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Table of contents
Intro to regression
Nonlinear regression
Curve fitting with Prism
Interpreting the results
Comparing two curves
Distributions of best-fit values
Radioligand binding
Saturation binding
Competitive binding

Kinetics of binding

Dose-response curves
Enzyme kinetics


Find Vmax & KM
Kinetics vs. binding
Lineweaver- Burk
Allosteric enzymes
Standard curves
More information
Search was created by GraphPad Software, Inc. Send comments or questions to the author of these pages, Dr. Harvey Motulsky, president of GraphPad Software.

In April 2003, GraphPad released Prism 4 and published Fitting Models to Biological Data using Linear and Nonlinear Regression. This book includes all the information that comprises, and much more. You can read this book as a pdf file.

Displaying enzyme kinetic data on a Lineweaver- Burk plot

The best way to analyze enzyme kinetic data is to fit the data directly to the Michaelis-Menten equation using nonlinear regression. Before nonlinear regression was available, investigators had to transform curved data into straight lines, so they could analyze with linear regression.

One way to do this is with a Lineweaver-Burk plot. Take the inverse of the Michaelis-Menten equation and simplify:

MathType Equation

Ignoring experimental error, a plot of 1/V vs. 1/S will be linear, with a Y-intercept of 1/Vmax and a slope equal to Km/Vmax. The X-intercept equals ?1/Km.

Use the Lineweaver-Burk plot only to display your data. Don't use the slope and intercept of a linear regression line to determine values for Vmax and KM. If you do this, you won't get the most accurate values for Vmax and KM. The problem is that the transformations (reciprocals) distort the experimental error, so the double-reciprocal plot does not obey the assumptions of linear regression. Use nonlinear regression to obtain the most accurate values of KM and Vmax (see Avoid Scatchard, Lineweaver-Burk and similar transforms).

Tip. You should analyze enzyme kinetic data with nonlinear regression, not with Lineweaver-Burk plots. Use Lineweaver-Burk plots to display data, not to analyze data.

To create a Lineweaver-Burk plot with Prism, start from a table where X is substrate concentration and Y is velocity. Click Analyze, and choose a built-in analysis. Then choose Transformations from the list of data manipulations. Check the option boxes to transform both X to be 1/X, and Y to be 1/Y. Be sure to check the option to create a new graph of the results.

From that graph, click Analyze and choose linear regression to superimpose the regression line. This linear regression line should NOT be used to obtain values for Vmax and Km. The X-intercept of the regression line will be near -1/KM, and the negative inverse of the slope will be near the Vmax. However, the Vmax and KM values determined directly with nonlinear regression will be more accurate. It is better to draw the line that corresponds to the nonlinear regression fit.

To create a Lineweaver-Burk line corresponding to the nonlinear regression fit, follow these steps:

1. Create a new data table, with numerical X values and single Y values.

2. Into row 1 enter X= -1/KM (previously determined by nonlinear regression), Y=0.

3. Into row 2 enter X=1/Smax  (Smax is the largest value of [substrate] you want to include on the graph) and Y=(1/Vmax)(1.0 + KM/Smax).

4. Note the name of this data table. Perhaps rename it to something appropriate.

5. Go to the Lineweaver-Burk graph.

6. Press Change, then Data on graph.

7. Add the new data table to the graph.

8. Press Change, then Symbols and lines.

9. Drop down the list of data sets, and select the one you noted in step 4.10. Choose to plot no symbols, but to connect with a line.

Allosteric enzymes  

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