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.

Min-Protein Oscillations in E. coli: Three-Dimensional Off-Lattice Stochastic Reaction-Diffusion Model

2006 ◽  
Vol 128 (1-2) ◽  
pp. 5-20 ◽  
Author(s):  
Vladimir Krstić ◽  
Željka Maglica ◽  
Hana Čipčić Paljetak ◽  
Boris Podobnik ◽  
Nenad Pavin
Keyword(s):  
Diffusion Model ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
E Coli ◽  
Reaction Diffusion Model ◽  
Stochastic Reaction

scholarly journals Microbial competition reduces interaction distances to the low µm-range

2020 ◽  
Author(s):  
Rinke J. van Tatenhove-Pel ◽  
Tomaž Rijavec ◽  
Aleš Lapanje ◽  
Iris van Swam ◽  
Emile Zwering ◽  
...  
Keyword(s):  
Effective Interaction ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Dimensional System ◽  
Cellular Interactions ◽  
Natural Ecosystems ◽  
Concentration Gradients ◽  
Reaction Diffusion Model ◽  
The Impact ◽  
Three Dimensional System

AbstractMetabolic interactions between cells affect microbial community compositions and hence their function in ecosystems. It is well-known that under competition for the exchanged metabolite, concentration gradients constrain the distances over which interactions can occur. However, interaction distances are typically quantified in two-dimensional systems or without accounting for competition or other metabolite-removal, conditions which may not very often match natural ecosystems. We here analyze the impact of cell-to-cell distance on unidirectional cross-feeding in a three-dimensional system with competition for the exchanged metabolite. Effective interaction distances were computed with a reaction-diffusion model and experimentally verified by growing a synthetic consortium of 1 µm-sized metabolite producer, receiver and competitor cells in different spatial structures. We show that receivers cannot interact with producers ∼15 µm away from them, as product concentration gradients flatten close to producer cells. We developed an aggregation protocol and created variants of the receiver cells’ import system, to show that within producer-receiver aggregates even low affinity receiver cells could interact with producers. These results show that competition or other metabolite-removal of a public good in a three-dimensional system reduces the interaction distance to the low micrometer-range, highlighting the importance of concentration gradients as physical constraint for cellular interactions.

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 A metabolic reaction–diffusion model for PKCα translocation via PIP2 hydrolysis in an endothelial cell

2020 ◽  
Vol 477 (20) ◽  
pp. 4071-4084
Author(s):  
Toshihiro Sera ◽  
Shiro Higa ◽  
Yan Zeshu ◽  
Kyosuke Takahi ◽  
Satoshi Miyamoto ◽  
...  
Keyword(s):  
Endothelial Cell ◽  
Cell Function ◽  
Cell Model ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Mathematical Framework ◽  
Metabolic Reaction ◽  
Membrane Domain ◽  
Reaction Diffusion Model ◽  
A Cell

Hydrolysis of the phospholipid phosphatidylinositol 4,5-bisphosphate (PIP2) at the cell membrane induces the release of inositol 1,4,5-trisphosphate (IP3) into the cytoplasm and diffusion of diacylglycerol (DAG) through the membrane, respectively. Release of IP3 subsequently increases Ca2+ levels in the cytoplasm, which results in activation of protein kinase C α (PKCα) by Ca2+ and DAG, and finally the translocation of PKCα from the cytoplasm to the membrane. In this study, we developed a metabolic reaction–diffusion framework to simulate PKCα translocation via PIP2 hydrolysis in an endothelial cell. A three-dimensional cell model, divided into membrane and cytoplasm domains, was reconstructed from confocal microscopy images. The associated metabolic reactions were divided into their corresponding domain; PIP2 hydrolysis at the membrane domain resulted in DAG diffusion at the membrane domain and IP3 release into the cytoplasm domain. In the cytoplasm domain, Ca2+ was released from the endoplasmic reticulum, and IP3, Ca2+, and PKCα diffused through the cytoplasm. PKCα bound Ca2+ at, and diffused through, the cytoplasm, and was finally activated by binding with DAG at the membrane. Using our model, we analyzed IP3 and DAG dynamics, Ca2+ waves, and PKCα translocation in response to a microscopic stimulus. We found a qualitative agreement between our simulation results and our experimental results obtained by live-cell imaging. Interestingly, our results suggest that PKCα translocation is dominated by DAG dynamics. This three-dimensional reaction–diffusion mathematical framework could be used to investigate the link between PKCα activation in a cell and cell function.

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.

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