17
Kinetics of Enzyme Reactions 3
Rate and order of chemical reactions, kinetics of zero order and 1st order reactions.
Mechanism of enzyme catalyzed reactions, activity and catalytic concentration of
enzymes, factors affecting the enzyme activity, Michaelis plot, KM, inhibitors.
Quantification of Enzymes
Expression of enzyme quantity Unit Dimension
Katal (kat) .........
Catalytic (enzyme) activity
International unit (U, IU) mol/min
Catalytic concentration ......... .........
Mass concentration g/L g/L
1. Derive the relation between the values of catalytic activity in kat and IU and vice versa.
Determination of Catalytic Activity
2. Characterize the main ways of catalytic activity measurement
a) Kinetic method .............................................................
b) Constant time method ............................................................
c) Immunochemical determination ............................................................
t
]P[
ionconcentratcatalytic
S P
E
t
tP]
P]
a) b)v0 v
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3. Lactate dehydrogenase has the catalytic activity 2 kat. How many molecules of lactate will be
formed from pyruvate in one minute, if an excess of substrate is present? (7.231019
)
4. How much product will be formed in an enzymatic reaction in 10 minutes, if the enzyme activity
is 10 kat? What experimental conditions must be kept to achieve the amount theoretically
calculated? (6 mmol)
5. Serum (0.1 mL) was added into a reaction mixture. After 10 minutes, exactly 610-3
mmol of the
product were determined. What is the catalytic concentration of the enzyme? Is the result different
from the activity determined by the kinetic method? (100 kat/L)
6. The reaction mixture contains 2.5 mL of a buffer, 0.2 mL of NAD+
solution, 0.1 mL of serum and
0.2 mL of lactate solution. The reaction proceeded exactly for 10 minutes and 0.0012 mol/L of
NADH was measured in the mixture. Calculate the catalytic activity and the catalytic
concentration of lactate dehydrogenase. (6 nkat, 60 kat/L)
7. Calculate the activity of catalase, if 6.72 L O2 was released in 10 minutes. In the reaction mixture
was an excess of H2O2 and the reaction proceeded under normal conditions. (1 nkat)
Optical (UV) Test
Use:
a) Determination of enzyme activities ­ NAD(P)-dependent dehydrogenases
­ coupled determination of other enzyme activities
b) Determination of substrate concentration ­ e.g. lactate
8. How will the absorbance at 340 nm change during the lactate determination when using the optical
test?
S
NAD(P)+
NAD(P)H + H+
P
NAD(P)H + H+
NAD(P)+
t
A340
~ionconcentratCatalytic
A340
t (s)0
v0
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Factors Affecting Rate of Enzyme Reactions
I. Substrate Concentration
The course of a mono-substrate enzyme reaction:
Michaelis Plot (Saturation Curve)
For steady state: [ES] = constant
Equation of Michaelis-Menten
[S] ... initial concentration of substrate
Vmax ... maximal initial velocity
9. Compare: kinetic curve: dependence of ............... on ..................
saturation curve: dependence of ............ on ..................
10. Suggest an experiment, which provides the data for the construction of the saturation curve.
11. What is the dimension of KM?
12. Characterize the three parts of the Michaelis-Menten plot for the values: a) [S] << KM
b) [S] >> KM. What are the reaction orders under these conditions?
13. Characterize the point on the saturation curve for the value [S] = KM.
14. Calculate the [S]/KM ratio, if the initial reaction rate v0 is: a) 90 % Vmax; b) 99 % Vmax. (a) 9; b) 99)
15. For which of the following substrates S1, S2 a S3 does an enzyme with a broad substrate specificity
have the highest affinity (KM1 = 400 mol/L, KM2 =1000 mol/L, KM3 = 60 mol/L)?
16. The enzyme -galactosidase has KM(lactose) = 400 mol/L. What concentration of lactose has to
be used to maintain a zero-order kinetic? ( KM, i.e. mmol/L
17. The KM of an enzyme was increased twice in comparison with the normal value due to a mutation.
What concentration of substrate must be used not to change the reaction rate?
18. L-Asparagin is necessary for proteosynthesis in some cancer cells. The enzyme asparaginase
converting Asn to Asp and ammonia is administered during the treatment of some leukaemia
types. The decrease of Asn in circulation occurs consequently and the proliferation of cells is
lowered. Which of the asparaginase forms will be the most suitable for the treatment if the Asn
concentration in blood is 0.2 mM?
a) KM = 0.2 mM; Vmax = 0.1 mM/h b) KM = 0.2 mM; Vmax = 0.5 mM/h
c) KM = 2 mM; Vmax = 0.1 mM/h d) KM = 0.1 mM; Vmax = 0.5 mM/h
19. Explain the term substrate specificity using hexokinase and glucokinase as examples.
]S[
[S]
M
max0
K
Vv
[S] (mol/L)
Vmax
v 0
V max
2
KM
E + S ES E + P
k2
k1
k 1
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Vmax = constant
positive
efector
negative
efector
no efectorPositive
effector
No effector
Negative
effector
Saturation Curve of Allosteric Enzymes
Allosteric effector
- low molecular compound (often intermediate or product)
- binding into another region different from the active site
- change of enzyme conformation change of activity
Allosteric enzyme
- usually more subunits (often regulatory and catalytic)
- regulatory functions in metabolism
II. Enzyme Concentration
In general: t0 ]E[kv
For a fully saturated enzyme ([E]t = [ES]): v0 = Vmax = kcat  [E]t
where [E]t = [E] + [ES];
kcat = Vmax / [E]t molecular activity (turnover number)
20. Construct the saturation curves for the three different enzyme concentrations ([E1] < [E2] < [E3]) of
the same enzyme and the same reaction type. How will KM, Vmax values change?
21. The molecular activity of carbonic anhydrase is 6105
s 1
. How many molecules of carbonic acid
were formed, if the reaction was catalyzed by one molecule of the enzyme for 10 milliseconds?
The enzyme is fully saturated. (6 000)
22. The molecular activity of lysozyme is 0.5 s 1
. How many glycosidic bonds would be hydrolyzed
by 1 mol of the enzyme in 1 minute? Assume that the enzyme would be saturated. (0.5 mol 1017
)
III. Temperature
IV. pH
V. Activators
23. In which way is the enzyme activity affected by: a) temperature; b) pH; c) activators?
Give examples.
24. What is Taq polymerase, at which method it is used?
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VI. Inhibitors
25. Explain the difference between the reversible and irreversible inhibition.
26. Give examples of irreversible inhibition.
27. What types of irreversible inhibition are distinguished?
28. Complete into the table, how are changed the values of KM and Vmax and give examples of
inhibitors.
Parameter Competitive inhibition Non-competitive inhibition
KM
Vmax
Inhibitor
29. Draw the course of competitive and non-competitive inhibition. Mark the values KM, Vmax into the
plots.
a) competitive inhibition b) non-competitive inhibition
30. Explain the terms: proenzyme, isoenzyme and isoform.
i = 0 i = 0