FODIS USER GUIDE

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Fodis
A Software for
Single Molecule Force Spectroscopy
(and Membrane Mechanics)

User Guide

Nicola Galvanetto

Trieste, Italy

October 2018

Contents
Preface

Installation

1 Basics
1.1 Software Framework . . . . . . . . . . . . . . . .
1.2 Open data . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Import traces (.txt files in Plain Format)
1.2.2 Open samples . . . . . . . . . . . . . . . .
1.3 Data saving . . . . . . . . . . . . . . . . . . . . .
1.4 Data pre-processing . . . . . . . . . . . . . . . .
1.5 Single trace representation - Plot data . . . . . .
1.5.1 Traces . . . . . . . . . . . . . . . . . . . .
1.5.2 Traces-Lc (Peaks automatic detection) . .
1.5.3 Dynamic persistence length . . . . . . . .
1.5.4 Contour length (Lc,Fc) . . . . . . . . . .
1.5.5 Contour length histogram . . . . . . . . .
1.5.6 Delta Lc histograms . . . . . . . . . . . .
1.6 Global trace representation . . . . . . . . . . . .
1.6.1 Global contour length histogram . . . . .
1.6.2 Global contour length histogram max . .
1.6.3 Global contour length - Force plot . . . .
1.6.4 Global delta Lc histograms (and plots) . .
1.6.5 Global peaks (or Global Matrix) . . . . .
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CONTENTS
1.6.6 Global persistence length
1.7 Graphical features . . . . . . . .
1.7.1 Density plots . . . . . . .
1.7.2 Parameters Box . . . . . .
1.7.3 Export plot . . . . . . . .
1.8 Selected & Valid Traces . . . . .
1.9 Trace filtering: basic tool . . . .
1.10 Align to zero . . . . . . . . . . .
1.11 Manual Alignment . . . . . . . .
1.12 Export Peaks Info (.txt, .xls) . .

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2 Advanced Tools
2.1 Unfolding Pathways Analysis . . . . . . . . .
2.1.1 Group division . . . . . . . . . . . . .
2.1.2 Path Plot . . . . . . . . . . . . . . . .
2.1.3 Combined Path Plot . . . . . . . . . .
2.1.4 Force-Lc segmentation plot (Thoma et
2.2 Fingerprint ROI . . . . . . . . . . . . . . . .
2.3 Automatic Alignment . . . . . . . . . . . . .
2.4 Selection through correlation . . . . . . . . .
2.5 Structural heterogeneity determination . . . .

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3 Membrane Mechanics
3.1 Import/Open breakthrough force curves . . . .
3.1.1 Import (plain format) . . . . . . . . . .
3.1.2 Open extension curves from AFM files
(only .txt exported from JPK, see 1.1.2)
3.2 Pre-processing . . . . . . . . . . . . . . . . . .
3.3 Analysis of the Breakthrough forces . . . . . .
3.4 Enhance Breakthrough forces detection . . . .
3.5 Export Breakthrough forces . . . . . . . . . . .
Bibliography

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Preface
Fodis (for “Force-distance software”) is a program for the analysis of Single Molecule Force Spectroscopy data. It is mainly intended for automated
analysis of force-distance curves of Protein Unfolding Events obtained during Atomic Force Spectroscopy experiments. However, it can be used for
visualization and organization of any force-distance curve. Fodis provides
a large number of force-curve visualization option, including function for
basic statistical analysis. Since the developers are active AFM users, the
program also contains some specific data processing methods intended for
protein unfolding studies. Fodis is Free and Open Source software, covered
by CC Public License. It was born in Matlab and we encourage thirdparties to participate in developing functions and modules. Being a free
software, it provides the source code to developers and users, which makes
easier both the verification of its data processing algorithms and any further
program improvements. Fodis was written in Matlab 2016b.

Installation
Fodis can be downloaded from https://github.com/nicolagalvanetto/
Fodis. Users need to
• unzip Fodis folder and move it to the Matlab Current Folder
• right clik on the folder and select Add to path folder and subfolders
• type Fodis in the Command Window and Enter
Fodis requires Matlab 2016b of newer versions. It also requires:
• Signal Processing Toolbox
• Statistics and Machine Learning Toolbox
• Image Processing Toolbox
Non-Matlab users working on Windows, Mac or Linux need to launch the
installer of their own version and follow the instructions. Please read the
README.txt file before installation.
For any problem related to the software, please use GitHub issue section
https://github.com/nicolagalvanetto/Fodis/issues.

Nomenclature
TSS

Tip Sample Separation: distance between the sample and the tip

Contour Length: length of the stretched polymer (segment)

Force: always referred in combination with Lc

F-d

Force-distance (curve): a SMFS trace

Persistence length

GHM

Global Histogram of the Maxima

CNG

Cyclic Nucleotide Gated channel

Chapter 1

Basics
In this chapter we present the basic working rules of the software and how
to use it.

