Activity-driven chromatin organization during interphase: Compaction, segregation, and entanglement suppression.

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 [Formula: see text] 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 ([Formula: see text]) longer than tens of minutes to be proportional to [Formula: see text]. 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.

Light-Induced Living Polymer Networks with Adaptive Functional Properties.

The advent of covalent adaptable networks (CANs) through the incorporation of dynamic covalent bonds has led to unprecedented properties of macromolecular systems, which can be engineered at the molecular level. Among the various types of stimuli that can be used to trigger chemical changes within polymer networks, light stands out for its remote and spatiotemporal control under ambient conditions. However, most examples of photoactive CANs need to be transparent and they exhibit slow response, side reactions, and limited light penetration. In this vein, it is interesting to understand how molecular engineering of optically active dynamic linkages that offer fast response to visible light can impart "living" characteristics to CANs, especially in opaque systems. Here, the use of carbazole-based thiuram disulfides (CTDs) that offer dual reactivity as photoactivated reshuffling linkages and iniferters under visible light irradiation is reported. The fast response to visible light activation of the CTDs leads to temporal control of shape manipulation, healing, and chain extension in the polymer networks, despite the lack of optical transparency. This strategy charts a promising avenue for manipulating multifunctional photoactivated CANs in a controlled manner.

Activity-driven chromatin organization during interphase: compaction, segregation, and entanglement suppression.

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 (kbp). 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 (Δt) longer than tens of minutes to be proportional to Δt1/3. 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.

Reactivity-Guided Depercolation Processes Determine Fracture Behavior in End-Linked Polymer Networks.

The fracture of polymer networks is tied to the molecular behavior of strands within the network, yet the specific molecular-level processes that determine the mechanical limits of a network remain elusive. Here, the question of reactivity-guided fracture is explored in otherwise indistinguishable end-linked networks by tuning the relative composition of strands with two different mechanochemical reactivities. Increasing the substitution of less mechanochemically reactive ("strong") strands into a network comprising more reactive ("weak") strands has a negligible impact on the fracture energy until the strong strand content reaches approximately 45%, at which point the fracture energy sharply increases with strong strand content. This aligns with the measured strong strand percolation threshold of 48 ± 3%, revealing that depercolation, or the loss of a percolated network structure, is a necessary criterion for crack propagation in a polymer network. Coarse-grained fracture simulations agree closely with the tearing energy trend observed experimentally, confirming that weak strand scissions dominate the failure until the strong strands approach percolation. The simulations further show that twice as many strands break in a mixture than in a pure network.

Nanocolloidal hydrogel mimics the structure and nonlinear mechanical properties of biological fibrous networks.

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.

An elastomer with ultrahigh strain-induced crystallization.

Strain-induced crystallization (SIC) prevalently strengthens, toughens, and enables an elastocaloric effect in elastomers. However, the crystallinity induced by mechanical stretching in common elastomers (e.g., natural rubber) is typically below 20%, and the stretchability plateaus due to trapped entanglements. We report a class of elastomers formed by end-linking and then deswelling star polymers with low defects and no trapped entanglements, which achieve strain-induced crystallinity of up to 50%. The deswollen end-linked star elastomer (DELSE) reaches an ultrahigh stretchability of 12.4 to 33.3, scaling beyond the saturated limit of common elastomers. The DELSE also exhibits a high fracture energy of 4.2 to 4.5 kJ m-2 while maintaining low hysteresis. The heightened SIC and stretchability synergistically promote a high elastocaloric effect with an adiabatic temperature change of 9.3°C.

How a Chain Can Be Extended While Its Bonds Are Compressed.

Extending polymer chains results in a positive chain tension, fch, primarily due to conformational restrictions. At the level of individual bonds, however, tension, fb, is either negative or positive and depends on both chain tension and bulk pressure. Typically, the chain and bond tension are assumed to be directly related. In specific systems, however, this dependence may not be intuitive, whereby fch increases while fb decreases; i.e., the entire chain is extended while bonds are compressed. Specifically, increasing the grafting density of a polymer brush results in chain extension along the direction perpendicular to the grafting surface while the underlying bonds are compressed. Similarly, upon compression of polymer networks, the extension of chains oriented in the "free" direction increases while their bonds are getting more compressed. We demonstrate this phenomenon in molecular dynamics simulations and explain it by the fact that the pressure contribution to fb is dominant over a wide range of network deformations and brush grafting densities.

Facile mechanochemical cycloreversion of polymer cross-linkers enhances tear resistance.

