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Surface : Volume Ratios
One of the most important mathematical concepts in Biology is the relationship between Surface Area and Internal Volume. Briefly stated this relationship says that for any 3-dimensional form, the ratio of Surface Area to Internal volume is NOT constant - it is inversely related to size. In other words, as size gets larger, the Surface Area becomes smaller relative to the Internal Volume.
In this numerical example a sphere is used, but the concept is the same
for any 3 dimensional object.
ASIDE: One of the best examples of how this mathematics applies to Biology is in Ecology. Bergmann's Rule and Allen's rule were first discovered by Ecologists, but their explanation is pure Geometry!! See Dr. Lott for an explanation and Dr. Dalby for actual examples! | ASIDE: Another excellent example of how this mathematics applies to Biology is the question of cell size - why are cells so small? Why is it impossible to have a giant amoeba which eats Manhattan? See Dr. Smith or Dr. Eggleton for an explanation! |
Insolubility of Hydrophilic and Hydrophobic Molecules
Suppose we consider the 9 small droplets of hydrophobic molecules - is there a difference in their surface areas if they are separated as 9 small droplets, or if they all fuse into a single large one? YES!
A single large droplet would have the same internal volume as 9 small ones, but considerably less surface area than the total surface area of the nine small ones.
Decrease in Surface Area 452.4 - 217.5 = 234.92 mm2 less surface area with a single large droplet instead of 9 small ones.
Per cent Decrease in Surface Area
234.92 / 452.4 = 51.9%. The decrease
in surface area is 51.9% of the total for the 9 small droplets.
This means
that 51.9% more water molecules can H-bond with each other if the hydrophobic
molecules are present in a single large droplet rather than 9 smaller
ones.
Therefore the
situation is this:
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