Biochemistry: Regulation of enzyme activity

Development of Complex Curricula for Molecular Bionics and Infobionics Programs within a consortial* framework**

Consortium leader

PETER PAZMANY CATHOLIC UNIVERSITY

Consortium members

SEMMELWEIS UNIVERSITY, DIALOG CAMPUS PUBLISHER

The Project has been realised with the support of the European Union and has been co-financed by the European Social Fund ***

**Molekuláris bionika és Infobionika Szakok tananyagának komplex fejlesztése konzorciumi keretben

***A projekt az Európai Unió támogatásával, az Európai Szociális Alap társfinanszírozásával valósul meg.

PETER PAZMANY CATHOLIC UNIVERSITY SEMMELWEIS

UNIVERSITY

Semmelweis University

ORGANIC AND BIOCHEMISTRY

Regulation of enzyme activity and its modelling

http://semmelweis-egyetem.hu/

(Szerves és biokémia)

(Enzimek szabályozása és ennek modellezése)

Krasimir Kolev

Biochemistry: Regulation of enzyme activity

Lecture objectives

At the end of the presentation the participant will be able:

1) To define the terms enzyme, cofactor, coenzyme 2) To discuss the classification of enzymes

3) To describe the connection between steady state and the regulation of metabolic pathways

4) To interpret the time scale of different regulatory mechanisms in metabolism 5) To define the term steady state of a single biochemical reaction

6) To list the conditions for optimal enzyme activity

7) To understand the relation between experimental data collection and models of reactions

8) To define models of enzyme-catalyzed reactions and characterize their adequateness

9) To apply kinetic parameters for the solution of biologically relevant questions 10) To discuss the general principles of enzyme regulation

Biochemistry: Regulation of enzyme activity

Structure of the active site

of the enzyme

• side chains of amino acids

• coenzymes^DEF (co-substrates)

• cofactors^DEF and prosthetic groups^DEF

Biochemistry: Regulation of enzyme activity

Coenzymes

molecules which participate in the catalytic mechanism and are changed in the course of the reaction, but are regenerated in an independent separate reaction

Example:

Biochemistry: Regulation of enzyme activity

Cofactors

molecules or ions which participate in the catalytic mechanism, but are not changed at the end of the reaction

Example: Zn²⁺ in the action of metalloproteases

Classification of enzymes

Biochemistry: Regulation of enzyme activity

Class Type of reaction Examples

1. oxidoreductases^DEF electron transfer dehydrogenases, oxidases, reductases, peroxidases, catalase, oxygenases, hydroxylases

2.transferases^DEF transfer of chemical groups transaldolase, transketolase, acyl-, methyl-, glucosyl and phosphoryl- transferases, kinases

3. hydrolases^DEF cleavage of chemical bonds accompanied by water addition

esterases, glucosidases, peptidases,

phosphatases, phospholipases, amidases, desaminases, ribonucleases

4. lyases^DEF cleavage of C-C or C-N bonds decarboxylases, aldolases, hydratases, dehydratases, synthases, lyases

5.isomerases^DEF transfer of a chemical group or a double bond within a molecule

racemases, eepimerases, isomerases, mutases

6. ligases^DEF formation of a C-C bond synthetases, carboxylases

Biochemistry: Regulation of enzyme activity

Hydroxylase (oxidoreductase)

Biochemistry: Regulation of enzyme activity

Kinase

(transferase)

Biochemistry: Regulation of enzyme activity

Protein phosphatase (hydrolase)

Biochemistry: Regulation of enzyme activity

Aldolase (lyase)

Biochemistry: Regulation of enzyme activity

Mutase (isomerase)

Biochemistry: Regulation of enzyme activity

Carboxylase (ligase)

Biochemistry: Regulation of enzyme activity

Metabolic steady state

and biochemical regulation

Fluxes in the citric acid cycle determined from the spread of ¹⁴C

Biochemistry: Regulation of enzyme activity

Time scale of biochemical process and their experimental

observation

Biochemistry: Regulation of enzyme activity

Kinetic steady state

of single enzyme-catalyzed reactions

1 2

1

k k

E S k ES E P

−

+ ←⎯ ⎯→ ⎯→ +

steady state

Biochemistry: Regulation of enzyme activity

Experimental data from continuous

and end-point

measurements

The product concentrations indicated by red asterisk are plotted as end-point velocity (product divided by time) in the right-hand side graph (sources of error!).

