Bài giảng Kỹ thuật phản ứng sinh học: Chương 2 - Bùi Hồng Quân

Bài giảng Kỹ thuật phản ứng sinh học: Chương 2 Động học phản ứng enzyme, cung cấp cho người học những kiến thức như: Các khái niệm cơ bản; Xúc tác sinh học; Phương trình Michelis Menten; Động học phản ứng enzyme. Mời các bạn cùng tham khảo!

Chương 2 Động học phản ứng enzyme

QUIZ

1 What is enzyme?

2 What is the function of enzyme?

3 What are the special characteristics of enzyme?

4 What kind of binding energy involve for the

formation of ES complexes (enzyme-substrate

• What characteristic features define enzymes?

• Can the rate of an enzyme-catalyzed reaction be

defined in a mathematical way?

• What equations define the kinetics of

enzyme-catalyzed reactions?

• What can be learned from the inhibition of

enzyme activity?

• What is the kinetic behavior of enzymes

catalyzing bimolecular reactions?

• How can enzymes be so specific?

• Are all enzymes proteins?

• Is it possible to design an enzyme to catalyze any

desired reaction?

Role of Bioprocess Engineering

 exploit advances in biology to create new products

 design biochemical processes & operate plants

 develop energy resources

 Develop new, environmentally friendly, and safer

processes to make the biochemical products that

people depend on

 Work in research and development laboratories,

creating polymeric materials with improved

performance and durability

 Work in manufacturing, making vaccines and antibiotics

 Invent new ways to keep our food and water supplies safe

Bioprocess Engineer’s Task

byproducts

bad (byproducts)

consumption

Enzymes

 There are many chemical compounds in the living

cell

 How they are manufactured and combined at

sufficient reaction rates under relatively mild

temperature and pressure?

 How does the cell select exactly which reactants will

be combined and which molecule will be

decomposed?

Catalysis by ENZYME

•Enzymes are biological catalysts that are protein

molecules in nature- react in mild condition

•They are produced by living cells (animal, plant, and

microorganism) and are absolutely essential as catalysts in biochemical reactions

•Almost every reaction in a cell requires the presence of a

specific enzyme – related to its particular protein structure

•A major function of enzymes in a living system is to

catalyze the making and breaking of chemical bonds

•Therefore, like any other catalysts, they increase the rate

of reaction without themselves undergoing permanent

chemical changes

Enzymes

Over 2000 enzymes have been identified

Often named by adding the - ‘ase’ to the name of substrate acted upon, or the reaction catalyzed such as urease, alcohol dehydrogenase

The majority of cellular reactions are catalyzed by enzymes

 Some protein enzyme required a non-protein group for their activity

Non protein group:

Cofactors : metal ions, Mg, Zn, Mn, Fe

FAD, CoA

Catalyze biochemical reactions

breaking, forming and rearranging bonds

Catalytic function – very specific and effective

(Specific because of conformational shape)

Dictated by the enzyme active site

Some active sites allow for multiple substrates

 Enzymes are catalysts

 Catalyst: chemical that changes the rate of a reaction without being consumed

 Recycled (used multiple times)

 Enzymes reduce the activation energy of a reaction

 Amount of energy that must be added to get a reaction to proceed

Catalysts

 A catalyst is unaltered during the course of a reaction and

functions in both the forward and reverse directions

In a chemical reaction, a catalyst increases the rate at which the reaction reaches equilibrium

 For a reaction to proceed from starting material to product,

the chemical transformations of bond-making and

bond-breaking require a minimal threshold amount of

energy, termed activation energy

 Generally, a catalyst serves to lower the activation energy of a particular reaction

Enzymes lower the activation energy of reaction

catalyzed

( They do this by binding to the substrate of the reaction,

and forming an enzyme-substrate (ES) complex)

Substrate binds to a specific site on the enzyme called

the active site

Multi-substrate reactions possible

 ‘Lock and key’ model

Enzyme Function

Enzyme lower the activation energy of the

reaction by binding the substrate and

enzymes

Enzyme lower the activation energy of the

reaction by binding the substrate and forming an

enzymes-substrate complex

The activation energy for

the decomposition of

hydrogen peroxide varies

depending on the type of

Comparison of activation energies in the uncatalyzed

Important Terms To Remember!

