of another, and two of a third. Porphyrin rings to which are attached that particular combination of sidechains are called "protoporphyrins."
Now this is the ticklish point. Which side-chains are attached to which positions in the porphyrin ring? To illustrate the difficulty, let's draw some pictures. Since this article concerns itself not with chemistry—despite appearances so far—but merely with some simple arithmetic, there is no need to make an accurate representation of the porphyrin ring. It will be sufficient to draw a ticktacktoe design (Figure 2). Topologically, we have achieved all that is necessary. The two ends of each of the four lines represent the eight positions to which sidechains can be attached.
 Figure 3a |
 Figure 3b |
Two possible arrangements of protoporphyrin side-chains.
(Note: The reader may think he can draw more arrangements than the fifteen stated in the article to be the number that can exist. So he can! However, the porphyrin ring possesses four-fold radial symmetry and front-back bilateral symmetry which reduces the number of different arrangements eightfold. Furthermore, certain arrangements could be ruled out for various chemical reasons. There remained, as stated, fifteen arrangements in all which could not be ruled out either by symmetry or by chemical reasoning.)
If we symbolize the side-chains as a, b, and c (four a's, two b', and two c's), several arrangements can be represented. Two of these are shown in Figures 3a and 3b. Altogether fifteen different and distinct arrangements can exist. Each arrangement represents a molecule with properties that are in some respects different from those of the molecules represented by
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