PETER PAZMANY CATHOLIC UNIVERSITYConsortium members

(1)

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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

(2)

Peter Pazmany Catholic University Faculty of Information Technology

INTRODUCTION TO BIOPHYSICS

ENZYMES

www.itk.ppke.hu

(Bevezetés a biofizikába)

(Enzimek)

GYÖRFFY DÁNIEL, ZÁVODSZKY PÉTER

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Introduction to biophysics: Enzymes

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Introduction

● Catalysts are substances that can accelerate reactions taking place spontaneously even in the absence of the catalyst

● Catalysts are reclaimed in unchanged form after the reaction occurs

● Enzymes are catalysts of biological processes

● Enzymes are proteins often containing cofactors such as metal ions

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● The substance converted in the reaction catalyzed by the enzyme is called the

substrate

● The substance produced in this reaction is called product

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Classification of enzymes

● Enzymes are classified into six groups based on the type of reaction catalyzed by them

● The coenzyme is responsible for the type of

reaction to be catalyzed while the apoenzyme determines the type of the substrate

converted in the reaction

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Classes of enzymes

Class Catalyzed reaction Example

Oxidoreductases Oxidation-reduction GAPDH

Transferases Group transfer ERK2

Hydrolases Hydrolysis Trypsin

Lyases Double bond formation or

removal Fumarase

Isomerases Isomerization Triose phosphate isomerase

Ligases Ligation DNA ligase

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GAPDH

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MAP kinase ERK2

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Trypsin

(10)

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Fumarase

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Triose phosphate isomerase

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DNA ligase

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Enzymes in action

● Enzymes can catalyze only reactions taking place spontaneously, i.e. in the absence of catalyst

● Reactions can take place spontaneously if the free energy of products is less than that of the reactants

● Thus, catalysts such as enzymes do not affect the thermodynamics of reactions but influence their kinetics

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● Usually, for a reaction to take place, an energy barrier must be passed

● The height of this barrier will determine the rate of the reaction

● The higher the barrier the slower the reaction

● Catalysts can make this barrier lower, and thus accelerate the reaction even by several orders of magnitude

● Now let us examine where this barrier comes from

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Recall: Arrhenius theory

● The Swedish chemist Arrhenius found a

relation between the rate of reaction and the temperature

● The Arrhenius equation says:

k = A e

^−E^a^/^{R T}

where k is the rate constant, E_a is the activation energy, R is the gas constant, T is the

temperature and A is a constant called Arrhenius constant or pre-exponential factor

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k as a function of T

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Recall: Boltzmann distribution

● Ludwig Boltzmann found the energy distribution of particles in a system at equilibrium

● The Boltzmann distribution is:

p  E

_i

= 1

Z e

⁻^Eⁱ^/^k ^B^T

where p(E_i) is the probability that a particle is in a state having E_ienergy, k_B is the Boltzmann

constant and Z is the partition function

(18)

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● The partition function

Z = ∑

i

e

⁻^Eⁱ^/^k^B^T

is the sum of the Boltzmann factors for all of the i states and serves as a scaling factor to ensure

that the sum of probabilities equals 1

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Boltzmann distribution

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● Thus, the rate of a reaction is proportional to the fraction of particles having an energy

higher than the activation energy

● Hence, if a catalyst lowers the activation

energy, a higher fraction of particles will have an energy higher than the activation energy thus, the rate of the reaction will be higher

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Fraction of particles of energy E in an uncatalyzed and a catalyzed reaction

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Recall: reaction profile

● The progress of a reaction can be

characterized by one or more reaction coordinates

● Now, let us consider a reaction with one reaction coordinate

● The free energy of the system can be plotted as a function of a reaction coordinate

● This plot is called reaction profile

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Reaction profile

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● The effect of a catalyst on the reaction profile is that it lowers the activation energy and thus lowers the barrier that must be passed for the system the reaction to occur

● It can be seen that a catalyst accelerates a reaction not only in one direction but in the opposite direction as well

● However, enzymes do not alter the reaction free energy ∆G_r, and therefore do not

influence whether the reaction occurs spontaneously

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Effect of a catalyst on the reaction profile

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Hypotheses for enzyme action

