Anomalous ion diffusion within skeletal muscle transverse tubule networks

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 high-frequency 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.

Using our model we found that the t-tubule network geometry reduced the K+ diffusion coefficient to 19-27% of its value in free solution, which is consistent with the experimentally observed value of 21% and is significantly smaller than existing theoretical values that range from 32-50%. We also found that diffusion in the t-tubules is anomalous for skeletal muscle fibres with a diameter of less than approximately 10-20 microm as a result of obstructed diffusion. We also observed that the [K+] within the interior of the t-tubule network during high-frequency activation is greater for fibres with a larger diameter. Smaller skeletal muscle fibres are therefore more resistant to membrane depolarization. Because the t-tubule network is anisotropic and inhomogeneous, we also found that the [K+] distribution generated within the network was irregular for fibres of small diameter.

Our model explains the measured effective diffusion coefficient for ions in skeletal muscle t-tubules.