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Understanding of the conformational ensemble of flexible polyelectrolytes, such as single-stranded nucleic acids (ssNAs), is complicated by the interplay of chain backbone entropy and salt-dependent electrostatic repulsions. Molecular elasticity measurements are sensitive probes of the statistical conformation of polymers and have elucidated ssNA conformation at low force, where electrostatic repulsion leads to a strong excluded volume effect, and at high force, where details of the backbone structure become important. Here, we report measurements of ssDNA and ssRNA elasticity in the intermediate-force regime, corresponding to 5- to 100-pN forces and 50-85% extension. These data are explained by a modified wormlike chain model incorporating an internal electrostatic tension. Fits to the elastic data show that the internal tension decreases with salt, from [Formula: see text]5 pN under 5 mM ionic strength to near zero at 1 M. This decrease is quantitatively described by an analytical model of electrostatic screening that ascribes to the polymer an effective charge density that is independent of force and salt. Our results thus connect microscopic chain physics to elasticity and structure at intermediate scales and provide a framework for understanding flexible polyelectrolyte elasticity across a broad range of relative extensions.

In mammalian cells, the cohesin protein complex is believed to translocate along chromatin during interphase to form dynamic loops through a process called active loop extrusion. Chromosome conformation capture and imaging experiments have suggested that chromatin adopts a compact structure with limited interpenetration between chromosomes and between chromosomal sections. We developed a theory demonstrating that active loop extrusion causes the apparent fractal dimension of chromatin to cross-over between two and four at contour lengths on the order of 30 kilo-base pairs. The anomalously high fractal dimension D = 4 is due to the inability of extruded loops to fully relax during active extrusion. Compaction on longer contour length scales extends within topologically associated domains (TADs), facilitating gene regulation by distal elements. Extrusion-induced compaction segregates TADs such that overlaps between TADs are reduced to less than 35% and increases the entanglement strand of chromatin by up to a factor of 50 to several Mega-base pairs. Furthermore, active loop extrusion couples cohesin motion to chromatin conformations formed by previously extruding cohesins and causes the mean square displacement of chromatin loci during lag times (Δ t) longer than tens of minutes to be proportional to Δ t 1/3. We validate our results with hybrid molecular dynamics--Monte Carlo simulations and show that our theory is consistent with experimental data. This work provides a theoretical basis for the compact organization of interphase chromatin, explaining the physical reason for TAD segregation and suppression of chromatin entanglements which contribute to efficient gene regulation. [ABSTRACT FROM AUTHOR]

Patterning of colloidal particles with chemically or topographically distinct surface domains (patches) has attracted intense research interest. Surface-patterned particles act as colloidal analogues of atoms and molecules, serve as model systems in studies of phase transitions in liquid systems, behave as 'colloidal surfactants' and function as templates for the synthesis of hybrid particles. The generation of micrometre- and submicrometre-sized patchy colloids is now efficient, but surface patterning of inorganic colloidal nanoparticles with dimensions of the order of tens of nanometres is uncommon. Such nanoparticles exhibit size- and shape-dependent optical, electronic and magnetic properties, and their assemblies show new collective properties. At present, nanoparticle patterning is limited to the generation of two-patch nanoparticles, and nanoparticles with surface ripples or a 'raspberry' surface morphology. Here we demonstrate nanoparticle surface patterning, which utilizes thermodynamically driven segregation of polymer ligands from a uniform polymer brush into surface-pinned micelles following a change in solvent quality. Patch formation is reversible but can be permanently preserved using a photocrosslinking step. The methodology offers the ability to control the dimensions of patches, their spatial distribution and the number of patches per nanoparticle, in agreement with a theoretical model. The versatility of the strategy is demonstrated by patterning nanoparticles with different dimensions, shapes and compositions, tethered with various types of polymers and subjected to different external stimuli. These patchy nanocolloids have potential applications in fundamental research, the self-assembly of nanomaterials, diagnostics, sensing and colloidal stabilization.

The active loop extrusion hypothesis proposes that chromatin threads through the cohesin protein complex into progressively larger loops until reaching specific boundary elements. We build upon this hypothesis and develop an analytical theory for active loop extrusion which predicts that loop formation probability is a nonmonotonic function of loop length and describes chromatin contact probabilities. We validate our model with Monte Carlo and hybrid Molecular Dynamics-Monte Carlo simulations and demonstrate that our theory recapitulates experimental chromatin conformation capture data. Our results support active loop extrusion as a mechanism for chromatin organization and provide an analytical description of chromatin organization that may be used to specifically modify chromatin contact probabilities. [ABSTRACT FROM AUTHOR]

