Computational Properties of Extracellular Calcium Dynamics

One fifth of the mammalian brain is comprised of extracellular space (ECS). The extracellular space is not empty, but instead comprises a complex network of proteins and a variety of molecular species. One extracellular species, calcium, holds a prominent position as one of the most important messengers known in the brain. However, calcium exists in low concentrations in the ECS, and its diffusion is slowed by the restricted volumes of the extracellular space – therefore, normal neural activity may cause calcium to flow out of the ECS faster than diffusion can fill it in. As opposed to the traditional view that extracellular calcium exists at a stable concentration, I explore the hypothesis that calcium concentrations may change. Such changes would be expected to carry significant functional impact, due to the many roles calcium plays. The hypothesis is explored both at the biophysical and theoretical levels. At the biophysical level, I explore the dynamics of external calcium changes under a wide range of reasonable parameter settings. At the theoretical level, I attempt to interpret how such fluctuations may serve as information-bearing signals in the nervous system. Specifically, I have employed Monte Carlo simulations, finite differencing schemes, and numerical analyses to develop a computational method capable of describing populations of neural elements, and the fluids that communicate through the spaces between them. Such a method has allowed me to address several issues, the broadest interpretations of which can be cast as a set of questions: • Is neural tissue engineered to allow – or prevent – fluctuations in extracellular ionic concentrations? • If fluctuations can occur, do they carry information? • What are the computations carried out by that flow of information? 3 Beginning with a model of pre-synaptic terminals, I show that reasonable assumptions about the kinetics of consumption and diffusion will lead to rapid, local changes in external calcium. The exact size of the calcium signal depends on several parameters. For example, the cleft width might be used by the tissue as a control parameter: changing the gap between elements can amplify or squelch the calcium signal. The distribution of calcium channels will also critically influence the calcium fluctuations: by clustering the channels, the local signal amplitude is greatly increased. In some circumstances, the density of the calcium channels can become high enough that the total calcium influx becomes limited by the speed of extracellular diffusion. I calculate that the …