Calcium-electrical interactions: An example of reaction-diffusion in the neuron simulator

To aid the study of chemical and electrical interactions in neurons, we extended the NEURON simulator to support models written in the systems biology markup language (SBML), models with stochastic diffusion, and three-dimensional models. As a demonstration of our new tools, we present a study of the interaction of calcium waves and electrical signaling in models of pyramidal cells taken from ModelDB [2] using endoplasmic reticulum (ER) calcium dynamics based on [1]. In these waves, calcium and inositol triphosphate (IP3) activate IP3 receptors (IP3R) which release calcium into the cytosol from the ER stores. Prolonged elevated calcium concentration deactivates the IP3R, and the calcium is resequestered in the ER by the SERCA pumps. Consistent with experimental results [3], in our model these waves are associated with a depolarization of the membrane potential and changes in neuronal excitability caused by altered calcium-dependent ion channel conductances. Conversely, back-propagating action potentials admit calcium which primes the ER stores and reduces the amount of IP3 necessary to initiate a wave. We then considered our model's response to pathological dysregulation of ER calcium dynamics, which occurs in many diseases as reviewed in [4]. Increasing IP3R activity or decreasing SERCA activity leads to a faster, spatially larger, and higher amplitude calcium wave, which leads to a more excitable cell. With increased SERCA activity, higher levels of IP3 are required to initiate calcium waves. References: 1. Fall et al. Cortically restricted production of IP3 leads to propagation of the fertilization Ca2+ wave along the cell surface in a model of the Xenopus egg. J Theor Biol 231(4):487-96, 2004. 2. Hines et al. ModelDB: A Database to Support Computational Neuroscience. J Comput Neurosci 17(1):7-11, 2004. 3. Sidiropoulou et al. Dopamine modulates an mGluR5-mediated depolarization underlying prefrontal persistent activity. Nat Neurosci 12(2):190-9, 2009. 4. Stutzmann and Mattson. Endoplasmic reticulum Ca(2+) handling in excitable cells in health and disease. Pharmacol Rev 63(3):700-27, 2011.