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Unformatted text preview: BIO5571 Cells as circuits. Page 1 2011 II. APPLYING ELECTRICAL CIRCUIT THEORY TO CELLS Equivalent circuit analysis often seems boring, difficult or uninformative when applied to cells, prompting the question Why bother? However, doing a circuit analysis is the only way to determine whether we actually understand properties of a cells membrane channels, and how the channels contribute to the physiological functioning of the cell. Biochemists have now identified many channel proteins of eukaryotic cells, but the central goal for a neurophysiologist is to determine the role of each channel in the overall function of a cell. Usually we start with observations of cell responses, so the goal is to determine the channels which underlie the particular membrane responses present in a given cell. The physical makeup of a cell membrane is quite different from that of the typical circuit-board in a stereo. Also, the membrane currents we are interested in are carried by ions, not by electrons. However, the principles of circuit analysis can be moved from one situation to another. Instead of electrons being moved through a resistor by an applied voltage, ions move through conductance pathways in the cell membrane down their electrochemical gradients. The fact that the ions are charged means that charges move across the membrane and so currents move across the membrane. The ability of ions to move across the cell membrane can be expressed either in terms of the resistance to movement (how hard it is to move an ion, or the membrane resistance to ion passage) or in terms of how easy it is to move the ion (the membrane conductance for that ion, or the inverse of the membrane resistance). In many contexts with cell membranes it is more natural to use membrane conductance in thinking about what determines the movement of ions. The fact that charges are separated across the membrane means that the cell membrane acts as a capacitor. Indeed, the capacitor is the critical element in the cell to convert ion movements into a membrane potential. Analysis of cell membrane properties in practice works backwards. An electrical engineer considers a bunch of circuit elements hooked together in a particular fashion, and predicts how the circuit will behave. The physiologist is given a cell behaving in some fashion, and has to deduce the elements of the circuit. The next, and essential, step is to determine that the deduced circuit actually behaves as the cell does under the experimental conditions used. Finally, the deduced circuit is used to predict the behavior expected in other experimental conditions. If the equivalent circuit has good predictive value, then it is likely to be an adequate description of the cell membrane electrical properties and it is possible to say This cell has one kind of voltage-gated sodium-selective channels with such-and-such gating properties, three kinds of voltage-gated potassium-selective channels .... Those interested in biology then go on to examine such voltage-gated potassium-selective channels ....
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- Fall '11