● Several hypotheses have been proposed to

explain how enzymes can accelerate reactions even by several orders of magnitude

● Enzymes often open up a by-pass pathway with lower activation energy for the reaction, which can thus proceed faster

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Transition state stabilization

● Let us consider the reaction to be catalyzed by an enzyme as

S ⇆

^K

‡

S

^‡



^k

‡

P

where S is the substrate, S^‡ is the transition state, P is the product, K^‡ is the equilibrium

constant for the formation of the transition state from the substrate, and k^‡ is the rate constant of the conversion of the transition state to the

product

(28)

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● It is assumed that the equilibrium step of the reaction is far faster than the second step

● Thus, the overall rate of the reaction can be approximated by

v = k [ S ]≈ k

^‡

[ S

^‡

]

● It can be seen that the rate of the overall

reaction is proportional to the concentration of the transition state

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● Since

K

^‡

= [ S

^‡

]

[ S ] =e

^− ^G^‡^/^RT

where ΔG^‡ is the activation free energy,

describing the stability of transition state relative to the substrate

● The more stable the transition state the higher its concentration

● Thus, enzymes accelerate reactions by stabilizing the transition state

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Enzyme-substrate complex

● In the course of catalysis, a complex of the enzyme and the substrate(s) is formed

● The transition state is also formed in an enzyme substrate complex

● The specificity of enzymes is brought about by the specific binding of substrate

● The region of the enzyme where the binding occurs is called the active site

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● To explain substrate specificity, several theories have been proposed

● The lock and key hypothesis assumes that the shape of the active site is a negative of the

shape of the substrate

● Later, several enzymes were found to be able to catalyze the reaction of substrates having significantly different shapes but not of

substances having almost the same shape as a known substrate

Lock and key hypothesis

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The lock and key hypothesis

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Induced fit hypothesis

● Due to the above mentioned difficulties, a new model has been proposed to better explain

substrate specificity

● This new model, called induced fit model

assumes that, when the substrate approaches the active site of the enzyme, a conformational change occurs in the enzyme, allowing the

binding based on shape complementarity

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The induced fit mechanism

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Transition state fit

● According to a more modern view, it is the

transition state whose shape fits the shape of the active site

● Thus, a lock and key binding occurs not

between the enzyme and the ground state but between the enzyme and the transition state of the substrate

(36)

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Transition state fit

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● The transition state is a high-energy state of the substrate

● According to the Boltzmann distribution, states with high energy have a low but non-zero

probability to occur

● Thus, a small amount of substrate molecules in the transition state is present in the medium

(38)

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● Transition state fit occurs when the enzyme selects a substrate molecule being in the

transition state for binding rather than molecules in the ground state

● Not only the enzyme can select from the

reservoir of substrate states but substrates can also select from the preexisting enzyme

conformations

● This mechanism is called conformational selection or fluctuation fit

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Conformational selection by the enzyme

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Conformational selection by the substrate

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Transition-state analogues

● Based on the model assuming the selective binding of the transition state by the enzyme, it has been proposed that analogues of the

transition state compounds, that is a

compound having similar conformation to it should be good inhibitors of the enzyme

● Indeed, several observations have been

accumulated that support the concept that transition state analogues are good inhibitors

(42)

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Abzymes

● The existence of abzymes lends further support for the transition state fit model

● Abzymes are catalytic antibodies

● They have catalytic activity for reactions for which they can selectively bind the transition state

● Immunizing animals by a transition state analogue, an effective enzyme can be

obtained

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Michaelis-Menten model for enzyme kinetics

● The Michaelis-Menten model of enzyme

kinetics accounts for dependence of the rate of the enzyme reactions on the substrate

concentration

● A steady-state approximation has been used to construct a model fitting well the experimental results for many enzymes

(44)

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Kinetic curves of an enzyme reaction

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● The following scheme can be proposed for a generic enzyme reaction

E  S ⇆

k₋₁ k₁

ES ⇆

k₋₂ k ₂

P

where E is the enzyme and S is the substrate in their free forms, ES is the enzyme-substrate

complex and P is the product

● The corresponding rate constants are also shown

(46)

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● Assuming that the rate of formation of product from the enzyme-substrate complex is far

higher than the rate of the reverse reaction, that is

k

₂

≫ k

₋₂

the general scheme of enzyme reactions can be simplified to be

E  S ⇆

k₁

ES 

^k ²

P

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● The rate of the reaction is assumed to be

v

₀

= k

₂

[ ES ]

