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Computer-interfaced Experiments - Conductivity Measurement

Enzyme Kinetics
Enzymatic Hydrolysis of Urea

Objectives: Determination of the Temperature Optimum, the Michaelis Constant Km and the Maximal Velocity Vmax, Competitive Inhibition

Peter Keusch



Datalogging and data analysis using Program CHEMEX and the Analog-Digital-Converter CHEMBOX
IBK electronic + informaticc
German version




Chemicals:
urea  (m.w. = 60.06 g / mol)
thiourea  (m.w. = 76.13 g / mol)
urease

Apparatus and glass wares:
2 magnetic stirrer hotplates
4 magnetic stirring bars
stirring bar remover
crystallizing dish d= 140 mm, h = 75 mm  (for water bath)
crystallizing dish d = 190 mm, h = 90 mm  (for water bath)
100 mL round bottom flask with center neck NS 29/32 and 2 angled side necks 14/23
6 beakers 100 mL
volumetric flask 1000 mL
2 contact thermometers
temperature sensor
conductivity measuring cell
volumetric pipette 10 mL
volumetric pipette 100 mL
2 pipette bulbs


Hazards and safety precautions:

Thiourea is toxic. Known animal carcinogen and probable human carcinogen. May cause irreversible effects. May affect fertility. May be fatal if swallowed. May cause allergic skin reaction. May cause skin ulcers, liver damage.

Handle as a carcinogen. Gloves, safety glasses, good ventilation. Protect against spills and the spread of dust.


Theoretical background:


equation


Urea is decomposed by the enzyme urease forming ammonia and carbon dioxide. Hence the reaction can be monitored by following the change in conductance of the reaction mixture with time. The conductance is proportional to the concentration of the ions formed during the reaction.


Kinetic equations (Download PDF file)


Preparation of the solutions:

Urea suspension: 1.2 g of urea are placed in a 1000 mL volumetric flask. Using a wash bottle the flask is carefully filled with distilled water to the mark etched on the neck. The concentration of the urea stock solution is 2 · 10 -2 mol / L. The test concentrations (1.5 · 10 -2,  10 -2,  7 · 10 -3  and   4 · 10 -3 molar solution) are prepared by diluting appropriate aliquots of the stock solution.

Urease suspension: 100 mg of the urease are suspended in 50 mL water in a 100 mL beaker while stirring.











Experiment set-up

Fig. 1: Experiment set-up


Experiment 1: Determination of the temperature optimum

Experimental procedure:

In addition to a conductivity measuring cell  (1)  a temperature sensor  (2)  is connected to the CHEMBOX via input Sensor1   (Fig. 1).

In the program CHEMEX the recording time is entered with 120 s and the measuring range is limited to 0 - 200 ms.

The flask placed in a water bath, is filled with 100 mL of urea solution (cS = 10 -2 mol / L). The two sensors are adjusted such that their terminals are immersed in the solution (at least 1 cm). Using a hotplate stirrer and a contact thermometer the water bath is warmed up to the desired reaction temperature (20, 30, 40, 50, 60 °C). Also the urease suspension is warmed up to the desired temperature  (Fig. 1).  The urea solution and the urease suspension both are allowed to equilibrate in the constant-temperature water bath. After thermal equilibrium has been reached 10 mL urease suspension are added to the urea solution. Immediately the sensing software is started.

The change in conductivity is displayed on the measuring screen  (Fig. 2).

Beginning at a reaction temperature of 40 °C, a freshly prepared urease suspension is to be used.



Fig 2: Realtime graph     conductivity curve  (T = 20 °C     cS = 10 -2 mol / L)



Data analysis using Excel (Download):


temperature
Fig. 3: Conductivity curves  (cS = 10 -2 mol / L)
T = 20 °C   (1)      30 °C   (2)      40 °C   (3)      50 °C   (4)     and     60 °C   (5)


Temperature [ °C ] 20 30 40 50 60
k [ mS · s -1 ] 0.000793 0.001515 0.002481 0.003865 0.003097
v [ mS · min -1 ] 0.04758 0.0909 0.14886 0.2319 0.18582
Tab. 1: Reaction velocity v

temperature optimum
Fig. 4: Effect of temperature on reaction velocity   (cS = 10 -2 mol / L)




For the temperature range 30 - 50 °C  (Tab. 1)  the activation energy is  38.1 kJ · mol-1   and the activation enthalpy is  35.5 kJ · mol-1. According to the Arrhenius and Eyring equation, respectively, the activation parameters are computed from the slope  m  of the straight lines in the plots of  lnk  and  lnk/T  respectively, versus  1/T  (Fig. 5):

E a  =  - m  ·  R =  4588,4  ·  8.3144  =  38.1 kJ · mol-1
DH ‡  =  4275,5   ·  8.3144  = 35.5 kJ · mol-1



Fig. 5: ARRHENIUS- (1) and EYRING-Plot (2)


Discussion:

Enzyme-catalyzed reactions have rates that increase with temperature, reach a maximum at the optimum temperature, and then decline as the enzyme is denatured. Animal enzymes often have temperature optima near 37 °C (especially human's since this is body temperature). The experimental results indicate enhanced resistance of urease to thermal denaturation. The temperature optimum is 50 °C. Above 50 °C the tertiary structure of the enzyme begins to degenerate and lose its activity.