The mechanical properties of covalent polymer networks often arise from the permanent end-linking or cross-linking of polymer strands, and molecular linkers that break more easily would likely produce materials that require less energy to tear. We report that cyclobutane-based mechanophore cross-linkers that break through force-triggered cycloreversion lead to networks that are up to nine times as tough as conventional analogs. The response is attributed to a combination of long, strong primary polymer strands and cross-linker scission forces that are approximately fivefold smaller than control cross-linkers at the same timescales. The enhanced toughness comes without the hysteresis associated with noncovalent cross-linking, and it is observed in two different acrylate elastomers, in fatigue as well as constant displacement rate tension, and in a gel as well as elastomers.

Theory of chromatin organization maintained by active loop extrusion.

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.

Entropic Mixing of Ring/Linear Polymer Blends.

The topological constraints of nonconcatenated ring polymers force them to form compact loopy globular conformations with much lower entropy than unconstrained ideal rings. The closed-loop structure of ring polymers also enables them to be threaded by linear polymers in ring/linear blends, resulting in less compact ring conformations with higher entropy. This conformational entropy increase promotes mixing rings with linear polymers. Here, using molecular dynamics simulations for bead-spring chains, ring/linear blends are shown to be significantly more miscible than linear/linear blends and that there is an entropic mixing, negative χ, for ring/linear blends compared to linear/linear and ring/ring blends. In analogy with small angle neutron scattering, the static structure function S(q) is measured, and the resulting data are fit to the random phase approximation model to determine χ. In the limit that the two components are the same, χ = 0 for the linear/linear and ring/ring blends as expected, while χ < 0 for the ring/linear blends. With increasing chain stiffness, χ for the ring/linear blends becomes more negative, varying reciprocally with the number of monomers between entanglements. Ring/linear blends are also shown to be more miscible than either ring/ring or linear/linear blends and stay in single phase for a wider range of increasing repulsion between the two components.

Elasticity of Slide-Ring Gels.

Slide-ring gels are polymer networks with cross-links that can slide along the chains. In contrast to conventional unentangled networks with cross-links fixed along the chains, the slide-ring networks are strain-softening and distribute tension much more uniformly between their strands due to the so-called "pulley effect". The sliding of cross-links also reduces the elastic modulus in comparison with the modulus of conventional networks with the same number density of cross-links and elastic strands. We develop a single-chain model to account for the redistribution of monomers between network strands of a primary chain. This model takes into account both the pulley effect and fluctuations in the number of monomers per network strand. The pulley effect leads to modulus reduction and uniform tension redistribution between network strands, while fluctuations in the number of strand monomers dominate the strain-softening, the magnitude of which decreases upon network swelling and increases upon deswelling.

Understanding Gas Transport in Polymer-Grafted Nanoparticle Assemblies.

We rationalize the unusual gas transport behavior of polymer-grafted nanoparticle (GNP) membranes. While gas permeabilities depend specifically on the chemistry of the polymers considered, we focus here on permeabilities relative to the corresponding pure polymer which show interesting, "universal" behavior. For a given NP radius, Rc, and for large enough areal grafting densities, σ, to be in the dense brush regime we find that gas permeability enhancements display a maximum as a function of the graft chain molecular weight, Mn. Based on a recently proposed theory for the structure of a spherical brush in a melt of GNPs, we conjecture that this peak permeability occurs when the densely grafted polymer brush has the highest, packing-induced extension free energy per chain. The corresponding brush thickness is predicted to be h max = 3 R c , independent of chain chemistry and σ, i.e., at an apparently universal value of the NP volume fraction (or loading), ϕNP, ϕNP,max = [Rc/(Rc + hmax)]3 ≈ 0.049. Motivated by this conclusion, we measured CO-2 and CH4 permeability enhancements across a variety of Rc, Mn and σ, and find that they behave in a similar manner when considered as a function of ϕNP, with a peak in the near vicinity of the predicted ϕNP,max. Thus, the chain length dependent extension free energy appears to be the critical variable in determining the gas permeability for these hybrid materials. The emerging picture is that these curved polymer brushes, at high enough σ behave akin to a two-layer transport medium - the region in the near vicinity of the NP surface is comprised of extended polymer chains which speed-up gas transport relative to the unperturbed melt. The chain extension free energy increases with increasing chain length, up to a maximum, and apparently leads to an increasing gas permeability. For long enough grafts, there is an outer region of chain segments that is akin to an unperturbed melt with slow gas transport. The permeability maximum and decreasing permeability with increasing chain length then follow naturally.

Fibrous hydrogels under biaxial confinement.

