BCM 254 & BCM 256

Alkaline Phosphatase Kinetics

Ina Keyser 10144383

University of Pretoria

14 May 2011

INDEX

1. INTRODUCTION 3a) Aim 4

2. METHOD 5a) Materials and Reagents 5b) Procedure

i. Determining the Optimal pH 5ii. Determining the Optimal Temperature 6

iii. Determining the Vmax and Km Values 63. RESULTS 7

a) Optimum pH 7b) Optimum Temperature 8c) Optimum Substrate Concentration 10d) Calculation of Vmax and Km Values 11

4. DISCUSSION 13a) Optimum pH 13b) Optimum Temperature 13c) Optimum Substrate Concentration 14

5. CONCLUTION 146. REFERENCES 16

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1. INTRODUCTION

Enzymes make up a large and diverse group of (mainly) proteins that are essential for metabolic functions in cells. These substrate-specific molecules function as catalysts in virtually all biochemical reactions by decreasing the activation energy required for the conversion of the substrates (or reagents) to products.

Enzymes are usually composed from amino-acids with R-groups, each with defining characteristics. The degree to which the R-groups of amino acids are protonated at a specific pH, determines the charge on those amino acids. And when present in an enzyme, the level of protonation of the various R-groups determines the degree of protonation and, therefore, the charge of the enzyme as a whole. The level of protonation of the individual R-groups, however, are responsible for the number and types of electrostatic interactions and hydrogen bonding; and in turn the three-dimensional structure of the enzyme. Should the pH of the existing environment change, the protonation of the R-groups will vary and the electrostatic interactions and hydrogen bonding will be redistributed so that the enzyme conformation changes as a whole. Not all the enzymes in the population undergo these changes in conformation. This result in either an increase or decrease in the number (concentration) of enzyme molecules present in the active conformation and can be used as a measure for the rate of the reaction.

For many enzymes the rate of catalysis, defined as the number of moles (n) of product formed per second (s), varies with the substrate (S) concentration. The extent of product (P) formation is determined as a function of time for a series of substrate concentrations. As expected in each case, the amount of product increases with time, although eventually a time is reached when there is no net change in the concentrations of S or P. The enzyme is still actively converting S into P and vice-versa, but the reaction has attained a dynamic equilibrium. [1]

The reaction to be investigated is that catalysed by alkaline phosphatase (AP). Alkaline phosphase is a hydrolase present in all tissues throughout the human body, but particularly concentrated in the liver, bile duct, kidneys, bone and in pregnant females – the placenta. It is responsible for the hydrolysis of phosphor-ester bonds, releasing a phosphate group and the alcohol derivative of the substrate. [1, 3] Alkaline phosphase needs Mg²⁺ ions to function and is inhibited by chelating agents (e.g. EDTA) and inorganic phosphate. In this experiment p-nitro phenol-phosphate will be used as a substrate for the synthesis of p-nitro phenol. P-Nitro phenol is yellow and p-nitro phenol-phosphate is colourless. It is therefore easy to perform a spectrophotometric enzyme assay.

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A spectrophotometer is a device used to measure light absorbency of a solution at a specific wavelength. When the enzymes act on the substrate to form product, the product causes the solution to display yellow. A sample of the solution can then absorb the light passing through the cuvette in the spectrophotometer and absorbency (dependent on the various [P]) can be obtained.

To produce an effective enzyme assay, the optimum pH and temperature (conditions at which enzyme function is optimal and therefore the highest [P] can be obtained) must be known. The product concentration value can be determined by using the Beer-Lambert’s Law. This law constitutes the empirical relationship between the absorption of light to the properties of the material it is directed through. With the environmental factors, pH and temperature, values an experiment van be conducted to determine the optimal [S].

The Michaelis-Menten and Lineweaver-Burke graphs can be plotted with the abovementioned data in order to calculate the Vmax and Km. Vmax is the theoretical maximum velocity of the reaction, since it never reaches this maximum, but approaches it asymptotically and therefore the [S] equals zero at this point. Half of the Vmax is taken to determine the corresponding [S] and is called the Km. Km, also referred to as the Michaelis constant is the [S] at which half of the enzyme active sites are occupied (or filled). The Km thus provides a measure of the [S] required for significant catalysis to occur. [2, 3]

a) Aim

To determine the kinetic parameters Vmax and Km of the non-allosteric enzyme, alkaline phosphatase, by investigating the optimum pH and temperature at which this enzyme functions.

