reversible changes in covalent bond

Phosphorylation-dephosphorylation

Adenylation or ADP-ribosylation also regulate enzyme activity

Methylation, acetylation, tyrosinolation, etc…do not regulate activity

1. Phosphorylation

Kinase : phosphorylation of other protein

Protein phosphatase : dephosphorylation

Human has 2000 kinase and 1000 protein phosphatase

Phosphorylation occurs on serine/threonine, tyrosine using ATP(GTP) as a substrate

4

6.2.1.2 Control by reversible changes in covalent bond

Ser/Thr phosphorylationinvolves in metabolic control, while Tyrphosphrylation in cell growth/differentiation

6.2.1.2 Control by reversible changes in covalent bond

Adenylylation on Tyr of glutamine synthase →Reducing enzyme activity

Nitrogenase from nitrogen-fixing bacteria is regulated by ADP-ribosylation on Arg →Reducing enzyme activity

Features

1. Rapid response and signal amplification

2. Continuous response

Ser/thr phos → in balance

Tyr phos → shift to dephosphorylation,

meaning the transient response

5

6.2.2 Control by Ligand binding

Conformation changes by ligand binding regulates enzyme activity

Firstly found in biosynthetic pathway

6.2.2 Control by Ligand binding

From Monod and Jacob

1. Effectors are structurally distinct from substrate or product, so they are unlikely bound to active site (allosteric)

2. Enzyme kinetics are sigmoidal rather than hyperbolic

3. Some treatments desensitize the enzymes to effector without losing enzyme activity

4. In general, the regulated enzymes are multimeric (structurally complex)

6

6.2.2.2 Kinetics of Ligand binding

Starting from Hb model

Allosteric effect

P + A PA

][]][[

PAAPK =

KAA

PAPPAY

+=

+=

][][

][][][

6.2.2.2 Kinetics of Ligand binding

Hill eq. (1910)

KAA

PAKPAY h

h

n

n

+=

+=

][][

][][

h = 1

h > 1

P + nA PAn

][]][[

n

n

PAAPK =

7

6.2.2.2 Kinetics of Ligand binding

KA

YY h][

1=

−

h : cooperativity

h is generally smaller than nh can be obtained by experiment

KAhY

Y log]log[)1

log( −=−

6.2.2.2 Kinetics of Ligand binding

Monod, Wyman, and Changeux (MWC) model

1. At lease one axis of symmetry

2. The conformation of each subunit is affected by others

3. Two conformation states, R and T

4. Either in R or T state, the symmetry is conserved - no ‘hybrid’ state

Fraction of subunitbound to substrate

8

6.2.2.2 Kinetics of Ligand binding

Two parameters are defined

a; conc. Free ligand, c=KR/KT, L=[T0]/[R0]

6.2.2.2 Kinetics of Ligand binding

L and c can be obtained experimentally (in hemoglobin, L=9050, c=0.014)

K system and V systema) No Substrate, no Effector

b) Adding substrate

c) Adding effector

9

6.2.2.2 Kinetics of Ligand binding

Koshland, Nemethy, and Filmer (KNF) model

“Induced-fit” hypothesis

1. Without substrate, the protein exist in one state

2. The conformational change is sequential

3. The intxns b/n subunits can be positive/negative

6.2.2.2 Kinetics of Ligand binding

Differences between MWC and KNF models

MWC model

KNF model

10

6.2.2.2 Kinetics of Ligand binding

The significance of the cooperativity in enzyme kinetics : small changes in [S] induce large changes in v

6.3 Control of metabolic pathways

Intrinsic control vs extrinsic control

Intrinsic control : Control of metabolic activity by metabolite concentrations (Unicellular organism)

Extrinsic control : Control of metabolic activity by extracellular signals, such as hormones or nervous stimulation (Multicellular organism)

Secondary signaling molecules : cyclic AMP, Ca2+, inositol 1,4,5-triphosphate, and diacylglycerol

