Anomalous ion diffusion within skeletal muscle transverse tubule networks

Abstract

Background: Skeletal muscle fibres contain transverse tubular (t-tubule) networks that allow electrical signals to rapidly propagate into the fibre. These electrical signals are generated by the transport of ions across the t-tubule membranes and this can result in significant changes in ion concentrations within the t-tubules during muscle excitation. During periods of repeated highfrequency activation of skeletal muscle the t-tubule K + concentration is believed to increase significantly and diffusive K + transport from the t-tubules into the interstitial space provides a mechanism for alleviating muscle membrane depolarization. However, the tortuous nature of the highly branched space-filling t-tubule network impedes the diffusion of material through the network. The effective diffusion coefficient for ions in the t-tubules has been measured to be approximately five times lower than in free solution, which is significantly different from existing theoretical values of the effective diffusion coefficient that range from 2-3 times lower than in free solution. To resolve this discrepancy, in this paper we study the process of diffusion within electron microscope scanned sections of the skeletal muscle t-tubule network using mathematical modelling and computer simulation techniques. Our model includes t-tubule geometry, tautness, hydrodynamic and non-planar network factors.

Cardiac BIN1 folds T-tubule membrane, controlling ion flux and limiting arrhythmia

“…In our model, the slow diffusion zone can only exchange with the rapid diffusion zone at the distal end of the T-tubule farthest from the extracellular space. The equations are: $$\frac{\partial c_{1}false(x,tfalse)}{\partial t}={\tau }_{Ca}{D}_{Ca}\frac{{\partial }^2{c}_{1}false(x,tfalse)}{\partial x^2}-\delta false(xfalse)·kfalse(c_{1}false(x,tfalse)-c_{2}false(tfalse)false)-\sigma c_1·c_E\frac{d{N}_{2}false(tfalse)}{dt}=kfalse(c_{1}false(0,tfalse)-c_{2}false(tfalse)false)\frac{\partial c_{E}false(x,tfalse)}{\partial t}={\tau }_E{D}_E\frac{{\partial }^2{c}_{E}false(x,tfalse)}{\partial x^2}-\sigma c_1·c_E$$ where k is the exchange rate between calcium in the slow and rapid diffusion zones, c 2 is the concentration of calcium in the slow diffusion zone (c 2 = N 2 /V 2 ), σ is a rate constant for Ca 2+ chelation by EGTA, D Ca 54 and D E 55 are the free diffusion constants of Ca 2+ and EGTA, respectively, and τ Ca and τ E are tortuosity factors for Ca 2+ and EGTA, respectively, that account for reduced diffusion in the T-tubule. The delta function, δ(x), indicates that compartment exchange only influences c 1 at the x = 0 end of the T-tubule.…”

Extracellular Potassium Homeostasis: Insights from Hypokalemic Periodic Paralysis

“…72 Several groups have shown that diffusion of extracellular potassium of skeletal muscle into systemic circulation is limited; the diffusion coefficient is less than 20% of its value in free solution. 73 …”

The effect of exercise training on transverse tubules in normal, remodeled, and reverse remodeled hearts

“…Transverse (T)-tubules; invaginations of the plasma membrane, allow this to occur uniformly across the whole cell (Brette and Orchard, 2003). This is made possible because (i) the T-tubules occur at ~2 μm intervals at approximately every z line and run deep into the interior of the cell, such that most sarcomeres are individually served by a singular T-tubule (Soeller and Cannell, 1999); (ii) sarcolemmal proteins that traffic ions across the plasma membrane are concentrated in the T-tubules (Brette and Orchard, 2003), and (iii) the T-tubules themselves constitute extracellular ion reservoirs that ensure a rapid access for transmembrane inward transport (Shorten and Soboleva, 2007; Swift et al, 2006). Thus, an intact network of T-tubules supports a rapid and coordinated contraction.…”