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We turn our attention next to molecules which have more than one stereocenter. We will start with a common four-carbon sugar called D-erythrose.
A note on sugar nomenclature: biochemists use a special system to refer to the stereochemistry of sugar molecules, employing names of historical origin in addition to the designators 'D' and 'L'. You will learn about this system if you take a biochemistry class. We will use the D/L designations here to refer to different sugars, but we won't worry about learning the system.
As you can see, D-erythrose is a chiral molecule: C2 and C3 are stereocenters, both of which have the R configuration. In addition, you should make a model to convince yourself that it is impossible to find a plane of symmetry through the molecule, regardless of the conformation. Does D-erythrose have an enantiomer? Of course it does – if it is a chiral molecule, it must. The enantiomer of erythrose is its mirror image, and is named L-erythrose (once again, you should use models to convince yourself that these mirror images of erythrose are not superimposable).
Notice that both chiral centers in L-erythrose both have the S configuration. In a pair of enantiomers, all of the chiral centers are of the opposite configuration.
What happens if we draw a stereoisomer of erythrose in which the configuration is S at C2 and R at C3? This stereoisomer, which is a sugar called D-threose, is not a mirror image of erythrose. D-threose is a diastereomer of both D-erythrose and L-erythrose.
The definition of diastereomers is simple: if two molecules are stereoisomers (same molecular formula, same connectivity, different arrangement of atoms in space) but are not enantiomers, then they are diastereomers by default. In practical terms, this means that at least one - but not all - of the chiral centers are opposite in a pair of diastereomers. By definition, two molecules that are diastereomers are not mirror images of each other.
L-threose, the enantiomer of D-threose, has the R configuration at C2 and the S configuration at C3. L-threose is a diastereomer of both erythrose enantiomers.
In general, a structure with n stereocenters will have 2n different stereoisomers. (We are not considering, for the time being, the stereochemistry of double bonds – that will come later). For example, let's consider the glucose molecule in its open-chain form (recall that many sugar molecules can exist in either an open-chain or a cyclic form). There are two enantiomers of glucose, called D-glucose and L-glucose. The D-enantiomer is the common sugar that our bodies use for energy. It has n = 4 stereocenters, so therefore there are 2n = 24 = 16 possible stereoisomers (including D-glucose itself).
In L-glucose, all of the stereocenters are inverted relative to D-glucose. That leaves 14 diastereomers of D-glucose: these are molecules in which at least one, but not all, of the stereocenters are inverted relative to D-glucose. One of these 14 diastereomers, a sugar called D-galactose, is shown above: in D-galactose, one of four stereocenters is inverted relative to D-glucose. Diastereomers which differ in only one stereocenter (out of two or more) are called epimers. D-glucose and D-galactose can therefore be refered to as epimers as well as diastereomers.
Exercise 3.10: Draw the structure of L-galactose, the enantiomer of D-galactose.
Exercise 3.11: Draw the structure of two more diastereomers of D-glucose. One should be an epimer.
In total, there are 210 = 1024 stereoisomers in the erythronolide B family: 1022 of these are diastereomers of the structure above, one is the enantiomer of the structure above, and the last is the structure above.
We know that enantiomers have identical physical properties and equal but opposite degrees of specific rotation. Diastereomers, in theory at least, have different physical properties – we stipulate ‘in theory’ because sometimes the physical properties of two or more diastereomers are so similar that it is very difficult to separate them. In addition, the specific rotations of diastereomers are unrelated – they could be the same sign or opposite signs, and similar in magnitude or very dissimilar.
It is a general rule that any molecule with at least one stereocenter is chiral – but as with most rules, there is an exception. Some molecules have more than one stereocenter but are actually achiral – these are called meso compounds. Tartaric acid, a byproduct of the wine-making process, provides a good example.
With two stereocenters, there should, in theory, be four stereoisomers of tartaric acid. In fact, there are only three. First of all, there is a pair of enantiomers with (2R,3R) and (2S, 3S) stereochemistry.
Now, carefully consider a (2S, 3R) stereoisomer. You may notice that, when it is rotated into just the right conformation, this isomer has a plane of symmetry passing through the C2-C3bond.
