scholarly journals Rethinking calcium profiles around single channels: the exponential and periodic calcium nanodomains

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Sergej L. Mironov
Keyword(s):  
Functional Role ◽  
Reaction Diffusion ◽  
Single Channels ◽  
Calcium Dependent ◽  
Physiological Processes ◽  
Nonlinear Reaction ◽  
Reaction Diffusion Model ◽  
Spatial Periodicity ◽  
Calcium Diffusion ◽  
Theoretical Predictions

AbstractMany fundamental calcium-dependent physiological processes are triggered by high local calcium levels that are established around the sites of calcium entry into the cell (channels). They are dubbed as calcium nanodomains but their exact profiles are still elusive. The concept of calcium nanodomains stems from a linear model of calcium diffusion and is only valid when calcium increases are smaller than the concentration of cytoplasmic buffers. Recent data indicates that much higher calcium levels cause buffer saturation. Therefore, I sought explicit solutions of a nonlinear reaction-diffusion model and found a dichotomous solution. For small fluxes, the steady state calcium profile is quasi-exponential, and when calcium exceeds buffer concentration a spatial periodicity appears. Analytical results are supported by Monte-Carlo simulations. I also imaged 1D- and radial calcium distributions around single α-synuclein channels in cell-free conditions. Measured Ca profiles are consistent with theoretical predictions. I propose that the periodic calcium patterns may well arise under certain conditions and their specific functional role has to be established.

scholarly journals Spatially periodic calcium profiles around single channels

2016 ◽  
Author(s):  
S. L. Mironov
Keyword(s):  
Calcium Binding ◽  
Linear Models ◽  
Single Channel ◽  
Reaction Diffusion ◽  
Diffusion Problem ◽  
Cell Physiology ◽  
Single Channels ◽  
Periodic Patterns ◽  
Calcium Diffusion ◽  
Spatially Periodic

AbstractThe concept of calcium nanodomains established around the sites of calcium entry into the cell is fundamental for mechanistic consideration of key physiological responses. It stems from linear models of calcium diffusion from single channel into the cytoplasm, but is only valid for calcium increases smaller than the concentration of calcium-binding species. Recent experiments indicate much higher calcium levels in the vicinity of channel exit that should cause buffer saturation. I here derive explicit solutions of respective non-linear reaction-diffusion problem and found dichotomous solution - for small fluxes the steady state calcium profiles have quasi-exponential form, whereas in the case of buffer saturation calcium distributions show spatial periodicity. These non-trivial and novel spatial calcium profiles are supported by Monte-Carlo simulations. Imaging of 1D- and radial distributions around single α-synuclein channels measured in cell-free conditions supports the theory. I suggest that periodic patterns may arise under different physiological conditions and play specific role in cell physiology.

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.

Traveling wavefronts of a nonlinear reaction–diffusion model of tumor growth under the acid environment

2014 ◽  
Vol 07 (03) ◽  
pp. 1450034
Author(s):  
Huiyan Zhu ◽  
Yang Luo ◽  
Xiufang Wang
Keyword(s):  
Diffusion Model ◽  
Perturbation Methods ◽  
Tumor Tissue ◽  
Reaction Diffusion ◽  
Traveling Wave Solution ◽  
Ion Concentration ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Reaction ◽  
Reaction Diffusion Model ◽  
Acid Environment

In this paper, a reaction–diffusion model describing temporal development of tumor tissue, normal tissue and excess H+ ion concentration is considered. Based on a combination of perturbation methods, the Fredholm theory and Banach fixed point theorem, we theoretically justify the existence of the traveling wave solution for this model.

scholarly journals Hereditary Evolution Processes Under Impulsive Effects

2021 ◽  
Vol 18 (3) ◽  
Author(s):  
Tiziana Cardinali ◽  
Paola Rubbioni
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Reaction Diffusion ◽  
Nonlinear Reaction ◽  
Reaction Diffusion Model ◽  
The Cauchy Problem ◽  
Semilinear Differential Equation ◽  
Impulsive Dynamics ◽  
Functional Delay ◽  
With Memory

AbstractIn this note, we deal with a model of population dynamics with memory effects subject to instantaneous external actions. We interpret the model as an impulsive Cauchy problem driven by a semilinear differential equation with functional delay. The existence of delayed impulsive solutions to the Cauchy problem leads to the presence of hereditary impulsive dynamics for the model. Furthermore, using the same procedure we study a nonlinear reaction–diffusion model.

scholarly journals A solvable nonlinear reaction-diffusion model

1995 ◽  
Vol 198 (2) ◽  
pp. 100-104 ◽  
Author(s):  
Max-Olivier Hongler ◽  
Ricardo Lima
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Nonlinear Reaction ◽  
Reaction Diffusion Model
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