Bi0157 Biochemistry Labs

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Wet Lab: Enzyme kinetics

Litterature: Horton, Chapter 5 (2nd and 3rd edition)

Introduction
In order to study the effects of different metabolites and conditions on enzymes and to determine how their activity is relevant to the functioning of a cell, it is necessary to be able to quantitate their activity how well they bind to substrates, and how fast they can turn over. This is the subject of enzyme kinetics, the study of enzymatic activity.

In this lab you will be looking at a reaction catalysed by BETA-GALACTOSIDASE. This enzyme recognises galactose in di-, oligo- and poly-saccharides and catalyses the hydrolysis of the glycosidic bond to beta-galactose. Many beta-galactosidases act on lactose, milk sugar, and those enzymes are also called lactases. Lactose is a disaccharide of galactose and glucose where galactose is bound by a beta-glycosidic bond to the hydroxyl on carbon 4 of glucose. Galactose and glucose are both aldo-hexoses and they differ only in the orientation of OH4 (the hydroxyl group on C4), which is axial in galactose and equatorial in glucose when the sugar is in its most stable chair conformation. The structure of lactose and its cleavage to galactose and glucose is shown in the figure below:

Beta-galactosidases are used in large scale in the dairy industry, for example for making low-lactose milk for people with lactose intolerance. Actually the majority of the world's adult population is intolerant to lactose. The enzyme used in this lab is from Aspergillus oryzae, a mould fungus ("mögelsvamp"). It is mainly used for hydrolysis of lactose in whey ("vassle"), which makes the whey sweeter and easier to concentrate. You can read more about the use of beta-galactosidase in the dairy industry on these web pages:

• http://www.fst.rdg.ac.uk/courses/fs560/topic1/t1f/t1f.htm
• http://www.sbu.ac.uk/biology/enztech/lactase.html

To make the measurements easy we will use an artificial substrate, p-nitrophenyl-beta-galactoside (pNP-Gal or pNPG), in which a chromophore, para-(or 4-)nitrophenol, is linked by a heteroglycosidic bond to beta-galactose. When the substrate is hydrolysed, p-nitrophenol is formed. At alkaline pH the phenolic proton dissociates (the pKa for p-nitrophenol is around 9) giving a phenolate anion with an intense yellow colour that can be easily measured in a spectrophotometer. The p-nitrophenyl group can not ionise as long as it is covalently bound to the galactose, only after hydrolysis will the colour develop. Such substrates are called chromogenic.

You will perform two experiments. In the first experiment you will determine the Michaelis constants Vmax and Km of beta-galactosidase for p-nitrophenyl-beta-galactoside. In the second you will perform the same experiment in the presence of an inhibitor, galactose, or another substrate, lactose. From the results you shall decide if the inhibition is competitive or non-competitive.

There are two methods of measuring the rate of a reaction. In the first, the rate of formation of a product (or of course disappearance of a substrate) is measured over a period of time, and from this the 'initial rate' is extrapolated, that is the rate of the reaction when the reaction was started and the concentration of substrate is known precisely.

The second method assumes that the amount of substrate is high enough such that its disappearance over a given period of time is insignificant (i.e. the rate of reaction is close to linear for the first stage of the reaction). After this fixed period of time the reaction is stopped and the concentration of formed product is measured. You will use this second method. The reaction is stopped by adding an equal volume of 0.5 M sodium carbonate to the reaction mixture. This will make the solution strongly alkaline. The high pH of 11-12 (you may check the actual pH if you want) will efficiently inactivate the enzyme and ensure that the colour is fully developed.

The way the rate of an enzyme-catalyzed reaction varies with the amount of substrate is described for a simple single-substrate reaction by the Michaelis-Menten equation:

v = V_max x S/(K_m + S)

where v is the rate of the reaction, V_max the maximum rate of reaction, S the substrate concentration and K_m a value related to how strongly the substrate is bound. By measuring the rate of reaction at different concentrations of substrate it is possible to construct a straight line (by transforming the above equation, for example using the Lineweaver-Burke method) and directly calculate the constants V_max and K_m.

• 0.1 M sodium acetate buffer pH 5.0 (NaAc), 10 ml
• 5 mM p-nitrophenyl-beta-galactoside (pNP-Gal) in buffer, 2 x 2.5 ml
• 1.5 µg/ml A. oryzae beta-galactosidase (Enz) in buffer, 5 ml
• 0.5 M Na₂CO₃, 12 ml
• 25 mM galactose (Gal) or 250 mM lactose (Lac) in buffer, 1.5 ml

         Blank

Na2CO3    500 µl
Enzyme    100 µl
pNPG        0 µl
Buffer    400 µl

The "Blank" is used to zero the spectrophotometer. Other things than substrate and prouct that are present in your solutions may absorb light and that must be compensated for. Save the blank and use also for experiment 2.

