Marginal nature of DNA solutions

Persistent draining crossover in DNA and other semi-flexible polymers: Evidence from hydrodynamic models and extensive measurements on DNA solutions

Although the scaling theory of polymer solutions has had many successes, this type of argument is deficient when applied to hydrodynamic solution properties. Since the foundation of polymer science, it has been appreciated that measurements of polymer size from diffusivity, sedimentation, and solution viscosity reflect a convolution of effects relating to polymer geometry and the strength of the hydrodynamic interactions within the polymer coil, i.e., "draining." Specifically, when polymers are expanded either by self-excluded volume interactions or inherent chain stiffness, the hydrodynamic interactions within the coil become weaker. This means there is no general relationship between static and hydrodynamic size measurements, e.g., the radius of gyration and the hydrodynamic radius. We study this problem by examining the hydrodynamic properties of duplex DNA in solution over a wide range of molecular masses both by hydrodynamic modeling using a numerical path-integration method and by comparing with extensive experimental observations. We also considered how excluded volume interactions influence the solution properties of DNA and confirm that excluded volume interactions are rather weak in duplex DNA in solution so that the simple worm-like chain model without excluded volume gives a good leading-order description of DNA for molar masses up to 10(7) or 10(8) g/mol or contour lengths between 5 μm and 50 μm. Since draining must also depend on the detailed chain monomer structure, future work aiming to characterize polymers in solution through hydrodynamic measurements will have to more carefully consider the relation between chain molecular structure and hydrodynamic solution properties. In particular, scaling theory is inadequate for quantitative polymer characterization.

Scanning fluorescence correlation spectroscopy as a versatile tool to measure static and dynamic properties of soft matter systems

We present the formalism and experimental implementation of scanning fluorescence correlation spectroscopy (SFCS) for the measurements of soft matter system structure and dynamics. We relate the SFCS function Fourier transform to the system intermediate scattering function and demonstrate how SFCS can be combined with specific labelling to measure the desired statistical and kinetic features of the system. Using DNA as a model polymer, we demonstrate the application of SFCS to measure (1) the static structure factor of the system, (2) polymer end-to-end distance distribution, and (3) polymer segmental dynamics in dilute and in dense solutions. The measured DNA end-to-end distance distributions are close to Gaussian. Implementing SFCS we obtain reliable data on segmental mean-square displacement kinetics in dense solutions, where the static FCS approach fails because of dye photobleaching. For moderate concentrations in the semidilute regime (at ∼7 overlap concentrations) segmental dynamics exhibit only weak entanglements. Both of these experimental findings are consistent with theoretical predictions of the weakness of excluded interactions in semiflexible polymers.

Transcription rates in DNA brushes

We theoretically predict the rate of transcription (TX) in DNA brushes by introducing the concept of TX dipoles that takes into account the unidirectional motion of enzymes (RNAP) along DNA during transcription as correlated pairs of sources and sinks in the relevant diffusion equation. Our theory predicts that the TX rates dramatically change upon the inversion of the orientation of the TX dipoles relative to the substrate because TX dipoles modulate the concentrations of RNAP in the solution. Comparing our theory with experiments suggests that, in some cases, DNA chain segments are relatively uniformly distributed in the brush, in contrast to the parabolic profile expected for flexible polymer brushes.

Entropy-driven collective interactions in DNA brushes on a biochip

Cell-free gene expression in localized DNA brushes on a biochip has been shown to depend on gene density and orientation, suggesting that brushes form compartments with partitioned conditions. At high density, the interplay of DNA entropic elasticity, electrostatics, and excluded volume interactions leads to collective conformations that affect the function of DNA-associated proteins. Hence, measuring the collective interactions in dense DNA, free of proteins, is essential for understanding crowded cellular environments and for the design of cell-free synthetic biochips. Here, we assembled dense DNA polymer brushes on a biochip along a density gradient and directly measured the collective extension of DNA using evanescent fluorescence. DNA of 1 kbp in a brush undergoes major conformational changes, from a relaxed random coil to a stretched configuration, following a universal function of density to ionic strength ratio with scaling exponent of 1/3. DNA extends because of the swelling force induced by the osmotic pressure of ions, which are trapped in the brush to maintain local charge neutrality, in competition with the restoring force of DNA entropic elasticity. The measurements reveal in DNA crossover between regimes of osmotic, salted, mushroom, and quasineutral brush. It is surprising to note that, at physiological ionic strength, DNA density does not induce collective stretch despite significant chain overlap, which implies that excluded volume interactions in DNA are weak.

Structure of DNA coils in dilute and semidilute solutions

We apply scanning fluorescence correlation spectroscopy to study the structure of individual DNA coils in dilute and semidilute solutions. In dilute solutions, over two decades in length, from 0.6 to 46 μm, DNA behave as ideal chains, in agreement with theoretical predictions and in disagreement with prior experiments. In semidilute solutions, up to very high densities, the structures of individual DNA coils are independent of concentration, unlike flexible coils that shrink with increasing density. Our experimental findings are consistent with the marginal solution theory of semiflexible polymers.

Polymer-induced entropic depletion potential

We study the effective interactions between nanoparticles immersed in an athermal polymer solution using Molecular dynamics. The directly measured polymer-induced depletion forces are well described with a scaling model in which the attraction between particles is caused by the depletion of concentration blobs and thus independent of the length of the polymer chains. We find strong evidence for a repulsive barrier which arises when the distance between the particles is of the order of the correlation length of the solution and which can be interpreted as a packing effect of concentration blobs. Interestingly, the scaling picture can be extended into the regime in which higher virial coefficients of the polymer solution become relevant. We derive a universal relation between the attraction force at the particle contact, f(0), and the osmotic pressure Π as f(0)∼Π(2/3), demonstrating its validity over a wide range of concentrations of the polymer solution.