scholarly journals Stochastic simulations reveal that dendritic spine morphology regulates synaptic plasticity in a deterministic manner

2021 ◽  
Author(s):  
Mason V. Holst ◽  
Miriam K. Bell ◽  
Christopher T Lee ◽  
Padmini Rangamani
Keyword(s):  
Dendritic Spines ◽  
Weight Change ◽  
Synaptic Weight ◽  
Calcium Influx ◽  
Reaction Diffusion ◽  
Stochastic Simulations ◽  
Calcium Dynamics ◽  
Spine Morphology ◽  
Reaction Diffusion Model ◽  
Realistic Geometries

Dendritic spines act as computational units and must adapt their responses according to their activation history. Calcium influx acts as the first signaling step during postsynaptic activation and is a determinant of synaptic weight change. Dendritic spines also come in a variety of sizes and shapes. To probe the relationship between calcium dynamics and spine morphology, we used a stochastic reaction-diffusion model of calcium dynamics in idealized and realistic geometries. We show that despite the stochastic nature of the various calcium channels, receptors, and pumps, spine size and shape can separately modulate calcium dynamics and subsequently synaptic weight updates in a deterministic manner. The relationships between calcium dynamics and spine morphology identified in idealized geometries also hold in realistic geometries suggesting that there are geometrically determined deterministic relationships that may modulate synaptic weight change.

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 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.

scholarly journals Nanoscale organization and calcium influx in dendritic spines guarantee ER store refilling without depletion

2021 ◽  
Author(s):  
Kanishka Basnayake ◽  
David Mazaud ◽  
Lilia Kushnireva ◽  
Alexis Bemelmans ◽  
nathalie Rouach ◽  
...  
Keyword(s):  
Dendritic Spines ◽  
Plasma Membranes ◽  
Calcium Release ◽  
Calcium Influx ◽  
Smooth Endoplasmic Reticulum ◽  
Super Resolution ◽  
Calcium Stores ◽  
Calcium Dynamics ◽  
Store Operated Calcium Entry ◽  
Critical Components

Dendritic spines are critical components of the neuronal synapse as they receive and transform the synaptic input into a succession of biochemical events regulated by calcium signaling. The spine apparatus (SA), an extension of smooth endoplasmic reticulum (ER), regulates slow and fast calcium dynamics in spines. Calcium release events from SA result in a rapid depletion of calcium ion reservoir, yet the next cycle of signaling requires replenishment of SA calcium stores. How dendritic spines achieve this without triggering calcium release remains unclear. Using computational modeling, calcium and STED super-resolution imaging, we showed that the refilling of calcium-deprived SA involves store-operated calcium entry during spontaneous calcium transients in spine heads. We identified two main conditions that guarantee SA replenishment without depletion: (1) a small amplitude and slow timescale for calcium influx, and (2) a close proximity between SA and plasma membranes. Thereby, molecular nano-organization creates the conditions for a clear separation between SA replenishment and depletion. We further conclude that the nanoscale organization of SA receptors underlies the specificity of calcium dynamics patterns during the induction of long-term synaptic changes.

scholarly journals How obstacles perturb population fronts and alter their genetic structure

2015 ◽  
Author(s):  
Wolfram Moebius ◽  
Andrew W. Murray ◽  
David R. Nelson
Keyword(s):  
Genetic Drift ◽  
Population Expansion ◽  
Reaction Diffusion ◽  
Constant Speed ◽  
Stochastic Simulations ◽  
Complex Environments ◽  
Front Width ◽  
Reaction Diffusion Model ◽  
Study Population ◽  
Experimental Findings

As populations spread into new territory, environmental heterogeneities can shape the population front and genetic composition. We study here the effect of one important building block of inhomogeneous environments, compact obstacles. With a combination of experiments, theory, and simulation, we show how isolated obstacles both create long-lived distortions of the front shape and amplify the effect of genetic drift. A system of bacteriophage T7 spreading on a spatially heterogeneous Escherichia coli lawn serves as an experimental model system to study population expansions. Using an inkjet printer, we create well-defined replicates of the lawn and quantitatively study the population expansion manifested in plaque growth. The transient perturbations of the plaque boundary found in the experiments are well described by a model in which the front moves with constant speed. Independent of the precise details of the expansion, we show that obstacles create a kink in the front that persists over large distances and is insensitive to the details of the obstacle's shape. The small deviations between experimental findings and the predictions of the constant speed model can be understood with a more general reaction-diffusion model, which reduces to the constant speed model when the obstacle size is large compared to the front width. Using this framework, we demonstrate that frontier alleles that just graze the side of an isolated obstacle increase in abundance, a phenomenon we call 'geometry-enhanced genetic drift', complementary to the founder effect associated with spatial bottlenecks. Bacterial range expansions around nutrient-poor barriers and stochastic simulations confirm this prediction, the latter highlight as well the effect of the obstacle on the genealogy of individuals at the front. We argue that related ideas and experimental techniques are applicable to a wide variety of more complex environments, leading to a better understanding of how environmental heterogeneities affect population range expansions.

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 Emergent three-dimensional sperm motility: coupling calcium dynamics and preferred curvature in a Kirchhoff rod model

2018 ◽  
Vol 36 (4) ◽  
pp. 439-469 ◽  
Author(s):  
Lucia Carichino ◽  
Sarah D Olson
Keyword(s):  
Sperm Motility ◽  
Calcium Concentration ◽  
Three Dimensional ◽  
Interaction Model ◽  
Reaction Diffusion ◽  
Calcium Dynamics ◽  
Elastic Rod ◽  
Sperm Flagellum ◽  
Kirchhoff Rod ◽  
Reaction Diffusion Model

AbstractChanges in calcium concentration along the sperm flagellum regulate sperm motility and hyperactivation, characterized by an increased flagellar bend amplitude and beat asymmetry, enabling the sperm to reach and penetrate the ovum (egg). The signalling pathways by which calcium increases within the flagellum are well established. However, the exact mechanisms of how calcium regulates flagellar bending are still under investigation. We extend our previous model of planar flagellar bending by developing a fluid-structure interaction model that couples the 3D motion of the flagellum in a viscous Newtonian fluid with the evolving calcium concentration. The flagellum is modelled as a Kirchhoff rod: an elastic rod with preferred curvature and twist. The calcium dynamics are represented as a 1D reaction–diffusion model on a moving domain, the flagellum. The two models are coupled assuming that the preferred curvature and twist of the sperm flagellum depend on the local calcium concentration. To investigate the effect of calcium on sperm motility, we compare model results of flagellar bend amplitude and swimming speed for three cases: planar, helical (spiral with equal amplitude in both directions), and quasi-planar (spiral with small amplitude in one direction). We observe that for the same parameters, the planar swimmer is faster and a turning motion is more clearly observed when calcium coupling is accounted for in the model. In the case of flagellar bending coupled to the calcium concentration, we observe emergent trajectories that can be characterized as a hypotrochoid for both quasi-planar and helical bending.

scholarly journals Stochastic Reaction-Diffusion Modeling of Calcium Dynamics in 3D-Dendritic Spines of Purkinje Cells

2021 ◽  
Vol 120 (3) ◽  
pp. 282a
Author(s):  
Victor Nicolai Friedhoff ◽  
Gabriela Antunes ◽  
Martin Falcke ◽  
Fábio Marques Simões de Souza
Keyword(s):  
Purkinje Cells ◽  
Dendritic Spines ◽  
Reaction Diffusion ◽  
Calcium Dynamics ◽  
Diffusion Modeling ◽  
Stochastic Reaction
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