• active site - a region of an enzyme comprised of different

amino acids where catalysis occurs or a small portion of the surface of an enzyme which a specific chemical reaction is

catalyzed

• substrate - the molecule being utilized and/or modified

by a particular enzyme at its active site

• co-factor - organic or inorganic molecules that are

required by some enzymes for activity These include

Mg2+, Fe2+, Zn2+ and larger molecules termed co-enzymes like nicotinamide adenine dinucleotide (NAD+), coenzyme A, and

many vitamins

Types of Enzymes

• holoenzyme - a complete, catalytically active enzyme

including all co-factors OR an enzyme containing a non protein group

• apoenzyme - the protein portion of a holoenzyme

minus the co-factors OR the protein part of holoenzyme

• (holoenzyme = apoenzyme+cofactor)

• isozyme - (or iso-enzyme) an enzyme that performs the

same or similar function of another enzyme that occur

in several different molecular forms

Nomenclature of enzyme

Originally enzymes were given non descriptive names such as:

rennin : curding of milk to start cheese

pepsin : hydrolyzes proteins at acidic pH

trypsin

Originally enzymes were given non descriptive names such as:

rennin : curding of milk to start cheese-making processor

pepsin : hydrolyzes proteins at acidic pH

trypsin : hydrolyzes proteins at mild alkaline pH

The nomenclature was later improved by adding the suffix -ase to the name of the substrate

with which the enzyme functions, or to the reaction that is catalyzed, for example:

The nomenclature was later improved by adding the suffix -ase to the name of the substrate

with which the enzyme functions, or to the reaction that is catalyzed, for example:

Alcohol

dehydrogenase

Glucose isomerase

Glucose oxidase

Lactic acid

dehydrogenase

Enzyme reactions are different from

chemical reactions, as follows:

1 An enzyme catalyst is highly specific , and catalyzes only one or

a small number of chemical reactions A great variety of enzymes

exist, which can catalyze a very wide range of reactions

2 The rate of an enzyme-catalyzed reaction is usually much faster

than that of the same reaction when directed by nonbiological catalysts

at mild reaction condition

3 A small amount of enzyme is required to produce a desired effect

4 Enzymes are comparatively sensitive or unstable molecules

and require care in their use

Enzymatic Reaction Principles

• Biochemically, enzymes are highly specific for their substrates and generally catalyze only one type of reaction

at rates thousands and millions times higher than

non-enzymatic reactions

• Two main principles to remember about enzymes are :

a) they act as CATALYSTS (they are not consumed in a

reaction and are regenerated to their starting state)

a) they INCREASE the rate of a reaction towards

equilibrium (ratio of substrate to product), but they do not determine the overall equilibrium of a reaction

Reaction Rates

including the concentration of substrate, temperature and pH

and temperature are in a defined environment (eg; pH

mathematically by combining the equilibrium constant, the

free energy change and first or second-order rate theory

Keq = e−∆Go/RT

activation energy, the faster the reaction rate , and vice versa

Specificity

catalyze similar reactions involving many different kinds of reactants

one reaction involving only certain substances

Binding Energy

 The interaction between enzyme and its substrate is usually by weak forces

 In most cases, Van der Waals forces and hydrogen

bonding are responsible for the formation of ES complexes

 The substrate binds to a specific site on the enzyme known

as the active site

Classification of Enzyme

Enzymes fall into 6 classes based on function

1 Oxidoreductases : which are involved in oxidation, reduction, and

electron or proton transfer reactions

2 Transferases : transfer of functional group

3 Hydrolases : which cleave various covalent bonds by hydrolysis

4 Lyases : catalyse reactions forming or breaking double bonds

5 Isomerases : catalyse isomerisation reactions

6 Ligases : join substituents together covalently

ENZYME KINETICS

Mathematical models of catalyzed reactions were first developed by Henri in 1902 and Michaelis & Menten in 1913

single-substrate-enzyme-Simple enzyme kinetics are now commonly referred to

as Michaelis-Menten or ‘saturation’ kinetics

At high substrate concentrations, all active sites on the enzyme are occupied by substrate – enzyme is

saturated

Models are based on data from batch reactors with

constant liquid volume in which the initial substrate,

[S0], and enzyme, [E0], concentrations are known

Enzyme Kinetics

•Enzyme kinetics deals with the rate of enzyme reaction

•Kinetic studies of enzymatic reactions provide

information about:

(1)the basic mechanism of the enzyme reaction and

(2) other parameters that characterize the properties of the enzyme

•The rate equations developed from the kinetic studies

can be applied in :

(1)calculating reaction time,

(2) yields, and

(3) optimum economic condition, which are important in

the design of an effective bioreactor

Assume that a substrate (S) is converted to a product (P) with the help

of an enzyme (E) in a reactor as:

