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 Correspondences between parameters in a reaction-diffusion model and connexin functions during zebrafish stripe formation

2021 ◽  
Author(s):  
Akiko Nakamasu
Keyword(s):  
Molecular Mechanisms ◽  
Reaction Diffusion ◽  
The Body ◽  
Pigment Cells ◽  
Turing Pattern ◽  
Reaction Diffusion Model ◽  
Spatial Periodicity ◽  
Pattern Formations ◽  
Mathematical Analyses ◽  
Spotted Pattern

Abstract Different diffusivities among interacting substances actualize the potential instability of a system. When these elicited instabilities manifested as forms of spatial periodicity, they are called Turing patterns. Simulations using general reaction-diffusion (RD) models have demonstrated that pigment patterns on the body trunk of growing fish follow a Turing pattern. Laser ablation experiments performed on zebrafish revealed apparent interactions among pigment cells, which allowed for a three-components RD model to be derived. However, the underlying molecular mechanisms responsible for Turing pattern formation in this system had been remained unknown. A zebrafish mutant with a spotted pattern was found to have a defect in Connexin41.8 (Cx41.8) which, together with Cx39.4, exists in pigment cells and controls pattern formations. Here, molecular-level evidence derived from connexin analyses was linked to the interactions among pigment cells described in previous RD modeling. Channels on pigment cells were generalized as “gates,” and the effects of respective gates were deduced. The model used partial differential equations (PDEs) to enable numerical and mathematical analyses of characteristics observed in the experiments. Furthermore, the improved PDE model included nonlinear reaction terms, enabled the consideration of the behavior of components.

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 Neuronal hibernation following hippocampal demyelination

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Selva Baltan ◽  
Safdar S. Jawaid ◽  
Anthony M. Chomyk ◽  
Grahame J. Kidd ◽  
Jacqueline Chen ◽  
...  
Keyword(s):  
Dendritic Spines ◽  
Hippocampal Neurons ◽  
Molecular Mechanisms ◽  
Three Dimensional ◽  
Long Term Potentiation ◽  
Synaptic Function ◽  
Mammalian Brain ◽  
Gene Transcript ◽  
Ca1 Neurons

AbstractCognitive dysfunction occurs in greater than 50% of individuals with multiple sclerosis (MS). Hippocampal demyelination is a prominent feature of postmortem MS brains and hippocampal atrophy correlates with cognitive decline in MS patients. Cellular and molecular mechanisms responsible for neuronal dysfunction in demyelinated hippocampi are not fully understood. Here we investigate a mouse model of hippocampal demyelination where twelve weeks of treatment with the oligodendrocyte toxin, cuprizone, demyelinates over 90% of the hippocampus and causes decreased memory/learning. Long-term potentiation (LTP) of hippocampal CA1 pyramidal neurons is considered to be a major cellular readout of learning and memory in the mammalian brain. In acute slices, we establish that hippocampal demyelination abolishes LTP and excitatory post-synaptic potentials of CA1 neurons, while pre-synaptic function of Schaeffer collateral fibers is preserved. Demyelination also reduced Ca2+-mediated firing of hippocampal neurons in vivo. Using three-dimensional electron microscopy, we investigated the number, shape (mushroom, stubby, thin), and post-synaptic densities (PSDs) of dendritic spines that facilitate LTP. Hippocampal demyelination did not alter the number of dendritic spines. Surprisingly, dendritic spines appeared to be more mature in demyelinated hippocampi, with a significant increase in mushroom-shaped spines, more perforated PSDs, and more astrocyte participation in the tripartite synapse. RNA sequencing experiments identified 400 altered transcripts in demyelinated hippocampi. Gene transcripts that regulate myelination, synaptic signaling, astrocyte function, and innate immunity were altered in demyelinated hippocampi. Hippocampal remyelination rescued synaptic transmission, LTP, and the majority of gene transcript changes. We establish that CA1 neurons projecting demyelinated axons silence their dendritic spines and hibernate in a state that may protect the demyelinated axon and facilitates functional recovery following remyelination.

scholarly journals Meta-modeling on detailed geography for accurate prediction of invasive alien species dispersal

