Biophysical Phantom Model

This is a phantom bursting model, (see Bertram et al, Biophys. J. 79:2880-2892, 2000 ) for pancreatic beta-cells in which the role of s_1 is played by cytosolic calcium (c) and the role of s_2 is played by ER calcium (cer) and the ADP/ATP ratio (a).

Reference: Bertram and Sherman, Bull. Math. Biol., 66:1313-1344 2004.

XPP files by figure:

• Basic Model (Figure 1; like Chay-Keizer negative feedback through cytosolic calcium only)
• Basic Model with Slow Calcium (Figure 3; Chay-Keizer with slow cytosolic calcium)
• ER Model - Fast Mode (Figure 6; model with cytosolic and ER calcium)
• ER Model - Medium Mode (Figure 8; model with cytosolic and ER calcium)
• ER Model - Addition of ACh (Figure 9; Store dumped but no ROC or SOC)
• ER Model - Muscarinic Bursting (Figure 11; Store dumped and ROC activated)
• ER/ATP Model - Slow Mode (Figure 13; c, cer, and a included)
• ER/ATP Model - Addition of Tg (Figure 14; medium bursting converted to fast by SERCA blockade)
• ER/ATP Model - Addition of Tg (Figure 15; slow bursting persists in face of SERCA blockade)
• ER/ATP Model - Triphasic Response to Glucose (Figure 16)
• ER/ATP Model - Addition of Tg and Tolbutamide (Figure 17; slow bursting persists in presence of both thapsigargin and tolbutamide)

Master file

• Combined Model (Choose File/Get set to get all three models and fast/medium/slow bursting)

Making Your Own Animations

The best way to see the animations is with XPP and its animator.

Download:

1. XPP file

   and

2. Animation script file

With these files you can view the moving slow manifold and nullcline in the V-w (omega) plane. The file is set to produce slow bursting with the ER/ATP model. To see animation choose View/Toons and read in the animation file from the animator File menu. File/Get set can be used to visualize other burst modes. You will need to adjust the parameters ttotal, wmin, and wmax to get the right scaling.

Saved Animations (Animated GIF files)

Warning: Some of these files are large, so make sure you have enough free memory (256 - 512 MB recommended). I recommend downloading the image file to your machine and playing there (eg., in Netscape right-click)

What you will see: Each animation has the time course in purple in the upper half and the v-w phaseplane in the lower half. The slow manifold (where v and n are at steady state) is in black and the w nullcline is in blue. The trajectory is red.