Why are cells so small? The answer to this question has as much to do with mathematics as biology. Imagine that a cell is shaped like a cube. As cell size increases, its surface area to volume ratio changes. The surface area and volume are calculated as shown in the figure below:
Questions:
1. List some of the things that cross a cell's membrane:
2. Why is it important that a cell have a large surface area relative to its volume? (In other words, a high surface area to volume ratio?)
3. Imagine that a cell's side could be any size that you wanted. Calculate what would happen to the surface area to volume ratio as the cell grows. Since we are assuming the cell to be cube shaped, all sides are equal so X=Length=Width=Height. The units here could be anything, since we're just hypothesizing.
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X |
6X2 |
X3 |
6X2 ÷ X3 |
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4a. What is happenning to the surface area to volume ratio as cell size increases?
As cells get larger, the surface area to volume ratio ______________________ (increases/decreases).
4b. Since transport of materials in and out of the cell can only happen at the cell's surface, what happens as cells get larger?
5. Take what you know about surface area to volume ratio and try to explain the following graph, which is known as the "mouse to elephant curve". Assume that metabolic rate relates to heat production and that all of these animals are trying to keep their bodies warm under the same environmental conditions. Note for example that an elephant has a mass (and volume) of more than 1000 times that of a mouse while its metabolic rate (and heat production) is only about 100 times that of a mouse. Why can an elephant heat itself more efficiently (per unit of mass) than a mouse?
6. "Bergman's Rule" says that among species of animals which have a global distribution, adult body size tends to be largest in the polar regions, medium in temperate climates and smallest in tropical ones. Although there are exceptions, this is generally true. Why should it be so?
7. Challenge Question: In one of my favorite old monster movies, Them, giant ants attack the city. Unfortunately, it could never happen. The incredible strength of the ant is dependent upon its small size. Scale him up to even human size and he'd collapse under his own weight on those skinny little legs. Volume (and therefore weight) scales to the power of 3 while surface area (and size) scale to the power of 2. Create a graph that shows why the giant ant can't destroy the city.