# Number of isomers in a 3-sugar oligosaccharide

I recently read that 12288 different oligosaccharides can be formed from the D-isomers of glucose, mannose and galactose. I wanted to try to calculate this, but I keep falling very short of this number.

Each molecule has the potential to form 6 unique bonds:

The disaccharide can form 13 unique bonds:

(Note, bonds formed by anomeric carbons shown with an arrow)

So, if a monosaccharide can form 6 different bonds, this means that:

6 possible bonds x 5 bonds on 2nd sugar x 2 anomers for seconds sugar = 60 possible disaccharides

Each of these disaccharides has 13 possible bonds it can make to a third saccharide:

13 bonds x 5 bonds of 3rd molecule x 2 anomers = 130 combinations for a single dissacharide.

130 combinations per disaccharide x 60 possible disaccharides =7800 isomers.

This is probably a counting error. But maybe I am missing a stereocenter?

• Do you have a reference for the 12,288 figure? I get twice that. Would like to look at work before posting. – user55119 Dec 18 '17 at 13:50
• Found it! Google stryer 12288 isomers. – user55119 Dec 18 '17 at 14:07