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CHAPTER 1:
ENZYME KINETICS AND
APPLICATIONS
ERT 317 BIOCHEMICAL ENGINEERING SEM 1 2012/13
Course details
Credit hours/Units : 4
Contact hours : 3 hr (L), 3 hr (P) and 1 hr (T) per week
Evaluations
Final Exam – 50%
Midterm Tests – 20%
Course works – 30%
Laboratories – 15%
Assignments – 15%
CARRY MARKS – 50%
Course details
Course Outcome (COs) will be covered:
CO1 – Ability to develop enzyme reactions based on
its kinetics study and applied catalysis
Course works (Overall evaluations)
Assignments - 2
Quizzes -1
Midterm test – 1
Class participations – Max. of 3 points
Important reminder
Attendance should not less than 80%, or else you will be barred from taking final examination.
Plagiarism and copying other students’ work is strictly prohibited especially in doing assignments and lab reports, or else both parties will get zero.
Cheating in quizzes and examinations is also prohibited, or else both parties will get zero.
Therefore, study hard and smart. Take note of the important chapters or things that will be highlighted throughout lectures.
Week 1 (10 - 21 Sept 2012)
Reading assignment:
1. Chapter 3, Bioprocess Engineering basic
Concepts. Shuler and Kargi (Main)
Kinetics of Enzyme Catalyzed
Reactions C1.1
Outline
Introduction to enzymes
Enzyme structure
Enzyme function
Enzyme kinetics
Michaelis-Menten Kinetics
The Rapid Equilibrium Assumption
The Quasi-Steady-State Assumption
Enzymes
Enzymes are usually proteins
Typically high molecular weight (15kDa – several
million kDa)
Over 2000 enzymes have been identified
Often named by adding the suffix ‘ase’ to the name of
substrate acted upon, or the reaction catalyzed such as
urease, alcohol dehydrogenase
Catalytic function – very specific and effective
The majority of cellular reactions are catalyzed by
enzymes
Enzyme Specificity
Absolute specificity – the enzyme will catalyze only one reaction
Group specificity – the enzyme will act only on molecules that have specific functional groups, such amino, phosphate or methyl groups
Linkage specificity – the enzyme will act on a particular type of chemical bond regardless of the rest of the molecular structure
Stereochemical specificity – the enzyme will act on a particular steric or optical isomer
Enzyme Structure
Some enzymes require a non-protein group for their
activity
Co-factors: metal and other chemical ions, such as
Mg2+, Zn 2+, Mn2+, Fe2+, Fe3+, Ca2+, K+
Co-enzymes: complex organic molecules such as NAD,
FAD, CoA, or some vitamins
Enzyme that contains a non-protein group is called
holoenzyme, the protein part of the holoenzyme is
called apoenyzme:
Apoenzyme + Co-factor = Holoenzyme
Enzyme Function
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
Lysozyme - Structure
The first enzyme structure to solved by X-ray
crystallography
Monomer of 14.9kDa
5 helices and a 3 stranded antiparallel sheet
Deep, long binding cleft, sufficient for
hexasaccaride – open at the ends
Catalytic residue Glu35 & Asp52
X-Ray structure of HEW
lysozyme.
a) The polypeptide chain
with a bound (NAG)6
substrate (green).
b) A ribbon diagram
highlighting the protein’s
secondary structure.
X-Ray structure of HEW lysozyme.
A computer-generated model showing the protein’s molecular
envelope (purple) and Ca backbone (blue).
Note: catalytic residue
Glu35 (yellow)
Asp52 (yellow)
Lysozyme - Function
Substrate
Products
Lysozyme catalyzes the hydrolysis of the b (1->4) glycosidic
bonds in bacterial cell wall peptidoglycans and chitin (fungal
cell walls)
Found in egg white, tears and mucus membranes, bacterial
viruses
Enzyme-Substrate Complex
Activation Energy
Potential-energy curves for the reaction of
substrate, S, to products, P.
Comparison of activation energies in the uncatalyzed
and catalyzed decompositions of ozone.
