Coupled systems: neural-glial networks and layered reaction-diffusion systems

Most of us are familiar with the fact that our brain contains a network of neurons. Perhaps less well known are the cells in the brain known as glial cells or, more specifically, astrocytes.  Neurons and astrocytes are chemically linked, resulting in a neural-glial network, just one biological example of a coupled system.  Though neuron-only networks have been well studied, less is known about neural-glial networks.  Another example of a coupled system is a pair of chemical reactions in thin gels that are linked by allowing diffusion between the gels.  Chemical reactions in a thin layer, known as reaction-diffusion systems, are a canonical example of a pattern forming system, but coupled reaction-diffusion systems have not been studied until quite recently, mostly via simulations.  We consider two approaches to better understand neural-glial networks and coupled reaction-diffusion systems with an eye to understanding coupled systems in general.  With these approaches, we show that the presence of coupling allows stabilization of firing patterns in the neural network and of spatial patterns in the reaction-diffusion system.