A Graphical Approach for Hybrid Simulation of 3D Diffusion Bio-Models via Coloured Hybrid Petri Nets

Table 2

Comparing model results with results from the literature.

Known behaviour (literature)	model Behaviour
In [40], channel opening and closing are based on the activity of subunits where the number of active subunits needs to be at least three for a channel to be opened.	Figure 4(a) shows the number of active subunits and Figure 4(b) the corresponding open channels, when the number of active subunits is more than three.
In [20], the channel opening and closing occur in a few seconds (e.g., a channel opens approximately every 0.02 s)	Figure 4(d) captures a small interval from the simulation time to show the period of channel opening and closing which occurs approximately every 0.02 s.
Opening a channel affects the calcium concentration in cytosol. It increases the value of calcium in cytosol [20].	Figure 5 illustrates the calcium concentration in cytosol at different points of simulation time (e.g., at opening and closing the channel) which shows that the value of calcium concentration increases with channel opening.
The results of the model in [20] showed that the opening and closing of the channels occur burst-like and in a stochastic way.	Figure 6(a) depicts the number of open channels inside a cluster which exhibits a similar burst and happens in a stochastic way.
In [20] it has been shown that the releasing of calcium affects the number of open channels. Thus, opening different numbers of channels leads to a variation in the calcium concentrations in the cytosol.	Figures 6(b)–6(f) describe the dynamics of calcium in cytosol inside a cube, where the calcium diffuses to the adjacent grid points, which increases the chance of channel opening at these points.
The results in [22] describe the dynamics of calcium as a wave form.	The wave-like shape can be clearly seen in Figure 6.
The behaviour observation described in [20] is very similar to the openings of the synchronized channels in many oscillating clusters, and the calcium concentration is abundant only in a small range during release due to channel opening.	Figure 7 presents the results of the experiment with multiclusters inside the cube which shows opening more than one cluster at the same time where the value of calcium is high at the center of the cluster (narrow range), while low calcium concentrations lead to the opening of other clusters.