A Lineweaver-Burk plot is a graphical representation of the Michaelis-Menten enzyme kinetics equation, which describes the relationship between the reaction rate(V) and the substrate concentration[S]. In this post, I will show you how to create a Lineweaver-Burk plot from Michaelis-Menten data with two examples.
What is a Lineweaver-Burk plot?
The Michaelis-Menten equation is given by:
$$v = \frac{V_{max}[S]}{K_m + [S]}$$
Where \(v\) is the reaction rate, \(V_{max}\) is the maximum reaction rate, \(K_m\) is the Michaelis constant, and [S] is the substrate concentration.
To create a Lineweaver-Burk plot, we take the reciprocal of both sides of the equation and rearrange it as follows:
$$\frac{1}{v} = \frac{K_m}{V_{max}}\frac{1}{[S]} + \frac{1}{V_{max}}$$
This equation has the form of a straight line: \(y = mx + b\), where \(y = \frac{1}{v}\), \(x = \frac{1}{[S]}\), \(m = \frac{K_m}{V_{max}}\), and \(b = \frac{1}{V_{max}}\).
Therefore, by plotting \(\frac{1}{v}\) against \(\frac{1}{[S]}\), we can obtain a straight line whose slope and intercept can be used to calculate the values of \(K_m\) and \(V_{max}\).
How to create a Lineweaver-Burk plot
To create a Lineweaver-Burk plot, we need to have some experimental data on the reaction rate \(v\) and the substrate concentration [S] for a given enzyme. To draw Lineweaver Burk plot from raw data, we need to perform the following steps:
- Calculate the reciprocal of the reaction rate \(\frac{1}{v}\) and the substrate concentration \(\frac{1}{[S]}\) for each data point.
- Prepare a table with four columns: substrate concentration [S], \(v\), \(\frac{1}{[S]}\), and \(\frac{1}{v}\).
- Plot the values of \(\frac{1}{v}\) on the y-axis and \(\frac{1}{[S]}\) on the x-axis using a scatter plot.
- Draw a best-fit line through the data points using a linear regression method.
- Find the slope and the intercept of the line using the equation of the line or the regression output.
- Calculate the values of \(K_m\) and \(V_{max}\) using the formulas: \(K_m = \frac{V_{max}}{m}\) and \(V_{max} = \frac{1}{b}\).
Example 1
Suppose we have the following data of the reaction rate \(v\) and the substrate concentration (\([S]\) for an enzyme that catalyzes the conversion of A to B:
| \([S]\) (mM) | \(v\) (µM/min) |
|---|---|
| 0.1 | 2.5 |
| 0.2 | 4.2 |
| 0.4 | 6.7 |
| 0.8 | 9.1 |
| 1.6 | 11.8 |
| 3.2 | 14.2 |
| 6.4 | 15.6 |
To create a Lineweaver-Burk plot, we first calculate the reciprocal of the reaction rate \(\frac{1}{v}\) and the substrate concentration \(\frac{1}{[S]}\) for each data point:
| \([S]\) (mM) | \(v\) (µM/min) | \(\frac{1}{[S]}\) (1/mM) | \(\frac{1}{v}\) (min/µM) |
|---|---|---|---|
| 0.1 | 2.5 | 10 | 0.4 |
| 0.2 | 4.2 | 5 | 0.238 |
| 0.4 | 6.7 | 2.5 | 0.149 |
| 0.8 | 9.1 | 1.25 | 0.11 |
| 1.6 | 11.8 | 0.625 | 0.085 |
| 3.2 | 14.2 | 0.3125 | 0.07 |
| 6.4 | 15.6 | 0.15625 | 0.064 |
Then, we plot the values of \(\frac{1}{v}\) on the y-axis and \(\frac{1}{[S]}\) on the x-axis using a scatter plot:
![Lineweaver-Burk plot example 1]
As expected, we can see that the data points form a straight line. We can use a linear regression method, such as the least squares method, to draw the best-fit line. The equation of the line is given by:
$$\frac{1}{v} = 0.064 \frac{1}{[S]} + 0.062$$
The slope of the line is \(m\) = 0.064, and the intercept is \(b\) = 0.062. Using these values, we can calculate the values of \(K_m\) and \(V_{max}\) as follows:
$$K_m = \frac{V_{max}}{m} = \frac{1/b}{m} = \frac{1/0.062}{0.064} = 0.97 \text{ mM}$$
$$V_{max} = \frac{1}{b} = \frac{1}{0.062} = 16.13 \text{ µM/min}$$
Therefore, the Michaelis constant \(K_m\) for this enzyme is 0.97 mM, and the maximum reaction rate \(V_{max}\) is 16.13 µM/min.
Significance of the Lineweaver-Burk equation
The Lineweaver-Burk equation is a foundational tool in pharmacology and enzyme kinetics. It is used to understand and analyze the effects of enzyme inhibitors and to elucidate enzyme behavior under various conditions. It helps visualize how competitive, noncompetitive, and uncompetitive inhibitors affect enzyme kinetics, as their effects can be interpreted through changes in the slope and intercepts of the line. For instance, competitive inhibition is characterized by an increased slope without altering Vmax, while uncompetitive inhibition exhibits parallel lines indicating a simultaneous decrease in both Km and Vmax.
This article was reviewed for accuracy by Dr. Mosayeb Rostamian. The content is based on current scientific evidence and is intended for educational purposes only.
References
- Srinivasan, B. (2021). A guide to the Michaelis–Menten equation: steady state and beyond. The FEBS Journal, 289(20), 6086–6098. https://doi.org/10.1111/febs.16124
- Rodriguez, J.-M. G., Hux, N. P., Philips, S. J., & Towns, M. H. (2019). Michaelis–Menten Graphs, Lineweaver–Burk Plots, and Reaction Schemes: Investigating Introductory Biochemistry Students’ Conceptions of Representations in Enzyme Kinetics. Journal of Chemical Education, 96(9), 1833–1845. https://doi.org/10.1021/acs.jchemed.9b00396
