Advanced Bioprocess Engineering
Enzymes & Enzymes Kinetics
Lecturer Dr. Kamal E. M. Elkahlout
Assistant 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 v
elo
city
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 v
elo
city
Substrate concentration
Vmax
The effect of pH
Optimum pH valuesE
nzy
me
acti
vity
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
En
zym
e ac
tivi
ty
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 inhibition
1. 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 ]K m [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 Experiment
Place 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 12.00
1/[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 m
v[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)
0 200.5 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
(m
in)
experimental data
regression
regressionS/v = 0.6S + 5.6
Allosteric Enzyme Kinetics
In 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 Enzymes
Can be irreversible (metals) or reversible (product, substrate, salt, etc.)
1. Competitive
2. Noncompetitive
3. Uncompetitive
Competitive InhibitionInhibitor is an analog of the substrate, and
binds to the active site of the enzyme.
E S ES P
I
EI
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 P
I
EI
I
ESIS
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
I
ESI
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 Inhibition
1/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 effects
At 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 ]
dtkd [E ], or [E] [E 0]e k dt , where kd Ade d
E dRT
Temperature EffectsEffect on rate is a combination of the two effects
v Ae E a
RT [E0 ]e k dt
Activation energy 10 kcal/mol
Deactivation energy 100 kcal/mol