Introduction Models >>Simulator<< Results References

The Simulator

The simulator is available as a Java applet. It incorporates both the first and second models, although it does not model the second model with uniformly increasing excitability. Only one set of parameters is used for both models - by setting the parameters of the second model appropriately, the first model can be simulated. The parameters are as follows:

grid size 100 100
cell density 0.2 0.18
degradation rate 0.5 0.5
diffusion rate 5 5
cAMP threshold min 10 4
cAMP threshold max 10 100
cAMP release time 2 1
cAMP released 1500 300
abs refractory time 20 8
rel refractory time 0 2
initial excitability 0 0
excitability incr 0 0.005
excitability decr 00.0005
random firers 1 -10

The values used are those specified in the papers, except in these cases:

Both models apparently ignore boundary conditions, and so does my simulator. cAMP simply diffuses off the edges of the grid. Both models also ignore chemotaxis until after the spiral wave pattern has formed, so my simulator ignores it as well.

I discretize my diffusion using the following update rule for each box b(i,j,t) of the grid at location (i,j) and time t:

b(i,j,t+1) = 0.5*b(i,j,t) + 0.125(b(i-1,j,t)+b(i+1,j,t)+b(i,j-1,t)+b(i,j+1,t))
I obtained this equation from lecture notes on discretizing the heat equation, which is very similar to the diffusion equation. The diffusion rate parameter is the number of diffusion time steps performed for each bion time step.


The simulator uses different colors to indicate a bion's state. Red through brown through yellow indicate different levels of excitability in the bion's excitable state. Red means the threshold is at its minimum value, brown an intermediate value, and yellow the maximum value. A bion is green while it is releasing cAMP. Blue means the bion is refractory. Relatively refractory is indicated with the appropriate color for the excitability of the bion. Note that the color schemes and merged-model parameter values end up making the first model's constant-threshold bions yellow but the second model's constant-threshold bions red.

The level of cAMP in a grid location is shown using a log scale of whiteness. The more cAMP, the more white the location is. As the cAMP diffuses and is degraded the location turns gray and finally black if no more cAMP is released in or near it.


The various parameters can be changed by typing in new values, or by using the "Inc/Dec" buttons. Left-clicking increases the parameter's value, and right-clicking lowers it. The "Update Parameters" button must be pressed to submit parameter value changes to the simulator.

The simulation can be controlled in VCR-style using the "Go", "Pause", "Step", and "Restart" buttons. The "Redraw" button is only provided to force repainting in case of Java refresh bugs.

The simulator displays messages on the Java console indicating errors (such as an invalid parameter value) and the time step of the simulation. A star is printed each time a cell randomly fires.

The parameters for the first model, the second model with constant excitability, and the second model with variable excitability are all pre-loadable using the buttons at the bottom of the control panel.

The repaint frequency parameter can be used to speed up long simulations by not redrawing the grid after every time step.

Introduction Models >>Simulator<< Results References