That means that this molecule is not chiral, even though it has two stereocenters! It also means that (2R,3S) tartaric acid and (2S,3R) tartaric acid are not enantiomers, as we might have expected – they are in fact the very same molecule, meso-tartaric acid. This achiral molecule is, however, still a diastereomer of both R,R and S,S tartaric acid. Notice that the two ‘stereocenters’ of (meso)-tartaric acid have the same four substituents – this is a prerequisite for meso compounds; otherwise there would be no plane of symmetry.
Cyclic compounds can also be meso. One of many such examples is cis-1,2-dihydroxycyclohexane. Note, however, that if the hydroxyl groups are trans to each other, the molecule is chiral.
Fortunately for overworked organic chemistry students, the meso compound is a very special case, and it is difficult to find many naturally occurring examples. They do, however, seem to like showing up in organic chemistry exam questions.
Exercise 3.12: Which of the molecules shown below are meso? Which are chiral? Which are achiral, but not meso?
Exercise 3.13: Draw the structure of another dimethylcyclopentane isomer that is meso (do not use structures from the previous problem).
As we saw with meso compounds, a molecule or group need not be chiral to have stereoisomers. Asymmetric alkene groups have a defined stereochemistry associated with their structure, but because of their flat geometry they have an inherent plane of symmetry and thus are not chiral. Consider, for example, two stereoisomeric forms of 2-butene.
The isomer on the left is cis-2-butene, while the isomer on the right is trans-2-butene. As we have learned already, the prefix trans means ‘opposite side’, and cis means ‘same side’. Because there is a barrier to rotation about the C2-C3 double bond, the cis and trans isomers are actually different stereoisomers, not just different conformations of the same molecule. Specifically, they fit the definition of diastereomers: they have the same connectivity but a different arrangement of atoms in space, and they are not mirror images.
Below are some examples of biomolecules that have diastereomeric alkene groups. Most naturally occurring unsaturated fatty acids have cis-double bonds, but trans-fatty acids, which are believed to be harmful, are found in margarine and some kinds of meat (see section 16.5D for more about the chemistry of trans-fats).
Retinal is a light-sensitive molecule, derived from vitamin A, that is found in the rod cells of the eye. When light enters the eye through the retina, the 11-cis diastereomer of retinal is converted to the all-trans diastereomer, changing the shape of the molecule and the way that it binds to the vision protein rhodopsin. This initiates a chain of events that leads to a signal being sent to the vision center of the brain.
While the terms cis and trans are quite clear in the examples above, in some cases they can be ambiguous, and a more rigorous stereochemical designation is required. To unambiguously designate overall alkene stereochemistry, it is best to use the designators 'E' and 'Z'. To use this naming system, we first decide which is the higher priority group on each carbon of the double bond, using the same priority rules that we learned for the R/S system. If the higher-priority groups are one the same side of the double bond, it is a Z-alkene, and if they are on the opposite side it is an E-alkene. Shown below is an example of an E-alkene: notice that, although the two methyl groups are on the same side (cis) relative to one another, the alkene has overall E stereochemistry according to the rules of the E/Z system because one of the methyl groups takes a lower priority.
Natural rubber is a polymer composed of five-carbon building blocks, called 'isoprene', that are linked with Z stereochemistry. The same isoprene building blocks can also be connected with E stereochemistry, leading to a polymer that is a precursor to cholesterol (and many other natural compounds found in all forms of life).
As a general rule, alkenes with the bulkiest groups on opposite sides of the double bond are more stable, due to reduced steric strain. The E (or trans) diastereomer of 2-butene, for example, is more stable than the Z (or cis) diastereomer.
In a reaction where either 2-butene isomer could form, it is the E isomer that will predominate (we'll see an example of this phenomenon when we study a reaction called an 'elimination' in section 14.3, and it will also be important when we look at the problem if trans fats in section 16.5D).
The compounds shown below were all isolated from natural sources and their structures reported in a recent issue of the Journal of Natural Products, an American Chemical Society publication. Label all alkene groups that are not inside 5- or 6-membered rings as E, Z, or N (neither E nor Z).
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