An Investigation into Enzyme Kinetics, Focusing on the Effect of pH and Time

1.0 Introduction

Enzymes are known as metabolic catalysts, advancing biological chemical reactions without being consumed, binding to substrates in order to create a product (Copeland, 2004) (Moore and Langley, 2011). This occurs via two models, lock and key and induced fit. The lock and key model, theorises that a specific substrate fits exact into a specific enzyme active site, while induced fit theorises that the active site changes shape to fit the substrate (Bettleheim et al., 2009). Enzymes have numerous practical uses, for example, in the process of making wine and cheese (Copeland, 2004). Enzyme kinetics aid in presenting catalysing enzymes in action and focus upon the factors that enzyme reaction rates depend on, which includes pH and time (Engel, 2013). Enzymes are particularly sensitive to changes in pH (Bisswanger, 2017). By researching into enzyme kinetics, industries can amplify yield and reduce the time taken to create a product.

Acid phosphatase is an enzyme which can be found within humans, working under the pH and temperature conditions of the body with traces of the enzyme being linked to skeletal diseases (Siller and Whyte, 2017).This information aids in how pharmaceutical tests are carried out for acid phosphatase, therefore, is an important scientific development (Siller and Whyte, 2017). To investigate how pH and time effect acid phosphatase, assays for both factors will be carried out.

Objectively, this report aims to investigate whether time and pH effect enzyme kinetics, by observing the initial rate of reaction and how it changes over time, from converted absorbance data.

2.0 Method and Materials.

Method and materials utilised for this experiment can be found in the “Introduction to Biochemistry Laboratory Manual 2018-2019”, under Experiment 4A and 4B. Some deviations to the methods have been made, for the method described in experiment 4B, a time span of 10 minutes was utilised to incubate the enzyme. This was chosen, as the method suggested to select a time span where the rate of the reaction became linear, from the data gained from experiment 4A. Utilising this data, a graph was constructed, which showed that the rate of reaction was most linear at 10 minutes. (Appendix 1).

2.1 Equations

Various equations aid in the interpretation of the data. pNP calibration data, provided in the laboratory manual, was used to convert the absorbance data into µmol of pNP produced. This calibration data was plotted, with the equation given by the graph being utilised to calculate the concentration of pNP produced (Appendix 2).

$\mathit{Conc}.=\frac{\mathit{Abs}.–0. 1067}{3.2565}$

This equation was utilised to carry out the conversion for both data sets.

Standard deviation was also utilised.

$\sqrt{\frac{\sum (x_1–\bar{x} {)}^2}{n–1}}$

Standard deviation allows for the variation of the results to be viewed, a smaller standard deviation is often desired as it means less outliers, resulting in more accurate data (Rumsey, 2016).

3.0 Results

Results show that for time, enzymes that were placed in the water bath for a longer duration, had a larger amount of µmol of pNP produced. Between five minutes to fifteen minutes, there is a linear phase (Figure 1).

Figure 1: µmol of pNP Produced Measured at Various Minute Intervals for an Enzyme Catalysed Reaction.

For the factor of pH, pH 7 has the largest amount pNP µmol produced per minute and is the optimum pH. This is where the concentration of pNP produced per minute peaks, then falls at pH 9. pH 9 has the lowest amount of pNP produced per minute (Figure 2).

Figure 2: µmol of pNP Produced per minute by Each pH of acid phosphatase in an Enzyme Catalysed Reaction.

4.0 Discussion

To summarize, a longer time period and a pH of 7 causes the greatest effect in the enzyme kinetics of acid phosphatase enzyme.

Models can help visualise enzyme kinetics. A widely used model is the Michealis-Menten kinetic model and equation (Norris and Malys, 2011). For enzymes to comply with the model K_m and V_max, kinetic parameters, must be obtained (Norris and Malys, 2011). K_m is the Michealis-Menten constant, which produces a rate of  ½ V_max and V_max, is the maximum rate in which an enzyme can be catalysed (Cornish-Bowden, 2015) (Moore and Langley, 2011). The Michealis-Menten equation can be plotted (Figure 3).  

$V_0=\frac{V_{\mathit{max}} \times \left[S\right]}{K_{\mathit{m }}+\left[S\right]}$

Figure 3: Michalis-Menten Equation plotted (Pharma Factz, 2014).

K_m is an important value, as it describes the binding within an enzyme substrate complex, a higher K_m means that the binding between the enzyme and substrate is weaker, a lower K_m means the binding is stronger (Moore and Langley, 2011). A high K_m or a weaker bind, means a larger concentration of substrate is required in order for ½ V_max to be reached (Moore and Langley, 2011).

Time scales have significant effect on enzyme kinetics. The graph below shows why this effect occurs (Figure 4).

Figure 4: Concentration of substrate [S] and product [P] measured over a period, during an enzyme catalysed reaction (Copeland, 2004).

Over time, as the concentration of product increases, the concentration of substrate decreases. Eventually, the substrate concentration will reach zero, therefore, the concentration of product can no longer increase. Less substrate means a decrease in collisions between substrate and enzyme per unit of time, so less product is formed (Copeland, 2004) (Birklett and Lester, 2002). The reaction will reach V_max as the concentration of product rises and reaches the optimum.

Enzymes kinetics are sensitive to any pH changes (Bisswanger, 2017). A bell curve can show this (Figure 5).

Figure 5: The first-rate constants dependence of pH (V_max/ K_s) on a linear scale (Marangoni, 2003).

