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 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 A Finite Element Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 717-725 ◽  
Author(s):  
Vidar Thomée
Keyword(s):  
Finite Element ◽  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Euler Approximation ◽  
Convection Diffusion ◽  
Time Stepping ◽  
Backward Euler ◽  
Spatially Periodic ◽  
Forward Euler

AbstractFor a spatially periodic convection-diffusion problem, we analyze a time stepping method based on Lie splitting of a spatially semidiscrete finite element solution on time steps of length k, using the backward Euler method for the diffusion part and a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {k/m} for the convection part. This complements earlier work on time splitting of the problem in a finite difference context.

scholarly journals Reduced basis approximations of the solutions to spectral fractional diffusion problems

2020 ◽  
Vol 28 (3) ◽  
pp. 147-160
Author(s):  
Andrea Bonito ◽  
Diane Guignard ◽  
Ashley R. Zhang
Keyword(s):  
Computational Cost ◽  
Fractional Power ◽  
Reaction Diffusion ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Quadrature Point ◽  
Reduced Basis ◽  
Fast Evaluation ◽  
Bottle Neck ◽  
Diffusion Problems

AbstractWe consider the numerical approximation of the spectral fractional diffusion problem based on the so called Balakrishnan representation. The latter consists of an improper integral approximated via quadratures. At each quadrature point, a reaction–diffusion problem must be approximated and is the method bottle neck. In this work, we propose to reduce the computational cost using a reduced basis strategy allowing for a fast evaluation of the reaction–diffusion problems. The reduced basis does not depend on the fractional power s for 0 < smin ⩽ s ⩽ smax < 1. It is built offline once for all and used online irrespectively of the fractional power. We analyze the reduced basis strategy and show its exponential convergence. The analytical results are illustrated with insightful numerical experiments.

scholarly journals A First-Order Explicit-Implicit Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 769-782
Author(s):  
Amiya K. Pani ◽  
Vidar Thomée ◽  
A. S. Vasudeva Murthy
Keyword(s):  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Second Order ◽  
Time Step ◽  
Convection Diffusion ◽  
First Order ◽  
Backward Euler ◽  
Strang Splitting ◽  
Spatially Periodic

AbstractWe analyze a second-order in space, first-order in time accurate finite difference method for a spatially periodic convection-diffusion problem. This method is a time stepping method based on the first-order Lie splitting of the spatially semidiscrete solution. In each time step, on an interval of length k, of this solution, the method uses the backward Euler method for the diffusion part, and then applies a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {\frac{k}{m}} for the convection part. With h the mesh width in space, this results in an error bound of the form {C_{0}h^{2}+C_{m}k} for appropriately smooth solutions, where {C_{m}\leq C^{\prime}+\frac{C^{\prime\prime}}{m}}. This work complements the earlier study [V. Thomée and A. S. Vasudeva Murthy, An explicit-implicit splitting method for a convection-diffusion problem, Comput. Methods Appl. Math. 19 2019, 2, 283–293] based on the second-order Strang splitting.

scholarly journals Functional A Posteriori Error Control for Conforming Mixed Approximations of Coercive Problems with Lower Order Terms

2016 ◽  
Vol 16 (4) ◽  
pp. 609-631 ◽  
Author(s):  
Immanuel Anjam ◽  
Dirk Pauly
Keyword(s):  
Error Control ◽  
A Posteriori Error Estimates ◽  
Reaction Diffusion ◽  
Posteriori Error ◽  
Diffusion Problem ◽  
Mixed Formulation ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Linear Partial Differential Equations ◽  
Primal And Dual

