Fig. 2

A simple example representing the operation of \({\mathcal {HPN^{C}}}\): (a) the \({\mathcal {HPN^{C}}}\) representation of spatial calcium dynamics, (b) the corresponding colour definitions, (c) a time course representing the number of channels in the open state, and (d) a matrix plot representing the calcium diffusion. In this model, we use three channels arranged in one cluster. The colour set chCS provides the number of channels (in this case three). The variable m is used in combination with the transition ch_open to model the transition of a certain channel. The coloured place open provides the total number of channels in the open state, which is used as a rate for the continuous transition Ca_inflow. The calcium is represented by the coloured place Ca, which when unfolded gives a number of places equal to the colours in the colour set Grid2D (in this case Grid2D is a two dimensional coloured set, each dimension being 100). Calcium diffusion is modelled via the continuous transition diffuse. When the continuous transition Ca_inflow fires, it adds calcium to the position of the cluster in the grid (here in the middle of the grid (50,50)). The calcium outflow is modelled by the continuous transition called Ca_pump