Step detection (membrane tether analysis) in AFM

"afmtether" is a Matlab, GUI-controlled application for the analysis of AFM force curves for discrete steps corresponding to disruption of single membrane tethers.

The program was written by Peter Nagy (email: peter.v.nagy@gmail.com, https://peternagyweb.hu)

The program can be started by typing "afmtether" at the Matlab command prompt. In addition to manual identification of discrete steps, two automatic step-detection algorithms are implemented in the program:

A comprehensive review about different step-detection algorithms has been published in Biophys. J.

The main panel of the program is shown below:

In this brief help you can find a step-by-step introduction to the major functionalities of the program.

You can select which parameters are plotted with the "X axis" and "Y axis" drop-down menus. The extension and retraction parts of the curves are plotted simultaneously, but only one of them is analyzed. The direction to be analyzed is selected in the "Direction" drop-down menu.

Set spring constant

The spring constant must be entered. The program saves the entered sping constant after pressing "Set". The saved spring constant will be displayed in the blue text field at the top of the main panel.

Read IBW file

The program can read Igor Binary Wave (IBW) files based on the submission of Jakub Bialek to Matlab Central. You have to click on the "Select an IBW file" button to select the IBW file to read followed by clicking on "Read". If you enter a variable name, the data will be saved into a Matlab variable and exported to the Matlab base workspace. This structure variable can be read the next time by clicking on "Read AFM data". Reading of this Matlab variable is faster than importing an IBW file, since the Matlab variable already contains the contact point, the baseline force and the spring constant. Specifying the variable is optional, since the program stores the data internally.

The spring constant must be entered before reading an IBW file. After reading the IBW file the "X axis" and "Y axis" drop-down menus will be populated and the contact point will be estimated based on the extension (approach) curve. If the Global Optimization Toolbox is installed in Matlab, the genetic algorithm will be used for detecting the contact point as a steep change in the slope of the curve shown by the red circle in the image below. If the Global Optimization Toolbox is not installed, the moving step fit algorithm will be applied. The moving step fit algorithm, also used for detecting severing of membrane tethers, is described below. After identifying the contact point the baseline force, corresponding to the mean force in the horizontal line distant to the contact point, is also determined.

Read AFM data

Data saved during reading an IBW file or exported by clicking on the button "Export and save" can be read from the Matlab base workspace. You have to specify the variable name and click on the "Read" button.

Read 2D array

2D arrays can be imported into the program from the Matlab work space. The imported data can be

There are two different ways of arranging the data:

Compensation

This part of the program can modify the contact point and make the baseline horizontal.

Find contact point

The genetic algorithm (if the Global Optimization Toolbox is installed in Matlab), the moving step fit algoritm and a manual approach are available. If the manual method is selected, the user has to move the red marker to the contact point in the graph below:

Make baseline horizontal

An automatic and a manual approach are available. The automatic approach makes the baseline horizontal by fitting a line on it. The baseline is defined as the section between the contact point and the beginning of extension in the deflection vs. rawZ plot or in the force vs. separation plot. Therefore, the contact point must be accurately defined for the automatic approach to work. In the manual approach the user must define the baseline by dragging the red and green markers in the graph below. The segment between the two markers will be made horizontal by fitting a line on it. The data point corresponding to the red marker will not be shifted, i.e. it is the reference point..The user is asked to select whether the baseline correction is performed in the deflection-rawZ or force-separation plot if both variable paris exist.

Smoothing

Three kinds of smoothing algorithm are implemented in the program:

The larger the filter size or filter SD, the more pronounced the smoothing effect is.

The unit of the numbers entered into the "Filter size" or "Filter SD" text boxes is "data point", i.e. if "2" is entered into the "Filter SD" box, the SD of the Gaussian filter will be two measured data points in the curve.

Smoothing will be carried out upon clicking the "Smooth" button and the smoothed curves will be added to the "Y axis" drop-down menu. The smoothed data will be stored in the structure variable which can be saved in the "Export and save" panel.

Manual analysis

By clicking on "Do it" the parameters selected in the "X axis" and "Y axis" drow-down menus will be plotted. Both the extension and retraction parts will be displayed, but only one of them, selected in the "Direction" drop-down menu, will be clickable and alalyzable. This curve will be dispayed in blue, whereas the other curve will be shown in black. The graph window is shown below:

Interaction with the graph:

Function of the buttons on the top of the graph window:

Moving step fit

The algorithm finds a step where fitting two lines with a common slope to a window of the data set produces a significantly better result than fitting a single line. The principle of the procedure is summerized in the figure below:

The difference between the quality of fits is expressed by θ according to the following equation:

where RSS and h stand for the residual sum of squares and the step height, respectively.

The panel from which moving step fit can be initiated is shown below:

If you press the "Do it" button, you will be asked to select a range to be analyzed:

You can select a range by clicking and dragging the mouse followed by pressing 'OK', or you can select the whole range by pressing 'Select whole range'.

Fitting will be performed in the selected range, and the identified steps will be shown in a plot whose appearance is similar to the one shown during manual analysis. The results of the automatic moving step fit are saved in the "movingstep" field of the structure variable. Any modification of the steps while interacting with the graph will not affect data saved in this field, only the data saved in the "steps" field.

Interaction with the graph:

The functions of the buttons shown above the graph are the same as those described for manual analysis.

Multi-step fit

The multi-step fitting algorithm incorporated into this program was written by Jacob Kerssemakers (j.w.j.kerssemakers@tudelft.nl).

The principle of the fitting algorithm is explained briefly below.

The algorithm begins fitting very few steps to the data set followed by increasing the number of fitted steps. If the number of found steps is smaller than the actual number of steps, underfitting is performed. On the other hand, in the case of overfitting the number of fitted steps is higher than the optimal. For each fit a quality factor is calculated according to the following equation:

where χ2counter fit,n is the χ2 deviation between the data set and an intentionally wrong fit with n number of steps and χ2best fit,n is the χ2 deviation between the data set and the best fit with n number of steps. The quality factor will have a maximum at the optimal number of steps.

After clicking on the "Do it" button

Export and save