CN2011 Handout 3 Cell shape

CN2011 Handout 3 Cell shape - BIO5571 III.A. Cell Size Cell...

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BIO5571 Cell shape. Page 1 2011 III. CELL SHAPE III.A. Cell Size The first morphological parameter considered is the size of a spherical cell. As you would expect, cell membrane properties scale with the surface area of the cell, since the circuit elements of the surface are in parallel to each other. To compare membrane properties between cells of different sizes, the following quantities are used: Specific membrane resistance R M ohm·cm 2 Specific membrane conductance G M S/cm 2 Specific membrane capacitance C M F/cm 2 For a spherical cell of radius a cm, r M = R M /(surface area) = R M / (4 π a 2 ) c M = C M × 4 π a 2 Most cells have C M ≈ 10 -6 F/cm 2 . Values for R M vary from ~10 3 ohm·cm 2 to ~5x10 4 ohm ·cm 2 . Cells with the lower values for R M are often called "leaky" cells, with the higher values "tight." III.B. Non-spherical cells - general points The basic point is fairly straightforward. For a spherical cell, the cell membrane resistance is larger than the resistance between any points in the cytoplasm or any points in the extracellular fluid immediately outside the cell membrane. Therefore, all of the membrane resistance and capacitance can be treated as being in parallel, and the entire cell can be viewed as being at the some potential. This is not true for many cells: the resistance between points in the cytoplasm can get quite large, and the cell is not necessarily equipotential. Therefore, we must be concerned about voltages and currents between points inside the cell, as well as across the cell membrane. This might appear to be a trivial problem, but it has many ramifications when it is considered carefully. The problem of current flow in cells of various shapes soon gets mathematically complicated. A book which deals with it in detail, but needs mathematical training to follow, is Electric Current Flow in Excitable Cells (Jack, Noble and Tsien, Clarendon Press, Oxford, 1975). The general approach is to divide a cell of complicated shape up into a large number of small pieces, and to use calculus to solve equations describing the current and voltage for each piece. In principle, this is analogous to assembling a large number of spherical cells with the appropriate circuit elements and hooking them together in a particular network. For example, after a spherical cell the next simplest cell is an infinitely long, uniform cable - a squid axon, an unbranched dendrite, or a muscle fiber, for examples. Such a structure could be represented by a strong of identical beads hooked together with internal longitudinal resistors r i and external resistors r x . In the mathematical analysis, each bead is made infinitesimally small and the resulting system of differential equations solved. However, an intuitive appreciation of the effects of cell geometry can be gained by applying principles discussed for spherical cells to the network of beads.
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Units for r i , r m and c M For the infinite linear cable r i : internal longitudinal resistance per unit length
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This note was uploaded on 02/27/2012 for the course BIO 5571 taught by Professor P.taghert during the Fall '11 term at Washington University in St. Louis.

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CN2011 Handout 3 Cell shape - BIO5571 III.A. Cell Size Cell...

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