Confinement of fibrous hydrogels in narrow capillaries is of great importance in biological and biomedical systems. Stretching and uniaxial compression of fibrous hydrogels have been extensively studied; however, their response to biaxial confinement in capillaries remains unexplored. Here, we show experimentally and theoretically that due to the asymmetry in the mechanical properties of the constituent filaments that are soft upon compression and stiff upon extension, filamentous gels respond to confinement in a qualitatively different manner than flexible-strand gels. Under strong confinement, fibrous gels exhibit a weak elongation and an asymptotic decrease to zero of their biaxial Poisson's ratio, which results in strong gel densification and a weak flux of liquid through the gel. These results shed light on the resistance of strained occlusive clots to lysis with therapeutic agents and stimulate the development of effective endovascular plugs from gels with fibrous structures for stopping vascular bleeding or suppressing blood supply to tumors.

Prospective validation of smartphone-based heart rate and respiratory rate measurement algorithms.

Background: Measuring vital signs plays a key role in both patient care and wellness, but can be challenging outside of medical settings due to the lack of specialized equipment. Methods: In this study, we prospectively evaluated smartphone camera-based techniques for measuring heart rate (HR) and respiratory rate (RR) for consumer wellness use. HR was measured by placing the finger over the rear-facing camera, while RR was measured via a video of the participants sitting still in front of the front-facing camera. Results: In the HR study of 95 participants (with a protocol that included both measurements at rest and post exercise), the mean absolute percent error (MAPE) ± standard deviation of the measurement was 1.6% ± 4.3%, which was significantly lower than the pre-specified goal of 5%. No significant differences in the MAPE were present across colorimeter-measured skin-tone subgroups: 1.8% ± 4.5% for very light to intermediate, 1.3% ± 3.3% for tan and brown, and 1.8% ± 4.9% for dark. In the RR study of 50 participants, the mean absolute error (MAE) was 0.78 ± 0.61 breaths/min, which was significantly lower than the pre-specified goal of 3 breaths/min. The MAE was low in both healthy participants (0.70 ± 0.67 breaths/min), and participants with chronic respiratory conditions (0.80 ± 0.60 breaths/min). Conclusions: These results validate the accuracy of our smartphone camera-based techniques to measure HR and RR across a range of pre-defined subgroups.

Mucus concentration-dependent biophysical abnormalities unify submucosal gland and superficial airway dysfunction in cystic fibrosis.

Cystic fibrosis (CF) is characterized by abnormal transepithelial ion transport. However, a description of CF lung disease pathophysiology unifying superficial epithelial and submucosal gland (SMG) dysfunctions has remained elusive. We hypothesized that biophysical abnormalities associated with CF mucus hyperconcentration provide a unifying mechanism. Studies of the anion secretion-inhibited pig airway model of CF revealed elevated SMG mucus concentrations, osmotic pressures, and SMG mucus accumulation. Human airway studies revealed hyperconcentrated CF SMG mucus with raised osmotic pressures and cohesive forces predicted to limit SMG mucus secretion/release. Using proline-rich protein 4 (PRR4) as a biomarker of SMG secretion, CF sputum proteomics analyses revealed markedly lower PRR4 levels compared to healthy and bronchiectasis controls, consistent with a failure of CF SMGs to secrete mucus onto airway surfaces. Raised mucus osmotic/cohesive forces, reflecting mucus hyperconcentration, provide a unifying mechanism that describes disease-initiating mucus accumulation on airway surfaces and in SMGs of the CF lung.

Where in the world are condensed counterions?

A scaling model of the concentration profiles of both condensed and free counterions is presented for solutions of spherical and cylindrical charged nanoparticles of different charge valences, nanoparticle sizes, and salt concentrations. The distribution of counterions for both spherical and cylindrical charged particles in salt-free solutions is determined by the condensation parameter γ0 defined as the ratio of nanoparticle valence Z0 to the number of Bjerrum lengths lB = e2/(εkT) per nanoparticle size (γ0 = Z0lB/(2r0) for spherical nanoparticles with radii r0 or γ0 = Z0lB/L for cylindrical particles with length L), where ε is solution dielectric permittivity, e is elementary charge and kT is thermal energy. Depending on the magnitudes of the condensation parameter γ0 and nanoparticle volume fraction ϕ, we find three qualitatively different regimes for the counterion distribution near charged particles: (i) weakly charged particles with no condensed counterions, (ii) regime of weak counterion condensation with less than half of the counterions condensed, and (iii) regime of strong counterion condensation with the majority of counterions condensed. The magnitude of electrostatic energy of a condensed counterion with respect to solution locations with zero electric field is larger than thermal energy kT, and the fraction of condensed counterions increases from less than half in the weak condensation regime to the majority of all counterions in the strong condensation regime. The condensed counterions are not bound to the nanoparticle surface but instead are localized within the condensed counterion zone near the charged particle. The thickness of the condensed counterion zone varies with the condensation parameter γ0, the nanoparticle shape and volume fraction ϕ, and the salt concentration and can be as narrow as Bjerrum length (∼nm) or as large as the particle size (∼L the length of charged cylinder).

