Electrophoretic mobility of linear and star-branched DNA in semidilute polymer solutions

Single molecule electrophoresis of star polymers through nanopores: Simulations

We study the translocation of charged star polymers through a solid-state nanopore using coarse-grained Langevin dynamics simulations, in the context of using nanopores as high-throughput devices to characterize polymers based on their architecture. The translocation is driven by an externally applied electric field. Our key observation is that translocation kinetics is highly sensitive to the functionality (number of arms) of the star polymer. The mean translocation time is found to vary non-monotonically with polymer functionality, exhibiting a critical value for which translocation is the fastest. The origin of this effect lies in the competition between the higher driving force inside the nanopore and inter-arm electrostatic repulsion in entering the pore, as the functionality is increased. Our simulations also show that the value of the critical functionality can be tuned by varying nanopore dimensions. Moreover, for narrow nanopores, star polymers above a threshold functionality do not translocate at all. These observations suggest the use of nanopores as a high-throughput low-cost analytical tool to characterize and separate star polymers.

Synthesis and Direct Observation of Thermoresponsive DNA Copolymers

Single-molecule techniques allow for the direct observation of long-chain macromolecules, and these methods can provide a molecular understanding of chemically heterogeneous and stimuli-response polymers. In this work, we report the synthesis and direct observation of thermoresponsive DNA copolymers using single-molecule techniques. DNA-PNIPAM copolymers are synthesized using a two-step strategy based on polymerase chain reaction (PCR) for generating linear DNA backbones containing non-natural nucleotides (dibenzocyclooctyne-dUTP), followed by grafting thermoresponsive side branches (poly(N-isopropylacrylamide), PNIPAM) onto DNA backbones using copper-free click chemistry. Single-molecule fluorescence microscopy is used to directly observe the stretching and relaxation dynamics of DNA-PNIPAM copolymers both below and above the lower critical solution temperature (LCST) of PNIPAM. Our results show that the intramolecular conformational dynamics of DNA-PNIPAM copolymers are affected by temperature, branch density, and branch molecular weight. Single-molecule experiments reveal an underlying molecular heterogeneity associated with polymer stretching and relaxation behavior, which arises in part due to heterogeneous chemical identity on DNA copolymer dynamics.

Topology-Controlled Relaxation Dynamics of Single Branched Polymers

In this work, we report the synthesis and direct observation of branched DNA polymers using single molecule techniques. Polymer topology plays a major role in determining the properties of advanced materials, yet understanding the dynamics of these complex macromolecules has been challenging. Here, we study the conformational relaxation dynamics of single surface-tethered comb polymers from high stretch in a microfluidic device. Our results show that the molecular topology of individual branched polymers plays a direct role on the relaxation dynamics of polymers with complex architectures. Macromolecular DNA combs are first synthesized using a hybrid enzymatic-synthetic approach, wherein chemically modified DNA branches and DNA backbones are generated in separate polymerase chain reactions, followed by a "graft-onto" reaction via strain-promoted [3 + 2] azide-alkyne cycloaddition. This method allows for the synthesis of branched polymers with nearly monodisperse backbone and branch molecular weights. Single molecule fluorescence microscopy is then used to directly visualize branched polymers, such that the backbone and side branches can be tracked independently using single- or dual-color fluorescence labeling. Using this approach, we characterize the molecular properties of branched polymers, including apparent contour length and branch grafting distributions. Finally, we study the relaxation dynamics of single comb polymers from high stretch following the cessation of fluid flow, and we find that polymer relaxation depends on branch grafting density and position of branch point along the main chain backbone. Overall, this work effectively extends single polymer dynamics to branched polymers, which allows for dynamic, molecular-scale observation of polymers with complex topologies.

Comparative gel electrophoresis analysis of helical junctions in RNA

Comparative gel electrophoresis provides information on the relative angles subtended between helical arms at a branchpoint in RNA. It is based upon the comparison of electrophoretic mobility in polyacrylamide gels of species containing two long arms, with the remaining one(s) being significantly shorter. Although the method currently lacks a really well-established basis of physical theory, it is very powerful, yet simple to apply. It has had a number of significant successes in RNA, DNA and DNA-protein complexes, and in all cases to date the results have stood the test of time and eventual comparison with crystallographic analysis.

