Advanced Bioprocess Engineering

Enzymes & Enzymes Kinetics

Lecturer Dr. Kamal E. M. ElkahloutAssistant Prof. of Biotechnology

ENZYMESBASICS AND INTRODUCTION

ENZYMES

A protein with catalytic properties due to its power of specific

activation

Chemical reactions

• Chemical reactions need an initial input of energy = THE ACTIVATION ENERGY

• During this part of the reaction the molecules are said to be in a transition state.

Reaction pathway

Making reactions go faster

• Increasing the temperature make molecules move faster

• Biological systems are very sensitive to temperature changes.

• Enzymes can increase the rate of reactions without increasing the temperature.

• They do this by lowering the activation energy. • They create a new reaction pathway “a short cut”

An enzyme controlled pathway

• Enzyme controlled reactions proceed 108 to 1011 times faster than corresponding non-enzymic reactions.

Enzyme structure• Enzymes are

proteins• They have a

globular shape• A complex 3-D

structure

Human pancreatic amylase

The active site• One part of an enzyme,

the active site, is particularly important

• The shape and the chemical environment inside the active site permits a chemical reaction to proceed more easily

Cofactors• An additional non-

protein molecule that is needed by some enzymes to help the reaction

• Tightly bound cofactors are called prosthetic groups

• Cofactors that are bound and released easily are called coenzymes

• Many vitamins are coenzymes

Nitrogenase enzyme with Fe, Mo and ADP cofactors

)

The substrate

• The substrate of an enzyme are the reactants that are activated by the enzyme

• Enzymes are specific to their substrates• The specificity is determined by the active

site

The Lock and Key Hypothesis• Fit between the substrate and the active site of the enzyme is

exact • Like a key fits into a lock very precisely• The key is analogous to the enzyme and the substrate

analogous to the lock. • Temporary structure called the enzyme-substrate complex

formed • Products have a different shape from the substrate • Once formed, they are released from the active site • Leaving it free to become attached to another substrate

The Lock and Key Hypothesis

Enzyme may be used again

Enzyme-substrate complex

E

S

P

E

E

P

Reaction coordinate

The Lock and Key Hypothesis

• This explains enzyme specificity• This explains the loss of activity when

enzymes denature

The Induced Fit Hypothesis• Some proteins can change their shape

(conformation)• When a substrate combines with an enzyme, it

induces a change in the enzyme’s conformation• The active site is then moulded into a precise

conformation• Making the chemical environment suitable for the

reaction• The bonds of the substrate are stretched to make

the reaction easier (lowers activation energy)

The Induced Fit Hypothesis

• This explains the enzymes that can react with a range of substrates of similar types

Hexokinase (a) without (b) with glucose substratehttp://www.biochem.arizona.edu/classes/bioc462/462a/NOTES/ENZYMES/enzyme_mechanism.html

Factors affecting Enzymes

• substrate concentration• pH• temperature• inhibitors

Substrate concentration: Non-enzymic reactions

• The increase in velocity is proportional to the substrate concentration

Rea

ctio

n ve

loci

ty

Substrate concentration

Substrate concentration: Enzymic reactions

• Faster reaction but it reaches a saturation point when all the enzyme molecules are occupied.

• If you alter the concentration of the enzyme then Vmax will change too.

Rea

ctio

n ve

loci

ty

Substrate concentration

Vmax

The effect of pH Optimum pH values

Enzy

me

activ

ity

Trypsin

Pepsin

pH1 3 5 7 9 11

The effect of pH

• Extreme pH levels will produce denaturation• The structure of the enzyme is changed • The active site is distorted and the substrate

molecules will no longer fit in it• At pH values slightly different from the enzyme’s

optimum value, small changes in the charges of the enzyme and it’s substrate molecules will occur

• This change in ionisation will affect the binding of the substrate with the active site.

The effect of temperature• Q10 (the temperature coefficient) = the increase

in reaction rate with a 10°C rise in temperature.• For chemical reactions the Q10 = 2 to 3

(the rate of the reaction doubles or triples with every 10°C rise in temperature)

• Enzyme-controlled reactions follow this rule as they are chemical reactions

• BUT at high temperatures proteins denature• The optimum temperature for an enzyme

controlled reaction will be a balance between the Q10 and denaturation.

