Structure of DNA coils in dilute and semidilute solutions

Polymer models with optimal good-solvent behavior

We consider three different continuum polymer models, which all depend on a tunable parameter r that determines the strength of the excluded-volume interactions. In the first model, chains are obtained by concatenating hard spherocylinders of height b and diameter rb (we call them thick self-avoiding chains). The other two models are generalizations of the tangent hard-sphere and of the Kremer-Grest models. We show that for a specific value [Formula: see text], all models show optimal behavior: asymptotic long-chain behavior is observed for relatively short chains. For [Formula: see text], instead, the behavior can be parametrized by using the two-parameter model, which also describes the thermal crossover close to the θ point. The bonds of the thick self-avoiding chains cannot cross each other, and therefore the model is suited for the investigation of topological properties and for dynamical studies. Such a model also provides a coarse-grained description of double-stranded DNA, so that we can use our results to discuss under which conditions DNA can be considered as a model good-solvent polymer.

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.

Self-avoiding wormlike chain model for double-stranded-DNA loop formation

We compute the effects of excluded volume on the probability for double-stranded DNA to form a loop. We utilize a Monte Carlo algorithm for generation of large ensembles of self-avoiding wormlike chains, which are used to compute the J factor for varying length scales. In the entropic regime, we confirm the scaling-theory prediction of a power-law drop off of -1.92, which is significantly stronger than the -1.5 power law predicted by the non-self-avoiding wormlike chain model. In the elastic regime, we find that the angle-independent end-to-end chain distribution is highly anisotropic. This anisotropy, combined with the excluded volume constraints, leads to an increase in the J factor of the self-avoiding wormlike chain by about half an order of magnitude relative to its non-self-avoiding counterpart. This increase could partially explain the anomalous results of recent cyclization experiments, in which short dsDNA molecules were found to have an increased propensity to form a loop.

Emergent properties of dense DNA phases toward artificial biosystems on a surface

CONSPECTUS: The expression of genes in a cell in response to external signals or internal programs occurs within an environment that is compartmentalized and dense. Reconstituting gene expression in man-made systems is relevant for the basic understanding of gene regulation, as well as for the development of applications in bio- and nanotechnology. DNA polymer brushes assembled on a surface emulate a dense cellular environment. In a regime of significant chain overlap, the highly charged nature of DNA, its entropic degrees of freedom, and its interaction with transcription/translation machinery lead to emergent collective biophysical and biochemical properties, which are summarized in this Account. First, we describe a single-step photolithographic biochip on which biomolecules can be immobilized. Then, we present the assembly of localized DNA brushes, a few kilo-base pairs long, with spatially varying density, reaching a DNA concentration of ∼10(7) base pairs/μm(3), which is comparable to the value in E. coli. We then summarize the response of brush height to changes in density and mono- and divalent ionic strength. The balance between entropic elasticity and swelling forces leads to a rich phase behavior. At no added salt, polymers are completely stretched due to the osmotic pressure of ions, and at high salt they assume a relaxed coil conformation. Midrange, the brush height scales with ratio of density and ionic strength to the third power, in agreement with the general theory of polyelectrolyte brushes. In response to trivalent cations, DNA brushes collapse into macroscopic dendritic condensates with hysteresis, coexistence, and a hierarchy of condensation with brush density. We next present an investigation of RNA transcription in the DNA brush. In general, the brush density entropically excludes macromolecules, depleting RNA polymerase concentration in the brush compared to the bulk, therefore reducing transcription rate. The orientation of transcription promoters with respect to the surface also affects the rate with a lower value for outward compared to inward transcription, likely due to local changes of RNA polymerase concentrations. We hypothesize that equalizing the macromolecular osmotic pressure between bulk and brush with the addition of inert macromolecules would overcome the entropic exclusion of DNA associated proteins, and lead to enhanced biochemical activity. Finally, we present protein synthesis cascades in DNA brushes patterned at close proximity, as a step toward biochemical signaling between brushes. Examining the synthesis of proteins polymerizing into crystalline tubes suggests that on-chip molecular traps serve as nucleation sites for protein assembly, thereby opening possibilities for reconstituting nanoscale protein assembly pathways.

Is DNA a Good Model Polymer?

The details surrounding the cross-over from wormlike-specific to universal polymeric behavior has been the subject of debate and confusion even for the simple case of a dilute, unconfined wormlike chain. We have directly computed the polymer size, form factor, free energy and Kirkwood diffusivity for unconfined wormlike chains as a function of molecular weight, focusing on persistence lengths and effective widths that represent single-stranded and double-stranded DNA in a high ionic strength buffer. To do so, we use a chain-growth Monte Carlo algorithm, the Pruned-Enriched Rosenbluth Method (PERM), which allows us to estimate equilibrium and near-equilibrium dynamic properties of wormlike chains over an extremely large range of contour lengths. From our calculations, we find that very large DNA chains (≈ 1,000,000 base pairs depending on the choice of size metric) are required to reach flexible, swollen non-draining coils. Furthermore, our results indicate that the commonly used model polymer λ-DNA (48,500 base pairs) does not exhibit "ideal" scaling, but exists in the middle of the transition to long-chain behavior. We subsequently conclude that typical DNA used in experiments are too short to serve as an accurate model of long-chain, universal polymer behavior.

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.