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Maybe a silly question but I was wondering about this. Trying to understand how small things are.

I have read that the DNA in a single cell if stretched out, would be about 6 feet long.

If you actually stretched it out and had something hold it - so that it was n a vertical line from about 6 ft to the floor, and then

  • would it cast a visible shadow?

  • if you waved your hand through it, would you be able to feel it?

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    $\begingroup$ Welcome to Biology.SE: I'm voting to close this question as off-topic because this is a question of physics and the strength of chemical bounds but not so much of biology. $\endgroup$ – Remi.b Apr 7 '17 at 17:21
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    $\begingroup$ @Remi.b I think we might be a bit overzealous in voting to close/migrate questions that could be appropriate here. I'd recommend we keep it open, I don't think it is any more relevant at physics or chemistry.se than it is here. $\endgroup$ – Bryan Krause Apr 7 '17 at 17:43
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    $\begingroup$ You should post this at physics.stackexchange.com Briefly, you should consider the fact that the width of the strand is an order of magnitude smaller than the wavelength of light, so even at very close range you won't get a shadow. Even much wider obstacles won't cast a shadow some distance away, and even if a small but much larger object than the DNA strand geometrically covers a light source, you may not get a shadow due to diffraction. If the angle subtended by the strand is smaller than the wavelength of light divided by the diameter, you'll see light diffracting around it. $\endgroup$ – Count Iblis Apr 7 '17 at 19:08
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    $\begingroup$ The energy needed to break chemical bonds is of the order of a few eV, so, you won't feel any resistance as your hand moves through a DNA strand. $\endgroup$ – Count Iblis Apr 7 '17 at 19:11
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    $\begingroup$ I don't see why people are retracting close votes. This question has nothing whatever to do with biology. At the least it should be migrated to Chemistry or Physics or somewhere where it would receive the scorn it deserves. Trying to understand how small things are indeed! Yes it is a silly question. $\endgroup$ – David Apr 8 '17 at 12:08
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Research on tactile detection has found humans can detect wrinkles in a surface on a nanoscale. One could argue that we may be able to feel a strand of DNA.

However, this research found only wrinkles of 10 nm were detectable. Therefore it is unlikely we would detect a DNA strand by simply touching it, considering DNA has a radius of one nanometer radius (10 ångströms).

We still may feel a pull of the strand depending on the tensile strength and bond strength but I'm not sure how those values relate to human perception.

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I originally thought it might be likely that the covalent phosphodiester bonds holding together the DNA backbone may not be able to support the weight of the polymer chain. I did a few napkin calculations to investigate the issue. Here is my analysis:

The nucleotide at the bottom of the chain has a certain very small weight, and will probably not break the bond to the nucleotide above it. The two bottom nucleotides weigh twice as much as the single bottom one, but that also probably won't break the bond above them. If you keep going up with this logic, you might reach a point where some number of nucleotides has enough weight to break the covalent bond above them, and that chain of nucleotides would fall to the floor (making a very tiny puddle).

The bonds in the sugar-phosphate backbone are: $...O-P-O-C-C-C-O-P-O...$ (just a random bit of the chain, where the carbons are 5', 4', 3' of a deoxyribose sugar). The lowest bond energy, thus the most easily broken, is $P-O$ at 335 kJ/mol (Ref). I'm taking this as this how much energy is required to break the DNA sugar-phosphate backbone (in a single place).

An experimentally derived estimate of the linear density of double stranded DNA is $2.1\cdot10^{12} \frac{g/mol}{m}$. So every meter of DNA weighs about a trillion g/mol. Does this sound like a lot? It's because that is the meter-weight of one mole of DNA helices. The linear density of one molecule of DNA helix can be found by dividing by avagadro's number: one molecule of DNA has a mass of $3.5\cdot10^{-12} g$ per meter.