2. METHOD

To conduct the experiment, it was very important to keep the laboratory work station neat and tidy, to clean all apparatus prior to the experiment with alcohol and distilled water and to dry these apparatus before starting with the experiment – it is of the utmost importance to uphold the principles of Good Lab Practice (GLP).

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a) Materials and Reagents

Materials: Spectrophotometer “Handy Step” 12 test tubes (in a

stand) 1 cuvette 1 “Handy Step” tip

(5ml) 2 beakers (20ml) Incubator (water bath)

with resettable temperature dial

Reagents:

5mM p-nitro phenol phosphate substrate standard

Buffers (with pH varying from 2 to 12)

Alkaline phosphate enzyme mixture

Distilled water (cleaning purpose)

Ethanol (cleaning purpose)

b) Procedure

i. Determining the Optimal pH

The spectrophotometer (SPM) was switched on and allowed to warm up for about 20 minutes. After warming up, the wavelength was set to 405nm. To determine the optimum pH, the temperature was kept constant at 35oC throughout the experiment and the substrate concentration in all the test tubes, 5mM of p-nitro phenol. The absorbance reading was zeroed by using a “blank”, i.e. distilled water. Eleven test tubes were used to conduct the experiment. For the first test tube p-nitro phenol phosphate (5mM), a buffer (with a pH of 2) and 10 units of the enzyme AP was added to make a final volume of 3ml. For the second test tube p-nitro phenol phosphate (5mM), a buffer (pH of 3) and 10 units of the enzyme AP was added to make a final volume of 3ml. The steps were repeated for the rest of the test tubes but each time a buffer, with a pH of 1 higher than the previous was added – resulting in test tube 11 ending with a pH of 12.

Once the enzyme was added to a test tube, the experiment for that particular test tube was immediately carried out. This ensured that the enzyme did not have extra time to allow for unaccounted formation of product, as this could lead to skewed results. Only when results are obtained at a particular pH can one then go on to make the next test substance at the differing pH.

The content of each test tube was then poured into the cuvette (one at a time) to determine the absorbencies of each test tube, respectively. The

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cuvette was placed into the spectrophotometer and the absorbance of each tube was recorded every minute for 10 minutes. After obtaining the results for each test tube, the product concentration was determined using Beer-Lamberts’ law: A=ƐCL. (where A was the absorbance, Ɛ the molar absorptivity, C the product concentration and L the wavelength). The product concentration was then plotted against pH and a standard curve was drawn. The peak of the curve indicated the optimum pH of alkaline phosphatase.

ii. Determining the Optimal Temperature

The spectrophotometer was switched on and allowed to warm up for 20 minutes. After warming up, the wavelength was set to 405nm. For determining the optimum temperature, the pH was kept constant at the newly found optimum pH (which was 8) throughout the experiment as well as the substrate concentration at 5mM. The absorbance reading on the spectrophotometer was zeroed using distilled water (the “blank”).

Seven test tubes were prepared by adding 5mM p-nitro phenol phosphate, a buffer which had a pH of 8 and 10 units of the enzyme alkaline phosphate into the test tubes - final volume was 3ml. Once the enzyme was added to test tube, the experiment for that particular test tube was carried out. This ensured that the enzyme did not have extra time to allow for unaccounted formation of product as this could lead to skewed results. Only when the results were obtained at a particular temperature can one go on to make the next test substance for the next temperature to be tested.