11

6.3 Control of metabolic pathways

1. Amplification

2. Signaling depending on the # of receptors/cell

3. One protein kinase activating many different enzymes

6.3 Control of metabolic pathways

6.3.1 General aspects of intrinsic control

Finding most economic way to regulate the flux

12

6.3 Control of metabolic pathways

Carbamoyl-phosphate synthase is inhibited by pyrimidines, but not by arginineCarbamoyl-phosphate synthase is activated by orinithineOther methods of regulation include isoenzymes(ex. Aromatic amino acid pathway)

6.3 Control of metabolic pathways

6.3.2 Amplification of signals

1. Substrate cycles

If E2 and E-2 are catalyzed by different enzymes,

AMP activates 1 and inhibits 2

13

6.3 Control of metabolic pathways

Control of glucose/glycogen metabolism in liver

Other examples include PEP/pyruvateinterconversion, fatty acid/triglycerol in adipose tissue, etc…Sometimes working as futile cycle

6.3 Control of metabolic pathways

2. Interconvertible enzyme cycle

Control of enzyme activities by covalent modification

0.5% changes of modifier can regulate enzyme activity from 10 to 90%

High ratios of [NADH]/[NAD+] and [acetylCoA]/[CoA] activate kinase and inactivates protein phosphatase

14

6.3 Control of metabolic pathways

1% increase of [cAMP] can convert 50% of phosphorylase b to a within 2 seconds

6.3 Control of metabolic pathways

3. Theoretical approach to analyze the metabolic pathways

1. Metabolic flux analysis

2. Metabolic control analysis

15

Metabolic Flux Analysis

X1 X2 X3v1 v2 v3 v4

211 vv

dtdX

−=

322 2vv

dtdX

−=

433 vv

dtdX

−=

vSdtdX

⋅=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−

−=

110002100011

S

V1 V2 V3 V4

X1

X2

X3

Example 1

322 XX →

Quasi Steady State Assumption

0=⋅= vSdtdX

01100

02100011

4

3

2

1

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−

−

vvvv

16

X1

X2X3

X4

v2v3

v4

v5

v6

v1

4322 XXX →+

0=⋅= vSdtdX

0

011000001100102010

000111

6

5

4

3

2

1

=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−−

−−−−

vvvvvv

Example 2

0

011000001100102010

000111

6

5

4

3

2

1

=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−−

−−−−

vvvvvv

0

001100000110100201

010011

6

1

5

4

3

2

=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−−

−−−−

vvvvvv

Type I Operation

17

0

001100000110100201

010011

6

1

5

4

3

2

=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−−

−−−−

vvvvvv

[ ] 0=⎥⎦

⎤⎢⎣

⎡

m

umu V

VSS

0=+ mmuu VSVS

mmuu VSVS −=

mmuu VSSV 1−−=

Example 3

Acetate(internal)

Glucose

G6P

F6P

Ru5P

X5P R5P

GAP

PEP

2 NADPHCO2

PEP

PYR

GAP S7P

PYR

AcCoA

ICT

SUC KG

OAA

F6P E4P

ATP

NADHATP

ATP

NADHCO2

ATP

Acetate(external)

Acetatefrom proteinproduction

CO2

CO2(internal)

CO2(external)

Biomass

NADH

AcCoA

ATPNADHCO2

NADHCO2

NADHFADH2

ATPNAD(P)H 2 ATP

*

qglc

v3

vpyr

vpdhvppc

vacev8

vtal

vtkt

v16v15

v14

v12

v11

vglyoxvict

vbiomass

vatp

vresp

qCO2

qace

vpgi

vpep

18

Jglc Jpgi J3 Jpep Jpyk Jpdh Jace J8 Jict J11 J12 Jppc J14 J15 J16 Jtkt Jtal Jresp Jatp Qco2 Qace Jbiomass

