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

Ion association in concentrated NaCI brines from ambient to supercritical conditions: results from classical molecular dynamics simulations

Highly concentrated NaCl brines are important geothermal fluids; chloride complexation of metals in such brines increases the solubility of minerals and plays a fundamental role in the genesis of hydrothermal ore deposits. There is experimental evidence that the molecular nature of the NaCl–water system changes over the pressure–temperature range of the Earth's crust. A transition of concentrated NaCl–H(2)O brines to a "hydrous molten salt" at high P and T has been argued to stabilize an aqueous fluid phase in the deep crust. In this work, we have done molecular dynamic simulations using classical potentials to determine the nature of concentrated (0.5–16 m) NaCl–water mixtures under ambient (25°C, 1 bar), hydrothermal (325°C, 1 kbar) and deep crustal (625°C, 15 kbar) conditions. We used the well-established SPCE model for water together with the Smith and Dang Lennard-Jones potentials for the ions (J. Chem. Phys., 1994, 100, 3757). With increasing temperature at 1 kbar, the dielectric constant of water decreases to give extensive ion-association and the formation of polyatomic (Na(n)Cl(m))(n-m )clusters in addition to simple NaCl ion pairs. Large polyatomic (Na(n)Cl(m))(n-m )clusters resemble what would be expected in a hydrous NaCl melt in which water and NaCl were completely miscible. Although ion association decreases with pressure, temperatures of 625°C are not enough to overcome pressures of 15 kbar; consequently, there is still enhanced Na–Cl association in brines under deep crustal conditions

Influence of the Water Content on the Diffusion Coefficients of Li⁺ and Water across Naphthalenic Based Copolyimide Cation-Exchange Membranes

The transport of lithium ions in cation-exchange membranes based on sulfonated copolyimide membranes is reported. Diffusion coefficients of lithium are estimated as a function of the water content in membranes by using pulsed field gradient (PFG) NMR and electrical conductivity techniques. It is found that the lithium transport slightly decreases with the diminution of water for membranes with water content lying in the range 14 < λ < 26.5, where λ is the number of molecules of water per fixed sulfonate group. For λ < 14, the value of the diffusion coefficient of lithium experiences a sharp decay with the reduction of water in the membranes. The dependence of the diffusion of lithium on the humidity of the membranes calculated from conductivity data using Nernst–Planck type equations follows a trend similar to that observed by NMR. The possible explanation of the fact that the Haven ratio is higher than the unit is discussed. The diffusion of water estimated by 1H PFG-NMR in membranes neutralized with lithium decreases as λ decreases, but the drop is sharper in the region where the decrease of the diffusion of protons of water also undergoes considerable reduction. The diffusion of lithium ions computed by full molecular dynamics is similar to that estimated by NMR. However, for membranes with medium and low concentration of water, steady state conditions are not reached in the computations and the diffusion coefficients obtained by MD simulation techniques are overestimated. The curves depicting the variation of the diffusion coefficient of water estimated by NMR and full dynamics follow parallel trends, though the values of the diffusion coefficient in the latter case are somewhat higher. The WAXS diffractograms of fully hydrated membranes exhibit the ionomer peak at q = 2.8 nm⁻1, the peak being shifted to higher q as the water content of the membranes decreases. The diffractograms present additional peaks at higher q, common to wet and dry membranes, but the peaks are better resolved in the wet membranes. The ionomer peak is not detected in the diffractograms of dry membranes.The authors acknowledge financial support provided by the DGICYT (Dirección General de Investigación Cientifíca y Tecnológica) through Grant MAT2011-29174-C02-02

Solvent structure, dynamics, and ion mobility in aqueous solutions at 25 c

-, Br -, and I -at infinite dilution by molecular dynamics simulation using the SPC/E model for water at 25°C and a reaction field for the long-range interactions. The ion mobilities show the same trends as the experimental results with distinct maxima for cations and anions. The mobilities (defined by u i ) D i /kT) of the corresponding uncharged species are also determined by simulation and are in qualitative agreement with Stokes&apos; law. The mobilities of Li + , Na + , K + , Rb + and F -increase on discharge, whereas Cl, Br, and I have smaller mobilities than the corresponding anions. The mobility of the fictitious I + ion, which differs from I -only in its charge, lies between that of I -and I in the order u I &lt; u I + &lt; u I -. The residence time of water in the first solvation shell of small cations (Li + and Na + ) and Ca 2+ decreases when the ions are discharged, while the opposite is observed on neutralizing I -, suggesting the formation of a solvent cage around the large uncharged I which partially breaks up on charging, increasing the mobility of the corresponding ion. The cage breakup is greater for I -than for I + which correlates with the asymmetry in the entropies of solvation of I -and I + , in SPC/E water on charge reversal, providing an explanation for the trends in the mobilities of I, I -, and I + . The residence times of water in the primary hydration shell around cations pass through a minimum as a function of size that correlates with the maximum in the corresponding solvation entropy, suggesting different types of hydration, i.e., electrostatic ion solvation (hydrophilic) and cage formation (hydrophobic) respectively for small and large cations. The results are in accord with recent calculations of the solvation entropy and free energy as continuous functions of the charge and size (Lynden-Bell, R. M.; Rasaiah, J. C. J. Chem. Phys. 1997, 107, 1981. Hydrophilic and hydrophobic solvation are reflected in the exchange dynamics of the water in the hydration shells around charged and uncharged solutes. The solvation dynamics of individual cations and anions are distinct at short times but characterized by the solvent at long times. Solvent dynamics, structure, and caging modulated by the charge and size of the ions are strongly implicated in determining their mobilities