Hybrid 1d/3d reaction-diffusion in the neuron simulator

Neuroscience simulators provide a framework for combining experimental observations to make predictions about neurons and networks of neurons that are impossible or impractical to measure directly with current technology. Each simulator necessarily has a domain of applicability. The NEURON simulator, used in over 1500 publications, has traditionally focused on problems dominated by electrophysiology, but we recently introduced a reaction-diffusion module to facilitate the specification of problems of that type. Stochastic 3D simulations are essential for studying highly localized phenomena (e.g. calcium microdomains), but this approach becomes computationally infeasible as the problem size increases, as is necessary for calcium waves which can spread over a large portion of a pyramidal cell's apical dendrite. Using a cartesian mesh and a deterministic solver provides well-understood accuracy and stability, but requires tiny voxels to represent the shape of the dendrites which in turn force small time steps to ensure stability. Tetrahedral meshes can represent the morphology more accurately with less compartments, but these present their own difficulties. To avoid these problems, we are introducing support for hybrid 1D-3D studies in NEURON. Each section of the morphology may be either simulated in 1D or 3D. Fluxes across a 1D-3D border are based on the concentrations in the end-segment of the 1D domain and on the edge disc of voxels in the 3D domain. We use a model of a propagating calcium wave to illustrate our approach. In the 1D version of our model, the gradient at the edge of the wave is sufficiently gradual that we did not expect significant variation across a dendrite. We verified this expectation with a 3D simulation stimulated by IP3 released at a single point. We then simulated calcium waves on traced pyramidal cells, with most of the dendrites in 1D and the soma and the proximal dendrites in 3D. By simulating the soma in 3D, we observed the wave slow and curve as it entered the soma. The speed of the wave as it enters the soma is a function of the amount of calcium sequestered in the ER, which is itself a function of previous electrical activity. The hybrid 1D/3D simulator provides a convenient and efficient tool for reaction-diffusion simulations that span multiple spatial scales.