The peak relates to the optimum pH of the enzyme being reached (Marangoni, 2003).  Acid phosphatase enzymes optimum pH is around 5.8, which means that V_max stops increasing around this point (Mobley et al., 1984). Changes in the pH of an enzymes environment causes a change within the enzymes conformation, effecting catalyst mechanisms (Bettleheim et al., 2009) (Bisswanger, 2017). If conditions are acidic, the substrate may gain a hydrogen ion and in alkaline conditions, the substrate may lose a hydrogen ion, meaning the enzyme and substrate can no longer bond, so little product is created and the concentration of product decreases (Clark, 2006). Enzymes also denature at heavily alkaline or acidic substances, due to the disruption of the ionic bonds in the enzymes structure, explaining as to why pH 7 was the optimum for acid phosphatase, as pH 9 was too alkaline (Bisswanger, 2017).

The experiment had several problems. The absorbance data gathered when using experiment 4As method, had noticeable outliers, decreasing the accuracy of the data. The error bars in Figure 2 vary in size, however, pH 3 and 9 have the largest bars. Large error bars are undesired because this may mean that outliers within the data have occurred (Rumsey, 2016). The likelihood is that these outliers where caused by errors in time keeping, therefore if repeated, the experiments method should be altered to allow for easier measurement and management of the incubation period. For both methods, when adding the enzyme into the microcentrifuge tubes within the water bath, water was observed spilling into the tubes. This could affect the enzymes and may have caused outliers within the data. Therefore, utmost care should be given when placing the enzyme within the tubes. The methods could be altered by taking the microcentrifuge tubes out of the water bath for a short period of time, adding the enzyme, then placing the tubes back inside the water bath, minimising the amount of water spilled into the tubes.

Additionally, only two factors effecting enzyme kinetics where explored. Temperature is also known to affect enzyme kinetics (Engel, 2013). Temperature could be explored by utilising water baths to incubate acid phosphatase at various temperatures and after the same set amount of time, the absorbance data can be gathered from a colourimeter, viewing how temperatures can affect enzymes. Data from different factors ensures a larger understanding in enzyme kinetics.

5.0 Conclusion

In conclusion, both temperature and pH are shown to affect the kinetics of acid phosphatase enzyme. More factors that effect enzyme kinetics, should be explored and data sets gathered to further understand the topic.

6.0 Appendix

6.1 Appendix

The graph below shows the pNP data found on page 22 of the laboratory manual plotted.

Relationship between pNP concentration (µmol) and absorbance (λ=410 nm).

6.2 Appendix 2

The absorbance data from experiment 4a plotted in order to discover the linear face of the rate of reaction.

Absorbance (λ=410) vs time (minutes).

7.0 References

• Bettleheim F., Brown W., Campbell M., Farell S., 2009. Introduction to Organic and Biochemistry, 7^th ed, Canada: Brooks/Cole Cengage learning, Pages: 349-350.
• Birklett J.W., Lester J.N., 2002. Microbiology and Chemistry for Environmental Scientists and Engineers., 2^nd ed, London and New York: Taylor and Francis Group, Pages: 139.
• Bisswanger H., 2017. Enzyme Kinetics: Principles and Methods, 3^rd ed, Weinheim: Wiley VCH, Pages: 145.
• The Effect of Changing Conditions in Enzyme Catalysis– Clark J., (2006). [Online] [Accessed: 07/05/2019] http://chemguide.co.uk/organicprops/aminoacids/enzymes2.html.
• Copeland A.C., 2004. Enzymes: A Practical Introduction to Structure, Mechanism, and Data Analysis., 2^nd ed, New York: Wiley VCH, Pages: 15,110.
• Cornish-Bowden A., 2015. One Hundred Years of Michealis Menten Kinetics, Perspectives in Science, Volume 4, Pages 3-9.
• Engel P.C., 2013. Enzyme Kinetics: The Steady State Approach, 2^nd ed, Springer-Science + Business Media B.V, Pages: 8.
• Marangoni A.G., 2003. Enzyme Kinetics: The Modern Approach, New Jersey: John Wiley and Sons, Pages: 80.
• Mobley D.M., Chengappa M.M., Kadel W.L., Stuart J.G., 1984. Effect of pH, Temperature and Media on Acid and Alkaline Phosphatase Activity in “Clinical” and “Nonclinical” isolates of Bordetella Bronchiseptica. Can J. Comp Med, Volume 48, Pages: 175-178.
• Moore J.T., Langely R.H., 2011. Biochemistry for Dummies,2^nd ed, Indianapolis: Wiley Publishing Inc., Pages: 82-83, 93-98.
• Norris G.S.M., Malys N., 2011. What is the true enzyme kinetics in the biological system? An investigation of macromolecular crowding effect upon enzyme kinetics of glucose-6-phosphate dehydrogenase. Biochemical and Biophysical Reasearch Communications, Volume 205, Issue 3, Pages: 388-322.
• Medicinal Chemistry-Understanding Enzyme Kinetics– Pharma Factz (2014). [Online][Accessed: 02/05/2019] https://pharmafactz.com/medicinal-chemistry-understanding-enzyme-kinetics/.
• Siller A.F, Whyte M.P., 2017. Alkaline Phosphatase: Discovery and Naming of Our Favourite Enzyme. JBMR, Volume 33, Issue 2, Pages: 362-364.
• Rumsey D., 2016. Statistics for dummies, 2^nd ed, John Wiley and Sons, (no page numbers).