Anomalous ion diffusion within skeletal muscle transverse tubule networks

<p>Abstract</p> <p>Background</p> <p>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.</p> <p>Results</p> <p>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 μm 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.</p> <p>Conclusion</p> <p>Our model explains the measured effective diffusion coefficient for ions in skeletal muscle t-tubules.</p

Using existing data to predict and quantify the risks of GM forage to a population of a non-target invertebrate species: A New Zealand case study

Determining the effects of genetically modified (GM) crops on non-target organisms is essential as many non-target species provide important ecological functions. However, it is simply not possible to collect field data on more than a few potential non-target species present in the receiving environment of a GM crop. While risk assessment must be rigorous, new approaches are necessary to improve the efficiency of the process. Utilisation of published information and existing data on the phenology and population dynamics of test species in the field can be combined with limited amounts of experimental biosafety data to predict possible outcomes on species persistence. This paper presents an example of an approach where data from laboratory experiments and field studies on phenology are combined using predictive modelling. Using the New Zealand native weevil species Nicaeana cervina as a case study, we could predict that oviposition rates of the weevil feeding on a GM ryegrass could be reduced by up to 30% without threat to populations of the weevil in pastoral ecosystems. In addition, an experimentally established correlation between feeding level and oviposition led to the prediction that a consistent reduction in feeding of 50% or higher indicated a significant risk to the species and could potentially lead to local extinctions. This approach to biosafety risk assessment, maximising the use of pre-existing field and laboratory data on non-target species, can make an important contribution to informed decision-making by regulatory authorities and developers of new technologies

The simulated steady state Kdistribution within a 10 μm × 10 μm section of the frog t-tubule network during repeated high-frequency activation of skeletal muscle

<p><b>Copyright information:</b></p><p>Taken from "Anomalous ion diffusion within skeletal muscle transverse tubule networks"</p><p>http://www.tbiomed.com/content/4/1/18</p><p>Theoretical Biology & Medical Modelling 2007;4():18-18.</p><p>Published online 17 May 2007</p><p>PMCID:PMC1899483.</p><p></p> The Kprofile across the fibre

The mean squared displacement (MSD) in Ktransport as a function of time for a random walk on the human t-tubule network (—) and an unrestricted random walk in two dimensions (– – –)

<p><b>Copyright information:</b></p><p>Taken from "Anomalous ion diffusion within skeletal muscle transverse tubule networks"</p><p>http://www.tbiomed.com/content/4/1/18</p><p>Theoretical Biology & Medical Modelling 2007;4():18-18.</p><p>Published online 17 May 2007</p><p>PMCID:PMC1899483.</p><p></p> The tubules significantly obstruct the transport of Kand the diffusion of Kin the t-tubule network is anomalous over short distances (i.e. the relationship between MSD and time is not linear as per standard Brownian diffusion (---))

The simulated steady state Kdistribution within a 35 μm × 35 μm section of the frog t-tubule network during repeated high-frequency activation of skeletal muscle

<p><b>Copyright information:</b></p><p>Taken from "Anomalous ion diffusion within skeletal muscle transverse tubule networks"</p><p>http://www.tbiomed.com/content/4/1/18</p><p>Theoretical Biology & Medical Modelling 2007;4():18-18.</p><p>Published online 17 May 2007</p><p>PMCID:PMC1899483.</p><p></p> The Kprofile across the fibre

A scanned section of the human skeletal muscle t-tubule network from Hayashi et al

<p><b>Copyright information:</b></p><p>Taken from "Anomalous ion diffusion within skeletal muscle transverse tubule networks"</p><p>http://www.tbiomed.com/content/4/1/18</p><p>Theoretical Biology & Medical Modelling 2007;4():18-18.</p><p>Published online 17 May 2007</p><p>PMCID:PMC1899483.</p><p></p> [8] (×8000; the scanned section is approximately 8 × 8 μm)

Simulated random walk of a single Kion within the human skeletal muscle t-tubule network (starting from the centre of the fibre)

<p><b>Copyright information:</b></p><p>Taken from "Anomalous ion diffusion within skeletal muscle transverse tubule networks"</p><p>http://www.tbiomed.com/content/4/1/18</p><p>Theoretical Biology & Medical Modelling 2007;4():18-18.</p><p>Published online 17 May 2007</p><p>PMCID:PMC1899483.</p><p></p

A reconstruction of the t-tubule network made by Peachey and Eisenberg 7 using electron microscope slices of frog sartorius muscle fibres (×1400; fibre is approximately 40 × 80 μm)

<p><b>Copyright information:</b></p><p>Taken from "Anomalous ion diffusion within skeletal muscle transverse tubule networks"</p><p>http://www.tbiomed.com/content/4/1/18</p><p>Theoretical Biology & Medical Modelling 2007;4():18-18.</p><p>Published online 17 May 2007</p><p>PMCID:PMC1899483.</p><p></p> Reprinted with permission from the Biophysical Society and L. D. Peachey