Extension, torque, and supercoiling in single, stretched, and twisted DNA molecules

Nanomechanics of negatively supercoiled diaminopurine-substituted DNA

Single molecule experiments have demonstrated a progressive transition from a B- to an L-form helix as DNA is gently stretched and progressively unwound. The particular sequence of a DNA segment defines both base stacking and hydrogen bonding that affect the partitioning and conformations of the two phases. Naturally or artificially modified bases alter H-bonds and base stacking and DNA with diaminopurine (DAP) replacing adenine was synthesized to produce linear fragments with triply hydrogen-bonded DAP:T base pairs. Both unmodified and DAP-substituted DNA transitioned from a B- to an L-helix under physiological conditions of mild tension and unwinding. This transition avoids writhing and the ease of this transition may prevent cumbersome topological rearrangements in genomic DNA that would require topoisomerase activity to resolve. L-DNA displayed about tenfold lower persistence length than B-DNA. However, left-handed DAP-substituted DNA was twice as stiff as unmodified L-DNA. Unmodified DNA and DAP-substituted DNA have very distinct mechanical characteristics at physiological levels of negative supercoiling and tension.

Dual high-stroke and high-work capacity artificial muscles inspired by DNA supercoiling

Powering miniature robots using actuating materials that mimic skeletal muscle is attractive because conventional mechanical drive systems cannot be readily downsized. However, muscle is not the only mechanically active system in nature, and the thousandfold contraction of eukaryotic DNA into the cell nucleus suggests an alternative mechanism for high-stroke artificial muscles. Our analysis reveals that the compaction of DNA generates a mass-normalized mechanical work output exceeding that of skeletal muscle, and this result inspired the development of composite double-helix fibers that reversibly convert twist to DNA-like plectonemic or solenoidal supercoils by simple swelling and deswelling. Our modeling-optimized twisted fibers give contraction strokes as high as 90% with a maximum gravimetric work 36 times higher than skeletal muscle. We found that our supercoiling coiled fibers simultaneously provide high stroke and high work capacity, which is rare in other artificial muscles.

Statistical mechanical model for a closed loop plectoneme with weak helix specific forces

We develop a statistical mechanical framework, based on a variational approximation, to describe closed loop plectonemes. This framework incorporates weak helix structure dependent forces into the determination of the free energy and average structure of a plectoneme. Notably, due to their chiral nature, helix structure dependent forces break the symmetry between left and right handed supercoiling. The theoretical approach, presented here, also provides a systematic way of enforcing the topological constraint of closed loop supercoiling in the variational approximation. At large plectoneme lengths, by considering correlation functions in an expansion in terms of the spatial mean twist density about its thermally averaged value, it can be argued that topological constraint may be approximated by replacing twist and writhe by their thermal averages. A Lagrange multiplier, containing the sum of average twist and writhe, can be added to the free energy to conveniently inforce this result. The average writhe can be calculated through the thermal average of the Gauss' integral in the variational approximation. Furthermore, this approach allows for a possible way to calculate finite size corrections due to the topological constraint. Using interaction energy terms from the mean-field Kornyshev-Leikin theory, for parameter values that correspond to weak helix dependent forces, we calculate the free energy, fluctuation magnitudes and mean geometric parameters for the plectoneme. We see a slight asymmetry, where interestingly, left handed supercoils have a looser structure than right handed ones, although with a lower free energy, unlike what the previous ground state calculations would suggest.