Let's take our vertical strip of DNA and imagine it is divided into two segments: an upper segment held by some vise, and a lower segment which dangles freely. The two segments are connected by a covalent bond of the sugar-phosphate backbone, specifically a $P-O$ bond. The lower segment has some mass $m$, and its weight $mg$ exerts a force against the bond ($F=mg$).

The bond requires energy $E=335 kJ/mol$ to break. This energy can be provided by the lower segment doing work to break the bond. Technically this work would be done by the force of gravity on the lower segment, which releases energy if the segment is moved closer the center of the earth. But the segment will only fall toward the earth of the energy released by that process overcomes the energy barrier $E$ of the bond holding the segments together.

Work is force times distance (roughly speaking), so what distance will the lower segment move in the process of breaking the bond? I think 1 angstrom (about a bond length) may be a reasonable approximation. That is, if we stretch the $P-O$ bond (which is already around 1.5 angstroms long) by 1 angstrom, it should be reasonable to say it is broken and the atoms will not re-attract each other (see Bond Dissociation graphs for details).

So! Our energy $E = 335 kJ/mol$ to break the bond will be supplied by work $W=Fd$, performed by the force of gravity $F=mg$, which acts for a relevant distance of $d=1$ angstroms $= 10^{-10} m$:

$$E=W=Fd=(mg)d$$

The mass of the lower segment is $m=\rho l$, where $\rho=2.1\cdot10^{12} g/mol/m$ is the linear density of the DNA segment and $l$ is the length of the segment. The question we should ask is "how long must the lower segment be for it to have enough weight to break the bond?" Well...

$$E=mgd=(\rho l)gd$$

$$l=\frac{E}{\rho gd} \\ = \frac{335\cdot10^3 J\cdot mol^{-1}}{(2.1\cdot10^{12} g\cdot mol^{-1} m^{-1})(9.8 m\cdot s^{-2})(10^{-10} m)} \cdot \frac{kg \cdot m^2 s^{-2}}{1 J} \cdot \frac{10^3 g}{1 kg} \\ = 1.6 \cdot 10^5 m$$

So, according to my admittedly crude approach, a segment of DNA would have to be on the order of 100,000 meters long to weigh enough to break the covalent bond holding it to the rest of the chain above it. I suppose this is a testament to the powerful strength of covalent bonds (or I've made some grave error somewhere in my physics). So my calculations suggest a 6-ft segment of DNA (magically extracted and assembled from trillions of humans cell) should have no problems holding together when you grip it in a tiny vise and hold it vertically.

I realize this was not exactly your question, but it was a practical consideration that I found myself investigating, and I figured I'd share my results.

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  • $\begingroup$ I have a sincere question. Did you consider the resonance effect of the phosphodiester linkage when you told the P--O bond energy was 335kJ? There would definitely be some resonance by the negatively charged oxygen. I'm sure that this would increase the bond dissociation energy, but not sure by how much though. $\endgroup$ – Twisted Genes Apr 8 '17 at 3:24
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    $\begingroup$ I did not consider it, but I'm not certain it is relevant. Here is a diagram for reference: (s3.amazonaws.com/chegg.media.images/board/681/…) On a given phosphate, the two oxygen atoms involved in the sugar-phosphate backbone are neutral, and participating in resonance would require them to become positive. The negative oxygen is much more likely (indeed, guaranteed) to participate in the resonance with the doubly-bonded oxygen, but neither of those last two oxygen sensor are involved in the bonding arrangement of the backbone. $\endgroup$ – electronpusher Apr 8 '17 at 6:57
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    $\begingroup$ Nice! I think the calculations are reasonable. I did something similar for a polyphosphate chain and found that its P-O bond should support an even longer polymer, about 1000km. And DNA should have higher linear density than polyphosphates, so your numbers make sense. I guess this is the reason for all the hoopla about nanomaterials --- pure molecules have incredible tensile strengths. (Yes, it's not really biology but it is kinda fun :) $\endgroup$ – Roland Apr 8 '17 at 9:37

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