         1     2     3     4     5     6     7     8     9    Control
Buffer  390   375   350   325   300   250   200   150   100   100
pNPG     10    25    50    75   100   150   200   250   300   300

Make sure that the solutions have reached room temperature before starting the reaction. The reaction is then started by adding 100 ul enzyme solution to the cuvettes 1 to 9, but not to the Control. After 10 minutes each reaction is stopped by adding 500 ul 0.5 M Na₂CO₃. This can be done as follows:

1. At t=0 minutes add enzyme to cuvette 1. Mix gently with the pipette.
   At t=0.5 minutes add enzyme to cuvette 2. Mix gently.
   ...
   At t=4.0 minutes start the reaction in cuvette 9 as before.
   
   
2. At t=10 minutes stop the reaction by adding 500 ul 0.5 M Na₂CO₃ to cuvette 1. Mix.
   At t=10.5 minutes stop the reaction in cuvette 2.
   ...
   At t=14.0 minutes stop the reaction in cuvette 9.

When you have stopped the reaction in cuvette 9, add 500 ul 0.5 M Na₂CO₃ to the 'Control', mix well and then add 100 ul enzyme solution. The 'Control' is used to measure possible background absorbance in the substrate solution. The substrate itself may absorb light and there may be product, free p-nitrophenol, present already before the reaction has started. Finally pNP-Gal is slowly hydrolysed in the strongly alkaline solution after sodium carbonate addition. By subtracting this background the corrected absorbance will only come from the amount of product formed by the added enzyme during the reaction time.

The absorbance of the solutions can now be measured in the spectrophotometer. Place the cuvettes so the light goes through 1 cm of liquid. The light path is thus 1 cm. Before measuring absorbance always:

• Make sure that the contents in the cuvette are well mixed;
• Make sure there are no visible air bubbles in the cuvette (these can be removed with a small pipette)
• Carefully wipe off the surfaces through which the light shall pass;
• Check that the surfaces are clear and there is no turbidity in the solution by looking through the cuvette immediately before you put it in the spectrophotometer.

Mix - Wipe - Look - Measure

Set the wavelength to 400 nm on the spectrophotometer. Zero using the 'blank'. Now read the absorbances of the reaction mixtures and record the results.

Measure the absorbance of the 'Control' and write down the value. If its absorbance is 0.02-0.03 or less the background can be ignored, but if larger, the background absorbance must be subtracted from the absorbance after the reaction. Note that the absorbance of the 'Control' is the background only for the highest substrate concentration. The background for the other concentrations can easily be extrapolated, since absorbance is directly proportional to the concentration.

Save the samples in the cuvettes until you have made Experiment 2, for visual comparison of the results.

Plot the absorbance vs. substrate volume on a scrap piece of paper. This will give you some idea if any of the points are spurious. Any reaction which looks suspicious can then be repeated if it seems necessary. Show the plot to the lab teacher before proceeding with Experiment 2.

Experiment 2
Before you start this experiment make sure that the results of Experiment 1 are acceptable.

Take a new set of cuvettes for Experiment 2. In order to investigate the effect of the inhibitor on the rate of the reaction, repeat Experiment 1, now with inhibitor. Include in the reaction mixture 100 ul inhibitor solution, maintaining the same volume as before in the reaction mixture. This means that you must take 100 ul less of the buffer. Make a quick plot as before to check if any reaction looks suspicious.

1. Calculate for each tube the concentration of pNP-Gal as it was in the cuvette at the start of the reaction (reaction volume 0.5 ml).
2. Calculate the background in each cuvette. The absorbance of the control is the background for cuvette 9. For cuvettes 1 to 8 it has to be extrapolated from the Control. See Appendix.
3. Calculate for each tube the rate of the reaction in terms of how many mol/dm³ of pNP-Gal that were hydrolysed per minute. The molar absorption coefficient of p-nitrophenol at high pH is 18,300 M^-1*cm^-1 at 400 nm (i.e. a 1 M solution of p-nitrophenol would have an absorbance of 18,300 - if that were possible to measure). Bear in mind the following points:
   - The final volume is 1.0 ml whereas the reaction volume is 0.5 ml
   - The reaction period was 10 minutes
   
4. The table in the Appendix gives you a hint on how to treat the data.

> From these values construct a Lineweaver-Burk plot for both experiments on the same piece of graph paper. Draw straight lines that fit best to your data. Remember that the data points far away from origo may deviate more than those closer to the y-axis. Read the Km and Vmax values for both experiments from the intercepts with the x- and y-axes.

1. What are the Km and Vmax (in mol*dm^-3 and mol*dm^-3*min^-1, respectively) of beta-galactosidase for pNP-Gal in the absence of any inhibitor?
2. What are the Km and Vmax in the presence of inhibitor? What was the concentration of inhibitor in the reaction mixture?
3. Is the inhibition competitive or non-competitive?
4. Calculate the value of kcat of beta-galactosidase for pNP-Gal (in the absence of any inhibitor). In order to do this you need to know the molar concentration of the enzyme in the reaction mixture, which can be derived from its concentration in the enzyme solution (in g/l) and the molecular mass of the protein. The mass of A. oryzae beta-galactosidase has been estimated at 105 kDa by analytical gel filtration (Tanaka et al., 1975).
5. Calculate the value of kcat/Km for the substrate pNP-Gal. What does this value mean?

