Principle, operation and calculation of Km value of alkaline phosphatase在线视频

Kinetics of enzyme-catalyzed reactions

is a study on the rate of enzymatic reactions and some factors

by which the rate is influenced.

such as the concentrations of substrates,

the concentrations of enzymes，activators，inhibitors，

pH and temperature in surroundings.

If we want to find the relationship

between the velocity and the concentration of substrate [S],

we can use the same concentration enzyme

to catalyze the reaction with the different concentration of substrate,

while the reaction temperature, pH are invariableness.

The velocity of a reaction is expressed

in terms of the changes in the concentration of substrate

or product per unit time.

So we can use the changes of concentration of product

or substrate over a given time period, and [S],

as two factors to draw different points in the graph,

and then to find the tendency.

We find the curve is a rectangular hy'perbola,

include three different stages,

the rate of the reaction is directly proportional to [S]

only when [S] is low,

we called the first-order reaction.

And this is a straight line from zero point.

When [S] is sufficiently high

so that the enzyme is saturated,

the reaction is zero-order reaction with respect to substrate. 

And this is a straight line

that parallel to the horizontal axis.

And the velocity is the Vmax.

At the intermediate [S]

the reaction is a mixed order reaction and formed a curve.

From the rectangular hyperbola

we find the velocity increase quickly

in the first-order reaction stage,

slowly in the mixed order reaction stage,

and has no change in the zero-order reaction stage.

How to use the mathematical method

to describe the relationship between velocity and [S]?

Michaelis and Menten

obtained the following rate versus substrate concentration equation:

This Michaelis-Menten equation

demonstrates that when v = ½Vmax,

the substrate concentration [S] is the same as the Km.  

So Km is defined as the substrate concentration

when the velocity of reaction is the half of the maximum value.

In a steady-state of reaction with constant of temperature,

pH and enzyme concentration,

the reaction velocity "v"

can be calculated by Michalis-Menten equation.

Km is a characteristic constant of an enzyme.

Different enzymes have different Km values.

different substrates of a single enzyme

will also have different Km values.

The Km of most pure enzymes lie in the range of 0.01-100 mmol/L.

The substrate concentration [S] is hyperbolic correlated

to velocity as shown in the figure.

It is difficult to get the precise value of Km from such a plot,

because it is difficult to plot a precise hy'perbola

by limited reactions at different substrate levels.

The Michaelis-Menten equation can be transformed simply

by taking reciprocal of both sides to form a Lineweaver-Burk equation.

If we take 1/v as the ordinate

and 1/[S] as the abscissa,

we can get a straight line plot.

This is called the Lineweaver-Burk plot or the double reciprocal plot.

This straight line has a slop of the ratio of km to Vmax (Km/Vmax),

an intercept of -1/Km on the 1/[S] axis,

and an intercept of 1/Vmax on the 1/v axis,

Therefore, the Km of an enzyme can be accurate determined

by a simple plot of double reciprocal diagram.

In the optimum conditions

(pH=10, 37 degrees celsius),

AKP catalyzes the hydrolysis of disodium phenyl phosphate

with liberation of phenol and disodium hydrogen phosphate.

Phenol can react with the 4-aminoantipyrene(AAP)

in the presence of po'tassium ferricya'nate of alkaline medium

as an oxidizing regent to form a quinone compound with red color.

This red colored compound may be used

as the basis of photometric determination.

In this experiment,

disodium phenyl phosphate is used as the substrate

and a series of increasing substrate concentration

is employed to determine the corresponding reaction velocities.

The amount of product is proportional to the colorimetric absorption.

The red compound has a maximum absorbance at 510nm.

So the A510 can reflect the concentration of phenol,

and the resulted product of AKP catalysis.

Thus, the plot 1/[S] versus 1/A

can get the straight line

and can be further used to calculatethe Km value of AKP.

Mark 8 clean dry medium test tubes,

mark 1-8, respectively.

Add reagents to the 8 tubes according to the table.

Incubated the tubes in 37 degrees celsius for 5 min,

mix well and keep in 37 degrees celsius water bath for 15 min,

take out the tube back,

mix well, incubated the tubes at room temperature for 10 min

for color development.

10 min later,

take the absorbance of tube 1-7 using tube 8 as blank.

Before use,

turn on the spectrophotometer for 30 min

to allow lamp and electronics warm up.

Set the wavelength knob to 510nm. 

Always hold the rough side of the cuvette in the whole process,

rinse the cuvette by pouring a little of corresponding reaction mix,  

empty cuvettes and fill them with testing samples

to 2/3 –3/4 height of the cuvettes.

Wipe any fingerprint or spills off the outside of cuvettes.

Insert blank,

No.1-3 cuvettes in sample drawer properly,

where mirror side of cuvettes face to light source.

Close the sample chamber cover,

press the 100% button to obtain a reading of 100% T. 

Press the MODE button to switch the spectrometer

to absorbance mode.

The reading of blank absorbance should be zero.  

Pull the sample drawer gently,

record the absorbance reading of sample 1-3 one by one.

Assay the remaining samples

using the same operation with the same blank.

Data Processing

Input the data of substrate concentration of tube 1-7,

and the corresponding absorbance value in an excel worksheet.

Calculate the reciprocal of [S] and A.

Draw a scatter diagram using 1/[S] and 1/A data,

Right click the mouse over one of the symbols.

Add a trendline on the scatter diagram by right click.

Adjust the diagram by extending 1 units on trendline.

Click display equation on chart

display R-squared value on chart. 

Check the equation and R-squared value boxes

in the pop-up window.

The resulted trendline is the desired image,

where R square value indicates linear correlation of 1/[S] and 1/A.

According to the Lineweaver-Burk equation,

the Y intercept is 1/Vmax,

the slop is Km/Vmax,

dividing slop to Y intercept results to Km.