Geometric principles of second messenger dynamics in dendritic spines

Abstract

Dendritic spines are small, bulbous protrusions along dendrites in neurons and play a critical role in synaptic transmission. Dendritic spines come in a variety of shapes that depend on their developmental state. Additionally, roughly 14–19% of mature spines have a specialized endoplasmic reticulum called the spine apparatus. How does the shape of a postsynaptic spine and its internal organization affect the spatio-temporal dynamics of short timescale signaling? Answers to this question are central to our understanding the initiation of synaptic transmission, learning, and memory formation. In this work, we investigated the effect of spine and spine apparatus size and shape on the spatio-temporal dynamics of second messengers using mathematical modeling using reaction-diffusion equations in idealized geometries (ellipsoids, spheres, and mushroom-shaped). Our analyses and simulations showed that in the short timescale, spine size and shape coupled with the spine apparatus geometries govern the spatiotemporal dynamics of second messengers. We show that the curvature of the geometries gives rise to pseudo-harmonic functions, which predict the locations of maximum and minimum concentrations along the spine head. Furthermore, we showed that the lifetime of the concentration gradient can be fine-tuned by localization of fluxes on the spine head and varying the relative curvatures and distances between the spine apparatus and the spine head. Thus, we have identified several key geometric determinants of how the spine head and spine apparatus may regulate the short timescale chemical dynamics of small molecules that control synaptic plasticity.

Bulk-surface coupling reconciles Min-protein pattern formationin vitroandin vivo

“…Intracellular pattern formation in general is based on cycling of proteins between cytosolic and membrane/cortex-bound states; see for example the Cdc42 system in budding yeast and fission yeast (33,58), the PAR system (46,59) in C. elegans, excitable RhoA pulses in C. elegans (60), Xenopus and starfish oocytes (61), and MARCKS dynamics in many cell types (62,63). Further examples include, intracellular signaling cascades (64)(65)(66)(67) and, potentially, intercellular signaling in tissues and biofilms. Our study shows that it is essential to explicitly take the bulk-surface coupling into account when one investigates such systems.…”

Mechanical principles governing the shapes of dendritic spines

“…Previously, we showed that the coupled dynamics of signaling and actin remodeling can alter spine volume in a biophysical model [67] without considering the geometry of the spines or considering the role of spine shape in regulating different signaling pathways [114][115][116][117][118]. In this work, we present a simplified mechanical model for studying the role of different force distributions and energy contributions that are associated with the different spine shapes noted in the literature.…”

3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

“…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 [112]. 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 [51,100,111,[117][118][119].…”