Anaphase A
Overview
This
software, written by Patrick Michael West Jr., is a simulation of the model for
Anaphase A described in Dr. L. John Gagliardi’s paper entitled “Electrostatic
Force in Prometaphase, Metaphase, and Anaphase A Chromosome Motions.” The purpose of this software is to
illustrate the viability of the model.
From biology we know what happens, but we do not know why it
happens. In light of Newtonian physics,
however, the simulation shows that, despite Debye screening, electrostatic
force is sufficient to drag the chromosome through the viscous medium of the
cytoplasm. The simulation further shows
that the “Negazone” (see “Probability Model” in “Setting Simulation Parameters”
section) can explain the localization of the disassembly to within a few dimer
lengths of each kinetochore, resulting in a motion that is
self-regulating. For comparison, a
simple “Relative Weights” probability model is also included.
About the Authors:
Dr. L. John Gagliardi is Chair of
the Physics Department at Rutgers University (Camden campus), and has long been
interested in the dynamics of mitotic motions.
Patrick Michael West Jr. holds a
degree in Electrical and Computer Engineering from Rutgers University and is
currently working on Advanced Processor Development at IBM, Poughkeepsie, NY.
System Requirements
1.
IBM compatible PC, 486
or higher processor with 8 MB of RAM.
2.
2MB free hard drive
space.
3.
3-½ inch, 1.44 MB floppy
drive (for floppy installation only).
4.
Internet access (for
download installation only).
5.
640 x 480 VGA adapter or
better.
6.
Microsoft Windows
95/98/2K, Millennium Edition, or above.
Installation
Via Internet Download:
1.
Click on “Download Now”
(below)
Download Now
2.
Save this file to the
Desktop on your machine
3.
After Downloading is
complete, double click the icon for Anaphase.exe on your Desktop.
4.
Follow onscreen
instructions.
5.
After installation is
complete, start program by clicking Start à Programs à Anaphase A à Anaphase A
From floppy disks:
1.
Insert Disk 1 into floppy drive A.
2.
Click Start àRun.
3.
Type “A:\Setup.exe” in
dialog box.
4.
Click “OK” button.
5.
Follow onscreen
instructions.
6.
After installation is
complete, start program by clicking Start à Programs à Anaphase A à Anaphase A
Using the Software
Display
Windows
The main screen has three large display windows. The first (leftmost) shows a cross sectional view of the structure, the center shows the current length of each protofilament, and the last (rightmost) provides the data from the most recent calculation. These three windows allow the user to monitor the progress of the simulation.
The first window shows a graphical representation of the cross section of the bundle of microtubules. The simulation considers a bundle of ten microtubules, which is shown as viewed from the kinetochore. Each individual protofilament is rendered in a shade of blue corresponding to its distance from the kinetochore; lighter shades are closer, and darker shades are farther. Initially, all protofilaments are in contact with the kinetochore and, therefore, rendered in the lightest shade of blue.
The center window shows the length of the 130 protofilaments. For each protofilament, the last five dimers are shown. A pair of red and blue line segments represents each dimer; the red segment represents the positively charged end of the dimer, and the blue segment represents the negatively charged end. The column of red segments at the far right of the window represents the positively charged ends of the microtubule stubs embedded in the kinetochore.
As the simulation progresses,
disassembly of the microtubules is represented graphically in the first two
windows. In the first window, when a
dimer has been selected for disassembly, a red flash occurs at its location,
and, then, its color is changed to the next darkest shade of blue. In the second window, the protofilament
containing the selected dimer is shortened by one pair of red and blue line
segments.
Disassemblies occur at the rightmost end of the protofilaments (nearest the kinetochore). After all dimers in contact with a kinetochore have been removed, a gap is created. This gap can be clearly seen in the second window. Once a gap exists, electrostatic interactions cause motion to occur.
The resulting motion is also represented graphically in the first two windows. In the first window, the color of all dimers is changed to the next lighter shade of blue. In the second window, the bundle configuration is advanced to the right until at least one dimer is in contact with the stubs in the kinetochore (at the far right of the window). Actually, the kinetochore is moving to the left, but is shown this way for simplicity.
Toolbar Buttons
The toolbar at the top of the screen can be used to access features of the software without going through the menu system. Clicking on a toolbar button will invoke the same action as selecting the corresponding menu option.
Run
Click the Run button to start the simulation.
Stop
Clicking the Stop button will stop the current simulation run. The simulation timer will be reset to zero, and all average values will also be reset to zero. In addition, final results of the run will be displayed in the Data Window. The current bundle configuration (lengths of microtubules), however, will be preserved.
TIP: Use the Pause button to freeze the simulation run without resetting values; the run will continue when Pause is released (clicked again).