If you measure the concentrations of substrate and product with

respect to time, the product concentration will increase and reach a maximum value, whereas the substrate concentration will decrease

as shown in Figure 2.1

The rate of reaction can be expressed in terms of either the change

of the substrate Cs or the product concentrations C P as follows:

Brown (1902) proposed that an enzyme forms a complex with its

substrate The complex then breaks down to the products and regenerates the free enzyme

The mechanism of one substrate-enzyme reaction can be expressed as:

change of the substrate Cs

product concentrations CP

One of the original theories to account for the formation

of the enzyme-substrate complex is the "lock and key"

theory

The enzyme represents the lock and substrate

represents the key

The main concept of this hypothesis is that there is a topographical, structural compatibility between an enzyme and a substrate which optimally favors the recognition of the substrate as shown in Figure 2.3

In multi substrate, enzyme-catalyzed reactions,

enzymes can hold substrates such that reactive

regions of substrates are close to each other and to

the enzyme’s active site, which is known as the

proximity effects (nearest in distance)

Multisubstrate

enzyme catalyst reaction

Alteration of active site

by activator

Also, enzymes can hold substrates at certain positions and

angles to improve the reaction rate, which is known as

the orientation effect

The reaction rate equation can be derived from the preceding mechanism based on the following

assumptions :

1 The total enzyme concentration stays constant

during the reaction,

2 The amount of an enzyme is very small compared to the amount of substrate Therefore, the formation of the enzyme substrate complex does not significantly deplete the substrate

3 The product concentration is so low that product

inhibition may be considered negligible

Michaelis - Menten or ‘saturation’

kinetics

Enzyme Substrate Complex

Product Substrate

2) The rate of the reverse reaction

of the second step is negligible (i.e k-2~0)

(Assumption 2 is typically only

valid when product (P)

accumulation is negligible, at

the beginning of the reaction)

This model are based on data from batch reactors with

constant liquid volume in which the initial substrate,[S 0 ], and enzyme [E 0 ], concentration are known

An enzyme solution has a fixed number of active sites to which

substrate can bind At high substrate concentrations, all these sites may be occupied by substrates or the enzyme is

Rate of product formation:

Rate of variation of the ES complex:

Since the enzyme is not consumed,

the conservation equation yields,

At this point, an assumption is required in order to

achieve an analytical solution

(1) Rapid-Equilibrium Assumption

(2) Quasi-Steady-State Assumption

Assumption

The Rapid Equilibrium Assumption

Henri and Michaelis and Menten used essentially this

approach

Assuming equilibrium in the first part of the reaction (E+S forms

ES), we can use the equilibrium coefficient to express [ES] in

terms of [S]

The equilibrium constant is:

Since , if the enzyme is conserved, then

(the prime (‘) indicates that

it was derived assuming

Vm= maximum forward rate of the

reaction (change with the addition of

additional enzyme but not addition of

substrate)

Rate of Reaction as a Function of

Substrate Concentration

 Briggs and Haldane first

E [

k ES





    

ES k

k ]

E ][

S [

k dt

ES

d

2 1

  1

2

Quasi-Steady-State Assumption

• Substituting , , and solve equation 2 for [ES],

Production formation kinetics,

 

] S

[ k

k k

] E ][

S [ ES

1

2 1

k dt

] P [

d dt

] S [

E [

k v

1 2

Substituting,

constant [K’m=k-1/k1] and Quasi-steady-state constant [K’m=k-1+k2/k1]

] E [ k

1

2

1 m

] S [

V v

m

m



 6

The "kinetic activator constant"

 Km is a constant

 Km is a constant derived from rate constants

 Km is, under true Michaelis-Menten conditions, an estimate of the dissociation constant of E from S

 Small Km means tight binding; high Km means weak binding

Km = ( k-1 + k2 )

k1

The Km values for some enzymes and their substrates

Glucokinase (hexokinase IV – liver)

High K , low affinity

The theoretical maximal velocity

 Vmax is a constant (at fixed conc of enzyme)

 Vmax is the theoretical maximal rate of the reaction - but it is

never achieved in reality

 To reach Vmax would require that ALL enzyme molecules are tightly bound with substrate

 Vmax is asymptotically approached as substrate is increased

The Turnover Number Defines the Activity of One

Enzyme Molecule

A measure of catalytic activity

 kcat, the turnover number, is the number of substrate molecules converted to product per enzyme molecule per unit of time, when E is saturated with substrate

 If the M-M model fits, k2 = kcat = Vmax/Et

 Values of kcat range from less than 1/sec to many millions per sec