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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]

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]

Fibrous networks formed by biological polymers such as collagen or fibrin exhibit nonlinear mechanical behavior. They undergo strong stiffening in response to weak shear and elongational strains, but soften under compressional strain, in striking difference with the response to the deformation of flexible-strand networks formed by molecules. The nonlinear properties of fibrous networks are attributed to the mechanical asymmetry of the constituent filaments, for which a stretching modulus is significantly larger than the bending modulus. Studies of the nonlinear mechanical behavior are generally performed on hydrogels formed by biological polymers, which offers limited control over network architecture. Here, we report an engineered covalently cross-linked nanofibrillar hydrogel derived from cellulose nanocrystals and gelatin. The variation in hydrogel composition provided a broad-range change in its shear modulus. The hydrogel exhibited both shear-stiffening and compression-induced softening, in agreement with the predictions of the affine model. The threshold nonlinear stress and strain were universal for the hydrogels with different compositions, which suggested that nonlinear mechanical properties are general for networks formed by rigid filaments. The experimental results were in agreement with an affine model describing deformation of the network formed by rigid filaments. Our results lend insight into the structural features that govern the nonlinear biomechanics of fibrous networks and provide a platform for future studies of the biological impact of nonlinear mechanical properties., Competing Interests: Competing interests statement:E.P. and E.K. have filed an International PCT patent application related to this work (Serial No. PCT/CA2018/050862, Filing Date: July 16, 2018).

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.