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Nick Pepper ◽  
Luca Gerardo-Giorda ◽  
Francesco Montomoli
Keyword(s):  
Invasive Species ◽  
Alien Species ◽  
Temporal Dynamics ◽  
Coupled Model ◽  
Reaction Diffusion ◽  
Model Complexity ◽  
Model Parameters ◽  
Northern Spain ◽  
Reaction Diffusion Model ◽  
The Impact

Abstract Invasive species are recognized as a significant threat to biodiversity. The mathematical modeling of their spatio-temporal dynamics can provide significant help to environmental managers in devising suitable control strategies. Several mathematical approaches have been proposed in recent decades to efficiently model the dispersal of invasive species. Relying on the assumption that the dispersal of an individual is random, but the density of individuals at the scale of the population can be considered smooth, reaction-diffusion models are a good trade-off between model complexity and flexibility for use in different situations. In this paper we present a continuous reaction-diffusion model coupled with arbitrary Polynomial Chaos (aPC) to assess the impact of uncertainties in the model parameters. We show how the finite elements framework is well-suited to handle important landscape heterogeneities as elevation and the complex geometries associated with the boundaries of an actual geographical region. We demonstrate the main capabilities of the proposed coupled model by assessing the uncertainties in the invasion of an alien species invading the Basque Country region in Northern Spain.

A REACTION–DIFFUSION MODEL FOR THE CONTROL OF CHOLERA EPIDEMIC

2016 ◽  
Vol 24 (04) ◽  
pp. 431-456 ◽  
Author(s):  
A. K. MISRA ◽  
ALOK GUPTA
Keyword(s):  
Temporal Dynamics ◽  
Temporal Distribution ◽  
Reaction Diffusion ◽  
Effective Control ◽  
Lytic Bacteriophage ◽  
Cholera Epidemic ◽  
Reaction Diffusion Model ◽  
Spatially Extended ◽  
Control Procedures ◽  
Spatio Temporal

Understanding the spatio-temporal dynamics of cholera outbreaks may help in devising more effective control procedures. In this paper, we have considered a reaction–diffusion system for biological control of cholera epidemic. Firstly, we have focused on temporal evolution of cholera in a region and its control using lytic bacteriophage in the aquatic reservoirs. Then, we have explored the effect of spatial dispersion of populations on the disease dynamics. We have observed the onset of sustained oscillations via Hopf-bifurcation for the endemic state of temporal system. This onset of fluctuations in populations depends upon the phage adsorption rate. But in the spatially extended setting, all the populations stabilize i.e., the spatio-temporal distribution of all the populations becomes uniform. Some numerical computations have been done to verify analytical results.

scholarly journals Correspondences between parameters in a reaction-diffusion model and connexin functions during zebrafish stripe formation

2021 ◽  
Author(s):  
Akiko Nakamasu
Keyword(s):  
Molecular Mechanisms ◽  
Reaction Diffusion ◽  
The Body ◽  
Pigment Cells ◽  
Turing Pattern ◽  
Reaction Diffusion Model ◽  
Spatial Periodicity ◽  
Pattern Formations ◽  
Mathematical Analyses ◽  
Spotted Pattern

Abstract Different diffusivities among interacting substances actualize the potential instability of a system. When these elicited instabilities manifested as forms of spatial periodicity, they are called Turing patterns. Simulations using general reaction-diffusion (RD) models have demonstrated that pigment patterns on the body trunk of growing fish follow a Turing pattern. Laser ablation experiments performed on zebrafish revealed apparent interactions among pigment cells, which allowed for a three-components RD model to be derived. However, the underlying molecular mechanisms responsible for Turing pattern formation in this system had been remained unknown. A zebrafish mutant with a spotted pattern was found to have a defect in Connexin41.8 (Cx41.8) which, together with Cx39.4, exists in pigment cells and controls pattern formations. Here, molecular-level evidence derived from connexin analyses was linked to the interactions among pigment cells described in previous RD modeling. Channels on pigment cells were generalized as “gates,” and the effects of respective gates were deduced. The model used partial differential equations (PDEs) to enable numerical and mathematical analyses of characteristics observed in the experiments. Furthermore, the improved PDE model included nonlinear reaction terms, enabled the consideration of the behavior of components.

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 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.

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