The mucus clearance system is the dominant mechanical host defense system of the human lung. Mucus is cleared from the lung by cilia and airflow, including both two-phase gas-liquid pumping and cough-dependent mechanisms, and mucus transport rates are heavily dependent on mucus concentration. Importantly, mucus transport rates are accurately predicted by the gel-on-brush model of the mucociliary apparatus from the relative osmotic moduli of the mucus and periciliary-glycocalyceal (PCL-G) layers. The fluid available to hydrate mucus is generated by transepithelial fluid transport. Feedback interactions between mucus concentrations and cilia beating, via purinergic signaling, coordinate Na+ absorptive vs Cl- secretory rates to maintain mucus hydration in health. In disease, mucus becomes hyperconcentrated (dehydrated). Multiple mechanisms derange the ion transport pathways that normally hydrate mucus in muco-obstructive lung diseases, e.g., cystic fibrosis (CF), chronic obstructive pulmonary disease (COPD), non-CF bronchiectasis (NCFB), and primary ciliary dyskinesia (PCD). A key step in muco-obstructive disease pathogenesis is the osmotic compression of the mucus layer onto the airway surface with the formation of adherent mucus plaques and plugs, particularly in distal airways. Mucus plaques create locally hypoxic conditions and produce airflow obstruction, inflammation, infection, and, ultimately, airway wall damage. Therapies to clear adherent mucus with hydrating and mucolytic agents are rational, and strategies to develop these agents are reviewed. [ABSTRACT FROM AUTHOR]

Self-organization of nanoparticles is an efficient strategy for producing nanostructures with complex, hierarchical architectures. The past decade has witnessed great progress in nanoparticle self-assembly, yet the quantitative prediction of the architecture of nanoparticle ensembles and of the kinetics of their formation remains a challenge. We report on the marked similarity between the self-assembly of metal nanoparticles and reaction-controlled step-growth polymerization. The nanoparticles act as multifunctional monomer units, which form reversible, noncovalent bonds at specific bond angles and organize themselves into a colloidal polymer. We show that the kinetics and statistics of step-growth polymerization enable a quantitative prediction of the architecture of linear, branched, and cyclic serf-assembled nanostructures; their aggregation numbers and size distribution; and the formation of structural isomers. 10.1126/science.1189457

Author(s): Sergei S. Sheiko (corresponding author) [1]; Frank C. Sun [1]; Adrian Randall [1]; David Shirvanyants [1]; Michael Rubinstein [1]; Hyung-il Lee [2]; Krzysztof Matyjaszewski [2] Covalent carbon-carbon bonds are [...]

A report of the results of static and dynamic light scattering investigations of polydimethyl siloxane (PDMS) solutions in both liquid and supercritical carbon dioxide (CO2) is presented. The study was performed below the theta point and it provided a quantitative information on the CO2 solvent quality over a large range of temperature (25-54 degree Celsius) and density (0.97-1.01 g/mL).

The effect of short-range interactions on polyelectrolyte adsorption at oppositely and similarly charged surfaces was studied. It was observed that the adsorption of polyelectrolytes at similarly charged surfaces could occur only within the range of surface charge densities where the short-range interactions dominate the electrostatic repulsion between adsorbed chains and the charged surface.

A study answers the conjecture that there are infinitely many pairs of primes for every even m. It is implied that such pairs of primes qualify as twin primes should m equal two. Thus, the number of pairs less than x is concluded to be similar to 2C2 times the quotient of x divided by (log x)squared. This conclusion is given a short heuristic proof, which in turn is generalized for a heuristic proof of the original conjecture. These proofs rely on a simple combinatorial problem and Dirichlet's Theorem.

The existence of infinitely many primes is proven by utilizing a set S of n distinct primes. Specifically, the study determines the number of positive integers less than or equal to x which are generated by S. The asymptotic answer then allows the conclusion that the number of primes cannot be finite. An alternative approach and a variation using prime pairs are also discussed. In fact, the simple formula f(S,x)

We present a comprehensive experimental rheological dataset for purified entangled ring polystyrenes and their blends with linear chains in nonlinear shear and elongation. In particular, data for the shear stress growth coefficient, steady-state shear viscosity, and first and second normal stress differences are obtained and discussed as functions of the shear rate, as well as molecular parameters (molar mass, blend composition, and decreasing molar mass of linear component in the blend). Over the extended parameter range investigated, rings do not exhibit clear transient undershoot in shear, in contrast to their linear counterparts and ring-linear blends. For the latter, the size of the undershoot and respective strain appear to increase with the shear rate. The universal scaling of the strain at overshoot and fractional overshoot (the ratio of the maximum to the steady-state shear stress growth coefficient) indicates subtle differences in the shear-rate dependence between rings and linear polymers or their blends. The shear thinning behavior of pure rings yields a slope nearly identical to predictions (−4/7) of a recent shear slit model and molecular dynamics simulations. Data for the second normal stress difference are reported for rings and ring-linear blends. While N2 is negative and its absolute value stays below that of N1, as for linear polymers, the ratio –N2/N1 is unambiguously larger for rings compared to linear polymer solutions with the same number of entanglements (almost by a factor of 2), in agreement with recent nonequilibrium molecular dynamics simulations. Furthermore, –N2 exhibits slightly weaker shear rate dependence compared to N1 at high rates, and the respective power-law exponents can be rationalized in view of the slit model (3/7) and simulations (0.6), although further work is needed to unravel the molecular original of the observed behavior. The comparison of shear and elongational stress growth coefficients for blends reflects the effect of ring-linear threading, which leads to significant viscosity enhancement in elongation. Along the same lines, the elongational stress is much larger than the first normal stress in shear, and their ratio is much larger for rings and ring-linear blends compared to linear polymers. This confirms the interlocking scenario of rings and their important role in mechanically reinforcing linear matrices. [ABSTRACT FROM AUTHOR]