Physiology and pathophysiology of human airway mucus.

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.

Toughening hydrogels through force-triggered chemical reactions that lengthen polymer strands.

The utility and lifetime of materials made from polymer networks, including hydrogels, depend on their capacity to stretch and resist tearing. In gels and elastomers, those mechanical properties are often limited by the covalent chemical structure of the polymer strands between cross-links, which is typically fixed during the material synthesis. We report polymer networks in which the constituent strands lengthen through force-coupled reactions that are triggered as the strands reach their nominal breaking point. In comparison with networks made from analogous control strands, reactive strand extensions of up to 40% lead to hydrogels that stretch 40 to 50% further and exhibit tear energies that are twice as large. The enhancements are synergistic with those provided by double-network architectures and complement other existing toughening strategies.

Universal Polymeric-to-Colloidal Transition in Melts of Hairy Nanoparticles.

Two different classes of hairy self-suspended nanoparticles in the melt state, polymer-grafted nanoparticles (GNPs) and star polymers, are shown to display universal dynamic behavior across a broad range of parameter space. Linear viscoelastic measurements on well-characterized silica-poly(methyl acrylate) GNPs with a fixed core radius (Rcore) and grafting density (or number of arms f) but varying arm degree of polymerization (Narm) show two distinctly different regimes of response. The colloidal Regime I with a small Narm (large core volume fraction) is characterized by predominant low-frequency solidlike colloidal plateau and ultraslow relaxation, while the polymeric Regime II with a large Narm (small core volume fractions) has a response dominated by the starlike relaxation of partially interpenetrated arms. The transition between the two regimes is marked by a crossover where both polymeric and colloidal modes are discerned albeit without a distinct colloidal plateau. Similarly, polybutadiene multiarm stars also exhibit the colloidal response of Regime I at very large f and small Narm. The star arm retraction model and a simple scaling model of nanoparticle escape from the cage of neighbors by overcoming a hopping potential barrier due to their elastic deformation quantitatively describe the linear response of the polymeric and colloidal regimes, respectively, in all these cases. The dynamic behavior of hairy nanoparticles of different chemistry and molecular characteristics, investigated here and reported in the literature, can be mapped onto a universal dynamic diagram of f/[Rcore3/ν0)1/4] as a function of (Narmν0f)/(Rcore3), where ν0 is the monomeric volume. In this diagram, the two regimes are separated by a line where the hopping potential ΔUhop is equal to the thermal energy, kBT. ΔUhop can be expressed as a function of the overcrowding parameter x (i.e., the ratio of f to the maximum number of unperturbed chains with Narm that can fill the volume occupied by the polymeric corona); hence, this crossing is shown to occur when x = 1. For x > 1, we have colloidal Regime I with an overcrowded volume, stretched arms, and ΔUhop > kBT, while polymeric Regime II is linked to x < 1. This single-material parameter x can provide the needed design principle to tailor the dynamics of this class of soft materials across a wide range of applications from membranes for gas separation to energy storage.

Dynamic Coupling in Unentangled Liquid Coacervates Formed by Oppositely Charged Polyelectrolytes.

We develop a scaling theory that predicts the dynamics of symmetric and asymmetric unentangled liquid coacervates formed by solutions of oppositely-charged polyelectrolytes. Symmetric coacervates made from oppositely-charged polyelectrolytes consist of polycations and polyanions with equal and opposite charge densities along their backbones. These symmetric coacervates can be described as mixtures of polyelectrolytes in the quasi-neutral regime with a single correlation length. Asymmetric coacervates are made from polycations and polyanions with unequal charge densities. The difference in charge densities results in a double semidilute structure of asymmetric coacervates with two correlation lengths, one for the high-charge-density and the other for the low-charge-density polyelectrolytes. We predict that the double-semidilute structure in asymmetric coacervates results in a dynamic coupling which increases the friction of the high-charge-density polyelectrolyte. This dynamic coupling increases the contribution to the zero-shear viscosity of the high-charge-density polyelectrolyte. The diffusion coefficient of the high-charge-density polyelectrolyte is predicted to depend on the concentration and degree of polymerization of the low-charge-density polyelectrolyte in the coacervate if the size of the low-charge-density polymer is smaller than the correlation length of the high-charge-density polymer. We also predict a non-monotonic salt concentration dependence of the zero-shear viscosity of asymmetric coacervates.