Electrical Properties of Cells
Electrical signals are fundamental to nervous system function.
The electrical properties of cells are important in determining how electrical signals spread along plasma membrane.
This Advanced Topic explores the electrical characteristics of cell membranes as electrical conductors and insulators.
These passive electrical properties arise from the physical properties of the membrane material and from the ion channels in the membrane.
The Cell Membrane as an Electrical Capacitor
An electrical capacitor is a charge-storing device, which consists of two conducting plates separated by an insulating barrier. Because the lipid bilayer of the plasma membrane forms an insulating barrier separating the electrically conductive salt solutions of the ICF and ECF, the plasma membrane behaves as a capacitor.
Capacitance is directly proportional to the area of the plates (bigger plates can store more charge) and inversely proportional to the distance separating the two plates.
Capacitance also depends on the characteristics of the insulating material between the plates, which is the lipid of the plasma membrane in cells.
The unit of capacitance is the farad (F): a 1 F capacitor can store 1 coulomb of charge when hooked up to a 1 V battery.
Biological membranes have a capacitance of approximately 10−6 F (that is, 1 microfarad, or μF) per cm2 of membrane area.
1 microfarad = 0.000001 coulomb/volt
From this value of membrane capacitance, the thickness of the insulating lipid portion of the membrane can be estimated using the following relation: (C-1) In this equation, x is the distance between the conducting plates (that is, the ICF and the ECF), C is the capacitance of the plasma membrane (1 μF/cm2 ), ε0 is the permittivity constant (8.85 × 10−8 μF/cm), and κ is the dielectric constant of the insulating material separating the two conducting plates (κ = 5 for membrane lipid).
The calculated membrane thickness is approximately 4.5 nm, which is similar to the membrane thickness of approximately 7.5 nm estimated with electron microscopy.
The thickness estimated from capacitance is less because it is determined by the insulating portion of the membrane, whereas the total membrane thickness, including associated proteins, is observed through the electron microscope.
Electrical Response of the Cell Membrane to Injected Current.
Many electrical signals in nerve cells arise when ion channels open in the plasma membrane, allowing a flow of electrical current, carried by ions, to move across the membrane and alter the membrane potential of the cell.
If a constant current, I, is injected into the cell, then charge, q, is added to the membrane capacitor at a constant rate (I = dq/dt). Because q = CVfor a capacitor, we obtain the result: (C-2) In other words, dV/dt is a constant, and voltage changes linearly (that is, at a constant rate) during injection of constant current.
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