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 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 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 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.

Geometry of Dendritic Spines Affects Calcium Dynamics in Hippocampal Neurons: Theory and Experiments

1999 ◽  
Vol 82 (1) ◽  
pp. 450-462 ◽  
Author(s):  
N. Volfovsky ◽  
H. Parnas ◽  
M. Segal ◽  
E. Korkotian
Keyword(s):  
Dendritic Spines ◽  
Dendritic Spine ◽  
Hippocampal Neurons ◽  
Laser Scanning ◽  
Nonlinear Differential Equations ◽  
Confocal Laser ◽  
Calcium Dynamics ◽  
Spine Head ◽  
The Impact ◽  
Cultured Hippocampal Neurons

The role of dendritic spine morphology in the regulation of the spatiotemporal distribution of free intracellular calcium concentration ([Ca2+]i) was examined in a unique axial-symmetrical model that focuses on spine–dendrite interactions, and the simulations of the model were compared with the behavior of real dendritic spines in cultured hippocampal neurons. A set of nonlinear differential equations describes the behavior of a spherical dendritic spine head, linked to a dendrite via a cylindrical spine neck. Mechanisms for handling of calcium (including internal stores, buffers, and efflux pathways) are placed in both the dendrites and spines. In response to a calcium surge, the magnitude and time course of the response in both the spine and the parent dendrite vary as a function of the length of the spine neck such that a short neck increases the magnitude of the response in the dendrite and speeds up the recovery in the spine head. The generality of the model, originally constructed for a case of release of calcium from stores, was tested in simulations of fast calcium influx through membrane channels and verified the impact of spine neck on calcium dynamics. Spatiotemporal distributions of [Ca2+]i, measured in individual dendritic spines of cultured hippocampal neurons injected with Calcium Green-1, were monitored with a confocal laser scanning microscope. Line scans of spines and dendrites at a <1-ms time resolution reveal simultaneous transient rises in [Ca2+]i in spines and their parent dendrites after application of caffeine or during spontaneous calcium transients associated with synaptic or action potential discharges. The magnitude of responses in the individual compartments, spine–dendrite disparity, and the temporal distribution of [Ca2+]i were different for spines with short and long necks, with the latter being more independent of the dendrite, in agreement with prediction of the model.

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 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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