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Monday, November 14, 2011

Better Biochemistry: Fischer Projections

Biochemistry is a three-dimensional subject but most of us aren't comfortable thinking in three dimensions. For example, we often have difficulty envisaging how a three-dimensional substrate binds to a three-dimensional enzyme.

The problem is exacerbated because we usually teach in two dimensions for simplicity—especially in textbooks.1 There are certain rules that have to be followed when displaying a three-dimensional object on a two-dimensional page. This is especially true for metabolites where the stereochemistry is crucial. One of these rules is called the Fischer projection.2

Most students (and faculty) don't understand the relationship between a two-dimensional Fischer projection and the three-dimensional molecule it's supposed to represent. This is unfortunate because it means they don't really understand the three-dimensional conformation of metabolites.

Let's look at a simple three-carbon compound—glyceraldehyde. There are two different versions of glyceraldehyde: D-glyceraldehyde and L-glyceraldehyde. The two different molecules cannot be superimposed, that's why you know that they are different molecules. Enzymes can tell the difference; that's why D-glyceraldehyde is a common metabolite and L-glyceraldehyde is rarely found in cells.

How do you represent these two molecules in two dimensions? You might think that you could just take the two molecules shown above and squash them down on a page to make an accurate two-dimensional representation. That appears to be what we've done in the drawings below. These representations are known as Fischer projections.

Unfortunately, it's not that simple. Here (left) are two different views of D-glyceraldehyde. (Convince yourself that these two molecules can be superimposed after rotating them around their single bonds.) Note that the right-hand version is the same as the molecule shown at the top of the page. In that conformation, the number 2 carbon atom projects out of the page toward you. In the left-hand version, the number 2 carbon atom projects into the plane of the page (screen). What this means is that the -OH group on this carbon atom is on the right in one molecule and on the left in the other. If we were to squash these molecules down on the page we'd get two-dimensional structures like those shown above.

But if those two-dimensional drawings are Fischer projections then they are supposed to be unambiguous. L-glyceraldehyde can only be L-glyceraldehyde in spite of the fact that we could rotate D-glyceraldehyde and squash it down on the paper to give a two-dimensional molecule with the C2 -OH group on the left. There must be a rule I haven't mentioned.

There is. In all Fischer projections, by definition, the carbon atom projects out of the page toward you. For each carbon atom, the two vertical bonds to adjacent atoms bend into the page and the two horizontal bonds project upward. If you follow this rule then the two-dimensional projections of L-glyceraldehyde and D-glyceraldehyde have to correspond to the three-dimensional molecules shown at the top of the page.

That seems simple enough, doesn't it? Yes it does, for three-carbon molecules. Let's see how it works for more complex sugars like glucose.

The Fischer projections below show the configurations of the eight D aldoses. (The ones in blue are the only sugars commonly found in cells.) These drawings should allow you to recognize any three-dimensional conformation of a D aldose as long as you remember the rule for Fischer projections.

But here's the catch. In a Fischer projection the configuration of atoms around each carbon is determined by the rule. What that means is that each of the six carbon atoms in D-allose projects out of the plane of the page (screen). If you think of that molecule in three-dimensions then you would have to visualize it folding back on itself into the page, The C1 and C6 atoms would bump into each other. In other words, the way we draw Fischer projections gives rise to an impossible conformation for molecules with four or more carbon atoms. You simply can't have a three-dimensional version that you could squash down on a page to make the Fischer projection.

The Fischer projections are artificial representations of the molecule. They are not supposed to represent a three-dimensional molecule.

All of the sugars shown above are D sugars because the position of the hydroxyl (-OH) groups on C5 resembles that of D-glyceraldehyde. That's the definition of a D sugar. Now you might think that all you have to do is change the position of the C5 hydroxyl group in order to make the corresponding L sugar. For example, just shift the C5 hydroxyl group on D-allose to the left-hand side and you get L-allose, right? Wrong!

If you did that, you'd end up with L-talose, not L-allose. That's because in the corresponding L sugars you have to change the configuration at every carbon atom, not just the C5 atom.

Now you know all the rules. Here's an example for you to examine (right). The difference between L-glucose and D-glucose follows directly from the rules. The similarity between the three-dimensional view of D-glucose (extended conformation) and the Fischer projection is harder, but it also follows the rule.

Now it's time to revisit Monday's Molecule #148 where most readers failed to get the right answer because they didn't know the rules.

Try and identify the two molecules shown below without peeking at the right answers from last Monday.

1. This is not a problem that can be solved by having more videos or getting students to look at three-dimensional objects on their computer monitors. Those methods are often distractions when you're trying to teach a fundamental principle or concept.

2. Named after Emil Fischer (1852-1919) who received the Nobel Prize in Chemistry in 1902.


Argon said...

"Most students (and faculty) don't understand the relationship between a two-dimensional Fischer projection and the three-dimensional molecule it's supposed to represent."

Hopefully, most students and faculty aren't chemists or biochemists. Now, if chemistry & biology/biochemistry students don't understand Fischer projection, then that's a worry.

Larry Moran said...

I was specifically referring to biochemistry students and faculty.

BTW, did you guess the correct molecules? Would you have got it right if you had tried last Monday?

DK said...

Guilty as charged. Like I said, I hate sugars :-)