The first test tube was incubated at 34oC, the second at 35oC, and the rest of the test tubes were incubated at 1 o C higher than the previous tube, up until 40oC. The cuvette was filled with each test tube substance, respectively, and then placed into the spectrophotometer for the absorbance of each tube to be recorded every 10 minutes. After obtaining the results for each test tube, the product concentration was determined using Beer-Lamberts’ law (as detailed in i. Determining the Optimal pH). The product concentration was then plotted against the temperature and a standard curve was constructed. The peak of the curve indicated the optimum temperature of alkaline phosphatase.

iii. Determining the Vmax and Km Values

The spectrophotometer was switched on and allowed to warm up for 20 minutes. After warming up, the wavelength was set to 405nm. During the experiment the pH of the buffer was kept constant at 8 and the temperature at 37oC. The absorbance reading on the spectrophotometer was zeroed by using a “blank”. Eight test tubes were used to conduct the experiment. The first tube was used as a control as no alkaline

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phosphatase was added. For the remaining seven test tubes, the substrate concentrations were changed. The second test tube was filled with 5mM p-nitro phenol phosphate, a buffer (pH 8) and 10 units of alkaline phosphatase, to make a total volume of 3 ml. The third test tube contained 10mM of p-nitro phenol and the rest of the test tubes 20mM, 30mM, 40mM, 50mM, 75mM and 100mM, respectively.

The absorbance of each test tube was recorded every minute for 10 minutes. After obtaining the results for each test tube, the product concentration was determined using Beer-Lambert’s law. The product concentration was then plotted against time and the gradients of the seven test tubes were determined to give the velocity of the reaction.

The velocity was then plotted against the corresponding substrate concentration, giving a graph known as a Michaelis-Menten graph. The Vmax and ⅟2 Vmax values were determined from the peak of the Michaelis-Menten graph. The Km value was determined using the ⅟2

Vmax value. The Lineweaver-Burke graph was then plotted using the same data used to obtain the Michaelis-Menton graph. The graph is a double reciprocal graph - as it is the inverse of the velocity of the reaction vs. the inverse of the substrate concentration.

3. RESULTS

a) Optimum pH

The absorbencies, and pH and the calculated p-nitro phenol concentrations are tabulated below (Table 1) and Graph 1 illustrates the relationship between the concentrations of p-nitro phenol in the eleven test tubes, respectively, and their corresponding pH.

Controls (constants): p-nitro phenol phosphate substrate concentration = 5mM Temperature = 37°C Alkaline phosphatase enzyme units used = 10

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C = A/εL

Table1: Absorbance, pH and p-Nitro Phenol Concentration of each Test Tube

Test Tube

Wavelength (nm)

Temperature (°C)

Absorbance

pH

[p-Nitro phenol] (mole/L)

1 405 37 0.275 2 3.612 405 37 0.275 3 3.613 405 37 0.275 4 3.614 405 37 0.337 5 4.435 405 37 0.39 6 5.126 405 37 0.41 7 5.387 405 37 0.43 8 5.658 405 37 0.412 9 5.419 405 37 0.43 10 5.65

10 405 37 0.41 11 5.3811 405 37 0.39 12 5.12

Graph 1: The Relationship between Product Concentration (mole/L x 10¯⁸ ) and pH

The optimum pH was found to be 8.

b) Optimum Temperature

8

0 2 4 6 8 10 12 140

1

2

3

4

5

6

The Relationship between p-Nitrophenol Concentration (mol/L x 10¯⁸) and pH

pH

p-N

itro

phen

ol C

once

ntra

tion

(mol

/Lx1

0¯⁸)

The absorbencies, and pH and the calculated p-nitro phenol concentrations are tabulated below (Table 2) and Graph 2 illustrates the relationship between the concentrations of p-nitro phenol in the seven test tubes, respectively, and their corresponding temperature.