The effect of temperature

Temperature / °C

Enzy

me

activ

ity

0 10 20 30 40 50

Q10 Denaturation

The effect of temperature

• For most enzymes the optimum temperature is about 30°C

• Many are a lot lower, cold water fish will die at 30°C because their enzymes denature

• A few bacteria have enzymes that can withstand very high temperatures up to 100°C

• Most enzymes however are fully denatured at 70°C

Inhibitors

• Inhibitors are chemicals that reduce the rate of enzymic reactions.

• The are usually specific and they work at low concentrations.

• They block the enzyme but they do not usually destroy it.

• Many drugs and poisons are inhibitors of enzymes in the nervous system.

The effect of enzyme inhibition

• Irreversible inhibitors: Combine with the functional groups of the amino acids in the active site, irreversibly.

Examples: nerve gases and pesticides, containing organophosphorus, combine with serine residues in the enzyme acetylcholine esterase.

The effect of enzyme inhibition

• Reversible inhibitors: These can be washed out of the solution of enzyme by dialysis.

There are two categories.

The effect of enzyme inhibition1. Competitive: These

compete with the substrate molecules for the active site.

The inhibitor’s action is proportional to its concentration.

Resembles the substrate’s structure closely.

Enzyme inhibitor complex

Reversible

reaction

E + I

EI

The effect of enzyme inhibition

Succinate

Fumarate + 2H++ 2e-Succinate

dehydrogenase

CH2COOH

CH2COOH

CHCOOH

CHCOOH

COOH

COOH

CH2

Malonate

The effect of enzyme inhibition2. Non-competitive: These are not influenced by the

concentration of the substrate. It inhibits by binding irreversibly to the enzyme but not at the active site.

Examples • Cyanide combines with the Iron in the enzymes

cytochrome oxidase.• Heavy metals, Ag or Hg, combine with –SH groups. These can be removed by using a chelating agent such as

EDTA.

Applications of inhibitors• Negative feedback: end point or end product

inhibition• Poisons snake bite, plant alkaloids and nerve

gases.• Medicine antibiotics, sulphonamides,

sedatives and stimulants

ENZYMESKINETICS OF ENZYME REACTIONS

INTRODUCTION• The objectives of studying kinetics: • 1) Gain an understanding of the mechanisms of

enzyme action; • 2) Illuminate the physiological roles of enzyme-

catalyzed reactions• 3) Manipulate enzyme properties for

biotechnological ends.

MICHAELIS–MENTEN KINETICS• Michaelis–Menten equation expresses the initial rate

(v) of a reaction at a concentration (S) of the substrate transformed in a reaction catalyzed by an enzyme at total concentration E0:

• The parameters are k2, the catalytic constant, and Km, the Michaelis constant.

v Vmax[S ]K m [S ]

k 2[E0][S ]Km [S ]

Michaelis-Menten Kinetics

Enzyme KineticsEnzymatic reaction

E + S ES E + Pk1

k-1

k2

Rate expression for product formation

v = dP/dt = k2(ES)

d(ES)/dt = k1(E)(S)-k-1(ES)-k2(ES)

Conservation of enzyme

(E) = (E0) – (ES)

Two Methods to Proceed• Rapid equilibrium assumption: define

equilibrium coefficient K’m = k-1/k1 = [E][S]/[ES]

• Quasi-steady state assumption[ES] = k1[E][S]/(k-1+k2)

• Both methods yield the same final equation

Michaelis- Menten Kinetics

Michaelis-Menten Kinetics

• When v= 1/2 Vmax, [S]= Km so Km is sometimes called the half-saturation constant and sometimes the Michaelis constant

v Vmax[S ]K m [S ]

k 2[E0][S ]Km [S ]

Michaelis-Menten Kinetics

• units on k2 are amount product per amount of enzyme per unit time (also called the “turnover number”). Units on E0 are amount of enzyme (moles, grams, units, etc.) per unit volume

• Km has the same units as [S] (mole/liter, etc.)

v Vmax [S ]Km [S ]

k 2[E0][S ]Km [S ]

Experimentally Determining Rate Parameters for Michaelis-Menten

Kinetics

Lineweaver-Burk Eadie-Hofstee Hanes- WoolfBatch Kinetics

Determining Parameters

• Rearrange the equation into a linear form.• Plot the data. • What kind of data would we have for an

experiment examining enzyme kinetics?• Describe an experiment.• The intercept and slope are related to the

parameter values.