Enzyme-Substrate Binding
Proximity effect:
In multi-substrate enzyme-catalyzed reactions, enzymes can hold substrates such that reactive regions of substrates are close to each other and to enzyme’s active site
Orientation effect:
Enzymes may hold the substrates at certain positions or angles to improve the reaction rate
Induced fit:
In some cases, formation of the ES complex causes slight changes in the 3D shape of the enzyme
May contribute to catalytic activity of the enzyme
INDUCED FIT
LOCK-AND-
KEY
The Conformational Change Induced in
Hexokinase by the Binding of a substrate, D-
Glucose
BINDING
CLEFT
CLEFT
CLOSES
Enzyme Kinetics
Mathematical models of single-substrate, enzyme-
catalyzed reactions were first developed by Henri in
1902 and Michaelis & Menten in 1913
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
Single-Substrate Enzyme Kinetics
It is assumed that:
The ES complex is established very rapidly
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
PEESSEk
k
k
2
1
1(3.1)
Rate of Reaction as a Function of
Substrate Concentration
Mechanistic Models for Simple Enzyme
Kinetics
The rate of product formation is:
Where v is the rate of product formation or substrate
consumption in moles/L-s
The rate constant k2 is often denoted as kcat in
biological literature
ESk
dt
Pdv 2 (3.2)
Mechanistic Models (cont’d)
The rate of variation of the ES complex is:
And since the enzyme is not consumed:
At this point, an assumption is required in order to
achieve an analytical solution
ESkESkSEk
dt
ESd211
ESEE 0
(3.3)
(3.4)
The Rapid Equilibrium Assumption
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
ES
SE
k
kKm
1
1'
ESEE 0
SK
SEES
Skk
SEES
m
'
0
11
0
(3.5)
(3.6)
(3.7)
The Rapid Equilibrium Assumption
Substitution Eq 3.7 into Eq 3.2 yields:
Where and is the maximum forward rate of the reaction
changes with the addition of additional enzyme, but not additional substrate
is called the Michaelis-Menten constant, and the prime(‘) indicates that it was derived assuming rapid equilibrium
A low value of suggests that the enzyme has a high affinity for the substrate
corresponds to the [S], such that
SK
SV
SK
SEk
dt
Pdv
m
m
m
''
02
02 EkVm mV
mV
'
mK
'
mK
'
mK2
' mm
VK
(3.8)
The Quasi-Steady-State Assumption
The assumption of rapid equilibrium is often not valid
The QSSA assumes that if the initial substrate
concentration greatly exceeds the initial enzyme
concentration , then
Computer simulations show that the QSSA holds, in a
closed system, after a brief transition period while the
reaction is initiated and equilibrium achieved
Applying the QSSA to Eq 3.3 gives us:
00 ES 0
dt
ESd
21
1
kk
SEkES
(3.9)
Formation of [ES] and Initiation of
Steady State
The Quasi-Steady-State Assumption
Substituting the enzyme conservation Eq 3.4 into Eq
3.9 yields
Solving Eq 3.10 for [ES]
Substituting Eq 3.11 into Eq 3.2
21
01
kk
SESEkES
Sk
kk
SEES
1
21
0
Sk
kk
SEk
dt
Pdv
1
21
2
(3.10)
(3.11)
(3.12a)
The Quasi-Steady-State Assumption
Therefore:
Where:
Eq 3.12b is the classic Michaelis-Menten equation for single-substrate enzyme kinetics
SK
SVv
m
m
02
1
21 and ,
EkV
k
kkK
m
m
(3.12b)
Outline
Simple enzyme kinetics
Complex enzyme kinetics
Allosteric enzymes
Inhibited enzyme kinetics
Competitive
Noncompetitive
Uncompetitive
Course details
Course Outcome (COs) will be covered:
CO1 – Ability to develop enzyme reactions based on
its kinetics study and applied catalysis
Course works (Overall evaluations)
Assignments 1 (Due Wed, 19/09)
Quizzes 1 (Wed, 19/09)
Midterm test – 1
Class participations – Max. of 3 points
Experimental Determination of
Michaelis-Menten Parameters
Determination of values for Km and Vm with high precision can be difficult
Experimental data are typically obtained from initial-rate experiments
Batch reactor charged with a known amount of substrate [S0] and enzyme [E0]
Product and/or substrate concentration plotted against time
Create many plots at different [S0] and enzyme [E0] and use to generate a plot as Figure 3.1
Cumbersome method of determining Km and Vm, therefore after methods have been developed
Lineweaver-Burk Plot
Eq 3.12b can be linearized in double-reciprocal form
A plot of 1/v versus 1/[S] yields a line with a slope of Km/Vm and a y-intercept of 1/Vm
Give good estmates of Vm but not necessarily Km
Data points at low substrate concentrations influence the slope and intercept more than data points at high [S]
SV
K
Vv
SK
SVv
m
m
m
m
m
111
(3.12b)
(3.13)
Lineweaver-Burk Plot
Lineweaver-Burk Plot with Actual
Experimental Data Sets
Eadie-Hofstee Plot
Eq 3.12b can be arranged as:
A plot of v versus v/[S] results in a line with slope –Km,
and a y-intercept of Vm
Eadie-Hofstee plots can be subjected to large errors,
since both coordinates contain v, but there is less bias on
points at low [S] than with Lineweaver-Burk plots
S
vKVv mm
(3.14)
Eadie-Hofstee Plot
Eadie-Hofstee Plot with Actual
Experimental Data Sets
Hanes-Woolf Plot
Rearrangement of Eq 3.12b yields:
A plot of [S]/v versus [S] results in a line of slope
1/Vm with a y-intercept of Km/Vm
This plot is used to determine Vm more accurately
than the previous two plots
S
VV
K
v
S
mm
m 1
(3.15)
Hanes-Woolf Plot
Hanes-Woolf Plot with Actual
Experimental Data Sets
Batch Kinetics
The time course of variation of [S] in a batch enzymatic reaction can be determined by integrating equation 3.12b to yield:
A plot 1/t (ln[S0]/[S]) versus {[S0]-[S]}/t results in a line of slope -1/Km with a y-intercept of Vm/Km
S
S
t
K
t
SSV
S
SKSStV
mm
mm
00
00
ln
ln
(3.16)
(3.17)
Complex Enzyme Kinetics: Allosteric
Enzymes
Allosteric enzymes:
Some enzymes posses more than one substrate binding
site
The binding of one substrate molecule to the enzyme
facilitates binding of other substrate molecules
This is known as allostery or cooperative binding
Often seen in regulatory enzymes
Allosteric Enzymes
Allos -other, steros –shape
The rate expression for allosteric enzymes is:
Where n = cooperativity coefficient and n>1 indicates positive cooperativity (=activator; n<1=inhibitor)
The cooperativity coefficient can be determined by rearranging 3.18:
And by plotting ln v/(Vm-v) versus ln [S]
nm
n
m
SK
SV
dt
Sdv
"
"lnlnln m
m
KSnvV
v
(3.18)
(3.19)
Allosteric Enzymes
Graphical Determination of the
Cooperativity Coefficient, n