1.1

Software Framework

The general architecture of Fodis
and the relationships among the
various blocks is shown in this flow
chart.
An ideal working session is here
presented. After the collection of
1000 Force-distance curves the user
imports these curves in Fodis.
The gray boxes represent the
input options (described in the
section 1.2 and 1.3: the data are
imported as they are.
If the imported data are in Volts
(rather than in Newton) or in the absolute height (rather than in Tip
Sample Separation(TSS)), it is possible to transform the force and position
units with the transformation module (section 1.4). Then, the traces
can be aligned, filtered and analyzed with all the tools available in
9

Fodis. Imagine a set 1000 consecutive Force-distance curves from a purple
membrane patch (like in the famous experiment by Oesterhelt et al. [1]).
The dataset contains many flat curves (without unfolding peaks), some
traces with only non-specific adhesion, some traces with random peaks
and some traces with real bacteriorhodopsin unfoldings. The basic filtering
tool (section 1.9) and the selection through correlation (section 2.4) can be
used to refine the selection of traces and go from 1000 to 10-20 traces. The
remaining traces can be aligned with the manual alignment (section 1.11)
or the automatic alignment (section 2.3). The user can then finalize his
analysis with the remaining tools, focusing on single traces or to population
statistics.

1.2

Open data

There are three modalities to import data and start working with Fodis.
• Import traces uploads matrices of numbers.
This is the most universal import option in
Fodis (see example below).
• Open samples uploads folders containing multiple files of single traces. The format allowed
is listed in the GUI menu.
• Load session uploads .afm files previously
generated by Fodis through Save session.
These files contain not only the saved dataset,
but also the specific configuration and parameters set in the previous working sessions.

1.2.1

Import traces (.txt files in Plain Format)

To import .txt files follow these rules:
• The .txt file must be organized in columns. The first column contains
the force values of the first trace in Newton, the second column contains tip-sample-separation values (or polymer extension) in meters,
and so on.
• Columns are space-separated.
• By convention, Fodis keep repulsive forces negative, attractive forces
positive.
• If different traces have different number of points, the number of rows
of the .txt will be equal to the number of point of the bigger trace.
Zeros must be added at the end of short traces to fill the gap (see
Figure).
N.B. If the user loads single traces (one couple of columns) with different number of rows, Fodis will manage the data anyway. The exported
file will be created following the aforementioned rules.

1.2.2

Open samples
Open-sample user interface is designed to
help the user uploading JPK or Bruker
files. First select the desired format on
the Select format menu and then Open
Folder. An example of the various files
can be found in additional datasets.

• JPK .txt: ASCII exported .txt files from JPK Data processing
• JPK .jpk-force
• Bruker .txt: with or without Header, ASCII exported in Display
Units (Fodis reads the metric prefix of the units)
• Bruker .spm (only for Windows in non-deployed versions):
Bruker raw files cannot be decoded without their proprietary .dll
libraries compiled in user’s machine.
Fodis can open .spm and .xyz (.084, .017, ...) files, but it requires
some additional installation steps.
1. Install Microsoft Windows SDK (Software Development Kit)
https://www.microsoft.com/en-us/download/details.aspx?
id=8279.
2. Install the Matlab compiler MinGW-w64: from Matlab Home >
Environment > Addons and search MinGW-w64 C/C++ Compiler or download it from https://it.mathworks.com/matlabcentral/
fileexchange/52848-matlab-support-for-mingw-w64-c-c++-compiler
3. Install Nanoscope
64 bit: ftp://anonymous@sboftp.bruker-nano.com/outgoing/
GPTech/Software/NanoScope_Analysis_x86_v180r2sr3.exe
32 bit: ftp://anonymous@sboftp.bruker-nano.com/outgoing/
GPTech/Software/NanoScope_Analysis_x64_v180r2sr3.exe
12

4. Install the AFM-Toolbox (chose custom and your Windows version) ftp://anonymous@sboftp.bruker-nano.com/outgoing/
GPTech/Software/AFM_MATLAB_Toolbox_Setup_for_NanoScope_
Analysis_v180r2sr3.exe
and follow the instruction to add the folder to the path.
For more information please contact fodis.help@gmail.com, and for
newer versions of Bruker’s software contact support.afm@bruker.
com.

1.3

Data saving

Any time, during a working session it is possible to save the data in two
different modalities (File > ...):
• Export traces generates a .txt of the same format presented in the
Import traces section. It is highly recommended to use this format
for portability reasons.
• Save session generates a .afm file that can be uploaded only by
Fodis through the Load session. These files contain not only the
current dataset, but also the specific configuration and parameters
set during the working session.
In case only partial information is needed, it is possible to Export plots or
Excel tabels (Tools > Export ...):
• Export plot generates a .fig, or any other file format for figures of
the current view.
• Export ‘Superimpose traces’ XY file generates a .txt two columns
file with all the points of the selected traces one after the other
(column1=TSS [m] ; column2=Force [N]).
• Export Peaks Info (comma separated values .txt) generates a
text file of comma separated values, that can be imported in Excel.
The file contains the list of selected traces and the relative Force,
Position and Slope of the peaks. See details in section 1.12.
• Export Peaks Info (Excel .xls) generates a .xls file containing
the list of selected traces and the relative Force, Position and Slope
of the peaks. (Due to Matlab-Excel poor compatibility this process
is slow). See details in section 1.12.