The uncatalyzed decomposition of urea in water has an activation energy of about  130 kJ, whereas in the presence of dissolved urease the activation energy is lowered to about  42 kJ.



Experiment 2: Determination of the Michaelis constant Km and the maximal velocity vmax

To determine the kinetic parameters Km and Vmax it is necessary to measure the enzyme reaction rate at different concentrations of substrate, while holding the enzyme concentration and all other conditions constant.

Procedure:

100 mL of urea solution are allowed to react with 10 mL of urease suspension at a temperature of 40 °C and 50 °C. The following substrate concentrations are used:
cS  =  4 · 10 -3,  7 · 10 -3  and  10 -2 mol / L.

Data analysis:


substrate concentration
Fig. 6: Effect of substrate concentration on velocity  (T = 50 °C)
cS  =  4 · 10 -3   (1)      7 · 10 -3   (2)      10 -2 mol / L   (3)


cS [ mol · L -1 ] 4 · 10 -3 7 · 10 -3 10 -2
k [ mS · s -1 ] 0.001868 0.002934 0.003865
v [ mS · min -1] 0.11208 0.17604 0.2319
Tab. 2: Reaction velocity at 50 °C
cS [ mol · L -1 ] 4 · 10 -3 7 · 10 -3 10 -2
k [ mS · s -1 ] 0.001214 0.001934 0.002481
v [ mS · min -1 ] 0.07284 0.11658 0.14886
Tab. 3: Reaction veloctiy v at 40 °C

According to equation (11)  Kinetic equations (Download PDF file)  1 / v  is plotted versus  1 / cS  (Fig. 7).  If the velocity constants k and the appropriate substrate concentrations  cS  are entered into the table of the Excel file  Lineweaver-Burk (Download)  (Tab. 4),  the values for the Michaelis constant Km and the maximal reaction veloctiy   vmax  will be calculated.


Excel file
Tab. 4: Excel file     Determination of  Km  and  vmax


Lineweaver-Burk
Fig. 7: Lineweaver-Burk plot     T = 50 °C  (1)     T = 40 °C  (2)


For the Michaelis constant  Km  a value of  2.41 · 10 -2 [ mol · L -1]  (Lit.: 2.5 · 10 -2 ) was obtained. The maximal reacktion velocity  vmax  amounts at 40 °C to  0.5118 [ mS · min -1 ]  and at 50 °C to  0.7868 [ mS · min -1].


The Michaelis constant Km equals the substrate concentration at half-maximal reaction velocity  vmax / 2  ( Fig. 8).  According to  ƒES  =  v / vmax Michaelis constant   allows the determination of the percentage of the occupied active centers for the different substrate conzentrations  (Fig. 9).


cS [ mol · L -1 ] 4 · 10 -3 7 · 10 -3 10 -2 1.5 · 10 -2 2 · 10 -2 2.41 · 10 -2  =  Km
v [ mS · min -1 ] 0.11208 0.17604 0.2319 0.30174 0.37148 0.3934
v / vmax 0.14245 0.22374 0.29474 0.38350 0.47214 0.5
Tab. 5: Percentage of the occupied active centers  ƒES  =  v / vmax    (T = 50 °C)

KM
Fig. 8: Plot of substrate concentration versus reaction velocity    (T = 50 °C)


besetzte Zentren
Fig. 9: Percentages of the occupied active centers  ƒES  =  v / vmax    (T = 50°C)



Experiment 3: Competitive inhibition with thiourea

Procedure:

In order to determine the competitive inhibition, 100 mL of a solution are used, which is eqiumolar in urea and thiourea. Also in this experiment are used the following concentrations:  cS  =  4 · 10 -3,  7 · 10 -3   and  10 -2mol / L. A mixture of 50 mL of urea solution and 50 mL of thiourea solution (identic concentrations) is mixed with 10 mL of urease suspension.

Data analysis:


Kompetitive Hemmung
Fig. 10: Competitive inhition     urea decomposition in presence of thiourea  (T = 50 °C)
cS  =  4 · 10 -3   (1)      7 · 10 -3   (2)      10 -2 mol / L   (3)


Lineweaver-Burk
Fig. 11: Lineweaver-Burk plot     competitive inhibition
1: urea     2: urea + thiourea


While vmax remains constant, the value for  Km  is doubled. The affinity of urea to the enzyme is reduced by half.

Thiourea is structurally related to the substrate (urea) and may be bound to the enzyme active center and competes with the substrate.

In the presence of an competitive inhibitor,  vmax  is not altered  ( vmax'  =  vmax )  because this is the velocity at high  cS  where the substrate will out compete the inhibitor for the active site. However, the apparent Michaelis-Menten constant  Km'  is altered.


Reference:
Computer-interfaced Experiments  Enzyme Kinetics: Enzymatic Decomposition of Hydrogen Peroxide
 Demonstration Experiment ob Video   Decomposition of Urea with Urease


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