Biochemistry: Regulation of enzyme activity

Modelling of steady state reactions

1 2

1

k k

E S k ES E P

−

+ ←⎯ ⎯→ ⎯→ +

The simplest reaction scheme:

0 0

0

. .( )

p t M

k E S P dP

dt K S P

= −

For any time point of a steady state window-frame:

+ −

where ^{1 2}

1 M

k k

K k

− +

= k_p=k₂

0

0 0 0

1 ln

. .

M

p t p t

K S

t P

k E k E S P

= +

−

Mathematical problem: no analytical integration for P as a function of t only for t as a function of P, which raises problems if the equation below is used for identification of kinetic parameters (conventional fitting procedures assume negligible errors in the independent variable)

Biochemistry: Regulation of enzyme activity

Effect of temperature on the rate of enzyme-catalyzed reactions

1 2

1

k k

E S k ES E P

−

+ ←⎯⎯→ ⎯→ +

For any rate constant in the scheme the Arrhenius equation

RT E_a

Ae k

−

= is valid, but enzymes are denatured in the course of time and denaturation is accelerated at higher temperatures.

Biochemistry: Regulation of enzyme activity

Effect of pH on the rate of enzyme-catalyzed reactions

The degree of protonation of the amino acid side chains determines the conformation of the active site as well as the interactions between enzyme and substrate.

Biochemistry: Regulation of enzyme activity

The isoelectric point of the common amino acids allows optimal enzyme action over a broad range of pH^DEF

chemical character at pH 7.4

Biochemistry: Regulation of enzyme activity

Michaelis-Menten model

steady state assumption (ES=const) + P~0

0 0

0

. .( )

p t M

k E S P dP

dt K S P

= −

+ −

0 0 0

. .

p t M

k E S dP

dt = K S +

complete course of reaction initial phase ΔP<0.1S₀

Biochemistry: Regulation of enzyme activity

Identification of kinetic parameters with non-linear regression

0 0 0

. .

p t m

k E S v = K S

+

max _p

.

V = k E V

K

Biochemistry: Regulation of enzyme activity

Identification of kinetic parameters with linear regression

max max 0

1 1 1

m

. K

v V = + V S

max

1 V

m

1

− K

Biochemistry: Regulation of enzyme activity

Discrepancies of kinetic parameters gained with non-linear and linear regression from the same experiment

Potential reasons:

1. violation of the model assumptions (e.g. v is calculated from non-linear stage of the progress curve as shown below) 2. the reciprocal transformation renders the slope more sensitive to v gained at low Swhich is measured with larger experimental error

Biochemistry: Regulation of enzyme activity

2

, , ,

2

1 1 ,

i M

n t

mean i j i j M

j i std j

P P

χ P

= =

⎡ − ⎤

= ⎢ ⎥

⎣ ⎦

∑∑

Goodness-of-fit of the model Chi

as a measure of goodness-of-fit

P_mean and P_std: mean and standard deviation of measured data

P^M: model values

Biochemistry: Regulation of enzyme activity

Comparison of different models 1.

The simplest scheme yields a poor fit

1 2

1

k k

E S

ES E P

−

+ ←⎯ ⎯→ ⎯→ +

1 2

1 m

k k

K k

− +

= k_p=k₂

0 0

0

. .( )

p t M

k E S P dP

dt K S P

= −

+ −

Biochemistry: Regulation of enzyme activity

Comparison of different models 2.