Controls (constants): p-nitro phenol phosphate substrate concentration = 5mM pH = 8 Alkaline phosphatase enzyme units used = 10

Table2: Absorbance, pH, Temperature and p-Nitro phenol Concentration of each Test Tube

Test Tube

Wavelength (nm)

Temperature (°C)

Absorbance

pH

[p-Nitro phenol] (mole/Lx10¯⁸)

1 405 34 0.412 8 5.42 405 35 0.405 8 5.323 405 36 0.417 8 5.484 405 37 0.43 8 5.655 405 38 0.417 8 5.486 405 39 0.405 8 5.327 405 40 0.412 8 5.4

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33 34 35 36 37 38 39 40 415.1

5.2

5.3

5.4

5.5

5.6

5.7

The Relationship between p-Nitrophenol Concentration (mol/Lx10¯⁸) and Temperature

(°C)

Temperature (°C)

p-N

itrop

heno

l Con

cent

ratio

n(m

ol/L

x10¯

⁸)

Graph 2: The Relationship between Product Concentration (mole/L x 10¯⁸ ) and Temperature (°C)

The optimum temperature was found to be 37°C.

c) Optimum Substrate

Graph 2 illustrates the relationship between the concentrations of p-nitro phenol phosphate and p-nitro phenol over a specific time period.

Controls (constants): Temperature = 37°C pH = 8 Alkaline phosphatase enzyme units used = 10

Graph 3: The Relationship between p-Nitro Phenol Phosphate (mM), p-Nitro Phenol Concentration (mole/Lx10¯⁸) and Time (minutes)

The optimum substrate concentration has been determined, is 100mM.

10

0 2 4 6 8 10 120

2

4

6

8

10

12

14

16

The Relasionship between p-Nitro Phenol Phosphate (mM), p-Nitro Phenol Concentration

(mole/Lx10¯⁸) and Time (minutes)

5mM10mM20mM30mM50mM75mM100mM

Time (minutes)

p-N

itro

Phe

nol C

once

ntra

tion

(mM

)

d) Calculation of Vmax and Km Values

The initial substrate concentrations and the correlating reaction velocities (mole/L/minute x10¯⁸) are tabulated in Table 3, and the relationship of these factors are illustrated with a Michaelis-Menten graph (Graph 4).

Table 3: Initial substrate concentrations (mM) and the correlating reaction velocities (mole/L/minute x10¯⁸) of each Test Tube

Substrate Concentration (mM) Reaction Velocity (mole/L/minute x10¯⁸)5 0.28

10 0.4720 0.6630 0.8650 0.9875 1.12

100 1.19

Graph 4: Michaelis-Menten Graph to illustrate the relationship between Vmax and Km

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0 20 40 60 80 100 1200

0.2

0.4

0.6

0.8

1

1.2

1.4

Michaelis-Menten Graph to illustrate the rela-tionship between Vmax and Km

p-Nitro Phenol Phosphate (mole/L x10¯⁸)Reac

tion

Velo

city

(mol

e/L/

min

ute

x10¯

⁸)

1/2Vmax = 0.595 x10¯⁸

Vmax = 1.19x10¯⁸

Km = 18

The Michaelis-Menten graph relates the initial rate Vo to the [S]. The above graph is a hyperbolic function, where the maximum rate is described as Vmax.

The mathematical relationship is as follows:

The following graph relates the inverse of the substrate concentrations (1/[S]) with the inverse of the reaction velocities (1/mole/L/minutes x10¯⁸). This Lineweaver-Burke graph gives a constant relationship as a “straight line” (constant) function.

Graph 5: Lineweaver-Burke graph gives a constant relationship between the inverse of the substrate concentrations (1/mM) with the inverse of the reaction velocities (1/mole/L/minutes x10¯⁸)

The Km was found to be 18mM and the Vmax 1.19x10¯⁸mM/minute.

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-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.250

0.5

1

1.5

2

2.5

3

3.5

4

Linewaever-Burke Graph to illustrate the rela-tionship between the 1/[S] (1/mM) and 1/V

(1/mole/L/minute x10¯⁸)

Inverse p-Nitro phenol phosphate (1/mM)Inve

rse

of th

e Re

actio

n Ve

locit

y (1

/mol

e/L/

min

ute

1/Vmax = 0.840

-1/Km = -0.06

Vmax [S]Vo = Km + [S]

1 Km + [S] ( Km) (1) 1 V = Vmax [S] = (Vmax) x [S] + Vmax

The mathematical relationship is as follows:

4. DISCUSSION

a) Optimum pH

The name alkaline phosphate indicates that the enzyme functions optimally at alkaline conditions. In determining the optimum pH, the enzyme and substrate concentration as well as the temperature were kept constant at the same time altering the pH and determining the highest product concentration by testing the absorbance of the solution containing p-nitro phenol and then using the Beer-Lambert’s law. The graph to obtain the optimum pH was drawn and the optimum pH was und to be at pH 8 and 10. Since alkaline phosphatase functions within the body (living tissue conditions) with an approximate pH of 8, a pH of 8 was used throughout the experiment.

