An open source LABVIEW platform for simulating image series of
fluorescent microtubules in gliding assays
Lawrence J. Herskowitz (lherskow@unm.edu), Steven J. Koch (sjkoch@unm.edu)
University of New Mexico, Center for High Technology Materials and Department of Physics and Astronomy
Abstract: We describe an open-source LabVIEW software platform for generating simulated images of microtubules in gliding
motility assays. We describe how the software works and how to obtain the software.
Introduction
Kinesin family proteins are motor proteins that are
able to use chemical energy to translocate on
microtubules. They are essential to many cellular
processes such as cell reproduction and axonal
transport (1; 2; 3). A technique that has proven very
valuable to studying kinesin’s physical properties is
the gliding motility assay (GMA) (4). In the GMA, the
kinesin tail is fixed to a slide with the motor domains
exposed to the solution. A solution of microtubule
with buffer and ATP are then added to the flow cell.
This allows the microtubules to be propelled by the kinesin motor domains as depicted in Figure 1.
Often the microtubules are labeled with dye molecules that allow them to be seen through fluorescence
microscopy (5). GMAs enable the study of many kinetic properties of wild type and mutant kinesins,
such as gliding speed, microtubule polarity, and force induction in the kinetic process (6; 7; 8; 9).
To extract information from these experiments, it is often imperative to track the moving microtubules
through a series of images, obtaining the position versus time of the microtubules. However, manual
tracking means going through hundreds of images and recording the position of the microtubule by
hand. This is a tedious and exhausting process, though it certainly has proven useful (10). The data are
also potentially more prone to selection bias and systematic and random errors than automated
tracking. Because of this several groups have developed microtubule tracking software (11; 12) (23). To
test the effectiveness of these tracking programs, many laboratories will track a stationary object. This
however is not ideal since it does not match experimental conditions well. To characterize the
systematic and random errors in the tracking algorithms, it is best to test them on a moving object. One
way this can be achieved is by moving a fixed microtubule with a piezoelectric stage. However, even in
that case it is difficult to completely eliminate drift and other effects. A simulated image series can
eliminate those problems and is often ideal for testing tracking algorithms (13). For this purpose we
developed an application that can generate microtubule images that mimic those captured from a
typical gliding motility assay. A simulated image is
shown in Figure 2A next to an actual gliding
motility assay image shown in Figure 2B.

The application was written in National Instruments LABVIEW 7.1. The user interface can be seen in the
Figure 3 with user inputs on the left and top and outputs on the right and bottom.
This paper is demarcated into two sections. Section 1 describes the process implemented to produce the
simulated image, the controls that the user can change, and the method for storing images and settings.
Section 2 provides instructions on how to obtain the open source code, the compiled application, and a
video tutorial.
SECTION 1
Algorithm Overview
Figure 4 shows a simplified diagram of the overall algorithm. This paper will go into detail of how each
step of the algorithm works. There is a main while loop seen in the diagram (see Reference (14) for a
LABVIEW video tutorial). In each iteration a frame is constructed and saved. Before the while loop is
entered, three initialization tasks are completed shown as subVIs I, II, III in the figure. (I) First the user
must create the trajectory the microtubule will follow in the image series that will be created. This is
done in the trajectory sub.vi. (II) Next using the settings in the “Physical Parameters” control the
program randomly sets the locations of the dye molecules along the microtubule length. (III) The third
task is to create a prototype Airy Disk from the “Airy Disk Parameters.” Each one of these subVIs is
completed only once for each set of images, prior to execution of the while loop that generates each of
the individual images.
In the while loop, first the absolute coordinates of the dye molecules are set in the subVI labeled “A” in
Figure 4. This VI, “Find Coord of Dyes.vi” has inputs of the microtubule trajectory, the index of the start
of the microtubule, speed, and length of the microtubule. SubVI A has three outputs: “Coordinates of
Dye Locations” (bundle of two double precision numbers), the “Index of Start of Microtubule for next
frame” (int32) and the “Index of End of Microtubule” (int32). The dye location coordinates determine
the locations of the centers of the airy disks in the simulated images. These are absolute coordinates
(relative to the top left of the image) instead of the relative coordinates with respect to the microtubule
end that the “Pick sites at random” subVI outputs. The second output, “Index of Start of Microtubule for
next frame,” goes into a shift register and replaces the previous iteration’s index for the start of the
microtubule. The distance the microtubule moves between frames is calculated from the speed inside of
this subVI. This is used to find the index along the trajectory the microtubule will start in the next frame.
The index of the end of the microtubule is calculated using the length of the microtubule value similar to
calculating the index for the next starting index.
After subVI A finishes, it passes parameters to subVI B, “Create high res image” including the
coordinates of the dye locations, a pointer to an image location and the user inputs “Photon
Parameters” and “Image Size.” Inside subVI B are the probability distribution function and the Monte
Carlo algorithm to randomly select the photon locations.
Next is subVI C, “Create low res noisy image,” with the inputs of “Image Size,” “Background Noise” and
the “High Res Image.” SubVI C resamples the high resolution image to create a lower resolution image