A product inhibition step improves the fit

1 2 3

1 3

k k k

k k

E S ES EP E P

− −

⎯→ ⎯→

+ ←⎯ ⎯→ ←⎯ +

( )

(

)

1 2 3

.

m

k k k

K k k k

− +

= +

2 3

2 3

.

p

k k k

k k

= +

3 3 i

K k

k

= −

0 0

0

. .( )

.(1 . )

p t

M i

k E S P dP

dt K K P S P

= −

+ + −

Biochemistry: Regulation of enzyme activity

Comparison of different models 3.

Acceptable fit in a model including irreversible enzyme inactivation

1 2 3

1 3

2 3

' '

k k k

k k

E S ES EP E P

J J

E S E P

− −

⎯→ ⎯→

+ ←⎯ ⎯→ ←⎯ +

↓ ↓

2 0 3

0

. ( )/ . . .

1 . ( )/

t t m t i

i m

dE J E S P K J E K P

dt K P S P K

− +

=− + + −

0 0

. .( )

.(1 . )

p t

m i

k E S P dP

dt K K P S P

= −

+ + −

Biochemistry: Regulation of enzyme activity

Differentiation of catalytic mechanisms based on kinetic data 1.

Sequential mechanism of a two-substrate reaction^DEF

Biochemistry: Regulation of enzyme activity

Differentiation of catalytic mechanisms based on kinetic data 2.

Ping-pong mechanism of a two-substrate reaction^DEF

Biochemistry: Regulation of enzyme activity

Practical applications of kinetic parameters 1.

Which compound is the physiological substrate of a metabolic pathway?

Necessary information: in vitro determined kinetic parameters + in vivo concentration data

substrate V_max (μmol.min^-1.g^-1) K_m (μM) intracellular

concentration (μM)

glucose 17 10 10

fructose 25 1000 1

Example: Parameters of brain hexokinase

Biochemistry: Regulation of enzyme activity

Practical applications of kinetic parameters 2.

Which step is rate-limiting in a metabolic pathway?

Necessary information: in vitro determined kinetic parameters + in vivo concentration data

N.B.: at steady state fluxes at all steps in a metabolic pathway are equal!

10,01 100 10,1

0,01 90 0,1

S ←⎯⎯ ⎯⎯⎯ ⎯ ←⎯⎯ ←⎯⎯ → ⎯⎯→ ⎯⎯→ A B P

Look for:

- non-equilibrium reaction

- in vivo V_max is relatively low compared to the neighboring reactions - [S]>>K_m

Biochemistry: Regulation of enzyme activity

Estimated displacement from equilibrium based on in vivo mass action ratio

ρ = K ^Γ

where Γ is the mass action ratio, K is

the equilibrium constant of the respective reaction

Candidates for rate-limiting role:

He (hexokinase)

Pf (phosphofruktokinase)

Biochemistry: Regulation of enzyme activity

In vivo V

as an additional indicator of rate-limiting role

V/J_gly: ratio of in vivo V_max to glycolytic flux

Biochemistry: Regulation of enzyme activity

A refined concept of rate-limiting reactions:

metabolic control coefficient

2 1

2

2 1

2 J

E

J J C J

E E E

−

= −

where C is the metabolic control coefficient of enzyme E when its activity is changed from value E₁ to E₂ (J₁ and J₂ are the respective pathway fluxes for the two enzyme activities)

1 ^J 2 ^J ... _n ^J 1 C + C + + C =

The sum of C of all enzymes in a pathway is 1. The value of C is an indicator of the relative contribution of an enzyme to the regulation of the pathway.

Biochemistry: Regulation of enzyme activity General schemes of enzyme regulation

(a) end-product inhibition (b) end-product inhibition +

coordination at branching points

Biochemistry: Regulation of enzyme activity

“Linear” inhibition 1.

Competitive inhibitor^DEF : a reversible inhibitor, which increases the K_m value and does not change the V_max value of the enzyme

max 0

0

.

(1 )

m

ic

dP V S

dt I

K S

K

=

+ +

(1 )

ic

K K I

= + K

Biochemistry: Regulation of enzyme activity

“Linear” inhibition 2.

