Nernst-Planck-Gaussian finite element modelling of Ca²⁺ electrodiffusion in amphibian striated muscle transverse tubule-sarcoplasmic reticular triadic junctional domains.

Abstract

<h4>Introduction</h4>Intracellular Ca²⁺ signalling regulates membrane permeabilities, enzyme activity, and gene transcription amongst other functions. Large transmembrane Ca²⁺ electrochemical gradients and low diffusibility between cell compartments potentially generate short-lived, localised, high-[Ca²⁺] microdomains. The highest concentration domains likely form between closely apposed membranes, as at amphibian skeletal muscle transverse tubule-sarcoplasmic reticular (T-SR, triad) junctions.<h4>Materials and methods</h4>Finite element computational analysis characterised the formation and steady state and kinetic properties of the Ca²⁺ microdomains using established empirical physiological and anatomical values. It progressively incorporated Fick diffusion and Nernst-Planck electrodiffusion gradients, K⁺, Cl^-, and Donnan protein, and calmodulin (CaM)-mediated Ca²⁺ buffering. It solved for temporal-spatial patterns of free and buffered Ca²⁺, Gaussian charge differences, and membrane potential changes, following Ca²⁺ release into the T-SR junction.<h4>Results</h4>Computational runs using established low and high Ca²⁺ diffusibility (<i>D</i> _Ca2+) limits both showed that voltages arising from intracytosolic total [Ca²⁺] gradients and the counterions little affected microdomain formation, although elevated <i>D</i> _Ca2+ reduced attained [Ca²⁺] and facilitated its kinetics. Contrastingly, adopting known cytosolic CaM concentrations and CaM-Ca²⁺ affinities markedly increased steady-state free ([Ca²⁺]_free) and total ([Ca²⁺]), albeit slowing microdomain formation, all to extents reduced by high <i>D</i> _Ca2+. However, both low and high <i>D</i> _Ca2+ yielded predictions of similar, physiologically effective, [Ca²⁺-CaM]. This Ca²⁺ trapping by the relatively immobile CaM particularly increased [Ca²⁺] at the junction centre. [Ca²⁺]_free, [Ca²⁺-CaM], [Ca²⁺], and microdomain kinetics all depended on both CaM-Ca²⁺ affinity and <i>D</i> _Ca2+. These changes accompanied only small Gaussian (∼6 mV) and surface charge (∼1 mV) effects on tubular transmembrane potential at either <i>D</i> _Ca2+.<h4>Conclusion</h4>These physical predictions of T-SR Ca²⁺ microdomain formation and properties are compatible with the microdomain roles in Ca²⁺ and Ca²⁺-CaM-mediated signalling but limited the effects on tubular transmembrane potentials. CaM emerges as a potential major regulator of both the kinetics and the extent of microdomain formation. These possible cellular Ca²⁺ signalling roles are discussed in relation to possible feedback modulation processes sensitive to the μM domain but not nM bulk cytosolic, [Ca²⁺]_free, and [Ca²⁺-CaM], including ryanodine receptor-mediated SR Ca²⁺ release; Na⁺, K⁺, and Cl^- channel-mediated membrane excitation and stabilisation; and Na⁺/Ca²⁺ exchange transport.