Entangled DNA Solutions Research Articles

Enzymatic cleaving of entangled DNA rings drives scale-dependent rheological trajectories.

DNA, which naturally occurs in linear, ring, and supercoiled topologies, frequently undergoes enzyme-driven topological conversion and fragmentation in vivo, enabling it to perform a variety of functions within the cell. In vitro, highly concentrated DNA polymers form entanglements that yield viscoelastic properties dependent on the topologies and lengths of the DNA. Enzyme-driven alterations of DNA size and shape therefore offer a means of designing active materials with programmable viscoelastic properties. Here, we incorporate multi-site restriction endonucleases into dense DNA solutions to linearize and fragment circular DNA molecules. We pair optical tweezers microrheology with differential dynamic microscopy and single-molecule tracking to measure the linear and nonlinear viscoelastic response and transport properties of entangled DNA solutions over a wide range of spatiotemporal scales throughout the course of enzymatic digestion. We show that, at short timescales, relative to the relaxation timescales of the polymers, digestion of these 'topologically-active' fluids initially causes an increase in elasticity and relaxation times followed by a gradual decrease. Conversely, for long timescales, linear viscoelastic moduli exhibit signatures of increasing elasticity. DNA diffusion, likewise, becomes increasingly slowed, in direct opposition to the short-time behavior. We hypothesize that this scale-dependent rheology arises from the population of small DNA fragments, which increases as digestion proceeds, driving self-association of larger fragments via depletion interactions, giving rise to slow relaxation modes of clusters of entangled chains, interspersed among shorter unentangled fragments. While these slow modes likely dominate at long times, they are presumably frozen out in the short-time limit, which instead probes the faster relaxation modes of the unentangled population.

Molecularly based criteria for shear banding in transient flow of entangled polymeric fluids

Dissipative particle dynamics simulations of polymeric melts in a start-up of shear flow as a function of ramp time to its steady state value is studied. Herein, we report the molecular findings showing the effect of ramp time on the formation of shear banded structures and chain relaxation behavior. Specifically, it is shown that shear banding emerges at a rapid start-up; however, homogeneous shear prevails when the deformation rate ramp time is sufficiently slow. This finding is in full consistency with prior continuum level linear stability analysis of shear banding in start-up of shear flows as well as experimental observations of entangled DNA and polymer solutions. Further, it has been revealed that the ratio of the longest chain orientation relaxation time to that of the time for the imposed deformation rate to reach its steady state value plays a central role in determining whether local strain inhomogeneities that lead to the formation of shear banded flow structures are created. In addition, we have shown that the gradient of the number of entanglements along the velocity gradient direction should reach a critical value for the creation of localized strain inhomogeneity. Moreover, the relation between the local process leading to shear banded flows and the relaxation mechanism of the chain is discussed. Overall, a molecular picture for the interrelation between the longest chain orientation and stress relaxation time, local inhomogeneities, and shear banding has been proposed and corroborated with extensive analysis.

Flow of DNA solutions in a microfluidic gradual contraction.

The flow of λ-DNA solutions in a gradual micro-contraction was investigated using direct measurement techniques. The effects on DNA transport in microscale flows are significant because the flow behavior is influenced by macromolecular conformations, both viscous and elastic forces dominate inertial forces at this length scale, and the fully extended length of the molecule approaches the characteristic channel length wc (L/wc ∼ 0.13). This study examines the flow of semi-dilute and entangled DNA solutions in a gradual planar micro-contraction for low Reynolds numbers (3.7 × 10(-6 )< Re < 3.1 × 10(-1)) and high Weissenberg numbers (0.4 < Wi < 446). The semi-dilute DNA solutions have modest elasticity number, El = Wi/Re = 55, and do not exhibit viscoelastic behavior. For the entangled DNA solutions, we access high elasticity numbers (7.9 × 10(3 )< El < 6.0 × 10(5)). Video microscopy and streak images of entangled DNA solution flow reveal highly elastic behavior evidenced by the presence of large, stable vortices symmetric about the centerline and upstream of the channel entrance. Micro-particle image velocimetry measurements are used to obtain high resolution, quantitative velocity measurements of the vortex growth in this micro-contraction flow. These direct measurements provide a deeper understanding of the underlying physics of macromolecular transport in microfluidic flow, which will enable the realization of enhanced designs of lab-on-a-chip systems.