1.4

Data pre-processing

To correctly analyze a Force-distance curve in Fodis, it must have in the
x-axis the Tip Sample Separation in meters (TSS) with the contact point
on the left, and in the y-axis the force in Newton (baseline corrected).
The imported data may not be ready for the analysis (wrong units, TSS
transformation needed, etc). To pre-process the curves please use this module that allows to perform 6 different type of transformations (go to Tools
> Pre-Processing (shift, TSS, Baseline)). By default, no transformation is active, but a message pops up suggesting the necessary transformations that needs to be performed.
1. Geometrical Adjustment: the mirroring option inverts the values
of the Force. The rotation option swaps the coordinates.
N.B. the curves must have the contact point on the left, and the
unfolding forces positive — tip-sample contact negative (as shown in
the figure).
2. X-axis Adjustment: the x-axis values are multiplied by the constant Height multiplier (which is automatically read in the import
15

files when present). This is necessary when the imported files contain only the non-corrected Height channel (e.g. in JPK files).
3. Y-axis Adjustment: if the vertical deflection of the cantilever is
imported in Volts, the curves need to be rescaled with the Sensitivity
constant. If the vertical deflection of the cantilever is imported in
meters, the curves need to be rescaled with the Spring constant. (The
constants are automatically read in the import files when present).
4. Subtract Baseline: if the Force values need to be vertically shifted,
this option finds the baseline averaging the final part of the curve
(red patch). The starting point and the ending point can be changed
in the edit boxes. The linear fit subtraction interpolate the final
part and allows to tilt the curve (Warning: curves with peaks within
the selected region will be shifted in an inconsistent way).
5. Find contact point finds the first positive value (starting from the
left).
6. From piezo height to TSS: it transforms the x-coordinate in tip
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sample separation (TSS). (The constant is automatically read in the
import files when present).
N.B. These transformations act on all Valid curves (see section 1.8).
Mark the curves as Not Valid to skip the transformations.

1.5

Single trace representation - Plot data

In this section we present all possible trace representations of single events
implemented in Fodis.
The plot-box at the top-left corner
controls the graph displayed in the
central panel. There are two major groups among these graphical representations: single trace representations and global representations of all
selected traces.

In the view-box, all the parameters necessary to control plotting range, marker size
and grid are present. To perform Export
plot click on tool in the menu bar: this
creates a Matlab figure containing all the objects present in the Fodis graphic panel.
N.B. Use the button Find my trace in case
no trace is visible in the screen.

1.5.1

Traces
Typical Force-tip sample separation curve: exact representation of input numbers. The
slide bar at the lower part
of the panel allows to move
across different loaded traces.

Trace smoothing performed through
a
discontinuity-preserving
filter
(Savitzky-Golay algorithm).
K is the polynomial order ot the interpolant curve while F is the number
of points used for interpolation (F
must be an odd number).
The smoothing acts on the trace shown in the screen when the check-box
is checked, after clicking the button Update. The button Update Sel performs the soothing onto all Selected curves (see section 1.8). To remove
the smoothing, uncheck the check-box and Update.

1.5.2

Traces-Lc (Peaks automatic detection)

Traces-Lc finds relevant peaks
and fits them with the WLC
equation.
Peak detection is
enhanced on smoothed traces.
The numbers reported in Lc
for Analysis are all detected
contour lengths (in nm) of plotted rainbow curves. In case
a peak is not detected, type
the number in the edit box and
then Enter or click the button
(red arrow) then click the peak
in the graph, and then Enter.
That new Lc will be saved for
all the following analyses.
N.B. The detection of the peaks is based on the Force-Lc profile shown in
section 1.5.4 (cyan line). The profile can be tuned acting on the parameters Threshold N points and Min peak proximity of the parameter box
(section 1.7.2) to enhance peaks detection.
19

1.5.3

Dynamic persistence length

The
persistence
length,
which is typically kept fixed
(p=0.4nm for a.a. chains),
in dynamic mode is relaxed
to find the best p-Lc couple
for each peak.
The final
parameters are plotted in the
legend.

1.5.4

Contour length (Lc,Fc)

This representation transforms every point above
a threshold force (in this
case 30 pN, tunable in
Parameters box Min F)
from F-tss space to FLc space according to
the transformation presented by Puncher and
colleagues [2, 3].
N.B. The detection of
the peaks is based on
the Force-Lc profile shown (cyan line). The profile can be tuned acting
on the parameters Threshold N points and Min peak proximity of the
parameter box (section 1.7.2) to enhance peaks detection.
20

1.5.5

Contour length histogram
This is the histogram of
Contour length (Lc,Fc)
representation.
It is also
called Barrier position histogram [2]. The red bars
represent the detected peaks.
Bin width can be tuned in
the Parameters box.

1.5.6

Delta Lc histograms
Delta Lc histograms shows
the value of the difference in
Lc between two consecutive
peaks. The first peak’s DeltaLc, by definition, is equal to
the first Lc.

1.6

Global trace representation

Single molecule force spectroscopy experiments generate a large amount of
data. Single trace representations are useful to establish the quality and
features of single events, but only a statistical evaluation of Lc distribution
or other specific features allows to perform a quantitative analysis. For this
reason, Fodis includes a variety of global representations for the population
of traces.
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1.6.1

Global contour length histogram
The
Global contour
length histogram is the
sum of all contour length
histograms, normalized on
the highest bin. Bin size can
be tuned in the Parameters
box.