Enzyme Kinetics ExperimentPlace enzyme and substrate (reactants) in a

constant temperature, well stirred vessel. Measure disappearance of reactant or formation of product with time.

Why constant temperature?

Why well stirred?

What about the medium? Buffer?

–Rewrite Michaelis-Menten rate expression

–Plot 1/v versus 1/[S]. Slope is Km/Vmax, intercept is 1/Vmax

Lineweaver-Burk (double reciprocal plot)

1v

K m

Vmax

1[S ]

1

Vmax

Graphical Solution

1/ V

1/ [S]

1/ Vmax

-1/ Km

1v

K m

Vmax

1[S ]

1

Vmax

Slope = Km/ Vmax

intercepts

Example: Lineweaver-Burk[S] x 10-5 M V, M/min x 10-5

1.0 1.17 1.5 1.50 2.0 1.75 2.5 1.94 3.0 2.10 3.5 2.23 4.0 2.33 4.5 2.42 5.0 2.50

Resulting PlotLineweaver-Burk Plot

y = 0.5686x + 2.8687

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

0.00 2.00 4.00 6.00 8.00 10.00 12.001/[S] x 10^(-4)

slope = Km/ Vmax= 0.5686

y intercept = 1/ Vmax= 2.8687

Michaelis-Menten Kinetics

v Vmax[S ]K m [S ]

k 2[E0][S ]Km [S ]

Fit to Data

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00[S] (M) x 10^(-5)

Vmax = 1/2.8687 x 10-4 = 3.49 x 10-5 M/min Km= 0.5686 x Vm = 1.98 x 10-5 M

Other Methods• Eadie-Hofstee plot

• Hanes- Woolf

[S ]v

Km

Vmax

1Vmax

[S ]

v Vmax K mv

[S ]

Comparison of Methods

• Lineweaver-Burk: supposedly gives good estimate for Vmax, error is not symmetric about data points, low [S] values get more weight

• Eadie-Hofstee: less bias at low [S]• Hanes-Woolf: more accurate for Vmax.• When trying to fit whole cell data – I don’t

have much luck with any of them!

Batch Kinetics

v d[S ]dt

Vmax[S ]K m [S ]

Vmaxt [S0] [S ] K m ln[S0 ][S ]

[S0] [S ]t

K m

tln[S0]

[S ]Vmax

integrate

rearrange

Inhibited Enzyme Kinetics

• Competitive Inhibition• Noncompetitive Inhibition• Uncompetitive Inhibition• Substrate Inhibition

Effects of Temperature and pH

Experiments: Initial rate at different substrate concentrations

E S1= 20 E S2=10 E S4=5E S3=6.7 E S5=4

Measure S for a short time period. Calculate v from:

v = [S(time 0) – S(time 1)]/delta time

Experiment Using S1

Time (min) S (g/L) 0 20

0.5 19.43

v= (20-19.3)g/L]/0.5 min = 1.14 g/L/min

Time (min) S (g/L) 0 10

0.5 9.565

v= (10-9.565)g/L]/0.5 min = 0.87 g/L/min

Experiment Using S2

Experimental DataS (mmol/L) v (mmol/L/min) 20 1.14 10 0.87 6.7 0.70 5.0 0.59 4.0 0.50

Problems with this method?

Rate is not measured at a constant substrate concentration – substrate decreasing. Must have sensitive assay for substrate to measure initial rates.

