# How many cis-trans isomers does 1-O-stearoyl-2-O-arachidonyl-phosphatidyl-inositol-4',5'-bisphosphate have?

I saw an exam that had a question asking the number of cis-trans-isomers of 1-O-stearoyl-2-O-arakidonyl-phosphatidyl-inositol-4',5'-bisphosphate:

The "correct" answer in the exam is 1023, but this is clearly not correct, because the stereoisomerism of the inositol ring is not called cis-trans-isomerism.

So, obviously only the arachidonyl chain has cis-trans isomerism. But if an isomer has several of the double bonds in trans orientation (not just one), is is still correct to call it a cis-trans isomer of the original molecule. If it is, I would say that this molecule has 15 cis-trans isomers. If it isn't I would say that it has only 4 cis-trans isomers.

Which one is correct?

• There can be cis and trans in the cyclic rings. The substituents can be axial or equatorial. Also, 15 is too low a number for the number of stereo isomers. Just consider the double bonds, you have four of them, each has two choices, cis or trans. That gives $2^4$ isomers on its own. Just 16 isomers from the double bond chain, there's way more possible from the ring. Keep trying, you'll get it soon. – Pritt Balagopal Jun 2 '17 at 9:44
• The isomerism in the ring is not called cis-trans-isomerism in this case. (See my other question at chemistry.stackexchange.com/questions/74853/…) And I would not say that the molecule is a cis-trans isomer of itself. Therefore it can't have more than 15 cis-trans isomers. – ttsc Jul 3 '17 at 18:27

## 1 Answer

Perhaps the answer is correct. If by cis/trans isomers the question includes the four stereogenic double bonds of the arachadonic acid chain and the six stereogenic carbons of the inositol ring, then there is a total of ten or 210=1024 isomers. But the answer is 1023 stereoisomers. That is because the question says "cis-trans-isomers OF...", which means NOT including the one shown. [210-1=1023.] Had the question asked "How many stereoisomers OF ...", then the lone stereogenic center of the glycerol moiety would have to be included. Then the answer would be 211-1=2047.

• The stereoisomerism of the inositol ring is not called cis-trans-isomerism. – ttsc Dec 7 '17 at 21:27
• Au contraire! Read the first sentence here in the IUPAC Gold Book. goldbook.iupac.org/html/C/C01092.html – user55119 Dec 7 '17 at 23:59
• Ok. I see your point. But what would you say about this: chemistry.stackexchange.com/questions/74853/… There everybody seems to agree that glucose and galactose are not cis-trans-isomers of each other. – ttsc Dec 8 '17 at 10:29
• I read your link. The problem with using cis/trans with a pyranose is that it is too cumbersome to express all of the relationships. As @NotEvans states cis/trans is usually reserved for rings with two substituents (and "simple" 1,2-disubstituted alkenes). It is more convenient to use glucose as a frame of reference and refer to D-galactose as the C4-epimer of D-glucose or alpha-D-mannose as the C1-epimer (anomer at C1) of beta-D-mannose. The point of the original exam question was to see if one recognizes elements of stereogenicity. Four double bonds would have been too trivial. – user55119 Dec 8 '17 at 16:02
• Yes, I understand that that's what the authors of the exam were thinking, but I'm interested in figuring out if they used the terms correctly. However, I have to admit that the IUPAC Gold Book definition seems like it would allow the interpretation of having 1023 cis-trans-isomers for this molecule. – ttsc Dec 8 '17 at 22:13