that matches experimental resolution, dictated by the user input. If selected, Gaussian noise is added to
the background. The output of subVI C is the final image.
SubVI D saves the image in a directory the user has chosen, and named after the frame number which is
the iteration number, such as 1.png. When the end of the microtubule index has reached the end of the
trajectory array, the while loop stops.
This section will be broken up into four segments to provide details of the above subVIs: Microtubule
Construction, Resampling and Noise Addition, Trajectory, and Saving. In each of these segments the
necessary user input is highlighted as well as a simplified version of the code.
Microtubule Construction
User Input:

This section will go into detail of how a single image of a microtubule is constructed. The coordinates for
the dyes need to be randomly selected along the length of the microtubule. The user can set the
microtubule length via the “Length of Microtubule” control. This control is in units of high resolution
pixels. This algorithm produces two images; a high resolution image and a lower resolution image. The
final image is the low resolution image. This allows for more accurate numerical estimation of the airy
disk probability density function which is implemented in the Monte Carlo algorithm. The “high res pix
per site” control dictates how many fluorescent dyes are theoretically possible to be found in each pixel.
For a typical fluorescent tubulin preparation (15), the molecules are attached to surface lysine residues
on the alpha/beta tubulin dimer. There is one dimer per 8 nm on a single protofilament. For a 13-
protofilament microtubule, there are thus approximately 1.5 dimers per nanometer. There also could be
multiple dye molecules on a single dimer, which would further reduce the number of high resolution
pixels per dye site. This control will change depending on the users desired nm/pixel ratio.

The first two controls thus dictate the microtubule length and the maximum number of dyes that can be
attached. In the example shown in the figure, there can be a maximum of 10,000 dyes. However in
practice, fluorescently labeled tubulin is mixed with unlabeled tubulin resulting in partially labeled
microtubules after polymerization. To mimic this, the program uses a Monte Carlo method to determine
if a given site will be labeled dependent on the fraction of dye control. A uniform random number from
0 to 1 is selected for each site. If that random number is lower than the user-set labeling fraction, the
site is deemed as labeled. If not the site is left as unlabeled. This code can be seen in Figure 6. There is
an indicator on the front panel seen to the right of the dynamic adjust control in Figure 3 which specifies
the number of dye molecules on the microtubule.
If the site is selected to be labeled, an airy disk is centered at that location. An airy disk represents the
fluorescent dye in the image plane since the dye emits light that is captured by the circular aperture of
the objective (16). Mathematically an airy disk is described with the following equation:

where is the maximum intensity of the airy disk center, is the Bessel function of the first kind in
circular coordinates, r is the radius in high res pixels, and k is what we have named the prefactor. It can
be calculated by

NA is the numerical aperture of the objective, and is the wavelength in nanometers. C is the
conversion factor from high resolution pixels to nanometers because we represent r in pixels. The first
zero for the airy disk can be calculated in nanometers using

where r0 is the distance to the first zero (17).

Since the microtubule is narrow compared to the airy disk radius, we treat it as a one-dimensional
object. So each airy disk location is recorded as a distance from the end of the microtubule, and these
relative distances along the contour remain fixed while the microtubule moves or curves during the
simulation.
This method of labeling dyes randomly along the microtubule is supported by prior experimental work.
A microtubule in a solution with a low concentration of fluorescent dyes looks speckled. Waterman-
Storer and Salmon studied this phenomenon and showed that this is caused by a non-uniform
distribution of the fluorescent dyes along the microtubule proto-filament in a purely stochastic process
(18).
User Input:

Since the airy disk intensity falls quickly, it is not necessary to calculate the airy disk over large values.
The numerical aperture and wavelength determines how quickly the airy disk reaches zero. A higher
numerical aperture or shorter wavelength means fewer pixels need to be calculated to get an accurate
representation than a higher numerical aperture and longer wavelength. This is illustrated in Figure 8. It
is obvious that the airy disk in 8A with a radius of 5.67 high res pixels (522.86 nm) needs fewer pixels
than 8B whose radius is 19.84 high res pixels (1,830 nm) to approximate the dye molecule. In the user
input image above, a square of -6 to 6 for both x and y values was chosen. This means that a 12 pixels x
12 pixel box centered at the airy disk’s center was used for each airy disk in the simulation which has the
same radius as Figure 8A. This is
done to ensure a shorter processing
time for the software. The radius of
the airy disk is calculated in both
nanometers and high res pixels. This
can be seen on the front panel in
Figure 3 below the number of dye
molecules indicator.

