A stochastic two-dimensional model of intercellular Ca²⁺ wave spread in glia

We describe a two-dimensional stochastic model of intercellular Ca²⁺ wave (ICW) spread in glia that includes contributions of external stimuli, ionotropic and metabotropic P2 receptors, exo- and ecto-nucleotidases, second messengers, and gap junctions. In this model, an initial stimulus evokes ATP and UTP release from a single cell. Agonists diffuse and are degraded both in bulk solution and at cell surfaces. Ca²⁺ elevation in individual cells is determined by bound agonist concentrations s and by number and features of P2 receptors summed with that generated by IP₃ diffusing through gap junction channels. Variability of ICWs is provided by randomly distributing a predetermined density of cells in a rectangular grid and by randomly selecting within intervals values characterizing the extracellular compartment, individual cells, and interconnections with neighboring cells. Variability intervals were obtained from experiments on astrocytoma cells transfected to express individual P2 receptors and/or the gap junction protein connexin43. The simulation program (available as Supplementary Material) permits individual alteration of ICW components, allowing comparison of simulations with data from cells expressing connexin43 and/or various P2 receptor subtypes. Such modeling is expected to be useful for testing phenomenological hypotheses and in understanding consequences of alteration of system components under experimental or pathological conditions.