## 4 Discussion
### Possible Biophysical Mechanism  
Nucleic acids have one key attribute which is mechanical stiffness, with DNA having similar elastic moduli to even the stiffer artificial polymers. A well-known measure of this stiffness is the persistence length--the distance over which the molecule maintains elastic integrity, even in aqueous solution. Going back decades, the persistence length has been an important metric in polymer science, and in recent years has been measured to be \(\approx\)50 nm (150 bp) in \(\beta\)-helicity dsDNA [14; 27], and \(\approx\)64 nm (237 bp) in \(\beta\)-helicity dsRNA [28; 29]. With 17-25 bp length, our si-RNA sample is entirely within this range, and three of the 50 bp sample strands are within this range, too. However, none of the 1-kbp DNA strands are, and certainly not the \(\lambda\)-DNA sample (48.5 kbp).  
On this basis, short strands of dsDNA or dsRNA can be thought of as stiff nanorods with three primary degrees of freedom: (1) compressional, (2) torsional (i.e., twisting), and (3) bending, each providing normal modes and natural resonant frequencies [30]. The compressional motion requires the highest force, so is thought to entail the highest resonant frequencies. Torsional and bending motions require much less force (or torque) and, hence, can display lower resonant frequencies, conceivably in the THz frequency range or lower, but still have high mechanical Q. Furthermore, a coupling between the torsional and bending motions has been identified, leading to the so-called Marko-Siggia model [31]. Although this model has been embellished several times in more recent years, the possibility of three normal modes remains. It also provides a plausible explanation for why, in the present work, we have seen three sharp signatures in the shorter nucleic samples.  
Of course, there is also the question of optical activity, since strong interaction with electromagnetic waves always requires polarity in the absorbing species. One source of polarity is the well-known sequence of polar hydrogen bonds between every base pair in the double strand. Another possibility is the following. At the physiologic, slightly basic pH levels of the present samples (7.2 for the si-RNA, 8.0 for the others), the phosphate groups in the backbone of every nucleic acid donate one proton to the aqueous solution, creating a sequence of single negative charges down each strand. When combined with a positive charge from a bound water layer, there will be a high degree of polarity because, like the hydrogen bond sequence, there will be at least one dipole per base pair in the molecule.  
There is also the issue of the remaining (weak) signatures that we observed in the larger sample, 1-kbp DNA. Historically, it is tempting to attribute these to the optically active phonon-like modes that have been discussed for decades, as described in the Introduction. However, their proximity in frequency to the sharp resonances of the smaller molecule samples suggests another possibility, which is coupled elastic modes. According to the \"worm-like chain\" model of polymer physics [32], the stiff sections of DNA or RNA approximately one persistence length long are loosely connected. In other words, the nano-mechanical resonators are coupled resonators, and from the principles of classical mechanics will yield more resonant modes with different frequencies than the uncoupled ones, including lower frequencies. However, by draining vibrational energy from the persistence length sections, the coupled modes should also be more heavily damped and thus have a lower Q, as we have seen experimentally. The higher damping may also explain the red-shift with increasing molecular length, as plotted in Figure 7.