AbstractThe results of this contribution are derived in the framework of functional type a posteriori error estimates. The error is measured in a combined norm which takes into account both the primal and dual variables denoted by x and y, respectively. Our first main result is an error equality for all equations of the class ${\mathrm{A}^{*}\mathrm{A}x+x=f}$ or in mixed formulation ${\mathrm{A}^{*}y+x=f}$, ${\mathrm{A}x=y}$, where the exact solution $(x,y)$ is in $D(\mathrm{A})\times D(\mathrm{A}^{*})$. Here ${\mathrm{A}}$ is a linear, densely defined and closed (usually a differential) operator and ${\mathrm{A}^{*}}$ its adjoint. In this paper we deal with very conforming mixed approximations, i.e., we assume that the approximation ${(\tilde{x},\tilde{y})}$ belongs to ${D(\mathrm{A})\times D(\mathrm{A}^{*})}$. In order to obtain the exact global error value of this approximation one only needs the problem data and the mixed approximation itself, i.e., we have the equality$\lvert x-\tilde{x}\rvert^{2}+\lvert\mathrm{A}(x-\tilde{x})\rvert^{2}+\lvert y-% \tilde{y}\rvert^{2}+\lvert\mathrm{A}^{*}(y-\tilde{y})\rvert^{2}=\mathcal{M}(% \tilde{x},\tilde{y}),$where ${\mathcal{M}(\tilde{x},\tilde{y}):=\lvert f-\tilde{x}-\mathrm{A}^{*}\tilde{y}% \rvert^{2}+\lvert\tilde{y}-\mathrm{A}\tilde{x}\rvert^{2}}$ contains only known data. Our second main result is an error estimate for all equations of the class ${\mathrm{A}^{*}\mathrm{A}x+ix=f}$ or in mixed formulation ${\mathrm{A}^{*}y+ix=f}$, ${\mathrm{A}x=y}$, where i is the imaginary unit. For this problem we have the two-sided estimate$\frac{\sqrt{2}}{\sqrt{2}+1}\mathcal{M}_{i}(\tilde{x},\tilde{y})\leq\lvert x-% \tilde{x}\rvert^{2}+\lvert\mathrm{A}(x-\tilde{x})\rvert^{2}+\lvert y-\tilde{y}% \rvert^{2}+\lvert\mathrm{A}^{*}(y-\tilde{y})\rvert^{2}\leq\frac{\sqrt{2}}{% \sqrt{2}-1}\mathcal{M}_{i}(\tilde{x},\tilde{y}),$where ${\mathcal{M}_{i}(\tilde{x},\tilde{y}):=\lvert f-i\tilde{x}-\mathrm{A}^{*}% \tilde{y}\rvert^{2}+\lvert\tilde{y}-\mathrm{A}\tilde{x}\rvert^{2}}$ contains only known data. We will point out a motivation for the study of the latter problems by time discretizations or time-harmonic ansatz of linear partial differential equations and we will present an extensive list of applications including the reaction-diffusion problem and the eddy current problem.

scholarly journals cAMP-dependent regulation of IKs single-channel kinetics

2017 ◽  
Vol 149 (8) ◽  
pp. 781-798 ◽  
Author(s):  
Emely Thompson ◽  
Jodene Eldstrom ◽  
Maartje Westhoff ◽  
Donald McAfee ◽  
Elise Balse ◽  
...  
Keyword(s):  
Action Potential ◽  
Single Channel ◽  
Cyclic Adenosine Monophosphate ◽  
Adenosine Monophosphate ◽  
Surface Expression ◽  
Voltage Sensor ◽  
Single Channels ◽  
Adrenergic Stimulation ◽  
Channel Opening ◽  
Sensor Activation

The delayed potassium rectifier current, IKs, is composed of KCNQ1 and KCNE1 subunits and plays an important role in cardiac action potential repolarization. During β-adrenergic stimulation, 3′-5′-cyclic adenosine monophosphate (cAMP)-dependent protein kinase A (PKA) phosphorylates KCNQ1, producing an increase in IKs current and a shortening of the action potential. Here, using cell-attached macropatches and single-channel recordings, we investigate the microscopic mechanisms underlying the cAMP-dependent increase in IKs current. A membrane-permeable cAMP analog, 8-(4-chlorophenylthio)-cAMP (8-CPT-cAMP), causes a marked leftward shift of the conductance–voltage relation in macropatches, with or without an increase in current size. Single channels exhibit fewer silent sweeps, reduced first latency to opening (control, 1.61 ± 0.13 s; cAMP, 1.06 ± 0.11 s), and increased higher-subconductance-level occupancy in the presence of cAMP. The E160R/R237E and S209F KCNQ1 mutants, which show fixed and enhanced voltage sensor activation, respectively, largely abolish the effect of cAMP. The phosphomimetic KCNQ1 mutations, S27D and S27D/S92D, are much less and not at all responsive, respectively, to the effects of PKA phosphorylation (first latency of S27D + KCNE1 channels: control, 1.81 ± 0.1 s; 8-CPT-cAMP, 1.44 ± 0.1 s, P &lt; 0.05; latency of S27D/S92D + KCNE1: control, 1.62 ± 0.1 s; cAMP, 1.43 ± 0.1 s, nonsignificant). Using total internal reflection fluorescence microscopy, we find no overall increase in surface expression of the channel during exposure to 8-CPT-cAMP. Our data suggest that the cAMP-dependent increase in IKs current is caused by an increase in the likelihood of channel opening, combined with faster openings and greater occupancy of higher subconductance levels, and is mediated by enhanced voltage sensor activation.