Photobleaching Correction in Fluorescence Correlation Spectroscopy

Fluorescence correlation spectroscopy (FCS) is a fluorescence technique conventionally used to study the kinetics of fluorescent molecules in a dilute solution. Being a non-invasive technique, FCS is now finding wider applications in the study of more complex systems like the dynamics of DNA or proteins in living cells and cell membranes. Unlike an ordinary dye solution, the dynamics of macromolecules like proteins or entangled DNA, in crowded environments is often slow and subdiffusive in nature. This in turn leads to longer residence times of the attached fluorophores in the excitation volume of the microscope. As a result, photobleaching becomes a problem: the number of photons available to calculate the intensity autocorrelation function is limited, and the decay of the fluorescence intensity itself contributes a spurious signal to the autocorrelation function that can easily obscure the signature of the molecular dynamics of interest.We present a method of calculating the intensity autocorrelation function from the arrival times of the photons on the detector that maximizes the information content while correcting for the effect of photobleaching to yield an autocorrelation function that reflects only the underlying dynamics of the sample. For this purpose, we determine the overall photobleaching rate by fitting a multi-exponential decay to the fluorescence intensity. Then we assign a weight to each photon using the reciprocal of this fit function. The autocorrelation function is then calculated from all photon pairs using the product of the individual photon weights. This gives late-arriving fluorescence photons that come from a partially photobleached sample a higher weight than those photons that arrived earlier, compensating for the loss of some of the fluorophores. We demonstrate the utility of this technique by acquiring artifact-free FCS data from entangled DNA solutions and from chromosomal DNA in E. coli.

Flow pattern and molecular visualization of DNA solutions through a 4:1 planar micro-contraction

The present work explores unusual flow behavior of entangled fluids in an abrupt contraction flow device. Fluorescent imaging was carried out on four different entangled DNA solutions with concentrations ranging from 0.1 to 1.0% (with a wide range of entanglements per chain Z = 7–55). For weakly entangled solutions ( Z < 30), vortex flow was dominant at high flow rates. However, for well-entangled DNA solutions ( Z ≥ 30), unusual time dependant shear banding was observed at the contraction entrance. Upon reducing the slip length by adding sucrose to the well-entangled DNA solution, vortex flow became dominant again. In vortex flow, most DNA chains remained coiled at the corner in regular recirculation. However, when jerky-shear-banding flow developed, significant stable stretching of DNA chains occurred at the center-line, with quasi-periodic switching between stretching and recoil at the corner.

Shear Banding or Not in Entangled DNA Solutions

Shear Banding or Not in Entangled DNA Solutions

Molecular Imaging of Slip in Entangled DNA Solution

This work obtains the first molecular imaging of wall slip in entangled solutions. Using a combination of confocal fluorescence microscopy and rheometry, molecular images were captured in the nonlinear response regime of entangled DNA solutions. Conformations of DNA molecules were imaged during shear to correlate with the magnitude of wall slip. Interfacial chain disentanglement results in wall slip beyond the stress overshoot. Sufficient disentanglement can produce tumbling of individual DNA in the entangled solutions.

Primitive chain network simulations for entangled DNA solutions

Molecular theories for polymer rheology are based on conformational dynamics of the polymeric chain. Hence, measurements directly related to molecular conformations appear more appealing than indirect ones obtained from rheology. In this study, primitive chain network simulations are compared to experimental data of entangled DNA solutions [Teixeira et al., Macromolecules 40, 2461 (2007)]. In addition to rheological comparisons of both linear and nonlinear viscoelasticities, a molecular extension measure obtained by Teixeira et al. through fluorescent microscopy is compared to simulations, in terms of both averages and distributions. The influence of flow on conformational distributions has never been simulated for the case of entangled polymers, and how DNA molecular individualism extends to the entangled regime is not known. The linear viscoelastic response and the viscosity growth curve in the nonlinear regime are found in good agreement with data for various DNA concentrations. Conversely, the molecular extension measure shows significant departures, even under equilibrium conditions. The reason for such discrepancies remains unknown.

Shear banding or not in entangled DNA solutions depending on the level of entanglement

Entangled DNA solutions are ideal as a model system to examine nonlinear shear flow behavior. Even when the number of entanglements per chain, Z, is higher than 100, the solution is still soft enough with an elastic plateau modulus under 100Pa and is thus amenable to experimental study by commercial rotational rheometry without ambiguity and uncertainty. We have investigated nonlinear flow behavior of three entangled DNA solutions with Z=24, 60, and 156, respectively, using a combination of particle-tracking velocimetric (PTV) and conventional rheometric measurements. We explore questions such as (a) whether shear banding also occurs in moderately entangled solutions, (b) whether creep results in development of nonlinear velocity profile, (c) whether shear banding produced in startup shear and creep persists at long times in steady state, and (d) whether these entangled solutions exhibit homogeneous shear at the upper end of the stress plateau region. We found that the first DNA solution (Z=24) only shows transient weakly inhomogeneous shear and steady linear velocity profile. In the more entangled solutions (Z=60 and 156), shear banding is observed in startup rate- and stress-controlled shear in the shear thinning regime. Shear homogeneity eventually returns at the upper end of the stress plateau (shear thinning) regime.

