Dendritic spine geometry and spine apparatus organization govern the spatiotemporal dynamics of calcium

Abstract

Dendritic spines are small subcompartments that protrude from the dendrites of neurons and are important for signaling activity and synaptic communication. These subcompartments have been characterized to have different shapes. While it is known that these shapes are associated with spine function, the specific nature of these shape-function relationships is not well understood. In this work, we systematically investigated the relationship between the shape and size of both the spine head and spine apparatus, a specialized endoplasmic reticulum compartment in the spine head, in modulating rapid calcium dynamics using mathematical modeling. We developed a spatial multi-compartment reaction-diffusion model of calcium dynamics in three dimensions with various flux sources including N-methyl-D-aspartate receptors (NMDAR), voltage sensitive calcium channels (VSCC), and different ion pumps on the plasma membrane. Using this model, we make several important predictions -first, the volume-to-surface area ratio of the spine regulates calcium dynamics, second, membrane fluxes impact calcium dynamics temporally and spatially in a nonlinear fashion, and finally the spine apparatus can act as a physical buffer for calcium by acting as a sink and rescaling the calcium concentration. These predictions set the stage for future experimental investigations of calcium dynamics in dendritic spines.Dendritic spine activity has numerous timescales with signaling pathways operating on the millisecond to the hour timescale following spine activation [1,10, 11]. Calcium dynamics are on the millisecond timescale, since calcium is the second messenger that floods the spine following the release of neurotransmitter from the presynaptic terminal. The temporal dynamics of calcium have provided valuable insight into the signaling dynamics in dendritic spines and it is quite clear that calcium dynamics are influenced by a large number of factors. Multiple studies have connected the electrical activity of the plasma membrane voltage to calcium dynamics of N-methyl-D-aspartate receptors (NMDAR) [12][13][14]. The electrophysiology of dendritic spines influences many signaling dynamics through voltage-sensitive (or voltage-dependent) ion channels [15] and thus models of these dynamics can be linked to downstream signaling.Calcium is critical for almost all the reactions in the brain [8] and is believed to accomplish a vast variety of functions through localization [16][17][18]. One possible way to achieve localization is by restricting the distance between the calcium source (often a channel) and the sink (calcium sensors and buffers). Thus, the localization of calcium can result from the location and mobility of different buffers and sensors [19]. Spatial models of calcium dynamics in dendritic spines that consider such effects have been proposed previously [6, 20, 21]. Spatial-temporal models of calcium dynamics have highlighted the role of calcium-induced cytosolic flow and calcium influx regulation by Ca 2+ -activated K + channels (SK channel...

GAMer 2: A System for 3D Mesh Processing of Cellular Electron Micrographs

“…For example, fluorescence experiments have shown that the dendritic spine necks act as a diffusion barrier to calcium ions, preventing ions from entering the dendritic shaft [59]. Complementary to this and other experiments, various physical models solving reaction-diffusion equations in idealized geometries have been developed to further interrogate the structure-function relationships [41,53,[64][65][66][67].…”

“…10, see also Movie S1 available online. Because the goal of this simulation was not to show biological accuracy, but rather to demonstrate that our pipeline is capable of producing biophysically relevant FEA simulations, we use a simplified version of the model found in Bell et al [53].…”

Geometric control of frequency modulation of cAMP oscillations due to Ca2+-bursts in dendritic spines

“…In addition to studying the spatiotemporal dynamics of cAMP in spines of different geometries, we also compare the peak time for each period, the peak concentration, and the Area Under the Curve (AUC) for each period. These metrics allow us to compare the oscillatory behaviors of cAMP in dendritic spines [35,36].…”

Geometric principles of second messenger dynamics in dendritic spines

“…Therefore, we chose a constant value of τ = 50 ms. Specialization of this model to Ca 2+ and cAM P can be found in Bell et al [50] and Ohadi et al [51,52], respectively.…”