User Input:

Generating the total probability density function for photon arrival in the image plane

After all the coordinates of all airy disks have been determined, the functions are added together. This is
shown in the equation below.

Here is the total intensity of all M airy disks added together. is the intensity profile of a single airy
disk. Its center is shifted inside the image by . is then normalized by numerical integration to
produce the probability density function (PDF) for photon arrival. Each pixel coordinate now represents
the probability of a given photon landing there.
Generating images based on PDF for photon arrival
Photon locations are randomly selected using a Monte Carlo method and the total photon PDF. To
minimize the number of random numbers needed for each photon arrival, all values in the two
dimensional PDF is flattened into a one-dimensional cumulative probability array. This is seen in Figure
10. Because the PDF was normalized, the last element in the cumulative probability array is 1. Each
element in the cumulative array has a corresponding pixel coordinate. For a given random number, the
index of the cumulative array element closest to that value (without exceeding it) is found by a binary
search algorithm. The value of pixel corresponding to that element is increased by an amount set by
“intensity per random number.” This method requires only one random number for each photon (19).
This code is shown in Figure 11.

The user chooses how many random numbers, or photons, used
for each image. Figure 12 represents what an image from this step
in the process looks like. The image produced is a floating point
image to allow for any number of photons per pixel. The image is
next cast to an 8-bit image, with a maximum pixel value of 255.
The user is given the option of dynamically adjusting the image so
that the maximum pixel value in the floating point image set to
255. If the user chooses not to do this, the image can mimic either
under- or over-exposure. The latter case will show saturated
pixels.
Resampling and Noise Addition
User Input:

After float image is cast into an 8 bit image, the image is then resampled into a lower resolution image
to match experimental resolution. The user inputs the x and y resolution of the higher resolution image
in “High Res X Image Size” and “High Res Y Image Size.” The user can then control how much the lower
resolution image will be in “X Resolution” and “Y Resolution.” This resampling into a lower resolution
image is done to allow for a more precise numerical integration to create the probability density
function.
User Input:

Finally, background noise can be added to the image depending on user settings. We add background
noise to the 8-bit resampled image. The user chooses the mean value and standard deviation of the

background noise Random noise is added to every pixel. The resulting image with its higher resolution
counterpart can be seen in Figure 15.
Because there are many parameters it is useful to view test images before creating the entire sequence
of images. This option is available to the user along with the additional ability to see what a single airy
disk looks like given the current relevant user settings. This allows the user to minimize the box
surrounding the airy disk and thus speed up subsequent simulations. Pressing “Test this set up”
produces a microtubule while “see this Airy Disk” shows what a single airy disk looks like. The maximum
intensity of the airy disk can be controlled with the “I0.” This only works with “See this Airy Disk” since
the sum of all the airy disks is normalized when constructing the microtubule image. These buttons can
be seen in Figure 3 below the “Let’s Make Some Magic” button.
Trajectory
The ultimate goal of this software is to produce a series of images that mimic microtubule motion in
gliding motility assays. This software contains a subVI that allows the user to create a trajectory that the
microtubule will follow throughout the frames. The trajectory can be composed of four different base
trajectories; a horizontal line, a vertical line, a sloped line, and a circle. The user can manipulate these
simpler paths to create elementary or more complicated trajectories as seen in the front panel image of
this subVI in Figure 16.

