PLANT BIOPHYSICS - Y. I. Posudin - 2004

I. PHYSICAL PROPERTIES OF PLANT CELLS AND TISSUES

4. ELECTROPHYSICAL PROPERTIES OF PLANTS

4.2. ELECTRICAL PROPERTIES OF THE CELL

Let us consider a spherical PLANT Cell AND estimate the resulting electrical charge that produces a typical transmembrane potential difference. The magnitude of the electrical charge of a sphere q is related to the capacitance of the sphere C and the potential difference Δφ across the plates of a spherical capacitor by the following relation:

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Suppose that the net charges with a density n are uniformly distributed throughout The Cell interior. Given that the charge inside a sphere is q = (4/3)nF (where F = 96487 C/mol is the Faraday constant), and the capacitance of the sphere is C = 4πr²C_s, with r being the radius of the sphere and C_s the specific membrane capacitance per unit area, we can formulate the expression for the potential difference in the case of a spherical capacitor:

This equation determines the potential difference between the center of the sphere and its outer surface. However, within the aqueous interior of the cell, charges are not uniformly distributed: they repel one another and accumulate on the inner surface of the sphere. Consequently, the potential difference actually drops across the limiting boundary of the sphere, that is, the membrane.

The electrical properties of Introduction/36.html">Biological Membranes are characterized by the following parameters: specific capacitance C_s = 0.5–1.3 µF·cm²; specific resistance R_s = 10²–10⁵ Ω·cm^-2. Let us discuss the fundamental passive electrical properties of cell membranes arising from their structural features. First, The Lipid Bilayer is impermeable to ions, which enables it to separate charges and act as a capacitor. Second, the lipid bilayer is embedded with Ion Channels through which inorganic ions can pass. The transfer of electric charges across the membrane can be represented as an equivalent electrical circuit consisting of a parallel combination of a capacitor C_M and a resistor R_M. The lipid bilayer acts as the capacitor, whereas the resistance corresponds to the conductance provided by the ion channels.

Let a spherical cell with a diameter of 30 µm have a transmembrane potential difference of -100 mV (a typical value for many Cells). Assuming that The cell membrane capacitance is C_s = 1 µF·cm² (or 10^-6 C·V^-1·cm^-2), let us calculate the average electric charge density within the cell that corresponds to this potential difference:

The negative sign indicates that there are more anions than cations inside the cell. Recall that the total ion concentration in plant cells is 0.1 mol.

Review Questions

1. Characterize the types of substance transport across membranes.

2. What are diffusion and osmotic equilibria?

3. Explain the physical principles underlying The formation of chemical and electrical gradients.

4. What does the Nernst equation describe?

5. What are the Resting Potential and the Action Potential?

6. Explain the main Methods for measuring membrane potentials.