G6P 1 -1 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -205

F6P 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -70.9

GAP 0 0 2 -1 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 -1625

PEP -1 0 0 1 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -519.1

PyR 1 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2832.8

AcCoA 0 0 0 0 0 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 -4028.8

OAA 0 0 0 0 0 0 0 -1 0 0 1 1 0 0 0 0 0 0 0 0 0 -1786.7

ICT 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0

KG 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 -1078.9

SUC 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0

Ru5P 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -1 0 0 0 0 0 0 0

R5P 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 -897.7

X5P 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0

S7P 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0

E4P 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -361

NAD(H)P 0 0 0 1 0 1 0 0 1 1 1 0 2 0 0 0 0 -1 0 0 0 -14678

ATP 0 0 -1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 2 -1 0 0 -18485

CO2 0 0 0 0 0 1 0 0 1 1 0 -1 1 0 0 0 0 0 0 -1 0 1793

acetate 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 387

Assumption : Vglyox = 0, Otherwise, Su is singular

mmuu VSSV 1−=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

=2.23.0

1

2CO

ace

glc

m

qqJ

V

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

0000788.056.735.3

0285.00285.00285.00992.0128.0226.0466.0466.0551.0551.0271.014.1363.063.1879.0856.0

16

15

14

12

11

8

3

Biomass

atp

resp

tal

tkt

ppc

ict

ace

pdh

pyr

pep

pgi

u

JJJJJJJJJJJJJ

JJJJJ

J

V

19

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

0000788.056.735.3

0285.00285.00285.00992.0128.0226.0466.0466.0551.0551.0271.014.1363.063.1879.0856.0

16

15

14

12

11

8

3

Biomass

atp

resp

tal

tkt

ppc

ict

ace

pdh

pyr

pep

pgi

u

JJJJJJJJJJJJJ

JJJJJ

J

V

Acetate(internal)

Glucose

G6P

F6P

Ru5P

X5P R5P

GAP

PEP

2 NADPHCO2

PEP

PYR

GAP S7P

PYR

AcCoA

ICT

SUC KG

OAA

F6P E4P

ATP

NADHATP

ATP

NADHCO2

ATP

Acetate(external)

Acetatefrom proteinproduction

CO2

CO2(internal)

CO2(external)

Biomass

NADH

AcCoA

ATPNADHCO2

NADHCO2

NADHFADH2

ATPNAD(P)H 2 ATP

*

qglc

v3

vpyr

vpdhvppc

vacev8

vtal

vtkt

v16v15

v14

v12

v11

vglyoxvict

vbiomass

vatp

vresp

qCO2

qace

vpgi

vpep

mmuu VSSV 1−=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

=35.3

237.01

resp

ppc

glc

m

JJJ

V

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

0000829.0204.032.242.7

0299.00299.00299.0104.0134.0500.0500.0590.0590.0174.010.1331.061.1873.0849.0

2

16

15

14

12

11

8

3

Biomass

ace

CO

atp

tal

tkt

ict

ace

pdh

pyr

pep

pgi

u

JqqJJJJJJJJJJ

JJJJJ

J

V

20

Metabolic Flux Analysis I

Mass Balance Equations

Quasi Steady State Approximation

Removing the Linearly Dependent

Reactions

Measure the Fluxes as many as Degree

of Freedom

Metabolic Flux Analysis II

Mass Balance Equations

Quasi Steady State Approximation

Removing the Linearly Dependent

Reactions

Measure the Fluxes as many as

Degree of Freedom

• More Constraints

• Optimal Solution

21

0=⋅= vSdtdX

max,0 ii vv ≤≤

max,0 jj vv ≤≤

max,0 kk vv ≤≤

Jbiomass Maximum

::

42 =+ yx )0,0( ≥≥ yx

x

y

Maxyx →+ 32

4

2

1

2

22

From Edwards and Palsson, PNAS, 97:5528

Summary : Metabolic Flux Analysis

Metabolic Flux Distribution

Maximum Yield

Predicting Growth Rates (wild type and

mutant)

Relying on Biochemical Knowledge

No Kinetics and Regulatory

Information

23

Metabolic Control Analysis

X1 X2 X3e1 e2 e3 e4

i

k

i

k

k

iJi Ed

JddEdJ

JEC k

lnln

==

Flux control coefficient

i

kvi dS

dvE k =Enzyme

FluxkJ

iCSlope =

Steady StateElasticity coefficient

Theorems 1=∑ JnC

0=∑ iS

Ji EC

Metabolic Control Analysis

Rate limiting enzyme

How the activity change in one enzyme can

affect on the overall pathway

Hard to estimate parameters