1.6.2

Global contour length histogram max

The Global contour length histogram of Maxima (also called Contour
length histogram by Kawamura and colleagues [4]) counts the detected
peaks of all selected traces (i.e. red bars shown in Contour length histograms
section). The resulting distribution can be fitted with the Gaussian Mixture Model (GMM) checking Tools > Automatic multi Gaussian option
on the menu bar. The GMM can be re-calculated with the button Update
in the Parameter box (the fitting procedure produces variable results, so
it may be useful to try different times). This representation is useful to
determine the probability of a certain unfolding event happening along the
Lc coordinate. (Bin size can be tuned in the Parameters box).
22

1.6.3

Global contour length - Force plot

The Lc - Force plot shows the contour length
vs Force of all detected peaks. This plot can
be used also to detect the detachment force in
binding experiments (e.g. with antibodies).

If the user is interested on the force distribution of a particular subgroup of peaks (i.e.
black rectangle), using Select Lc-F button
it is possible to select a region (draw a rectangle and double click inside de area). A force
distribution of the selected points will be automatically generated.

1.6.4

Global delta Lc histograms (and plots)

Delta Lc is defined as the Lc
difference between two consecutive peaks. On the left,
histogram of all Delta Lc values of the population.
N.B. Right clicking on the
graphs allows the user to
change the view to Delta
Lc-Fc or Lc-Delta Lc.
23

The Lc-Delta Lc plot shows
the scatter plot of all detected peaks.
If the user
wants the Delta Lc distribution of a particular subgroup
of peaks (i.e. red rectangle),
using Select dLc button it
is possible to select a region
(draw a rectangle and double
click inside de area). A Delta
Lc distribution of the selected
points will be automatically
generated.

1.6.5

Global peaks (or Global Matrix)
Automatically detected peaks are
used to form a string of ones and zeros for each trace (zeros where there
are no peaks, ones where there are a
peak). It is a sort of binarized coding
for the traces. Each string is therefore
plotted one above the other in Global
peaks with white pixels for zeros and
black pixels for ones.

1.6.6

Global persistence length
All the peaks of the population are
fitted with two free parameters persistence length (p) and Lc as
described in Dynamic persistence
length- and plotted. This allows to
find correlations between the peaks
positions and their curvature(i.e. p).
24

1.7
1.7.1

Graphical features
Density plots
A heat map is plotted when the
Density plot check box is selected.
The image is constituted by pixels
(Resolution) and the color of the
pixel is proportional to the number of points contained in the pixel
area. Ratio reference changes the
heat map color limits. The Points
Density plot highlights each point
with the color of the corresponding
pixel. Density plot is available for:
• Superimpose Traces
• Superimpose Lc
• Global delta Lc histograms
(Lc - Delta Lc)

1.7.2

Parameters Box

Many parameters can be set to tune both graphical views and threshold
limits (parameters not described here will be discussed later).
• Min F: minimum value of force valid for peaks detection or Lc evaluation;
• Max F: maximum value of force valid for peaks detection or Lc evaluation;
• Min peak proximity: minimum interval for automatic peaks detection (it tunes the sharpness of the cyan line in Contour length
(Lc,Fc) plot, section 1.5.4);
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• Threshold N points: parameter related to peaks detection. The
automatic peaks detection operate on the Contour length (Lc,Fc)
plot (section 1.5.4). N is the number of points that are removed
from each bin (Lc bin size) after the transformation in Lc-Fc, to
reduce the detection of spurious and isolated peaks caused by noise
fluctuations.
N.B. This number highly depends on the sampling rate of the curves.
A heuristic rule could be to chose this value proportional to the total
number of points of the curve:
T hreshold N points ∼

T otal P oints N umber
;
1000

N.B.2 Breakthrough force detection [for Membrane studies (see
section 3.4)].
• Max Lc: maximum value of Lc taken into account;
• Min Lc for Delta Lc: minimum value of Lc taken into account for
Delta Lc plots;
26

• Max Lc for Delta Lc: maximum value of Lc taken into account for
Delta Lc plots;
• Lc bin size: bin width of Lc histograms or Global Lc representations;
• Fc bin size: bin width of Force histograms or Global Force representations;
• Delta Lc bin size: bin width of Delta Lc histograms or Global
Delta Lc representations;
• Persistence Length p: fixed value of persistence length for Lc evaluation;
• p step (free p): minimum step when evaluating free persistence
length (dynamic persistence length);
• Min p (free p): minimum value for dynamic persistence length
algorithm;
• Max p (free p): maximum value for dynamic persistence length
algorithm;
• Lc for Analysis: detected Lc values of a current trace (they can
be edited);
• Update: after parameters changes, click this button to update displayed results.

1.7.3

Export plot

Every plot can be extracted and saved individually in Matlab format .fig,
or any other file format for figures, from the menu bar Tools > Export
plot.
It is also possible to export the Superimpose traces plot as a single
X-Y .txt file with Export ’Superimpose traces’ file.