0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20 25

S (g/L)

S/v

(min

)

experimental dataregression

regressionS/v = 0.6S + 5.6

Allosteric Enzyme KineticsIn an enzyme with more than one substrate binding site, binding of one substrate molecule affects the binding of another.

n>1, cooperation; n<1, interference

v d[S ]dt

V max[S]n

Kmn [S ]n

Allosteric EnzymesShape of rate curve is sigmoidal

Michaelis-Menten

Allosteric

Inhibition of EnzymesCan be irreversible (metals) or reversible (product, substrate, salt, etc.)

1. Competitive2. Noncompetitive3. Uncompetitive

Competitive InhibitionInhibitor is an analog of the substrate, and

binds to the active site of the enzyme.

E S ES PIEI

K m [E ][S ][ES ]

K I [E ][I ][EI ]

[E0 ] [E ] [ES ] [EI ]

v k 2[ES]

What assumption have we make in defining the parameters on the right?

Competitive Inhibition

Competitive InhibitionRate is given by:

v Vmax[S ]

K m 1I

K I

[S ]

Vmax[S ]K m,app [S ]

What is the magnitude of Km,app relative to Km and what will be the effect on v? How could you run a process to minimize the effects of this type of inhibition?

Competitive Inhibition1/v

Vmax is unchanged

I > 0

I=0

1/Vmax

1/[S]-1/Km,app-1/Km

Practice deriving kinetic expressions

Derive competitive inhibition equation (3.22 in your text)? Write down all assumptions.

Noncompetitive InhibitionInhibitor binds to the enzyme, but not at the active site. However, the enzyme affinity for substrate is reduced.

K m [E ][S ][ES ]

[EI ][S ][ESI ]

K I [E ][I ][EI ]

[ES ][I ][ESI ]

[E0 ] [E ] [ES ] [EI ] [ESI ]

v k 2[ES]

E S ES PIEI

IESIS

Noncompetitive Inhibition

Cofactors and Coenzymes

Holoenzymes- three parts• Apoenzyme- Protein portion• Cofactor- inorganic ion (ex: metal ions),

improve the fit of enzyme with substrate• Coenzyme- nonprotein organic molecule

(ex: NAD- nicotinamide adenine dinucleotide), many synthesized from vitamins (why vitamins are essential)

Rate is given by:

v Vmax

1[I ]K I

1

K m[S ]

Vmax,app

1K m

[S ]

Noncompetitive Inhibition

Question: What is the magnitude of Vmax,app relative to Vmax, and what will be the effect of v? How can you moderate the effects of this type of inhibition.

Noncompetitive Inhibition

1/v

Km is unchanged

I > 0

I=0

1/Vmax

1/[S]-1/Km

1/Vmax,app

Uncompetitive InhibitionInhibitor binds only to ES complex, and not to E alone.

K m [E ][S ][ES ]

K I [E ][I ][EI ]

[E0 ] [E ] [ES ] [ESI ]

v k 2[ES]

E S ES P

IESI

Uncompetitive InhibitionRate is given by:

v

Vmax

1[I ]K I

[S ]

K m

1[I ]K I

[S ]

Vmax,app [S ]K m ,app [S ]

What is the magnitude of Vmax,app relative to Vmax? What is the magnitude of Km,app relative to Km?

Uncompetitive Inhibition1/v

I > 0

I=0

1/Vmax

1/[S]-1/Km

1/Vmax,app

-1/Km,app

Substrate Inhibition

v Vmax [S ]

K m [S ] [S]2

KS i

[S ]max. rate K mK Si

No substrate inhibition

Substrate inhibition

S

v

Enzyme Deactivation

• Enzymes are denatured by–Temperature–pH–Radiation–Irreversible binding by inhibitors

• Temperature can both increase (thermal activation) and decrease (thermal denaturation) rate

Temperature effectsAt moderate temperatures, higher temperatures give higher rates.

At higher temperatures, rate starts to decrease as enzyme denatures faster

v k 2[E ], where k2 Ae E a

RT

d[E ]dt

kd [E ], or [E] [E 0]e k dt , where kd Ade d E d

RT

Temperature EffectsEffect on rate is a combination of the two effects

v Ae Ea

RT [E0 ]e k dt

Activation energy 10 kcal/mol

Deactivation energy 100 kcal/mol