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Register a new userChain conformation of ring polymers under a cylindrical nanochannel confinement
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We investigate the chain conformation of ring polymers confined to a cylindrical nanochannel using both theoretical analysis and three dimensional Langevin dynamics simulations. We predict that the longitudinal size of a ring polymer scales with the chain length and the diameter of the channel in the same manner as that for linear chains based on scaling analysis and Flory-type theory. Moreover, Flory-type theory also gives the ratio of the longitudinal sizes for a ring polymer and a linear chain with identical chain length. These theoretical predictions are confirmed by numerical simulations. Finally, our simulation results show that this ratio first decreases and then saturates with increasing the chain stiffness, which has interpreted the discrepancy in experiments. Our results have biological significance.
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Using analytical techniques and Langevin dynamics simulations, we investigate the dynamics of polymer translocation through a nanochannel embedded in two dimensions under an applied external field. We examine the translocation time for various ratio of the channel length $L$ to the polymer length $N$. For short channels $Lll N$, the translocation time $tau sim N^{1+ u}$ under weak driving force $F$, while $tausim F^{-1}L$ for long channels $Lgg N$, independent of the chain length $N$. Moreover, we observe a minimum of translocation time as a function of $L/N$ for different driving forces and channel widths. These results are interpreted by the waiting time of a single segment.
We investigate the ejection dynamics of a ring polymer out of a cylindrical nanochannel using both theoretical analysis and three dimensional Langevin dynamics simulations. The ejection dynamics for ring polymers shows two regimes like for linear polymers, depending on the relative length of the chain compared with the channel. For long chains with length $N$ larger than the critical chain length $N_{c}$, at which the chain just fully occupies the nanochannel, the ejection for ring polymers is faster compared with linear chains of identical length due to a larger entropic pulling force; while for short chains ($N<N_c$), it takes longer time for ring polymers to eject out of the channel due to a longer distance to be diffused to reach the exit of the channel before experiencing the entropic pulling force. These results can help understand many biological processes, such as bacterial chromosome segregation.
Single molecule force spectroscopy of DNA strands adsorbed at surfaces is a powerful technique used in air or liquid environments to quantify their mechanical properties. Although the force responses are limited to unfolding events so far, single base detection might be possible in more drastic cleanliness conditions such as ultra high vacuum. Here, we report on high resolution imaging and pulling attempts at low temperature (5K) of a single strand DNA (ssDNA) molecules composed of 20 cytosine bases adsorbed on Au(111) by scanning probe microscopy and numerical calculations. Using electrospray deposition technique, the ssDNA were successfully transferred from solution onto a surface kept in ultra high vacuum. Real space characterizations reveal that the ssDNA have an amorphous structure on gold in agreement with numerical calculations. Subsequent substrate annealing promotes the desorption of solvent molecules, DNA as individual molecules as well as the formation of DNA self assemblies. Furthermore, pulling experiments by force spectroscopy have been conducted to measure the mechanical response of the ssDNA while detaching. A periodic pattern of 0.2 to 0.3nm is observed in the force curve which arises from the stick slip of single nucleotide bases over the gold. Although an intra molecular response is obtained in the force curve, a clear distinction of each nucleotide detachment is not possible due the complex structure of ssDNA adsorbed on gold.
Hydrodynamic interactions as modeled by Multi-Particle Collision Dynamics can dramatically influence the dynamics of fully flexible, ring-shaped polymers in ways not known for any other polymer architecture or topology. We show that steady shear leads to an inflation scenario exclusive to ring polymers, which depends not only on Weissenberg number but also on contour length of the ring. By analyzing velocity fields of the solvent around the polymer, we show the existence of a hydrodynamic pocket which allows the polymer to self-stabilize at a certain alignment angle to the flow axis. This self-induced stabilization is accompanied by transitioning of the ring to a non-Brownian particle and a cessation of tumbling. The ring swells significantly in the vorticity direction, and the horseshoe regions on the stretched and swollen ring are effectively locked in place relative to the rings center-of-mass. The observed effect is exclusive to ring polymers and stems from an interplay between hydrodynamic interactions and topology. Furthermore, knots tied onto such rings can serve as additional stabilization anchors. Under strong shear, the knotted section is pulled tight and remains well-localized while tank-treading from one horseshoe region to the opposite one in sudden bursts. We find knotted polymers of high contour length behave very similarly to unknotted rings of the same contour length, but small knotted rings feature a host of different configurations. We propose a filtering technique for rings and chains based on our observations and suggest that strong shear could be used to tighten knots on rings.
Molecular dynamics simulations confirm recent extensional flow experiments showing ring polymer melts exhibit strong extension-rate thickening of the viscosity at Weissenberg numbers $Wi<<1$. Thickening coincides with the extreme elongation of a minority population of rings that grows with $Wi$. The large susceptibility of some rings to extend is due to a flow-driven formation of topological links that connect multiple rings into supramolecular chains. Links form spontaneously with a longer delay at lower $Wi$ and are pulled tight and stabilized by the flow. Once linked, these composite objects experience larger drag forces than individual rings, driving their strong elongation. The fraction of linked rings generated by flow depends non-monotonically on $Wi$, increasing to a maximum when $Wisim1$ before rapidly decreasing when the strain rate approaches the relaxation rate of the smallest ring loops $sim 1/tau_e$.
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