1.8

Selected & Valid Traces

Loaded traces have a visibility label. There are only three possible labels:
• Selected
• Valid
• Not Valid

By default, loaded traces are all Selected. Global representations act on
Selected (that is a sub-group of Valid). All Valid traces are displayed
moving the slide bar. Not Valid traces are not shown. Filtering procedures described in the next section and chapter, filter out traces labeling
them as Not Valid.
Details Box shows the numbers:
85 Selected,
101 Valid,
122 Valid plus Not Valid, i.e. all loaded
data.
Trace Selection Box allows
to edit the list of Selected
traces.
The Remove[r]
check box removes the current trace from the selection (to Valid but not
Selected). Offset add a
shift to all selected traces. Selected Traces edit box lists the indexes of
Selected curves. It allows also, by changing the list, to add or to remove
traces from Selected group.

In the Filter menu bar the user can manage
the visibility labels of loaded data:

• Move ALL to valid: all Not Valid are labeled Valid;

• Move all Valid to Selected: all Valid are labeled Selected;

• Move not-Selected to not-Valid: all Valid but not Selected are
set Not Valid;

• Swap Valid and not Valid: all Valid, therefore also Selected, are
labeled Not Valid, and vice versa;

• Swap Selected and not Selected: all Selected are labeled Valid,
and vice versa; Not Valid remains unchanged.

1.9

Trace filtering: basic tool

SMFS experiments typically generate a large amount of data. In this section we present a basic filtering tool that allows the user to select traces
upon two characteristics: points position in F-tss space and peaks position. Traces that do not satisfy desired requirements will be labeled as Not
Valid.
29

The top panel displays single traces. On this panel, the user can draw
two kinds of rectangular ROIs: mandatory regions (green) and forbidden
regions (red). Green ROIs define Force and tss intervals in which at least
one point of the trace must fall into, otherwise the trace is filtered out.
Red ROIs define Force and tss intervals in which no point of the trace can
fall into, otherwise the trace is filtered out. The ROIs are equal for all
the traces. To draw a ROI, the user needs to click on Draw Rectangle
ROI and then move on the panel and click&drag; to erase a ROI, just click
Erase ROI. Multiple ROIs can be drawn.
The bottom panel displays the single contour length histograms in red and
the detected peaks in black. Color limits are set by the four edit boxes on
the right. The Blue section defines the area in which at least one peak of
the trace must fall, otherwise the trace is filtered out. The Pink section
defines the area in which the last peak of the trace must fall, i.e. no peaks
on higher Lc values, otherwise the trace is filtered out.
N.B. We suggest to perform this filtering procedure with traces smoothed
with Savitzky-Golay algorithm in order to enhance peaks detection.
Once all the desired limits have been set, Compute Filter finds the traces
30

to be removed and Update Valid Traces updates the Not Valid group.

1.10

Align to zero

Loaded traces can be all aligned to a zero position. There are two zero
definitions:
• Align to zero
• Align to first
positive force

Align to zero finds the average value of tss corresponding to negative
forces between -200pN and -400pN, and translates each trace accordingly.
Sometimes this procedure may not work because the contact phases are
not homogeneous: in this case Align to first positive force sets to
zero the tss corresponding to the first positive value of Force of each trace.

1.11

Manual Alignment

Manual Alignment tool (accessible from the menu bar Align > Manual
alignment) allows the user to slightly refine the relative shift among valid
traces, typically caused by misalignment of the base line. The graphical
panel shows three traces of different colors:
• Yellow - chosen trace, its number is visible in the Frame text box;
• Green - template trace, editable in the Template edit box;
• Pink - trace(s) saved on screen, Keep on screen check box.
Traces can be moved only horizontally, both with the Translate slide bar
and clicking&dragging on the graphic panel. Only chosen trace (yellow
trace) can be translated. To move across valid traces, use Frame slide
bar. Select box contains all the information related to Selected traces,
the chosen trace can be removed editing the selected edit box or by clicking
on Remove trace check box. View box allows to decide the trace representation and to set an Lc of reference.

1.12

Export Peaks Info (.txt, .xls)

The following description is valid for both .xls files and comma separated
.txt files (imported in Excel).
The files generated in Tools > Export Peaks Info contain the geometrical information of Selected traces.
• The first column contains the reference number of the Selected
traces.
32

• Contour length (m): the first group lists the contour length of each
peak identified in the traces. The parameters for peaks identification
can be tuned as explained in section 1.5.4.
• Force (N): the second group lists the rupture force of the peaks
reported above.
• Slope keq (nN/nm): the third group lists the slope calculated on
the last 20 points before the rupture. This value can be used to
calculate the loading rate before the rupture re as follows [7]:
re =

ksamp · v
1+

ksamp
kcant

, where

ksamp =

keq · kcant
kcant − keq

where keq is the slope, kcant is the spring constant of the cantilever
and v is the pulling velocity.

Chapter 2

Advanced Tools
In this chapter we describe the tools implemented in Fodis. These tools
were developed in order to solve some common issues in SMFS experiments,
like clustering and alignment.

2.1

Unfolding Pathways Analysis

Given a population of traces that represent the unfolding of a certain protein, an important issue in SMFS is to determine how this unfolding happens. Global representations presented in Chapter 1, for instance, are very
useful to generate statistics in an aggregated fashion. Here, with Unfolding
Pathways Analysis we intend to present three representations that, in spite
of being global, show unfolding pathways in a disaggregated fashion.