Analysis of branched nucleic acid structure using comparative gel electrophoresis

Electrophoresis in polyacrylamide gels provides a simple yet powerful means of analyzing the relative disposition of helical arms in branched nucleic acids. The electrophoretic mobility of DNA or RNA with a central discontinuity is determined by the angle subtended between the arms radiating from the branchpoint. In a multi-helical branchpoint, comparative gel electrophoresis can provide a relative measure of all the inter-helical angles and thus the shape and symmetry of the molecule. Using the long-short arm approach, the electrophoretic mobility of all the species with two helical arms that are longer than all others is compared. This can be done as a function of conditions, allowing the analysis of ion-dependent folding of branched DNA and RNA species. Notable successes for the technique include the four-way (Holliday) junction in DNA and helical junctions in functionally significant RNA species such as ribozymes. Many of these structures have subsequently been proved correct by crystallography or other methods, up to 10 years later in the case of the Holliday junction. Just as important, the technique has not failed to date. Comparative gel electrophoresis can provide a window on both fast and slow conformational equilibria such as conformer exchange in four-way DNA junctions. But perhaps the biggest test of the approach has been to deduce the structures of complexes of four-way DNA junctions with proteins. Two recent crystallographic structures show that the global structures were correctly deduced by electrophoresis, proving the worth of the method even in these rather complex systems. Comparative gel electrophoresis is a robust method for the analysis of branched nucleic acids and their complexes.

Barrier crossing by a star polymer

We analyze the dynamics of a star polymer of F arms trapped in a double well potential. Initially the molecule is confined to one of the minima and can cross over the barrier to the other side. We use the continuum version of the Rouse-Ham model and calculate the rate of crossing using the multidimensional approach due to Langer [Ann. Phys. (N.Y.) 54, 258 (1969)]. Finding the transition state for the process is shown to be equivalent to the solution of Newton's equations for F independent particles, moving in an inverted potential. For each star polymer, there is a critical barrier top curvature, below which the star crosses over in coiled conformation. The value of the critical curvature is determined by the first Rouse mode of the star. If the curvature is greater than this critical value, the saddle point for the crossing is a stretched conformation of the star. For the coiled transition state, the activation energy is proportional to the total arm length of the star. For the stretched transition state, as one increases the length of an arm of the star, the activation energy at first increases and then decreases. This results from the fact that in the stretched state, only one arm of the polymer is stretched across the top of the barrier, while others need not be. We calculate the rate by expanding the energy around the saddle up to second order in the fluctuations. As we use the continuum model, there are infinite modes for the polymer and, consequently, the prefactor has infinite products. We show that these infinite products can be reduced to a simple expression, and evaluated easily. However, the rate diverges near NTc due to the multifurcation, which results in more than one unstable mode. The cure for this divergence is to keep terms up to fourth order in the expansion of energy for these modes. Performing this, we have calculated the rate as a function of the length of the star. It is found that the rate has a nonmonotonic dependence on the length, suggesting that longer stars may actually cross over the barrier faster.

Brownian dynamics simulations of polyelectrolyte molecules traveling through an entropic trap array during electrophoresis

Using Brownian dynamics simulations of wormlike chain bead-spring models, the dynamics of linear and star-branched polyelectrolyte molecules traveling through an array of entropic traps during electrophoresis have been investigated. First, the effectiveness of using coarse-grained bead-spring systems for linear molecules to model the electrophoretic process was demonstrated and compared to previous bead-rod (Kramers) chain simulations by Panwar and Kumar [Macromolecules 39, 1297 (2006)]. Second, the coarse-grained bead-spring model has been extended to investigate the effect of branching on the dynamics of molecules through the entropic trap array. Initial studies indicate the reduced mobility of star-branched molecules as compared to equivalent linear molecules. The radius of gyration of the polymer molecule appears to be the dominating factor governing the time scales encountered during traversal of the entropic trapping array.