The flow of current through an ionic channel is studied using the energetic variational approach of Liu applied to the primitive (implicit solvent) model of ionic solutions. This approach allows the derivation of self-consistent (Euler-Lagrange) equations to describe the flow of spheres through channels. The partial differential equations derived involve the global interactions of the spheres and are replaced here with a local approximation that we call steric PNP (Poisson-Nernst-Planck) (Lin, T. C.; Eisenberg, B. To be submitted for publication, 2012). Kong combining rules are used and a range of values of steric interaction parameters are studied. These parameters change the energetics of steric interaction but have no effect on diffusion coefficients in models and simulations. Calculations are made for the calcium (EEEE, EEEA) and sodium channels (DEKA) previously studied in Monte Carlo simulations with comparable results. The biological function is quite sensitive to the steric interaction parameters, and we speculate that a wide range of the function of channels and transporters, even enzymes, might depend on such terms. We point out that classical theories of channels, transporters, and enzymes depend on ideal representations of ionic solutions in which nothing interacts with nothing, even in the enormous concentrations found near and in these proteins or near electrodes in electrochemical cells for that matter. We suggest that a theory designed to handle interactions might be more appropriate. We show that one such theory is feasible and computable: steric PNP allows a direct comparison with experiments measuring flows as well as equilibrium properties. Steric PNP combines atomic and macroscales in a computable formulation that allows the calculation of the macroscopic effects of changes in atomic scale structures (size ~/= 10(-10) meters) studied very extensively in channology and molecular biology.
The action potential of nerve and muscle is produced by voltage-sensitive channels that include a specialized device to sense voltage. The voltage sensor depends on the movement of charges in the changing electric field as suggested by Hodgkin and Huxley. Gating currents of the voltage sensor are now known to depend on the movements of positively charged arginines through the hydrophobic plug of a voltage sensor domain. Transient movements of these permanently charged arginines, caused by the change of transmembrane potential V, further drag the S4 segment and induce opening/closing of the ion conduction pore by moving the S4-S5 linker. This moving permanent charge induces capacitive current flow everywhere. Everything interacts with everything else in the voltage sensor and protein, and so it must also happen in its mathematical model. A Poisson-Nernst-Planck (PNP)-steric model of arginines and a mechanical model for the S4 segment are combined using energy variational methods in which all densities and movements of charge satisfy conservation laws, which are expressed as partial differential equations in space and time. The model computes gating current flowing in the baths produced by arginines moving in the voltage sensor. The model also captures the capacitive pile up of ions in the vestibules that link the bulk solution to the hydrophobic plug. Our model reproduces the signature properties of gating current: 1) equality of ON and OFF charge Q in integrals of gating current, 2) saturating voltage dependence in the Q(charge)-voltage curve, and 3) many (but not all) details of the shape of gating current as a function of voltage. Our results agree qualitatively with experiments and can be improved by adding more details of the structure and its correlated movements. The proposed continuum model is a promising tool to explore the dynamics and mechanism of the voltage sensor.
Incorporation of surface-based capacitances (C/S) simulated by Helmholtz models with pore size distribution obtained from the non-local density functional theory precisely predicts the double-layer capacitance of distinct forms of carbon.
n the basis of the ESVEM trial, d,l-sotalol has been approved for the treatment of life-threatening ventricular tachycardia (VT) and ventricular fibrillation (VF). 1,2 It has been shown that d,l-sotalol reduces the complexity of epicardial activation patterns and prolonged wavelength (WL) during VF in isolated rabbit hearts. 3 Recently, Pak et al reported that d,l-sotalol at therapeutic doses (≤10 mg/L) effectively terminated VF/VT by flattening the action potential duration restitution (APDR) in isolated swine ventricles. 4 However, the effects of d,l-sotalol at therapeutic concentrations on the wavefront characteristics of VF and the genesis of electrophysiological heterogeneity (such as action potential duration (APD) dispersion and spatial heterogeneity of restitutions) are still not completely understood.We previously demonstrated that 2 types of VF exist in the same isolated rabbit heart. 5 As APDR was flattened by low-dose methoxyverapamil (D600), multiple-wavelet type 1 VF was converted to VT. A further increase of D600 concentration converted VT to a slower (type 2) VF with a stationary or slow drifting mother rotor. During type 2 VF, an anatomical structure (the papillary muscle (PM)), always served as an anchoring site for the mother rotor. 6,7 We hypothesized that d,l-sotalol at therapeutic concentrations, with both its effects of APDR flattening and WL prolongation, would also convert a preexisting type 1 VF into a regular rhythm, finally leading to termination of the ventricular tachyarrhythmia. To test this hypothesis, an optical mapping system was used to record epicardial activation patterns during d,l-sotalol infusion in isolated rabbit hearts. The aims of this study were to determine (1) whether or not acute administration of d,l-sotalol can effectively convert a preexisting VF into VT before its termination, and (2) the wavefront characteristics of VF and the electrophysiological heterogeneity during d,l-sotalol infusion with therapeutic concentrations. MethodsThis research protocol was approved by the Institutional Animal Care and Use Committee of Taichung Veterans General Hospital and followed the guidelines of American (Received June 5, 2008; revised manuscript received July 19, 2008; accepted August 5, 2008; released online November 13, 2008
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