Vm Responses of an Active Cell

When an active cell is field stimulated, the ion channels all along the cell length activate and inactivate to varying degrees as the cell is polarized. As a result, different regions of the cell have different membrane resistance (Rm). Moreover, as the channels gate, Rm dynamically changes with time. Therefore, Rm is a function of space and time, that is, Rm = Rm(x,t). Consequently the transmembrane current (im = Vm/Rm) integrated over the entire cell can have a time-varying nonzero value, that is,

where ds is the elemental membrane area. Note that in the case of a passive cell Im is always zero since either the im is zero, or ims in the regions symmetrically located about the cell center are equal and opposite. A nonzero Im for an active cell results in a net charge transfer from or into the cell and causes a change in and hence a change in Vm. However, because the intracellular space is small and highly conductive, any such change in (and Vm) is uniform along the cell length (i.e., ^ is only a function of t). Thus, Vm for an active cell is given by

Figure 2 presents two possible situations during field stimulation. Figure 2a presents the case of a cell in which the inward current in the negatively polarized regions exceeds the outward current in the positively polarized regions. The Im is inward, and therefore the ^ increases with time. Consequently, the Vm from the various sites show a parallel positive x— x, -;—^ x=+x1

Figure 1: Physical basis of a passive cell's polarization. (a) Shows the schematic of a cell of length L with origin at x = 0. The cell is stimulated with a uniform electric field Eo in the indicated direction, and the steady-state extracellular potential (<e) and intracellular potential (<) are shown in (b), top subpanel. The <e varies linearly along the cell length, and the < stays isopotential at zero. The resulting transmembrane potential (Vm = < — <e) is shown in (b), bottom subpanel. (c) Shows the result of a hypothetical experiment in which the cell shown in (a) is stimulated with a field pulse shown in (c), top row. The responses corresponding to three sites on the cell (overlaid circles; x = —x1, 0 and +x1) are shown in (c), bottom three rows

Figure 1: Physical basis of a passive cell's polarization. (a) Shows the schematic of a cell of length L with origin at x = 0. The cell is stimulated with a uniform electric field Eo in the indicated direction, and the steady-state extracellular potential (<e) and intracellular potential (<) are shown in (b), top subpanel. The <e varies linearly along the cell length, and the < stays isopotential at zero. The resulting transmembrane potential (Vm = < — <e) is shown in (b), bottom subpanel. (c) Shows the result of a hypothetical experiment in which the cell shown in (a) is stimulated with a field pulse shown in (c), top row. The responses corresponding to three sites on the cell (overlaid circles; x = —x1, 0 and +x1) are shown in (c), bottom three rows shift during the field pulse. Figure 2b depicts a situation in which the Im is outward, and therefore Vm shows a negative shift with time.

In the next section we will turn to experimental examination of Vm responses during field stimulation of a cardiac cell and attempt to understand them in the context of theoretical framework described above.

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