Fast Synchronization of Ultradian Oscillators Controlled by Delta-Notch Signaling with Cis-Inhibition

While it is known that a large fraction of vertebrate genes are under the control of a gene regulatory network (GRN) forming a clock with circadian periodicity, shorter period oscillatory genes like the Hairy-enhancer-of split (Hes) genes are discussed mostly in connection with the embryonic process of somitogenesis. They form the core of the somitogenesis-clock, which orchestrates the periodic separation of somites from the presomitic mesoderm (PSM). The formation of sharp boundaries between the blocks of many cells works only when the oscillators in the cells forming the boundary are synchronized. It has been shown experimentally that Delta-Notch (D/N) signaling is responsible for this synchronization. This process has to happen rather fast as a cell experiences at most five oscillations from its ‘birth’ to its incorporation into a somite. Computer simulations describing synchronized oscillators with classical modes of D/N-interaction have difficulties to achieve synchronization in an appropriate time. One approach to solving this problem of modeling fast synchronization in the PSM was the consideration of cell movements. Here we show that fast synchronization of Hes-type oscillators can be achieved without cell movements by including D/N cis-inhibition, wherein the mutual interaction of DELTA and NOTCH in the same cell leads to a titration of ligand against receptor so that only one sort of molecule prevails. Consequently, the symmetry between sender and receiver is partially broken and one cell becomes preferentially sender or receiver at a given moment, which leads to faster entrainment of oscillators. Although not yet confirmed by experiment, the proposed mechanism of enhanced synchronization of mesenchymal cells in the PSM would be a new distinct developmental mechanism employing D/N cis-inhibition. Consequently, the way in which Delta-Notch signaling was modeled so far should be carefully reconsidered.


Simulation Program Mini-Manual System Requirements
We implemented our simulation program as a Java application on a dual core processor machine using jdk1.6 and Java3D version 1.5.2. To run it we use an amount of 1500MB of the memory allocation pool (java virtual machine options: -Xms1500m -Xmx1500m).

Installation and Starting the Application
To run the application you need to install the packed file SIM13.zip, which can be downloaded from http://www.helmholtzmuenchen.de/fileadmin/IEG/ZIP/downloads/simulation13/SIM13.zip.
After unpacking the file you get a directory (SIM/) with the following configuration: • Subdirectory ICONS/ contains figures used to design the graphical user interface of the simulation program.
• Subdirectory j3d_lib/ contains the java3d (resp. java bindings to OpenGL) jar files needed to make the application run under Mac OS X 10.8+ (see SIM/README for more details).
• Subdirectory sim_lib/ contains all supplementary jar files used by the application.  • Executable file sim.jar contains the simulation program.
• Executable batch file startSIM.bat starts the application on Windows.
• Executable shell script startSim_linux.sh starts the application on Linux.
• Executable shell script startSim_macosx.sh starts the application on Mac OS X.
Please read the file SIM/README for more details.

Starting the Simulation
The application provides a graphical user interface (GUI), on which the parameter values needed to start the simulation can be changed. The buttons to start and stop the simulation are on the bar at the bottom of the GUI: • By clicking on 'start' the simulation starts with the configuration status described on the parameter panel (see chapter Using the Graphical User Interface).
• Button 'cancel' terminates the Java application.
• It is possible to return from the simulation panel to the parameter panel by clicking 'return'.

Using the Graphical User Interface (GUI)
The picture below shows the part of the GUI containing information about the genes building the gene regulatory network (GRN) and its interactions.
• To change the oscillation period all parameters can be scaled by the 'scaling factor'-value, which is equivalent to scaling by time. To do so proceed as Reset to the default value saved in configfile.

follows:
1. Change the value and press ENTER to continue.

A pop-up window informs you what effect the value change has. Click
OK to continue or just close the window to cancel the action.
• The 'initial noise percent' is a simple measure for the initial noise, i.e. by selecting the 'initial noise'-option we add to the initial concentration value the entered percentage of the initial value multiplied by a random value between zero and one.
• By clicking 'save all model parameters' an update of the configuration file sim_model/<model_description>/configfile occurs. All modifications made on Start with initial noise means: <initial value> = <initial value> * (1 + <random value> * <initial noise percent>) the GUI can be thus used by another program run. The old configuration file will be moved to OLD/configfile.OLD<index>.
• All network genes are described on panels sharing the same space. Selecting the corresponding tab can access the parameters of one gene. The color of the selected tab indicates for which gene the concentration values of mRNA or protein are visualized during the simulation run or whether gradient genes are coupled or not.
Cyan color tags the gene which gene product is shown during the simulation.
A dark gray colored tab indicates that gradient genes are coupled.
Clicking on the corresponding check box can change the status of each gene.
The simulation shows the mRNA of Notch1.

Dark/light color means high/low concentration.
A scaling value is needed since the Java color components should be in the range of [0.0, 1.0].
The Fgf8 protein is coupled on the decay rate of the Hes7 mRNA in cytoplasm 1. We simulate a gene knock out by setting the mRNA transcription rate to 0.

2.
Gene excluded from network means that no computation would be done for its products. In case of Delta-Notch genes the elimination of Dll1 (Notch1) from the GRN implies also the elimination of Notch1 (Dll1) and

NICD.
3. In case of Fgf8 a partial inhibition is also supplied, which means that the protein production rate can be reduced by a defined amount at a defined time step during the simulation.
Gene panels contain also information about gene promoter.
If no selection is made the gene status doesn't change by clicking the OK button.
Change the promoter term by changing the value of n, since its generic form is: h7term*[(1-n)*nicdterm+n*f8term] Select the 'mitosis' check box to simulate mitosis, which is done by setting the transcription rate to 0 for the selected genes. During the simulation the cells undergoing mitosis are colored orange.
The lower part of the GUI is reserved for general settings like the layout of the proliferating cells and the way they proliferate.
Click on button to show promoter parameters.
Switch promoter on or off.

Number of intermediate states during cell division
Defines the position of the initial configuration of cells.
Defines the direction in which the emerging cells grow.

Number of rows
The growth zone describes the region where a new cell randomly arises in each column.
The direct neighbors (cyan) of a cell (red); the maximum number of 6 neighbors is reached in case of 3dimensional structures.
The 'plot data for cells' field gives users the option to output the oscillators numerical data, which means that after each step of the Runge-Kutta method used to solve the system of differential equations modeling the GRN, the data will be written to a file, which can be read by an appropriate program (like gnuplot) to visualize the time course of the concentrations. Clears the list of cells selected to plot their numerical data.
The numerical data of this cell would be saved to the file named CELL<index_of_cell>/cell<index_of_cell>, at which the cell index corresponds to the random order of cells appearance. To select a cell for plotting its numerical data enter the cell index and enter return (important). options are selected.
As we use a simple 4 th order Runge-Kutta Algorithm and most decay terms are linear (i.e. not saturated, we would otherwise introduce even more unknown constants) negative concentrations can be induced by choosing parameters or noise, which stray too wide from the standard values.
If negative values occur during the simulation a pop-up warning window informs the user about which cells (together with their neighbors) are involved, giving him the opportunity to return and choose another parameter values or cancel the application.