● Since we do not know the concentration of the enzyme-substrate complex, we need to

express it in terms of the known quantities such as the initial substrate or enzyme

concentration

d [ ES ]

d t = k

₁

[ E ][ S ]−  ^k

−1

 k

₂

 ^[ ^ES ^]

(48)

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● Making use of the steady state approximation, i.e. that the concentration of the enzyme-

substrate complex does not change for a wide time range

d [ ES ]

d t =0

and thus

k

₁

[ E ][ S ]=  ^k

−1

 k

₂

 ^[ ^ES ^]

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● After rearrangement we obtain

[ E ][ S ]/[ ES ]=  ^k

−1

 k

₂

 ^/ ^k

1

● If we define a new constant called Michaelis constant, K_M

K

_M

=  ^k

−1

k

₂

 ^/ ^k

1

we get a simpler equation

[ ES ]= [ E ][ S ]

K

_M

(50)

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● The concentration of the free enzyme can be obtained from the equation

[ E ]=[ E ]

_T

−[ ES ]

where [E]_T is the total enzyme concentration

● Since the total amount of the enzyme does not change through the reaction, it will be equal to the amount of enzyme initially put into the

reaction mixture

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● Substituting the expression for the enzyme

concentration into the equation above, we get

[ ES ]=  ^[ ^E ^]

T

−[ ES ]  ^[ ^S ^]

K

_M

● Solving the equation for [ES], we obtain

[ ES ]=[ E ]

_T

[ S ]

[ S ] K

_M

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● Substituting this expression into the equation for the reaction rate, we obtain

v

₀

= k

₂

[ E ]

_T

[ S ]

[ S ] K

_M

● The reaction can proceed with the maximal

speed when all of the enzyme molecules are in complex with a substrate molecule, that is

when

[ ES ]=[ E ]

_T

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● Thus the maximal velocity is

v

_max

= k

₂

[ E ]

_T

● Based on this, the relationship between the maximal and the actual velocity is

v

₀

= v

_max

[ S ]

[ S ] K

_M

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● It can be seen in the equation above that K_M corresponds to the substrate concentration where the rate of reaction is half of the

maximal rate

● It also shows that the Michaelis constant is an important kinetic property of enzymes

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The rate of the reaction as a function of the substrate concentration

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● If the substrate concentration is far lower than the Michaelis constant, that is

[ S ]≪ K

_M

then the rate of reaction is approximately

v

₀

≈ v

_max

K

_M

[ S ]

● It can be seen that at low substrate

concentration, the reaction is first-order with

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● On the other hand, if the substrate

concentration is far higher than the Michaelis constant, that is

[ S ]≫ K

_M

then the rate of reaction is approximately

v

₀

≈ v

_max

● It can be seen that at high substrate

concentration, the reaction is zeroth-order with respect to the substrate

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Catalytic efficiency

● The turnover number of an enzyme is the

number of molecules converted into a product in unit time when the enzyme is fully saturated by the substrate

● The turnover number is equal to the rate constant k₂ which is also called k_cat

● The maximal velocity, v_max in terms of k_cat is

v

_max

= k

_cat

[ E ]

_T

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● When the substrate concentration is far lower than the Michaelis constant, the enzymatic

rate is much less than k_cat

● From equation

v

₀

= k

_cat

[ ES ]

and

[ ES ]= [ E ][ S ] K

_M

we can obtain a new equation

(60)

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● k_cat/K_M behaves as a second-order rate constant for the reaction between the substrate and the free enzyme, and thus can serve as a measure of catalytic efficiency

● The physical limit on the value of k_cat/K_M is the rate constant of formation of the enzyme-

substrate complex which cannot be faster than

v

₀

= k

_cat

K

_M

[ E ][ S ]

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Inhibitors

● Enzymes can be inhibited by specific inhibitors

● Two main classes of inhibitors can be distinguished

– Competitive inhibitors

– Non-competitive inhibitors

● Competitive inhibitors use the same binding site on the enzyme as the substrate and a

competition occurs between the substrate and the inhibitor for the binding site

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● Non-competitive inhibitors bind to a different site on the enzyme than the substrate