Prepare your report according to the general guidelines in "How to write a lab report".

The report should include:

1. In the Abstract, which enzyme from which organism, which substrate and which inhibitor, the most important results (Km and kcat without inhibitor, Ki if calculated, how Vmax and Km changed in the experiment with inhibitor) and conclusions (which type of competition).
   
   
2. The results of the calculations above in the Results section.
   
   
3. Tables with raw data and calculated values for both experiments, either the Appendix forms filled in by hand and supplied as Appendices, or as tables in the Results section.
   
   
4. The plots of the rate of the reaction, V, vs. concentration of substrate, [S], (in M, mM or uM) for both experiments in the same diagram. Indicate the Vmax values by horisontal lines from the y-axis through the diagram. Indicate Km by vertical lines from the Km values on the x-axis up to the respective experimental curves and by horisontal lines from the y-axis at Vmax/2 to the respective experimental curves. For each experiment the two lines should intersect on the experimental curve. Remember units on both axes.
   
   
5. The Lineweaver-Burk plot for both experiments in one graph, and if necessary, one Lineweaver-Burk plot for experiment 1 alone from which the values of Km and Vmax may be estimated. Remember units on both axes.

...AND DONT FORGET UNITS : g/mol, mM, mg/ml, nm, M-1*cm-1 etc.

Optional
The ambitious student may also calculate the inhibitor constant, Ki, for the inhibitor, which is a measure of how strongly the inhibitor is bound. The value of Ki corresponds to the inhibitor concentration when half of the enzyme molecules bind an inhibitor molecule (half-saturation concentration). If the inhibition is pure competitive or non-competitive, then Ki is the same as the dissociation constant, Kd, for the enzyme-inhibitor complex. The relationship between the Vmax and Km values in the absence and presence of the inhibitor are different for the two types of inhibition:

Competitive: Km(with) = Km(without)*(1+([I]/Ki))

Non-competitive: Vmax(with) = Vmax(without)/(1+([I]/Ki))

You may also look up some published data on the beta-galactosidase enzyme. In the abstract for the reference Tanaka et al (1975) you will find the Km value for a related substrate, oNP-Gal. Search for the article in Medline http://www.ncbi.nlm.nih.gov/entrez/query.fcgi

Supplementary information
The substrate was from Sigma, cat. no. N-1252, p-nitrophenyl-beta-D-galacto-pyranoside, (1 g, price Aug 2001 SEK 330:-). FW 301 g/mol + 1 mol/mol water = 319 g/mol. For a 5 mM solution dissolve 160 mg in 100 ml 0.1 M NaAc pH 5.0. The substrate is sensitive to contamination by possible environmental beta-galactosidase and the substrate may undergo slow hydrolysis even in the absence of enzyme. May be kept a week or so in the fridge. Freeze for longer time storage.

The enzyme was from Sigma, cat. no. G-5160, beta-galactosidase from Aspergillus oryzae, standardised with starch (25,000 units, price Aug 2001 SEK 276:-). The enzyme solution was prepared by dissolving 0.01 g/l powder in 0.1 M NaAc, pH 5.0. The protein content was estimated at 15% by measuring A280 and assuming an avarage protein absorbtion coefficient of 1.5 liter*g^-1*cm^-1. The enzyme concentration is thus given as 1.5 µg/ml. It may, however, be significantly lower since this is a crude enzyme prep, but we will use this value until an accurate determination of the beta-galactosidase content can be performed. The solution is stable at least a week in the fridge. I am not sure if the solution can be frozen.

More about the properties of A. oryzae beta-galactosidase and comparison of specificity with beta-gal from other organisms can be found in Zeleny et al. (1997).

Several beta-galactosidases have high transglycosylation activity and have succesfully been applied for synthesis of oligosaccharides. A rather recent study on this is presented in Boon et al. (2000).

A very valuable source for information on enzymes is the Worthington Biochemical Corp. web site. There you can find manuals for assaying several useful enzymes and also loads of references. Unfortunately the manual for beta-galactosidase describes the E. coli enzyme which is less stable, but there are references also for the A. oryzae enzyme. http://www.worthington-biochem.com/manual/G/BG.html

• Boon, M.A., Janssen, A.E.M. and van 't Riet, K. (2000) Effect of temperature and enzyme origin on the enzymatic synthesis of oligosaccharides. Enz. Microb. Technol. 26, 271-281.
• Tanaka, Y., Kagamaiishi, A., Kiuchi, A. and Horiuchi, T. (1975) Purification and properties of beta-galactosidase from Aspergillus oryzae. J. Biochem. (Tokyo) 77, 241-247.
• Zeleny, R., Altmann, F., and Praznik, W. (1997) A capillary electrophoresis study on the specificity of beta-galactosidases from Aspergillus oryzae, Escherichia coli, Streptococcus pneumoniae, and Canavalia ensiformis (Jack bean). Anal. Biochem. 246, 96-101.

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Original lab by Tom Taylor
Modified by Jerry Stahlberg
Page updated 2004.10.21 by Tom Taylor
Copyright © 1998-2000. Department of Molecular Biology SLU. All rights reserved.