Diacetyl and the Aroma of Butter

diacetyl
Diacetyl, also known as 2,3-butanedione. It’s called a dione because of the presence of two ketone groups. A ketone is a compound that, between two carbon atoms, sandwiches a carbonyl group (a carbon atom double-bonded to oxygen).  If the carbonyl is sandwiched between an oxygen and a carbon within a ringed structure, we have a lactone. Aldehydes have a carbonyl attached to at least 1 hydrogen. Aldehydes, ketones and lactones and other organics make up buttery aromas.

Some textbooks mistakenly attribute butter’s aroma solely to diacetyl, a compound with a pair of ketone groups. Diacetyl does indeed have a buttery smell, but gas chromatography olfactometry reveals a more complete profile of the smell of butter. Complimenting diacetyl in sour cream butter are a pair of other key compounds, also formed by lactic acid- fermenting bacteria. Known as butanoic acid and δ-decalactone, they contribute cheesy and peachy notes, respectively. Sweet cream butter’s smell is defined by lactones and sulphurous compounds while aldehydes are found in butter oil’s aroma. Heat up the butter and the caramel-like furanone, the potato-like methional and then the cheesy 3-methylbutanoic acid will surface.

Small amounts of diacetyl are also found naturally in a variety of other foods aside from butter including cheeses and other dairy products, and it’s also in beer and wine.  Depending on the type of beer, diacetyl is not always desirable. In wine however it lends a smooth, buttery taste. Interestingly our threshold for detection of diacetyl in wine varies with the type. It’s low in Chardonnay (0.2 ppm) but higher in Merlots and Sauvignon. Apparently diacetyl  binds to sulfur dioxide, whose concentration varies from one wine to another.

But why is diacetyl’s presence fairly common? Glucose is life’s most important investment of chemical energy. But cells can’t burn it in a crude manner as if it were wood or fossil fuels in the hands of humans. That would release only heat, would be too disruptive and too limiting. Instead the energy has to be invested in other compounds such as ATP that can then both facilitate constructive reactions and release heat slowly. Whether or not oxygen is present, the 6-carbon molecule, glucose, is, in a series of steps, first converted to a pair of 3-carbon atoms known as pyruvate. In oxygen’s presence, pyruvate will enter the citric acid cycle and lead to the production of lots of ATP. On the other hand, the absence of oxygen will lead to less productive options known as fermentation. Fermenters start with pyruvate, obtaining it either from glycolysis or from citric acid. But certain bacteria, while investing in ATP also produce lactic acid, acetate, 2,3-butanediol or, like yeasts, even alcohol. Diacetyl trickles out of that reaction-ensemble, coming from a side-reaction that releases diacetyl and CO2 from a 5-carbon molecule, which is in turn made partly from pyruvate.

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From the New England Journal of Medicine: the difference between a healthy bronchiole and one that’s been permanently constricted. Bronchioles are the part of the lung connecting its main branches to its air sacs.

As long as there’s more profit to be gained, industry is too often ready to cater to consumers’ laziness. Why oblige them to add their own butter to popcorn or flavors to coffee when part of butter’s aroma can be prepackaged? Unfortunately diacetyl has been shown to be an occupational hazard for workers in factories handling the compound. Repeated exposure to elevated concentrations of diacetyl leads to permanent shortness of breath from obliterative bronchiolitis, a condition involving scarring and constriction of the bronchioles. Some companies have stopped using diacetyl altogether. Those who persist have to make sure that a limit of 5 parts per billion for up to 8 hours a day and 40 hours per week is not surpassed. All the energy that goes into mass-producing diacetyl and all the physical suffering and regulations could be saved and avoided if people buttered their own popcorn or ate the unadulterated version while learning about diacetyl’s chemistry.

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Fun With Shapes and Numbers

In the diagram below, in between two circles, each with a radius of 1 meter, three smaller circles are squeezed in, centred at C1 , C2 and C3. If you imagine it was possible to continue drawing and squeezing in more circles until you had a billion of them, how much space would be left between the top of the smallest circle and point A? And what ubiquitous thing’s diameter is very close to that distance?

circlePuzzle
What could fit into the tiny space between point A and the smallest of a billion circles squeezed into the space between the two large circles, one of which is centered at B? Diagram by the author.

This is a variation of an old problem, and although the situation is often used as an example of a non-geometric series in calculus books, it could also be solved with some basic algebra and induction. And for that reason, versions of the puzzle have appeared in math competitions for bright kids who have yet to venture into calculus.

Let’s begin by solving for the radius of the first circle (the red one centered at C1). If we come with expressions or numbers for all three sides,  we could apply the Pythagorean theorem to triangle ABC1.

Notice that AC1 ‘s length can simply be obtained by subtracting the radius of the red circle from the 1-meter length of the square’s side, which we obtain from the radius of the large, identical circles.

AC1 = 1 – r1.

Since AB² + AC1 ² = BC1 ²,  where the hypotenuse, BC1 , is simply the sum of the radii, we obtain:

1² + (1 – r1) ² = (1 + r1) ²

Solving for r1 yields  r1 = 1/4 so the red circle’s diameter = d1  = 2 * 1/4 =  1/2 .

Not to bore you, we will walk through the steps only one more time to obtain the diameter, d2, of the blue circle centered at C2.

We add the red circle’s obtained diameter of  1/2 to the radius of  the blue circle, r2 , and then subtract the sum from 1 meter to obtain AC2.

AC2 = 1 – (1/2 + r2 )=   1/2 – r2

Then we apply the Pythagorean theorem to the second triangle, ABC2,

AB² + AC2 ² = BC2 ²,  or:

1² + ( 1/2 – r2) ² = (1 + r2) ²

1 + 1/4 – r2 + r2 ² = 1 + 2r2 + r2 ²

1/4 = 3r2

r2 = 1/12

so the blue circle’s diameter = 2 * 1/12 = d2 = 1/6.

As promised, without going through the similar details, d3 = 1/12 and for a fourth circle that we squeeze in, d4 will be 1/20.

Now a pattern becomes apparent. For the diameter of the nth circle, dn,  dn = 1/n(n+1). But if you did not realize that, you could still solve the problem. After all, we’re interested in the leftover distance between the top of the billionth circle and point A.

After we squeezed in one circle , we had a diameter of  1/2 . After squeezing in a pair, the sum of the two circles’ diameters 1/21/6 = 2/3. Squeeze in three circles and the sum is  1/21/6 + 1/12 = 3/4 .  A fourth insertion yields 1/21/6 + 1/12 + 1/20 = 48/60 = 4/5.

So for squeezing in an n-number of  circles, the sum of the diameters is n/n+1 and since the side of the square is 1 meter in length, the remaining distance will be 1 – n/n+1. Using a common denominator, that expression is equal to n+1 -n/n+1 = 1/n+1.  For a billion circles then, the leftover distance would be

1/1 000 000 000 +1 = 1/1 000 000 001 meters,

which is extremely close to being to a nanometer.

Alpha-D-glucose-3D-balls
α-D-Glucopyranose, the hexagonal form of glucose. Image from Wikimedia commons.

1/1 000 000 000 meters or 1 nanometer, is a little more than three times the size of a single water molecule, and just slightly wider than the ring of one glucose molecule, the fuel for all brains, including those that devised and solved this puzzle. And use up just an extra iota of  glucose to realize that the leftover space would be long enough but not wide enough to accommodate the entire molecule. Finally, imagine a circle for every person alive on Earth in 2050, about 9.4 billion, and the distance remaining between the smallest circle and point A will only as big as the diameter of the smallest and most common atom in the universe.

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