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Page 34

		1.3.4— Examples of Power Law Scalings of Spatial Objects: The Surfaces of Cell Membranes

		Membranes encase living cells, as well as form different compartments within cells. Paumgartner, Losa, and Weibel measured the total surface area of such membranes from photographs taken with an electron microscope. The magnification of the electron microscope set the spatial resolution of the measurement of the surface area.

		As the magnification was increased, then more undulations in the membranes were detected, and the amount of membrane surface measured increased.

		They found that the surface area measured at resolution r of the endoplasmic reticulum, the outer mitochondrial membrane, and the inner mitochondrial membrane each had a power law scaling of the form that was proportional to rb, where the value of b was different for each type of membrane.

		This power law scaling of the membrane surface area with the resolution r used to measure it appears as a straight line on a plot of versus Log [r]. The slope of these lines, which is equal to the value of b, is different for each type of membrane.

 

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