Transmembrane current flow

The time course of an action potential reflects net current flow and thus the balance of open ion channels. The rate of change of membrane voltage is proportional to transmembrane current flow, according to the equation ... 

Electronics to hold transmembrane potential (Vm) constant and measure current flowing across membrane... 

The above expression can be derived from the Nernst-Planck equations with the assumption that concentration does not vary with time. In addition the space dimension of Equation 22.4 is reduced to a two-compartment — cell interior and exterior — model. Thus the steady-state of Equation 22.4 teUs us that when there is no net current flow, the transmembrane potential will equal a quantity called the Nernst potential E = (RT/ZiP) ln([C]o/[C],) z, is the valence of the ion, [C,]o is the concentration of the ion on the outside, and [C,] is the concentration on the inside. Quantities such as ion mobility are effectively lumped into a nonlinear time-varying conductance (G,m hf). 

I-V curves for these artificial ion channels were obtained by mounting the membrane sample between the two halves of a U-tube conductivity cell. Each half-cell was filled with 5 mL of a 10 mM pH = 7 phosphate buffer that was also 100 mM in KCl. A Ag/AgCl reference electrode was inserted into each half-cell solution, and a Keithley Instruments 6487 picoammeter/voltage source was used to apply the desired transmembrane potential and measure the resulting ionic current flowing through the gold nanotube. 

Vm Is Set at a Constant Level Once Fm is set constant, the capacitive current is zero. This means that the current recorded via the recording pipette equals the transmembrane current (current carried by ions flowing through channels and ions transported by pumps) or briefly speaking, the current recorded is the transmembrane current. 

We have carried out simulations under two different conditions. In the first a circular isochrone with an assumed spatial rising phase for is assumed and the resulting transmembrane and longitudinal currents determined for each conductivity case. The objective was to hold all conditions constant except the conductivities to see the effect of the latter on patterns of current flow. (In this we tactily assume that the initial transmembrane potential distribution, while based on observed waveforms, could be specified arbitrarily). 

Figure 1 is the current flow map for a two-dimensional cardiac tissue with nominal conductivity that arises from an assumed circular isochrone, where the rising phase of the transmembrane action potential in the radial direction was assumed to follow a typical behavior as given by the equation... 

Figures. Current flow map for reciprocal anisotropy (g = 2 x 10 Siemens/mm, g,. = 2 x 10"- g = 2 X 10 goy = 2 X 10 " ). Intracellular, interstitial and transmembrane currents are shown. outward...

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