2.1.1

Group division

The first step in an Unfolding Pathways Analysis is to identify different
groups of traces depending on the position of their force peaks.
35

The idea is to generate a
graphical representation of
the different unfolding pathways of a set of traces, and
cluster them. Starting from
Global Histogram of Maxima
(GHM), we can divide the
Lc coordinates in intervals
(different colors).

The extremities of each interval can be set in the Path
Interval edit box. Intervals
cannot overlap.
Auto Intervals automatically generate the intervals writing the corresponding string. The borders are identified as the minima of the Gaussians
sum generated over the GHM (section 1.6.2).
Then, the string can be edited following this simple rule:
min1-max1,min2-max2,... in nm; max(n)≤min(n+1)
The intervals can be also chosen equally spaced by inserting only one integer:
N : divide Lc coordinates in N equal intervals.
Once the intervals have been chosen, the user can update the group division
by clicking on Update Grouping. Then checking Enable Group Division
it is possible to move across different resulting groups with the menu Show
Group Nr.

2.1.2

Path Plot

The Path Plot is a representation that clusters a population of traces depending on the position and on the number of Force peaks. Group divi36

sion, and resulting Path Plot generation (Path Analysis > Path Plot),
is based on the following 5 steps.

Traces are fitted with the WLC model, transformed into Lc histograms
and grouped in the Global Histogram (or GHM).

The Global Histogram is divided into intervals according to the main
ensembles of occurring events, to partition the Lc coordinates in regions
with distinct maxima.

Following the aforementioned rule, in this explanatory panel, we selected 5 intervals 90-118,118-155,155-200,200-247,247-285nm.
37

On the base of this division, each trace is coded in a binary string of
5 digits: 0 is assigned if no force peak is detected within the interval, 1 is
assigned if at least one event is detected. From each string, we created two
additional sequences: # and Pn. # is the sequence referred to the order of
appearance of the force peak along the trace (in a trace with 2 peaks, the
1st peak has #=1 and the 2nd peak has #=2). Pn refers to the interval
position occupied by a peak (a peak that falls within the 3rd interval has
Pn=3).

Traces so coded are finally plotted as broken lines into an orthogonal
#-Pn space, the line-width is proportional to the number of traces that
follow the same path. This method provides a representation to distinguish
different unfolding behaviors/clusters of a given set of traces, based on the
number and position of occurrence of unfolding events.

Path Plot of a larger population
The previous example shows how the Path Plot is constructed, now we
present how it looks when generated on a larger dataset (CNG dataset).
38

Each line width is proportional to the number of traces that cover that
specific path. The size of the point at a node is proportional to the number
of traces that pass through that node.

By Enabling Group Division we can select only one group, the 18th
in this case. We can see the peaks distribution and relative Path Plot of
7 traces that has no peak in intervals 3 and 4, indeed, in the Path Plot
representation, it does not have any node in the 3rd and 4th intervals.

2.1.3

Combined Path Plot

Similar to the Path plot, the Combined Path Plot displays the #-Pn space
but with no color distinction. Each segment-width is proportional to the
absolute number of traces that travel over that particular segment path.

2.1.4

Force-Lc segmentation plot (Thoma et al.)

Thoma and colleagues, in 2017, presented a different Unfolding Pathways Analysis based on the Contour length position and average
Force of Force peaks [6]. In this representation, the points coordinates
40

are the average Force and Contour length of each different class (intervals of different colors in the figure below); the segments connect the
points showing the distribution of the unfolding pathways. The groupdivision implemented in Fodis is based on the partition shown in section
2.1.1. This representation can be generated clicking (Path Analysis >
Force-Lc segmentation plot). The radius of the points is proportional
to the number of Force peaks that are present in the relative intervals;
the width of the segments is proportional to the number of Force-distance
curves that show that specific point-to-point pathway.
N.B. This analysis is enabled only after setting the intervals (section 2.1.1).

Global force plot and group division

Thoma plot relative to the above population of peaks
41

2.2

Fingerprint ROI

Fingerprint ROI is a tool intended to find specific pattern over the
population of traces. It is accessible from the menu bar Selection >
Fingerprint ROI.
This graphic interface shows the plot panel and the slide bar. The general
idea behind this tool is to evaluate how many points of a trace fall into
the drawn area (pink area). By clicking the Brush area button, move
the mouse cursor on the graph and finally click&drag to draw a continuous
ROI. The user can draw as many ROIs as needed just by clicking the button
Brush area for any new ROI. The Delete area button deletes all ROIs
previously drawn. Once all desired ROIs have been drawn, the evaluation
can start. Lag allowed edit box sets how many nm each trace is shifted
from its starting position. The maximum value of intersection between
ROIs and a trace is saved and displayed with Compute similarity. The
Threshold score edit box sets the threshold value of the score: the Update
Traces button filters out all the traces that score lower than the threshold
value and then they are available in the main Fodis interface.
42

2.3

Automatic Alignment

The Automatic Alignment (menu bar Align > Automatic Alignment) is
a tool intended to solve the critical and highly operator-dependent issue of
traces alignment.

Align to a reference trace
The Align to this trace option takes the contour length histogram of
the current trace (the trace in the view box) and it calculates the cross
correlation of all contour length histograms against the current trace. After
this process, all the traces will be horizontally shifted to maximize the cross
correlation against the current trace.

