## How strongly do you have to pull on a covalent bond to break it?

The first time I saw just how large our chromosomes are, the thought struck me (as it probably struck many of you).  Why don’t they fall apart?  Are covalent bonds strong enough to hold them together?  The most boring part of chemistry (for me) is calorimetry measuring heats of formation and indirectly just how much energy it takes to break a given bond.

Force is not the same thing as energy, but there is a way to convert the kiloCalories (energy) in a given bond into the force needed to break it.  The units of energy are those of work, namely force times distance.   Figure that if you stretch a bond by one Angstrom (10^-10 meters) you’ve broken it.

Now the X chromosome (our largest) contains 155,000,000 nitrogen bases + deoxyribose + phosphate + potassium.  (Why potassium rather than sodium?. Because potassium is the main intracellular cation, and sodium is the dominant cation outside cells).  What is it’s mass?

Figuring things out in Daltons, potassium is 40, PO2 is 63, deoxyribose 131.  How to account for the 4 bases (adenine 135, thymine 126, cytosine 111, Adenine 151)?  I averaged them — which isn’t quite kosher as our DNA doesn’t contain 25% of each base, but close enough — so the average nucleotide has a mass of 131 Daltons.

What is the mass of a Dalton in grams?   A dalton is 1/12 the weight of a mole of carbon 12 or one gram.  So how much does an atom of hydrogen weigh?  (Better — what is its mass?) — it’s 1/Avogadro’s number or 1/(6.023 x 10^23 grams).

So the average nucleotide (base sugar phosphate + potassium) has a mass of 362 Daltons or 362/6.023 x 10^23) grams

Multiply this by 155,000,000 and you get 9316 * 10^6 * 10^-23 or (roughly) 10^13 grams (If I’ve done everything correctly) or 10^-16 kiloGrams.

Force = Mass * acceleration.  The acceleration of gravity is 9.81 meters/second^2.

Force (in Newtons) is Kilograms * Meters/second^2.

If we suspend one strand of our X chromosome and let gravity pull on it, the topmost bond has a force of

10^-16 kilograms * 9.81  — roughly 10^-15 Newtons pulling on it. Now let the force pull one of the bonds at the top apart a distance of 1 Angstrom (10^-10 meters).   We’ve done work of 10^-25 Newton* meters on our one molecule of the X chromosome.  Well 1 Newton*meter is 1 Joule. But the energy of bonds are given in kiloJoules/Mole and also we’re talking about one molecule here.

Single bond energies are 65 *4.184 for C-N, 80 * 4.184 for C – C and 78 * 4.184 for C – O.  The energies were given in kiloCalories/mole so you need to multiply by 4.184 to get joules (and another 10^3 to get kiloJoules).   I’m not sure what the value for the P – O bond is.  From here it looks like the C – O bond is the weakest link (Why not C – N?   All nucleotides are joined to the ribose by a C – N bond aren’t they?   Because all nucleotides hang off the sugar phosphate backbone, so they aren’t pulled on by the mass of the chromosome.).

So the energy to break one C – O bond in a molecule is 78 * 4.184 * 10^3/Avogadro’s number (in Joules)

78 * 4.184 * 10^3/6.023 * 10^23 = 54 * 10^-20  Joules.  But the whole mass of the chromosome pulling on the C – O bond and stretching it by 1 Angstrom exerts only 10^-25 Joules.  Far from enough.

It’s been a fun calculation, and I hope I did it right.  Please correct me if I’ve screwed up.

So has anyone broken a covalent bond by stretching it?  People doing single molecule studies do all sorts of nasty things to the molecule — stretching, twisting etc. etc.  But these always involve the noncovalent interactions a found in the secondary and tertiary structure of proteins.

The answer is yes, amazingly enough.  See Science vol. 329 pp. 1057 – 1060 ’10.  A polybutadiene polymer was treated with a difluorocarbene forming difluorocyclopropanes along the polymer backbone.  They were able to open up the cyclopropane by stretching it, forming a diradical (for which they had convincing spectroscopic and chemical evidence).  The initial cyclopropane had its links to the rest of the chain trans (as the polymer has trans double bonds), but when the diradical formed and was allowed to collapse back to form a cyclopropane again, the links were cis.  So the polymer contracted after pulling on it.  Ain’t chemistry grand ?