Change Parameters
Clicking the Change Parameters button opens the Change Parameters dialog box. If the simulation is running, the current run will be paused until the dialog box is closed. More information on the Change Parameters dialog box can be found under “Setting Simulation Parameters.”
Auto-Slow-Mo
Clicking the Automatic Slow Motion button enables/disables this feature. When enabled, the simulation display rate is slowed while chromosomal motion is occurring. That is, while motion is occurring, the data, for each iteration, are displayed for the length of the “Display Hold Time” (settable via the Change Parameters dialog box). This feature allows the calculations to be observed and verified. If necessary, the Pause button can be used to extend the hold time of a particular program iteration (even indefinitely) to facilitate verification of the dynamics. When chromosomal motion is not occurring, execution proceeds at the normal rate (limited only by the host machine).
Pause
Clicking the Pause button enables/disables the Pause feature. Pause simply freezes the simulation run so that the current state may be analyzed. When released, the run resumes unaltered.
Exit
Clicking the Exit button closes the simulation and returns control to Windows.
Setting Simulation Parameters
The simulation parameters can be set via the Change Parameters dialog box, which is accessible via either the Change Parameters toolbar button or the Set Parameters selection in the Options menu. Changes to the simulation parameters are effective immediately upon closing the dialog box. If a simulation run is in progress, the run will resume with the new parameters in effect. However, the average values for the current run will not be reset; sometimes, the results can be undesirable. To start a new simulation run, click the stop button followed by the run button.
Number of Seconds to Simulate
This field sets the number of seconds to be simulated. If a simulation run is in progress, its termination time can be extended or truncated using this feature. If this parameter is set to a value less than the current number of seconds already simulated by a run in progress, the current run will be terminated upon closing the dialog box.
Average Disassembly Rate
This field sets the average number of dimers per microtubule disassembling per second. This parameter is used to synchronize the probability model to the simulation timeline.
Number of Electron Charges
This parameter specifies the number of electron charges associated with the terminal end of the dimer. This parameter is used in the force calculation.
Radius of Dimer Cap
This parameter specifies the radius of the dimer cap for use in the force calculation.
Static Time Interval
This field allows the static time interval to be set. The static time interval is the (simulated) time between iterations while no chromosomal motion is occurring. Under this condition, disassembly of dimers is the only activity.
Dynamic Time Interval
This field allows the dynamic time interval to be set. The dynamic time interval is the (simulated) time between program iterations while chromosomal motion is occurring. While chromosomal motion is occurring, force, velocity, and acceleration are being calculated. In addition, disassembly may also occur, which would affect these calculations.
Display Hold Time
This parameter sets the length of time to hold the display when Auto-Slow-Motion is enabled. When Auto-Slow-Motion is enabled, the simulation display rate is slowed while chromosomal motion is occurring. That is, while motion is occurring, the data, for each iteration, are displayed for the length of the “Display Hold Time”.
Probability Model
This section allows the probability model to be selected and adjusted. One of two probability models, Relative Weights and Negazone, may be selected. For each, the characteristics of the model may be adjusted at runtime.
The Relative Weights model (somewhat artificially) assigns weights to dimers based on their column position with respect to the kinetochore; column 5 is closest to the kinetochore, and column 1 is farthest. By giving dimers in column 5 a greater relative weight than those in column 1, the simulation can be made to disassemble more frequently near the terminal end. The program sums the relative weights for each dimer to obtain the total weight. Then, the interval between 0 and 1 is divided in ranges corresponding to each dimer. The width of each dimer’s range is equal to its relative weight divided by the total weight. To select a dimer for disassembly, the program selects a (pseudo) random number between 0 and 1, determines which dimer’s range it falls in, and removes that dimer.
The Negazone model assigns weights to dimers based on the proximity of the terminal dimers of its nearest neighbors. A dimer whose neighbors have terminal dimers aligned with its bond site is more likely to disassemble than one whose neighbors have terminal dimers far from its bond site. The reason for this increased likelihood is that the negative charge at the end of a dimer depresses the local pH, increasing disassembly probability of nearby dimers. Value 1 represents the contribution for a neighboring dimer closest to the bond site, and Value 5, the farthest. Each dimer’s weight is calculated by summing the contributions from its two neighbors. Additional contributions are added for those dimers that have neighbors in adjacent microtubules (unless “Ignore Neighboring Microtubules” is selected). Once the weight for each dimer has been determined, the dimer to be removed is selected in the same manner as for the Relative Weights model.
Relative Weights
This section allows the weights for each column to be adjusted.
Negazone
As discussed above, this section allows the contributions from nearest neighbors to be adjusted.