Reference-free Alignment
This tool is based on the work of Bosshart and colleagues [3], with some
specific improvements developed to extend its applicability to more general
SMFS datasets.
In particular, they proposed an algorithm consisting of 4 steps. Starting
from the contour length histogram of every trace, they:
• subdivided the traces into groups of homogeneous traces (i.e. traces
with the same number of peaks);
• recursively aligned traces into the same group with the maximumcorrelation principle, building an average contour-length reference for
each group;
• formed a global reference;
• aligned all the traces of the dataset to the global reference.
To this remarkable computational procedure, we added two features that
help to manage a larger variety of traces that do not display regular occurrence of peaks.
1. In addition to the contour-length histogram, we assign to every trace
a zero-point, that is the point of tip-sample contact. Given the correlation curve of two traces, we then multiply the correlation curve with
43

a Gaussian curve centered at the point in which the zero-points of
the two traces match with each other (red Gaussian curve). The idea
is to apply a “potential well” to reduce the maximum displacement
of the two zeros.
2. Group division proposed by Bosshart and colleagues works only if all
the traces with the same number of peaks have the peaks in the same
position, but this is not generally true for F-D curves of the same
protein. Therefore, we used a group division following the method
described in the Path Plot section. In this way, we imposed two
constrains for a given trace to be part of a given group: to have
a specific number of peaks and to have those peaks in a specific
position.
N.B. Group division is done as shown in Path Plot section, with
custom or equally-spaced intervals.
The user performing Automatic Alignment (menu bar Align > Automatic
Alignment) in Fodis is guided across the aforementioned steps with the help
of two Graphic Interfaces.

Graphic interface 1 for global reference construction
44

The first interface helps the user to set all relevant parameters for the
formation of the global reference. The Histogram Customization box is
crucial to determine the shape of the histograms to be aligned. Default
parameters are generally adequate, but in case of some specific requirements, the user is allowed to change them. The Alignment Valid range
edit boxes set the limits over which histograms are set to zero. Gaussian
std. sets the standard deviation of the Gaussian ”potential” and Nr. of
Iterations sets how many iterations the algorithm executes: iterations
are time consuming, but only one iteration generally gives unstable results.
Use the button Align! to execute the algorithm, Skip if first alignment
has already been performed thus to go directly to the second Alignment
interface.

Graphic interface 2 for global reference tuning
The scope of the second alignment step is to prepare the desired global
reference (i.e. the reference histogram onto which every single histogram
is finally aligned). Default parameters should be adequate, but for specific
requirements, it is possible to change some settings.
The tuning process consists of:
• tuning shape of the blue profiles (i.e. group references, resulting his45

tograms from alignment intra-group). This can be done in the Group
Histograms Customization box moving through different groups
with the slide bar.
N.B. Group division is done as shown in the Path Plot section, with
custom or equally-spaced intervals;
• tuning shape of the red profile (i.e. global reference) and pink profile
(i.e. binarized reference). This can be done in Reference Histogram
Customization box.
The global reference is the weighted average of group references. The
binarized reference is based on the global reference. It contains peaks
found in the global reference, but they are leveled and normalized.
Align to Global-Custom Reference to finally re-align all the traces
to the reference.

2.4

Selection through correlation

A common problem in SMFS is finding and isolating relevant traces among
all collected data. The Basic Filtering Tool described in Chapter 1 allows
the operator to filter out traces longer or shorter than the expected ones;
the Fingerprint ROI tool, described in this Chapter, looks at a specific
pattern drawn by the user and can list the traces accordingly. All these
tools need the intervention of the user to choose some specific interval or
shape, in contrast with the purpose of an unsupervised filtering procedure.

The Selection through correlation (Selection > *) calculates the cross
correlation between every couple of loaded (Valid) traces forming a symmetric similarity matrix. This matrix can then be sorted (ordered) with
the MATLAB function symamd (symmetric approximate minimum permutation algorithm).
The slide bars change the visualized contour length histograms. The blue
curve in the top-right panel is the calculated cross correlation of the two
visualized histograms of trace 1 and trace 2. The diamond points the maximum value, the red area is the Gaussian curve that weights the correlation
(as described in Automaic Alignment).
47

• Single trace correlation button displays the values of correlation
relative to trace 1 (the one shown in the upper panel);
• Sort Correlation Matrix applies the symmetric approximate minimum permutation algorithm to the similarity matrix (i.e. it changes
the order of the traces to find clusters of similar traces);
• Global Correlation shows the similarity matrix ;
• Sigma determines the width of the Gaussian curve that weights the
correlation curve;
• Min is the threshold value for the similarity matrix ;
• Max Lag is the maximum lag allowed when calculating the correlation
between two traces.

Similarity matrix

Sorted similarity matrix

At this point the user has two options: he can decide to select a specific cluster in the sorted similarity matrix, or he can select traces similar
to the reference trace 1 (the trace visualized in the upper panel).

