Lecture – 4 The Kinetics of Enzyme-Catalyzed Reactions

Dr. AKM Shafiqul IslamSchool of Bioprocess Engineering

University Malaysia Perlis08.01.10

Michaelis-Menten Kinetics

• Enzyme E and substrate S combine to form a complex ES, which then dissociates into product P and free or uncombined enzyme E:

Michaelis-Menten Kinetics

• Equilibrium Constant

• Enzyme balance

• Decomposition of the complex to product and free enzyme is irreversible.

• Product formation Rate, v

Michaelis-Menten Kinetics

• Solving the equations

• Substitute e in following equation

esee o

mKk

k

es

se

1

1

sK

sese

m 0

Michaelis-Menten Kinetics

• From Product formation equation

sK

sek

m 0

2

sK

svv

m max

02max Where ekv

Quasi-steady-state Approximation

• Briggs and Haldane first proposed Quasi-steady-state assumption

• Applying mass balance for substrate and intermediate

esksekdt

dsv 11

eskksekdt

esd211

Quasi-steady-state Approximation

• In a batch reactor at closed system [E0] is considered very small compared STherefore, d(es)/dt ≈0

From equation

21

1

kk

sekes

eskksekdt

esd211

Quasi-steady-state Approximation

• Substituting e

Production formation kinetics

s

kkkse

es

1

21

0

eskdt

dp

dt

dsv 2

skkk

sek

121

02

/

Quasi-steady-state Approximation

Substituting

There is difference between Michaelis-Menten and Quasi-steady-state constant.

02max ekv

1

21m and

k

kkK

sK

svv

m max

Evaluation of Parameters in Michaelis-Menten Equation

Lineweaver-Burk plots are convenient for determination of Km

• Double reciprocal plot

Eadie–Hofstee plot

plot v versus v/[S] gives a line of slope –Km and y-axis intercept of Vm

Hanes–Woolf plot

• Plot of [S]/v versus [S] gives line of slope I/Vm and y-axis intercept of Km/Vm.

• This plot is used to determine Vm more accurately.

Modulation and Regulation of Enzyme Activity

• Chemical species other than the substrate can combine with enzymes to alter or modulate their catalytic activity.

• Such substances are called modulators or effectors, may be normal constituents of the cell.

• They enter from the cell's environment or act on isolated enzymes.

Modulation and Regulation of Enzyme Activity

• The combination of an enzyme with an modulator is chemical reaction

• Modulator can be fully reversible, partially reversible, or essentially irreversible.

• Examples of irreversible inhibitors include poisons such as cyanide ions, which deactivate xanthine oxidase,

• Nerve gases, which deactivate cholinesterases (enzymes which are part of nerve transmission).

Modulation and Regulation of Enzyme Activity

• Reversible modulation of enzyme activity is one control mechanism employed by the cell to achieve efficient use of nutrients.

• The enzyme regulation involve interconnected networks of reactions with several control loops

Modulation and Regulation of Enzyme Activity

• Example, five-step sequence for the biosynthesis of the amino acid L-isoleucine. Regulation of this sequence is achieved by feedback inhibition:

Modulation and Regulation of Enzyme Activity

The final product, L-isoleucine, inhibits the activity of the first enzyme. Thus, if the final product begins to build up, the biosynthesis process will be stopped

Modulation and Regulation of Enzyme Activity

• enzyme-substrate inhibitors systems classify by their influence on the Michaelis-Menten equation parameters vmax and Km

• Reversible inhibitors are termed competitive if their presence increases the value of Km but does not alter vmax The effect of such inhibitors can be countered or reversed by increasing the substrate concentration.

• On the other hand, by rendering the enzyme or the enzyme-substrate complex inactive, a noncompetitive inhibitor decreases the vmax of the enzyme but does not alter the Km value.

Mechanisms of Reversible Enzyme Modulation

• Many competitive inhibitors bear close relationships to the normal substrates. This are called substrate analogs. It is thought that these inhibitors have the key to fit into the enzyme active site, or lock, But the key is not quite right so the lock does not work; i.e., no chemical reaction results.

Mechanisms of Reversible Enzyme Modulation

• For example, inhibition of succinic acid dehydrogenation by malonic acid:The malonic acid can complex with succinic dehydrogenase, but it does not react

Mechanisms of Reversible Enzyme Modulation

• How the sulfa-drug act against bacteria?The action of one of the sulfa drugs, sulfanilamide, is due to its effect as a competitive inhibitor.

Mechanisms of Reversible Enzyme Modulation

• Sulfanilamide is very similar in structure to p-aminobenzoic acid, an important vitamin for many bacteria.

By inhibiting the enzyme which causes p-aminobenzoic acid to react to give folic acid, the sulfa drug can block the biochemical machinery of the bacterium and kill it.

• Some noncompetitive inhibition and is thought to be the dominant mechanism for noncompetitive inhibition and activation. These are called allosteric control

• An enzyme which possesses sites for modulation as well as catalysis has consequently been named an allosteric enzyme.