Analyzing Enzyme Kinetics: Substrate Concentration and Inhibition Effects

Abstract

The aim of these experiments was to identify the effect on enzyme catalysed reactions by changing the substrate concentration and adding an inhibitor. From which the type of inhibition was obtained. The timed assay of the series of control and experimental tubes that contained a buffer, substrate and distilled water allowed the data collection of the amount of product PNP. Spectrometry was used to measure the absorbance of solutions in the control and experimental test tubes. The rate of reaction for each tube of presence and absence of inhibitor was calculated using the amount of product and absorbance.

Using the data collected the Vmax and Km value was calculated. Vmax value of 0.012µmoles/minute and 0.013µmoles/minute and Km values of 0.11mM 0.81mM, respectively for without inhibitor and with inhibitor. These values identified that the inhibitor was competitive.

Introduction

Enzyme kinetics can be described as the study of rates of enzyme-catalysed reactions (Berg et al., 2019). Increasing substrate concentration increases the rate of reaction.

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However, if all the enzymes present have formed an enzyme-substrate complex, the increase in substrate concentration does not affect the rate of reaction (Berg et al., 2019). Knowing that the enzyme concentration is fixed the initial rate differs hyperbolically with the substrate concentration (Walker and Wilson, 2010).

Michaelis-Menten equation expresses the basic concepts of enzyme kinetics. The equation displays the relationship between initial rate and substrate concentration under specific parameters (Walker and Wilson, 2010). The equation includes the initial rate (v), value of initial rate when all active sites have substrate bound (Vmax), Michaelis constant (Km) and substrate concentration ([S]) (Walker and Wilson, 2010). Figure 1 shows how to estimate Vmax and Km value from

Michaelis-Menten Plot

Inhibitors bind to enzymes (like a substrate), but they are substances that prevents the enzymes activities. The inhibitors are either irreversible or reversible. (Berg et al, 2019). Competitive inhibitor binds at the active site of the enzyme and does not allow the substrate to bind to the enzyme (Berg et al, 2019). Non-competitive inhibitor binds at another site on the enzyme, both the substrate and inhibitor bind to active sites (Berg et al, 2019). The Lineweaver-Burk plot is essential in identifying the type of inhibition and whether an inhibitor is present or not (Wilkinson, 1970)

The experiment aimed to establish the effect of substrate concentration and presence of inhibitor on rate of reaction, from which the Vmax and Km value was found. Also, to identify the inhibitor used as competitive or non-competitive. In these experiments the enzyme was acid phosphatase, the substrate was p-nitrophenyl phosphate (PNPP) and the product formed in this reaction is p-nitrophenol (PNP).

Results

The following tables and figures display the results of the experiments performed, to determine the effect of substrate concentration and presence of inhibitor on enzyme activity.

Table 1: The absorbance result at different amounts of PNP

To identify the relationship between absorbance and the known amount of PNP, in tubes labelled 1-7, different amounts of PNP concentration of 1mM and distilled water was added (as per lab book). Then the absorbance was measured using a spectrophotometer.

Figure 1 demonstrates a linear relationship, that satisfies the Beer-Lambert Law (absorbance is directly proportional to concentration). Increasing the amount of PNP, increase the absorbance. At 0.05µmoles the absorbance is 0.135Au, and at 0.20µmoles the absorbance is 0.518Au. The line equation represents the absorbance (y), gradient (m), concentration/amount of PNP (x) and y-intercept (c). The equation can be used to determine the concentration of unknown solutions.

Table 2: Rate of reaction at different substrate concentration when an inhibitor is not present

Absorbance/(gradient ) = 0.113/2.5873 = 4.36 x 10-2

(4.36 x 10^(-2))/15 = 2.91 x 10-3 µmoles PNP/minute

In order to determine the effect of varying substrate concentration on rate of reaction, sets of control and experimental tubes containing citrate buffer and different amounts of PNPP at concentration of 10mM and distilled water was incubated (as per lab book). Both control and experimental tubes were incubated (at 37°C) for 10 minutes. During the further 15 minute of incubation enzyme solution was added. Results collected was used to determine effect of substrate concentration on enzyme activity (as per lab book).

Increasing substrate concentration does increase rate of reaction but the increase in rate of reaction is reduced after 0.5mM. The Vmax and Km value was estimated using Figure 2 as the Vmax value is the rate of reaction when the substrate concentration becomes infinity.

Estimated Vmax and Km value from Figure 2:

Vmax = 0.013µmoles/min

Km: Vmax/2 = 0.013/2 = 0.0065 µmoles/min

Km = 0.15 mM

Table 3: 1/V and 1/[S] of enzyme activity for without an inhibitor

Table 4: 1/V and 1/[S] of enzyme activity for with an inhibitor

To determine the type of inhibition another experiment was conducted in which phosphate-containing citrate buffer (instead of normal citrate buffer), 10mm PNPP and distilled water was added to a series of test tube (as per lab book). The tubes were incubated for 10 minutes then 15 minutes; during this time the enzyme solution was added (as per lab book). The amount of PNP produced was calculated. Absorbance at 400nm was also measured. Using the data collected from this experiment and results from Table 2 1/V and 1/[S] was calculated.

The Lineweaver-Burk plot in Figure 3 shows a steep increase for the absence of inhibitor and a steady increase for with the inhibitor. Gradient of 62.616 and 8.8195 represents this respectively for with and without inhibitor. Lineweaver-Burk plot allows accurate measurement of Vmax and Km value.

Calculation of Vmax and Km value for no inhibitor:

Calculated Vmax: 1/Vmax = 81.024

Vmax = 1/81.024 = 0.0123 µmoles/min

Calculated Km: (-1)/Km

X = (-c)/m = (-81.024)/8.8195 = -9.19 (2dp)

Km = (-1)/(-9.19) = 0.11 mM (2dp)

Calculation of Vmax and Km value for with inhibitor:

Calculated Vmax: 1/Vmax = 77.027

Vmax = 1/77.027 = 0.0130 µmoles/min

Calculated Km: (-1)/Km

X = (-c)/m = (-77.027)/62.616 = -1.23 (2dp)

Km = (-1)/(-1.23) = 0.81 mM (2dp)

Discussion

The study confirmed that increasing substrate concentration enhances reaction rates until enzyme saturation occurs. Competitive inhibitors increase the apparent Km value without affecting Vmax, as observed in our experiments. The Lineweaver-Burk plot facilitated accurate Vmax and Km determination, reinforcing the identification of competitive inhibition.

Conclusion

This investigation successfully elucidated the dynamics of enzyme kinetics in response to varying substrate concentrations and the presence of competitive inhibitors. By calculating Vmax and Km values, it was possible to classify the inhibitor type and further understand enzyme-substrate interactions. Future work could explore other enzyme systems and inhibitor types to broaden our understanding of enzyme kinetics.