Non-competitive inhibitor^DEF : a reversible inhibitor, which decreases the V_max value and does not change the K_m value of the enzyme

max 0

0 app

.

m

dP V S dt = K S

+

max max

1

app

i

V V

I K

=

+

Biochemistry: Regulation of enzyme activity

Allosteric

effectors

Binding to a site different from the catalytic site may result in either activation (A) or inhibition (I).

Biochemistry: Regulation of enzyme activity

Cooperativity

Binding of a single effector to an allosteric site changes the binding of substrates to multiple sites on different subunits.

Biochemistry: Regulation of enzyme activity Models of cooperativity 1.

Symmetric model

Models of cooperativity 2.

Sequential model

Biochemistry: Regulation of enzyme activity

Biochemistry: Regulation of enzyme activity

Regulation of enzyme activity through specialized subunits

Example: activation of cAMP-dependent

protein kinase

Biochemistry: Regulation of enzyme activity

Regulation of enzyme activity through reversible covalent modification

phosphorylation dephosphorylation

Biochemistry: Regulation of enzyme activity

Regulation of enzyme activity through irreversible covalent modification

Example: activation of prothrombin by a specific protease (factor Xa)

N.B. Cleaved peptide bonds cannot be

resealed.

Messages to take home

1) Enzymes accelerate the rate of the reactions, but do not change their equilibrium state

2) The classification of enzymes is based on the type of the catalyzed reaction 3) Metabolic pathways are typically in a steady state with all reactions

proceeding at the same rate and external regulators shift the pathway from one steady state to another

4) Metabolic pathways are regulated through changes of enzyme activities by inhibitors and activators or covalent modification, as well as through control of enzyme synthesis and degradation

5) A single biochemical reaction is in steady state, if the rates of formation and breakdown of the enzyme-substrate complex are equal

6) Major factors affecting enzyme activity: concentration of enzyme and substrate, temperature, pH

7) Mathematical models of enzyme-catalyzed reactions allow prediction of the responses of metabolic pathways in the living organisms.

Biochemistry: Regulation of enzyme activity

Biochemistry: Regulation of enzyme activity

Comprehension problem 1

Which statement is true regarding the role of ATP in the hexokinase catalyzed reaction?

1. coenzyme 2. cosubstrate 3. cofactor

4. prosthetic group

5. maintains coupling-in-series of the catalyzed reaction in the metabolic pathway

A. 1 B. 1,2 C. 1,2,3 D. 1,2,3,4 E. 1,2,3,4,5

Biochemistry: Regulation of enzyme activity

Comprehension problem 2

1. Classify the enzyme catalyzing the reaction below!

2. Define the role of ATP

A 1. oxidoreductase 2. cofactor B 1. transferase 2. cofactor

C 1. ligase 2. coenzyme

D 1. transferase 2. coenzyme

E 1. lyase 2. cofactor

Biochemistry: Regulation of enzyme activity

Comprehension problem 3

1. Classify the enzyme catalyzing the reaction below!

2. Define the role of NAD

A 1. oxidoreductase 2. cofactor B 1. transferase 2. cofactor

C 1. ligase 2. coenzyme

D 1. transferase 2. coenzyme

E 1. oxidoreductase 2. coenzyme

Biochemistry: Regulation of enzyme activity

Comprehension problem 4

1. Classify the enzyme catalyzing the reaction below!

2. Define the role of biotin

A 1. oxidoreductase 2. cofactor B 1. transferase 2. cofactor

C 1. ligase 2. cofactor

D 1. transferase 2. coenzyme

E 1. lyase 2. cofactor

Biochemistry: Regulation of enzyme activity

Comprehension problem 5

Select the pairs of time intervals and equations which apply to the enzyme-catalyzed reaction presented in the figure below!

1: 2 min/Eq.(I) 2: 5 min/Eq.(II) 3: 10 min/Eq.(I) 4: 15 min/Eq.(II) 5: 20 min/Eq.(II)

A: 1 B: 1,2 C: 1,2,3 D: 1,3 E: 4,5

0 0

0

. .( )

.( ): ^{p t}

M

k E S P Eq I dP

dt K S P

= −

+ −

0 0

0

. .