Enzymes are composed from amino acids with defined characteristics. Interactions such as hydrogen bonds, disulphide bonds, ionic interactions and hydrophobic interactions between different amino acids side chains in the protein determine the specific three dimensional structure of the enzyme. Since an increase in pH will lower the hydrogen ion concentration and vice versa, this results in a disturbing of the bonds keeping the enzyme in a correct conformation and thereby changing the three dimensional structure of the enzyme and so affecting the binding ability of the substrate too.

b) Optimum Temperature

Alkaline phosphatase is found in the human body and will therefore be expected to function optimally at or around 370C, since this is the temperature of the body under normal living conditions. In determining the optimum temperature, the substrate and enzyme concentrations were kept constant as well as the pH (at 8),m while varying the values of the temperature. The Beer-Lambert’s law was used to calculate the product concentrations which were then plotted against the corresponding temperature. The optimum temperature was found to be 37°C, which corresponds with the theoretical (human body) temperature, as expected.

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Def k 2 + k -1

Km = k1 ≈ KD

c) Optimum Substrate Concentration

In determining the optimum substrate concentration, the pH was kept constant at 8 and the temperature at 370C. In this part of the experiment, the substrate concentration was the variable. The reaction velocities were determined by calculating the gradients of the graph and the optimum substrate concentration was found to be 100mM.

This makes sense, because the more substrate available for the enzyme to bind to, the more products can be synthetized – therefore the absorbencies were read to determine the [P].

This process is summarized by the following equation:

5. CONCLUTION

We were able to successfully accomplish our aim of determining KM (which we found to be 18mM) and the Vmax (which we found as 1.19 x 10-8 mMmin-1).We can therefore conclude that at a p-nitro phenol phosphate concentration of 18nM, 50% of the alkaline phosphate enzyme active sites are occupied by substrate. (Km is a measure of how tightly substrate is bound to the enzyme. The greater the Km, the less tightly the substrate is bound to the enzyme.)Km is also the dissociation constant of the ES-complex, when we assume k-1 >> k2.Vmax is related to the turnover number of an enzyme, a quantity equal to the catalytic constant k2. The constant is referred to as kcat. The turnover number is the moles p-nitro phenol phosphate that reacts to form p-nitro phenol per mole of alkaline phosphate per unit time (assuming that AP is fully saturated with p-nitro phenol phosphate and thus the reaction is proceeding at a maximum rate).

We have to note that this methodology of determining enzymatic kinetic parameters is only suitable when we investigate non-allosteric enzymes. When dealing with allosteric enzymes, it is difficult to account for the effect of cooperation displayed by the enzyme.

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K1 k2

E + S ES E + P k-1

Def

Vmax = kcat [E]tot

Lineweaver-Burke plots by virtue of their reciprocal nature are prone to error, as they increase small errors in measurement. Also most points on the graph are found to the right of the y-axis (owing to the limiting solubility not allowing large values of [S] and therefore a small 1/[S] value) calling for extrapolation to obtain the x and y intercepts. This explains why the 1/Vmax values for 0 and 0.01 concentration had the same value of 0.84. This is the only manner to allow for further extrapolation to determine the x intercept (-1/Km).

6. REFERENCES

1. Campbell, Farrell. Biochemistry. 6th Ed. Belmont. Brooks/Cole. 2008: 144-164.2. Wikipedia. Alkaline Phosphate [cited 2009 April 24].

http://en.wikipedia.org/wiki/Alkaline_phosphate.3. Berg Jm, Tymoczko JL, Stryer P and Lubert C. Biochemistry. 5th Ed. New York:

W.H. Freeman and Co: 2002. http://www.ncbi.nlm.nih.gov/.

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