• Manual Select Valid Group button: the sorted similarity matrix
pops up and, with the cursor, the user can select a cluster of traces
48

(click-drag&drop plus double-click on the segment). The operation
can be performed multiple times just by clicking again the button
Manual Select Valid Group. The Delete button deletes the selection. The selected group of traces (identified by a X) will be visible
in the main interface only after clicking Update traces. If the selection does not satisfy the user, he can Filter > Move ALL to Valid
and redo all the process.
• Select Traces above Min corr Value button allows to select the
traces above the Min threshold, that are similar to the reference trace
(trace shown in the upper panel). The selected traces are previously
visible clicking Single trace correlation button.
A further refinement of the calculation of the correlation is possible
tuning the contour length histograms with the options:
• Filter trace applies a smoothing filter to the contour length histogram of every trace;
• Gaussian substitution substitutes a sum of Gaussian curves to
each contour length histograms. It detects the peaks with the parameters on the right.

2.5

Structural heterogeneity determination

Hinkzewski and colleagues in 2016 found a function that give information
about the structural heterogeneity of a protein [5]. This function Ω can be
determined performing SMFS at different pulling speed. To perform this
analysis in Fodis go to Tools > Structural heterogeneity.

Global Contour length-Force plot
(section 1.6.3 ).
The user have to select the region of interest containing the Force peaks,
and double click inside the region. Fodis will compute Ω. Then the user
have to repeat the procedure to the same Force peaks obtained at a different
pulling speed, saving and comparing the Ω graphs.

Ω function of the force

Chapter 3

Membrane Mechanics
In this chapter we describe the tools for the analysis of breakthrough force:
• determination of the Breakthrough force of a membrane;
• 2D mapping of the Breakthrough force of a membrane;
• line tension;
• spreading pressure.

3.1
3.1.1

Import/Open breakthrough force curves
Import (plain format)
From File > Import traces you can open
the curves in plain format (see section 1.2.1).

3.1.2

Open extension curves from AFM files
(only .txt exported from JPK, see 1.1.2)
From File > Open samples you
can choose to open the extension
curves. Select the folder with the
data and Import Traces.

3.2

Pre-processing

First set the baseline to zero and then align to the maximum positive.
You could also transform the x axis to Tip-sample-separation.
N.B. If your force is negative (upside down) use Mirror (F -> -F)
since the tool for membrane mechanics only recognizes the breakthrough
forces in the positive region.
Then you can align the traces to the surface position with Align to
maximum value.

3.3

Analysis of the Breakthrough forces

Once all the curves are loaded and aligned go to the menu bar for Membranes
> Force Break Membrane. Fodis will generate the statistical analysis of
all the valid curves.

• Figure 1: Breakthrough force map (if the JPK .txt contain the position of the curves);
• Figure 2: scatter plot of the detected Breakthrough forces (Force and
position);
• Figure 3: histogram of the detected Breakthrough forces (Force only;
orange curve: curve described in [8]);
• Parameters: set the experimental parameters of your experiment and
then tune the surface energy S and the Line tension G in order
to fit the distribution with the orange cure in Figure 3.
The correct line tension and spreading pressure of your
membrane are the ones that best fit the cyan distribution.
54

3.4

Enhance Breakthrough forces detection

If the number of points in the previous histogram/scatterplot is too low
(too high), it means that the detection of the Breakthrough forces of your
set of curves is not optimal. So you probably need to tune the parameter
Threshold N points which set the threshold for the prominence of the
Breakthrough events.
• Reduce Threshold N points and click for Membranes > Force
Break Membrane again to increase the number of detected Breakthrough events.
• Increase Threshold N points and click for Membranes > Force
Break Membrane again to reduce the number of detected Breakthrough events.

3.5

Export Breakthrough forces
You can export the values of position and
Breakthrough Forces in a .txt file from
for Membranes > Export position/
Break force.
Column1=position [m] ; Column2=Force
[N].

Bibliography
[1] Oesterhelt, F., et al. ”Unfolding pathways of individual bacteriorhodopsins.” Science 288.5463 (2000): 143-146.
[2] Puchner, Elias M., et al. ”Comparing proteins by their unfolding pattern.” Biophysical journal 95.1 (2008): 426-434.
[3] Bosshart, Patrick D., Patrick LTM Frederix, and Andreas Engel. ”Reference-free alignment and sorting of single-molecule
force spectroscopy data.” Biophysical journal 102.9 (2012):
2202-2211.
[4] Kawamura, Shiho, et al. ”Kinetic, energetic, and mechanical
differences between dark-state rhodopsin and opsin.” Structure 21.3 (2013): 426-437.
[5] Hinczewski, Michael, Changbong Hyeon, and D. Thirumalai.
”Directly measuring single-molecule heterogeneity using force
spectroscopy.” Proceedings of the National Academy of Sciences 113.27 (2016): E3852-E3861.
[6] Thoma, Johannes, et al. ”Maltoporin LamB Unfolds beta
Hairpins along Mechanical Stress-Dependent Unfolding Pathways.” Structure (2017).
[7] Bizzarri, Anna Rita, and Salvatore Cannistraro, eds. Dynamic force spectroscopy and biomolecular recognition. CRC
Press, 2012..
57

[8] S.Loi, G.Sun, V.Franz, H.-J.Butt, Rupture of molecular thin films observed in atomic force microscopy.
II.Experiment,
Phys.Rev.E66(2002)031602,
https://
doi.org/10.1103/PhysRevE.66.031602

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