Exploring the transition from wall slip to bulk shearing banding in well-entangled DNA solutions

In this study we have carried out a combination of rheometric and particle-tracking velocimetric (PTV) measurements to investigate nonlinear rheological behavior of three entangled DNA solutions (with ca. 150 entanglements per chain) and, in particular, to explore a transformation from slip-dominated steady-state flow to bulk shear inhomogeneity. In the stress plateau regime, an elastic recoil-like response occurs transiently at either interfaces or sample interior after stress overshoot during a startup shear. In both startup shear and creep mode, wall slip, bulk shear banding or a combination of both have been observed in both transient and steady states. The water-based solution shows massive wall slip allowing the bulk to remain in the Newtonian flow regime. Use of glycerol as a solvent can effectively reduce interfacial slip, permitting bulk shear banding to develop in both controlled-rate and controlled-stress modes. For the glycerol based solution, a sufficiently high Weissenberg number can attain in the rheometer where PTV observations reveal homogenous shear in steady state.

Self-Diffusion in Binary Blends of Cyclic and Linear Polymers

A lattice model is used to estimate the self-diffusivity of entangled cyclic and linear polymers in blends of varying compositions. To interpret simulation results, we suggest a minimal model based on the physical idea that constraints imposed on a cyclic polymer by infiltrating linear chains have to be released, before it can diffuse beyond a radius of gyration. Both, the simulation, and recently reported experimental data on entangled DNA solutions support the simple model over a wide range of blend compositions, concentrations, and molecular weights.

Role of Electrostatic Interactions in Shear Banding of Entangled DNA Solutions

Role of Electrostatic Interactions in Shear Banding of Entangled DNA Solutions

Observations of Wall Slip and Shear Banding in an Entangled DNA Solution

: We have studied nonlinear flow behavior of entangled DNA solutions using particle tracking velocimetry in Couette and cone/plate geometries. At apparent shear rate γ app 40 s -1 , the velocity profile progressively curves and becomes banded with a sharp interface after hundreds of strain units. In the steady state, the thickness of high-shear band increases linearly with the apparent shear rate. At γ yapp = 1000 s -1 , the velocity profile returns to linearity.

Strong effects of molecular topology on diffusion of entangled DNA molecules

When long polymers such as DNA are in a highly concentrated state they may become entangled, leading to restricted self-diffusion. Here, we investigate the effect of molecular topology on diffusion in concentrated DNA solutions and find surprisingly large effects, even with molecules of modest length and concentration. We measured the diffusion coefficients of linear and relaxed circular molecules by tracking the Brownian motion of single molecules with fluorescence microscopy. Four possible cases were compared: linear molecules surrounded by linear molecules, circular molecules surrounded by linear molecules, linear molecules surrounded by circles, and circles surrounded by circles. In measurements with 45-kbp DNA at 1 mg/ml, we found that circles diffused approximately 100 times slower when surrounded by linear molecules than when surrounded by circles. In contrast, linear and circular molecules diffused at nearly the same rate when surrounded by circles, and circles diffused approximately 10 times slower than linears when surrounded by linears. Thus, diffusion in entangled DNA solutions strongly depends on topology of both the diffusing molecule and the surrounding molecules. This effect also strongly depends on DNA concentration and length. The differences largely disappeared when the concentration was lowered to 0.1 mg/ml or when the DNA length was lowered to 6 kb. Present theories cannot fully explain these effects.

FRAP and FCS studies of self-diffusion and mutual diffusion in entangled DNA solutions

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTFRAP and FCS studies of self-diffusion and mutual diffusion in entangled DNA solutionsBethe A. Scalettar, John E. Hearst, and Melvin P. KleinCite this: Macromolecules 1989, 22, 12, 4550–4559Publication Date (Print):December 1, 1989Publication History Published online1 May 2002Published inissue 1 December 1989https://doi.org/10.1021/ma00202a030RIGHTS & PERMISSIONSArticle Views327Altmetric-Citations44LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (1 MB) Get e-Alerts Get e-Alerts