.( ): ^{p t}

M

k E S Eq II dP

dt = K S +

Biochemistry: Regulation of enzyme activity

Comprehension problem 6

Select the factors which affect the rate of enzyme-catalyzed reactions!

1: substrate concentration 2: enzyme concentration 3: pH

4: temperature

5: coenzyme concentration

A: 1,2 B: 1,2,3 C:1,3,4 D: 1,2,3,4 E:all

Biochemistry: Regulation of enzyme activity

Comprehension problem 7

Which statement applies to the steady state approach in the models of enzyme-catalyzed reactions!

A: The change of substrate concentration is 0 B: The change of product concentration is 0 C: The change of enzyme concentration is 0

D: The change of enzyme-substrate complex concentration is 0

E: All of the above conditions should be valid

Biochemistry: Regulation of enzyme activity

Comprehension problem 8

Which statement applies to the steady state approach in the models of enzyme-catalyzed reactions!

A: The rate of formation of the enzyme-substrate complex is higher than the rate of product formation

B: The rate of formation of the enzyme-substrate complex is equal to the rate of product formation

C: The rate of formation of the enzyme-substrate complex is lower than the rate of product formation

D: The rate of degradation of the enzyme-substrate complex is lower than the rate of product formation

E: None of the above statements applies

Biochemistry: Regulation of enzyme activity

Comprehension problem 9

Which condition should be valid for the application of the equation to describe the rate of an enzyme- catalyzed reaction?

A: the reaction should be reversible under the conditions of the experiment

B: the reaction should be irreversible under the conditions of the experiment

C: S

>>K

D: S

<K

E: None of the above

0 0 0

. .

p t M

k E S v= K S

+

Biochemistry: Regulation of enzyme activity

Comprehension problem 10

The identification of the physiological substrate of an enzyme requires knowledge of

1. the in vitro determined value of K

for this substrate 2. the in vivo determined value of V

for this substrate 3. the in vitro determined value of k

for this substrate 4. the in vivo substrate concentration

A: 1,2 B: 1,3 C: 1,2,4 D: 1,3,4 E: 2,4

Biochemistry: Regulation of enzyme activity

Comprehension problem 11

Which statement is true regarding the rate-limiting step of a metabolic pathway?

1. the in vivo rate of this reaction is significantly lower than the rate of the rest of the reactions

2. the in vivo V

of this reaction is significantly lower than the V

of the rest of the reactions

3. the K

of this enzyme is significantly lower than the K

of the rest of the enzymes in the pathway

4. the K

of this reaction is significantly lower than the in vivo concentration of the substrate of this reaction

5. the K

of this reaction is significantly higher than the in vivo concentration of the substrate of this reaction

A: 1,2 B: 1,2,3 C: 1,2,4 D: 2,3,5 E: 2,4

Biochemistry: Regulation of enzyme activity

Comprehension problem 12

What can happen with the enzyme activity, if one of the amino acid residues in the enzyme structure is modified as shown below?

1. activation 2. inhibition

3. decrease in K

4. increase in K

5. change in V

A: 1,2 B: 1,3,5 C: 2,4,5 D: 3,5 E: all

Biochemistry: Regulation of enzyme activity

Comprehension problem 13

Define the type of inhibitor based on the experimental results below

A: competitive

B: non-competitive

C: uncompetitive

D: mixed type

E: irreversible

Biochemistry: Regulation of enzyme activity

Comprehension problem 14

Define the type of inhibitor based on the experimental results below

A: competitive

B: non-competitive

C: uncompetitive

D: mixed type

E: irreversible

Biochemistry: Regulation of enzyme activity

Recommended literature

Orvosi Biokémia (Ed. Ádám Veronika): pp. 30-43

Biochemistry: Regulation of enzyme activity

Answers to comprehension problems

1. B; 2. D; 3. E; 4. C; 5. D; 6. E; 7. D; 8. A; 9. B; 10. D; 11. E; 12. E; 13. A; 14. B