Calcium 'impedance mismatch' – the role of geometry on diffusion dynamics

Calcium (Ca) is a major intracellular second messenger. As such, it is heavily regulated within a neuron and is thought of as forming a partnership with membrane voltage in providing the major state variables across the dendritic tree of a pyramidal cell. In many pyramidal cells, regenerative calcium waves propagate through a portion of the morphology in response to a multitude of factors, including inputs to metabotropic glutamate receptors providing IP3 that releases Ca from intracellular stores, and contributions from plasma membrane Ca fluxes from both NMDA receptors and voltage-sensitive calcium channels. We have begun to explore these complex interactions using a new version of the NEURON simulator, a widely used tool for the computational study of neuronal electrophysiology, now being extended to provide a specialized reaction-diffusion syntax. In NEURON version 7.3, diffusion was restricted to one-dimension. It has now been extended to also support 3D simulation in the developmental version available online. Prior experimental observations demonstrated that Ca waves often approach the soma but rarely enter it, even though the soma can sustain wave propagation. We investigated the specific role of geometry in wave blocking by varying apical dendrite broadening as well as the specifics of the shape of the dendrite-soma connection in a deterministic simulation of diffusion augmented by calcium-induced calcium release. Abrupt expansions in geometry slowed or blocked wave propagation in a parameter-dependent fashion in a manner reminiscent of the membrane depolarization failures seen due to electrical impedance mismatch, which occurs where small low-current-sourcing dendrites attempt to drive the much larger somatic membrane. We therefore characterize this is a [Ca]-impedance mismatch and compare and contrast with the voltage impedance mismatch at transition points, using identical geometry.