scholarly journals Geometric principles of second messenger dynamics in dendritic spines

2018 ◽  
Author(s):  
Andrea Cugno ◽  
Thomas M. Bartol ◽  
Terrence J. Sejnowski ◽  
Ravi Iyengar ◽  
Padmini Rangamani
Keyword(s):  
Synaptic Transmission ◽  
Dendritic Spines ◽  
Temporal Dynamics ◽  
Second Messengers ◽  
Developmental State ◽  
Size And Shape ◽  
Spine Head ◽  
Short Timescale ◽  
Spine Apparatus ◽  
Spatio Temporal

AbstractDendritic 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.

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

2019 ◽  
Vol 151 (8) ◽  
pp. 1017-1034 ◽  
Author(s):  
Miriam Bell ◽  
Tom Bartol ◽  
Terrence Sejnowski ◽  
Padmini Rangamani
Keyword(s):  
Dendritic Spines ◽  
Reaction Diffusion ◽  
Three Dimensions ◽  
Experimental Investigations ◽  
Calcium Dynamics ◽  
Surface Area Ratio ◽  
Spine Head ◽  
Reaction Diffusion Model ◽  
Spine Apparatus ◽  
Spine Function

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 within the spine head, in modulating rapid calcium dynamics using mathematical modeling. We developed a spatial multicompartment reaction–diffusion model of calcium dynamics in three dimensions with various flux sources, including N-methyl-D-aspartate receptors (NMDARs), voltage-sensitive calcium channels (VSCCs), 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. 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.

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

2019 ◽  
Author(s):  
D. Ohadi ◽  
P. Rangamani
Keyword(s):  
Dendritic Spines ◽  
Molecular Mechanisms ◽  
Neuronal Development ◽  
Temporal Dynamics ◽  
Second Messengers ◽  
Reaction Diffusion ◽  
Long Term Potentiation ◽  
Dynamic Interactions ◽  
Neck Size ◽  
Reaction Diffusion Model

ABSTRACTThe spatiotemporal regulation of cAMP and its dynamic interactions with other second messengers such as calcium are critical features of signaling specificity required for neuronal development and connectivity. cAMP is known to contribute to long-term potentiation and memory formation by controlling the formation and regulation of dendritic spines. Despite the recent advances in biosensing techniques for monitoring spatiotemporal cAMP dynamics, the underlying molecular mechanisms that attribute to the subcellular modulation of cAMP remain unknown. In the present work, we model the spatio-temporal dynamics of calcium-induced cAMP signaling pathway in dendritic spines. Using a 3D reaction-diffusion model, we investigate the effect of different spatial characteristics of cAMP dynamics that may be responsible for subcellular regulation of cAMP concentrations. Our model predicts that the volume-to-surface ratio of the spine, regulated through the spine head size, spine neck size, and the presence of physical barriers (spine apparatus) is an important regulator of cAMP dynamics. Furthermore, localization of the enzymes responsible for the synthesis and degradation of cAMP in different compartments also modulates the oscillatory patterns of cAMP through exponential relationships. Our findings shed light on the significance of complex geometric and localization relationships for cAMP dynamics in dendritic spines.

scholarly journals Mathematical Model of the Spatio-Temporal Dynamics of Second Messengers in Visual Transduction

2003 ◽  
Vol 85 (3) ◽  
pp. 1358-1376 ◽  
Author(s):  
D. Andreucci ◽  
P. Bisegna ◽  
G. Caruso ◽  
H.E. Hamm ◽  
E. DiBenedetto
Keyword(s):  
Mathematical Model ◽  
Temporal Dynamics ◽  
Second Messengers ◽  
Visual Transduction ◽  
Spatio Temporal

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

2018 ◽  
Author(s):  
Miriam Bell ◽  
Tom Bartol ◽  
Terrence Sejnowski ◽  
Padmini Rangamani
Keyword(s):  
Dendritic Spines ◽  
Reaction Diffusion ◽  
Three Dimensions ◽  
Experimental Investigations ◽  
Calcium Dynamics ◽  
Surface Area Ratio ◽  
Spine Head ◽  
Reaction Diffusion Model ◽  
Spine Apparatus ◽  
Spine Function

AbstractDendritic 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.

Spatial and temporal dynamics of Pacific capelin Mallotus catervarius in the Gulf of Alaska: implications for ecosystem-based fisheries management

2020 ◽  
Vol 637 ◽  
pp. 117-140 ◽  
Author(s):  
DW McGowan ◽  
ED Goldstein ◽  
ML Arimitsu ◽  
AL Deary ◽  
O Ormseth ◽  
...  
Keyword(s):  
Temporal Dynamics ◽  
Marine Ecosystem ◽  
Gulf Of Alaska ◽  
Data Series ◽  
Limited Information ◽  
Important Species ◽  
Multiple Data ◽  
Spatial And Temporal Dynamics ◽  
Spawning Areas ◽  
Spatio Temporal

Pacific capelin Mallotus catervarius are planktivorous small pelagic fish that serve an intermediate trophic role in marine food webs. Due to the lack of a directed fishery or monitoring of capelin in the Northeast Pacific, limited information is available on their distribution and abundance, and how spatio-temporal fluctuations in capelin density affect their availability as prey. To provide information on life history, spatial patterns, and population dynamics of capelin in the Gulf of Alaska (GOA), we modeled distributions of spawning habitat and larval dispersal, and synthesized spatially indexed data from multiple independent sources from 1996 to 2016. Potential capelin spawning areas were broadly distributed across the GOA. Models of larval drift show the GOA’s advective circulation patterns disperse capelin larvae over the continental shelf and upper slope, indicating potential connections between spawning areas and observed offshore distributions that are influenced by the location and timing of spawning. Spatial overlap in composite distributions of larval and age-1+ fish was used to identify core areas where capelin consistently occur and concentrate. Capelin primarily occupy shelf waters near the Kodiak Archipelago, and are patchily distributed across the GOA shelf and inshore waters. Interannual variations in abundance along with spatio-temporal differences in density indicate that the availability of capelin to predators and monitoring surveys is highly variable in the GOA. We demonstrate that the limitations of individual data series can be compensated for by integrating multiple data sources to monitor fluctuations in distributions and abundance trends of an ecologically important species across a large marine ecosystem.

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