The simplest paths are the horizontal and the vertical line. For the horizontal line, the user inputs the
starting point coordinate (x,y) and the ending x coordinate. The vertical line is very similar in that it
needs the user to input the starting point coordinate (x,y), but it needs the ending y coordinate instead
of x. The sloped line needs both the x and y coordinates for the starting and ending points. It will output
the slope of the line for reference. For a circular arc, the user specifies the origin, radius, and angles to
start and end the arc. These angles can vary from -2 to 2 .
To make creating more complicated trajectories easier, each one of these paths have an option to
automatically link to the existing path. For the horizontal and vertical line this only means that the
starting point is set automatically to be the last point of the semi-completed path. For the sloped line,
the starting point is set just like the horizontal line, but the slope is also set to the slope of the incoming
path. It won’t set the slope automatically if the incoming slope is horizontal or vertical. To best attach a
circle to the trajectory, the program can set the starting point on the circle so the incoming trajectory
has the same slope as the tangential line to the circle. This ensures a smooth transition into the circle.
Since there are two points on the circle with the same slope, the user can choose which point to use.
This trajectory subVI also allows the user to load a trajectory previously made and edit that path. The
user can also save the completed trajectory as a .dat file in a chosen directory. The main program will
automatically save the trajectory in the same directory as the images.
Speed
User Input:
See Figure 5
The microtubule will have a fixed speed (see “Updates” section at end of manuscript), defined by the
user in units of high res pixel/frame. In the case shown in Figure 5 the user has chosen a speed of 2 high
res pixels/frame. The amount of resampling will determine the speed in the final, lower resolution
images. With the settings shown earlier in Figure 5, the tracked speed is 1 low res pixels/frame.
In each image frame, the microtubule dye molecules coordinates will be moved along the trajectory a
distance specified by the speed. Since the airy disks are labeled by their distance from the start of the
microtubule and not from a location on the image, their relative distances remain unchanged despite
curves along the trajectory. The program calculates the distances between adjacent points on the
trajectory. Using this array of distances it is able to set the front of the microtubule and quickly search
for points that are certain distances away from the start. The code is shown in Figure 17.
Finally, when satisfied with the settings and trajectory, the user presses the “Let’s Make Some Magic”
button which can be seen in Figure 3 to the right of Image Size parameters. The program runs and saves
images until it reaches the end of the trajectory. Currently the user cannot stop the simulations early.
Pressing the stop button will stop the entire program but will only be responsive after all the images
have been created.

Saving images and user settings
User Input:

This software saves the images in a directory that is specified in “Directory for Storing Images.” The
images are .pngs and are named after the frame number. The parameters used to create the
microtubule as well as the trajectory are saved. The parameters are saved in an .ini file while the
trajectory is saved as a .dat file.
This speed of this software is dependent on the user parameters. For example a higher number of
photons will slow down the algorithm proportionally. A larger box around the center of the airy disk will
also slow down the simulation. With the settings shown in this paper, the software creates an image in
about 350 milliseconds on our Intel Core 2 Duo CPU running Windows XP.
Section 2
How to obtain code and a video tutorial
This code is available from sourceforge at https://sourceforge.net/projects/simulatingimage/files/. The
VIs used to create this program are available for download in the Simulating Images folder. LabVIEW and
the Vision Development Module are required to view and edit the source code. An executable version of
this program is also available in Executable Folder found in the Simulating Images directory. A $420 “NI
Vision Development Module Run-Time License” is required to run the executable.
http://sine.ni.com/nips/cds/view/p/lang/en/nid/207700
A video tutorial created by CamStudio is also available in the Tutorial Folder in the same directory. The
.ini file that saved the settings used to create the images found in this paper and the trajectory shown
above are located in Settings for Paper folder inside this directory.
Prior Attempts
This report describes our second attempt to create images of microtubules. The first attempt followed
more closely to the steps taken in the Cheezum paper (13). We found the stochastic method we report
here more satisfying as far as mimicking our experimental data. However the other process, based on
convolutions of a line or rectangle with an airy disk worked well. We do not describe those methods
here, but out work can be seen in LJH’s open notebook, dates 11/12/2009

(http://openwetware.org/wiki/User:TheLarry/Notebook/Larrys_Notebook/2009/11/12) through
11/18/2009 (http://openwetware.org/wiki/User:TheLarry/Notebook/Larrys_Notebook/2009/11/18).
Updates
Since writing this pre-print, we have added features to this software. For example, the ability to pause or
switch speeds. Also, the ability for speed to vary according to Poisson stepping. The updates may be
reflected in the code and thus some figures may be slightly outdated.
Conclusion
This software can create a series of images of a microtubule moving along a user specified trajectory.
This can be used to test tracking software designed for gliding motility assays or other microtubule
assays. It is possible to adapt this software to create images of other polymeric protein structures such
as f-actin and some cytoskeletal proteins (20; 21). However it is not equipped to handle these yet. The
code is freely are available at SourceForge under an MIT license for reuse and adaptation.
Acknowledgements
This research was funded through DTRA CB Basic Research Program under Grant No. HDTRA1-09-1-008.
The authors would also like to acknowledge Anthony Salvagno for creating Figure 1. Haiqing Liu for
providing the kinesin for the gliding motility assays. Andy Maloney for performing the gliding motility
assays especially for providing the image in Figure 2B.


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