Chapter 22, Problem 40PP

Converting dc to ac. An individual cell such as an egg cell (an ovum, produced in the ovaries} is commonly organized spatially, as manifested in part by asymmetries in the cell membrane. These asymmetries include non-uniform distributions of ion transport mechanisms, which result in a net electric current entering one region of the membrane and leaving another. These steady cellular currents may regulate cell polarity, leading (in the case of eggs) to embryonic polarity; therefore, scientists are interested in measuring them.

These cellular currents move in loops through extracellular fluid. Ohm’s law requires that there be a voltage difference between any two points in this current-carrying fluid surrounding cells. Although the currents may be significant, the extracellular voltage differences are tiny—on the order of nanovolts. If we can map the voltage differences in the fluid outside a cell, we can calculate the current density by using Ohm’s law, assuming that the resistivity of the fluid is known. We cannot measure these voltage differences by spacing two electrodes 10 or 20 μm apart because the dc impedance (the resistance) of such electrodes is high and the inherent noise in signals detected at the electrodes far exceeds the cellular voltages.

One successful method of measurement uses an electrode with a ball-shaped end made of platinum that is moved sinusoidally between two points in the fluid outside a ceil. The electric potential that the electrode measures, with respect to a distant reference electrode, also varies sinusoidally. The dc potential difference between the two extremes (the two points in the fluid) is then converted to a sine-wave ac potential difference. The platinum electrode behaves as a capacitor in series with the resistance of the extracellular fluid. This resistance, called the access resistance (R _A), has a value of about ρ/10a, where ρ is the resistivity of the fluid (usually expressed in ω·cm) and a is the radius of the ball electrode, The platinum bail typically has a diameter of 20 μm and a capacitance of 10 nF; the resistivity of many biological fluids is 100 ω·cm.

40. What is the dc Impedance of the electrode, assuming that it behaves as an ideal capacitor?

1. A.    0
2. B.     Infinite
3. C.     $\sqrt{2}$ × 10⁴Ω
4. D.    $\sqrt{2}$ × 10⁶Ω