● They cause a conformational change in the

enzyme, leading to a reduction of the action of the enzyme

● Competitive and non-competitive inhibitors have a different effect on the kinetics of the enzyme reaction and thus they can be

kinetically distinguished

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● In the case of a competitive inhibitor, if the

concentration of substrate is high enough, the maximal velocity, v_max, can be attained but the substrate concentration where the velocity is the half of v_max, K_M, will be higher

● In the case of non-competitive inhibitors, the maximum velocity v_max cannot be attained even at very high substrate concentration, but the substrate concentration where the velocity is the half of the modified maximal velocity is unchanged

(64)

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Competitive inhibitor

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Non competitive inhibitor

(66)

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Catalytic strategies

● The function of enzymes is based on one or more of a few strategies

– Through covalent catalysis, a reactive group of the active site becomes covalently modified

• In the active site of trypsin, the catalytic serine residue forms an acyl-enzyme intermediate with the N-terminal part of the cleaved polypeptide chain

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Acyl-enzyme intermediate in the active site of trypsin

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– In acid-base catalysis, a proton transfer occurs where the donor or acceptor group is not water

– Metal ions can take part in the catalytic reactions in several ways, for example they can supply positive charge if the intermediate is negatively charged, or they can take part in the substrate binding

– The enzyme can help substrates to approach each other in a proper orientation, entropically decreasing the activation free energy

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Ribozymes

● Catalytic capability is a property not

exclusively of proteins but also of RNAs

● Several catalytic RNAs called ribozymes are known

● Ribozymes take part mainly in the catalysis of reactions related to RNA conversion

● Ribozymes are important constituents of ribosomes, the molecular machines

responsible for protein synthesis

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Large subunit of a bacterial ribosome

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Small subunit of a bacterial ribosome

(72)

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● Another important process catalyzed partly by ribozymes is splicing through which exons are cleaved out from the premature mRNA

molecule

● Inspired by the discovery of catalytic RNAs, an evolutionary concept called the RNA world was proposed

● According to these hypothesis, at an earlier stage of evolution, it was RNA that was

responsible for catalysis and information storage instead of proteins and DNA,

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RNA splicing

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● The RNA world hypothesis is supported by the existence of catalytic RNAs and the fact that many enzymes have a coenzyme, i.e. a

ribonucleotide derivative such as NAD, the most important electron carrier molecule of the cell and ATP, the most important energy currency

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Adenosine triphosphate (ATP)

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Nicotinamid adenine dinucleotide (NAD)

PETER PAZMANY CATHOLIC UNIVERSITYConsortium members

ENZYMES

Introduction

Classification of enzymes

Enzymes in action

Recall: Arrhenius theory

k = A e

Recall: Boltzmann distribution

p  E

= 1

Z e

Z = ∑

e

Recall: reaction profile

Hypotheses for enzyme action

Transition state stabilization

S ⇆

S



P

v = k [ S ]≈ k

[ S

]

K

= [ S

]

[ S ] =e

Enzyme-substrate complex

Lock and key hypothesis

Induced fit hypothesis

Transition-state analogues

Abzymes

Michaelis-Menten model for enzyme kinetics

E  S ⇆

ES ⇆

P

k

≫ k

E  S ⇆

ES 

P

v

= k

[ ES ]

d [ ES ]

d t = k

[ E ][ S ]−  k

 k

 [ ES ]

d [ ES ]

d t =0

k

[ E ][ S ]=  k

 k

 [ ES ]

[ E ][ S ]/[ ES ]=  k

 k

 / k

K

=  k

k

 / k

[ ES ]= [ E ][ S ]

K

[ E ]=[ E ]

−[ ES ]

[ ES ]=  [ E ]

−[ ES ]  [ S ]

K

[ ES ]=[ E ]

[ S ]

[ S ] K

v

= k

[ E ]

[ S ]

[ S ] K

[ ES ]=[ E ]

v

= k

[ E ][ S ]−  ^k

 ^[ ^ES ^]

[ E ][ S ]=  ^k

 ^[ ^ES ^]

[ E ][ S ]/[ ES ]=  ^k

 ^/ ^k

=  ^k

 ^/ ^k

[ ES ]=  ^[ ^E ^]

−[ ES ]  ^[ ^S ^]