scholarly journals Caffeine-induced inhibition of inositol(1,4,5)-trisphosphate-gated calcium channels from cerebellum.

1994 ◽  
Vol 5 (1) ◽  
pp. 97-103 ◽  
Author(s):  
I Bezprozvanny ◽  
S Bezprozvannaya ◽  
B E Ehrlich
Keyword(s):  
Lipid Bilayers ◽  
Inhibitory Action ◽  
Single Channel ◽  
Ryanodine Receptors ◽  
Single Channels ◽  
Ca Channels ◽  
Open Time ◽  
Inositol 1,4,5 Trisphosphate ◽  
Insp3 Receptors ◽  
Intracellular Ca

Effects of the xanthine drug caffeine on inositol (1,4,5)-trisphosphate (InsP3)-gated calcium (Ca) channels from canine cerebellum were studied using single channels incorporated into planar lipid bilayers. Caffeine, used widely as an agonist of ryanodine receptors, inhibited the activity of InsP3-gated Ca channels in a noncooperative fashion with half-inhibition at 1.64 mM caffeine. The frequency of channel openings was decreased more than threefold after addition of 5 mM caffeine; there was only a small effect on mean open time of the channels, and the single channel conductance was unchanged. Increased InsP3 concentration overcame the inhibitory action of caffeine, but caffeine did not reduce specific [3H]InsP3 binding to the receptor. The inhibitory action of caffeine on InsP3 receptors suggests that the action of caffeine on the intracellular Ca pool must be interpreted with caution when both ryanodine receptors and InsP3 receptors are present in the cell.

scholarly journals Effects of Strontium on the Permeation and Gating Phenotype of Calcium Channels in Hair Cells

2008 ◽  
Vol 100 (4) ◽  
pp. 2115-2124 ◽  
Author(s):  
Adrian Rodriguez-Contreras ◽  
Ping Lv ◽  
Jun Zhu ◽  
Hyo Jeong Kim ◽  
Ebenezer N. Yamoah
Keyword(s):  
Hair Cell ◽  
Single Channel ◽  
Single Channels ◽  
Physiological Concentration ◽  
Closed State ◽  
Dependent Inactivation ◽  
Intracellular Ca ◽  
High Concentrations ◽  
Latency Distributions ◽  
Channel Properties

To minimize the effects of Ca2+ buffering and signaling, this study sought to examine single Ca2+ channel properties using Sr2+ ions, which substitute well for Ca2+ but bind weakly to intracellular Ca2+ buffers. Two single-channel fluctuations were distinguished by their sensitivity to dihydropyridine agonist (L-type) and insensitivity toward dihydropyridine antagonist (non-L-type). The L- and non-L-type single channels were observed with single-channel conductances of 16 and 19 pS at 70 mM Sr2+ and 11 and 13 pS at 5 mM Sr2+, respectively. We obtained KD estimates of 5.2 and 1.9 mM for Sr2+ for L- and non-L-type channels, respectively. At Ca2+ concentration of ∼2 mM, the single-channel conductances of Sr2+ for the L-type channel was ∼1.5 and 4.0 pS for the non-L-type channels. Thus the limits of single-channel microdomain at the membrane potential of a hair cell (e.g., −65 mV) for Sr2+ ranges from 800 to 2,000 ion/ms, assuming an ECa of 100 mV. The channels are ≥4-fold more sensitive at the physiological concentration ranges than at concentrations >10 mM. Additionally, the channels have the propensity to dwell in the closed state at high concentrations of Sr2+, which is reflected in the time constant of the first latency distributions. It is concluded that the concentration of the permeant ion modulates the gating of hair cell Ca2+ channels. Finally, the closed state/s that is/are altered by high concentrations of Sr2+ may represent divalent ion-dependent inactivation of the L-type channel.

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