Polymer dynamics are of central importance in materials science, mechanical engineering, biology and medicine. The dynamics of macromolecular solutions and melts in shear flow are typically studied using bulk experimental methods such as light and neutron scattering and birefringence. But the effect of shear on the conformation and dynamics of individual polymers is still not well understood. Here we describe observations of the real-time dynamics of individual, flexible polymers (fluorescently labelled DNA molecules) under a shear flow. The sheared polymers exhibit many types of extended conformation with an overall orientation ranging from parallel to perpendicular with respect to the flow direction. For shear rates much smaller than the inverse of the relaxation time of the molecule, the relative populations of these two main types of conformation are controlled by the rate of the shear flow. These results question the adequacy of assumptions made in standard models of polymer dynamics.
We detail the design of an electromagnetic assembly capable of generating a constant magnetic field superimposed to a large magnetic field gradient (between 40 and 100 T/m), which was uniform over a large gap (between 1.5 and 2 cm). Large gaps allowed the use of wide high numerical-aperture lenses to track microspheres attached to DNA molecules with an inverted light microscope. Given the geometric constraints of the microscope, computer-aided design was used to optimize the magnetic field gradient linearity, homogeneity, and amplitude, as well as the arrangement of the magnetic coils, the currents, and the mechanical stability of the assembly. The assembly was used to apply forces of controlled amplitude, direction, and time dependence on superparamagnetic microspheres by using magnetic coils instead of permanent magnets. A streptavidin-coated microsphere was attached to the 3′ end of a λ-phage DNA molecule through a single biotin molecule. The 5′ end of the λ-phage DNA molecule was tethered to a glass coverslip by conjugating the DNA’s overhang to a complementary 12 base-pair primer, which was itself cross-linked to a heterobifunctional group placed on the glass coverslip. By tracking the centroid of this microsphere, the mechanical response of a single λ-phage DNA molecule was measured as a function of the applied magnetic force. The resulting force-extension curve was fitted with the worm-like-chain model to obtain λ-phage DNA’s persistence length and contour length, which were in agreement with previous reports.
Random walks have been used to describe a wide variety of systems ranging from cell colonies to polymers. Sixty-five years ago, Kuhn [Kuhn, W. (1934) Kolloid-Z. 68, 2-11] made the prediction, backed later by computer simulations, that the overall shape of a random-walk polymer is aspherical, yet no experimental work has directly tested Kuhn's general idea and subsequent computer simulations. By using fluorescence microscopy, we monitored the conformation of individual, long, random-walk polymers (fluorescently labeled DNA molecules) at equilibrium. We found that a polymer most frequently adopts highly extended, nonfractal structures with a strongly anisotropic shape. The ensemble-average ratio of the lengths of the long and short axes of the best-fit ellipse of the polymer was much larger than unity. R andom walks have been extensively used to describe a multitude of phenomena, ranging from cell migration within connective tissues, to Markov processes in DNA sequences, to time series in the stock market, to diffusion in gas, liquids, and solids (1-5). Sixty-five years ago, Kuhn (6) predicted that the shape of a random-walk polymer is not spherically symmetric, i.e., a regular random walk has an overall shape which is anisotropic. The intuitive idea of a spherical shape is based on a flexible polymer (or a random walk) having an isotropic end-to-end vector distribution and on the implicit rotational averaging typically done in polymer theories and experiments (7-10), yet the shape of individual polymers has not been probed directly (5, 9).The lack of direct conformational information has so far prevented a direct test of Kuhn's prediction (6), which is supported by computer simulations (11-16) and analytical calculations (5). Bulk measurements such as light scattering and rheology (17, 18) are inappropriate to probe the behavior of individual polymers in solution. These bulk experimental methods average the orientation, shape, and dynamics of a large ensemble of molecules simultaneously. Here, by monitoring the conformation, orientation, and dynamics of individual flexible polymers in dilute solutions, we directly measure the distributions of conformational parameters. We therefore test Kuhn's central prediction directly. Materials and MethodsLight microscopy (Nikon) equipped with a ϫ100, n.a. 1.30, oil-immersion lens was used to monitor the conformation of individual, fluorescently labeled DNA molecules at equilibrium. We used monodisperse Coliphage T2-phage DNA (T2-DNA) molecules (19) suspended at a concentration Ϸ20 ng͞ml (much smaller than the overlap concentration Ϸ0.13 mg͞ml) in Tris⅐EDTA buffer and an oxygen-scavenging system to reduce photobleaching (20)(21)(22). DNA molecules were stained with an intercalating dye (YOYO-1, Molecular Probes), which we verified did not affect the overall shape distribution of DNA. T2-DNA is a highly flexible polymer with a contour length of L Ϸ 56 m and a persistence length of l p Ϸ 52 nm. Hence, this polymer is a linear sequence of Ϸ1,075 (ϭ L͞l P Ͼ Ͼ 1) statistical segme...
The chromatographic purification of biological macromolecules requires a novel approach to overcome some of the pore size limitations of commercially available resins. Membrane adsorbers offer the potential for better resolution as well as productivity. Sharp peaks are gained by the rapid exchange rate with the adsorbing membranes associated with the convective flow path, in contrast to the pore diffusion requirement for resin exchange. The resolution advantage is preserved even when the very short bed heights of membranes are exploited for the purpose of exceptionally high flow rates and productivity. Breakthrough experiments were used to assess the membrane dynamic loading capacities of flexible macromolecules using supercoiled (SC) DNA as a model system. In contrast to reports for smaller biomolecules such as proteins and antibodies, the dynamic capacity for DNA was found to be highly dependent on flow rates and concentrations. Increasing flow rates induced DNA elongation, which increased the surface coverage and, in turn, lowered the capacity. Increasing concentrations beyond C*, the overlap concentration, led to exclusion-volume interactions, which reduced the size of DNA and increased the membrane adsorber capacity. In the chromatographic mode, membranes with a strongly positive charge were able to resolve various isoforms of DNA, surpassing the capabilities of analogous chromatographic resins. In this study, we found that the convective-flow-induced-structural behavior of DNA is responsible for the resolution in separation.
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