Michael Rubinstein

Both polymer size and chain elasticity depend on long-range bond correlations, which determine the chain Kuhn length. These correlations are gradually cut off with increasing externally applied force or polymer confinement, thereby decreasing the effective Kuhn length. We develop a theory for the strain-dependent Kuhn length and validate it with simulations. Our model explains why the Kuhn length obtained from single-molecule force spectroscopy experiments is smaller than the Kuhn length determined from scattering measurements of unperturbed chains. Finally, we propose a crossover function for the Kuhn length as a function of applied force, which can be used for the interpretation of force-extension curves.

The stretchability (ability to be elongated) and toughness (capacity to absorb energy before breaking) of polymer network materials, such as elastomers and hydrogels, often determine their utility and lifetime. Direct correlations between the molecular behavior of polymer network components and the physical properties of the network inform the design of materials with enhanced performance, extended lifetime, and minimized waste stream. Here, we report the impact of the fused ring size in bicyclic cyclobutane mechanophores within the strands of polymer network gels. The mechanophores and their polymer strands share the same initial covalent contour length, whereas the capacity for reactive strand extension (RSE) is varied by changing the size of the ring fused to the cyclobutane from 5 to 12 carbon atoms. We observe the first evidence of covalent RSE effects in a single-network gel, and strands with greater RSE lead to gels with greater stretchability and toughness. The same qualitative correlation between molecular and macroscopic extension is also observed in DN hydrogels with mechanophores in the prestretched first network.

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.

Pressure differentials across polymer solutions cause fluid flow. We develop a theory for the spatial variation of polymer concentration in solutions under steady flow between two interfaces permeable to the solvent but not to the polymer. The balance between the external pressure gradient and the osmotic pressure gradient of the polymer solution determines the concentration profile, which increases from the solvent inlet towards the solvent outlet. We find that even if the solution is dilute on average, a semidilute region with overlapping polymers could develop near the outlet. Conversely, even if the solution is semidilute on average, a dilute region with non-overlapping polymers could develop near the solvent inlet. The spatial dependence of polymer concentration implies that polymer dynamics could be significantly slower at the outlet. We apply our theory to the distribution of mucin polymers in human airway mucus. This work suggests that although the average mucin concentration could be near overlap in healthy physiological conditions, water evaporation causes a layer of higher mucin concentration near the air-mucus interface and a dilute mucus layer near the cell surface. On the other hand, even if the average mucin concentration in some diseased states might compress the periciliary layer (PCL), the evaporation-driven redistribution of mucins could sufficiently decrease the concentration near the PCL, delaying the onset of PCL collapse and permitting mucociliary clearance.

In the present work, we investigate the nonlinear shear rheology of unentangled polymer melts. We use linear polystyrenes with molar mass of 10 kg/mol, 20 kg/mol, or 30 kg/mol. The measurements of shear and normal stress are performed using cone-and-partitioned-plate rheometry. While the linear viscoelastic response is consistent with predictions of the Rouse model, in the nonlinear regime, the Cox-Merz rule is not fully validated, despite a universal thinning exponent of -0.5. These experimental results are analyzed using the recent shear slit model of Parisi et al. and molecular dynamics simulations. A new molecular picture is proposed to explain the origin of the transient stress overshoot, based on the concept of the advection time that marks the transition between affine and non-affine deformation. Finally, a simple model is developed, by combining Rouse relaxation modes, chain confinement to shear slit in the velocity gradient direction and tension blobs in the velocity direction. The predictions of this model for shear viscosity are in excellent agreement with the experimental data and consistent with simulations.

Polymers are an effective test bed for studying topological constraints in condensed matter due to a wide array of synthetically available chain topologies. When linear and ring polymers are blended together, emergent rheological properties are observed as the blend can be more viscous than either of the individual components. This emergent behavior arises since ring-linear blends can form long-lived topological constraints as the linear polymers thread the ring polymers. Here, we demonstrate how the Gauss linking integral can be used to efficiently evaluate the relaxation of topological constraints in ring-linear polymer blends. For majority-linear blends, the relaxation rate of topological constraints depends primarily on reptation of the linear polymers, resulting in the diffusive time τ_{d,R} for rings of length N_{R} blended with linear chains of length N_{l} to scale as τ_{d,R}∼N_{R}^{2}N_{L}^{3.4}.

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.

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.

Polymers are an effective test-bed for studying topological constraints in condensed matter due to a wide array of synthetically-available chain topologies. When linear and ring polymers are blended together, emergent rheological properties are observed as the blend can be more viscous than either of the individual components. This emergent behavior arises since ring-linear blends can form long-lived topological constraints as the linear polymers thread the ring polymers. Here, we demonstrate how the Gauss linking integral can be used to efficiently evaluate the relaxation of topological constraints in ring-linear polymer blends. For majority-linear blends, the relaxation rate of topological constraints depends primarily on reptation of the linear polymers, resulting in the diffusive time $τ_{d,R}$ for rings of length $N_R$ blended with linear chains of length $N_l$ to scale as $τ_{d,R}\sim N_R^2N_L^{3.4}$.

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.

ABSTRACT 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 (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. SIGNIFICANCE STATEMENT During interphase, cells must compact chromatin such that gene promoters and their regulatory elements frequently contact each other in space. However, cells also need to insulate promoters from regulatory elements in other genomic sections. Using polymer physics theory and computer simulations, we propose that the cohesin protein complex actively extrudes chromatin into topologically associated domains (TADs) with an anomalously high fractal dimension of D ≈ 4 while suppressing spatial overlap between different TADs. Our model suggests that the fast kinetics of active loop extrusion compared to the slow relaxation of chromatin loops maintains a dense chromatin organization. This work presents a physical framework explaining how cohesin contributes to effective transcriptional regulation.

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.

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.

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.

Both polymer size and chain elasticity depend on long-range bond correlations. These correlations are gradually cut off for higher externally applied force thus increasing chain stiffness. We develop a theory for tension-dependent elasticity and validate it with simulations. Our model explains the higher stiffness measured in single-molecule force spectroscopy experiments compared with scattering experiments of unperturbed chains.

An equilibrium statistical mechanical theory for the formation of reversible networks in two-component solutions of associative polymers is presented to account for the phase behavior due to hydrogen-bonding, metal–ligand, electrostatic, or other pairwise heterotypic associative interactions. We derive explicit analytical expressions for the binding statistics, gelation condition, and free energy, in which we consider polymers of types A and B with many associating groups per chain and consider only A–B association between the groups. The free energy is approximated at the mean-field level, considering overlapping polymer chains with an ideal gas of “stickers” capable of intermolecular association. It is shown that the number of associations is maximized at stoichiometric conditions between A and B associative groups. Accordingly, homogeneous networks are most easily formed near stoichiometric conditions between A and B associative groups, resulting in a re-entrant sol–gel–sol transition as the overall composition is altered. Association and reversible network formation are found to be accompanied by a tendency for phase separation. These results demonstrate that reversibly associating polymers have a large parameter space in terms of molecular design, binding energy, and mixture compositions. Our predictions are expected to be useful in the rational design of interacting polymer mixtures and the formation of reversible networks.

Extending polymer chains results in a positive chain tension, f ch, primarily due to conformational restrictions. At the level of individual bonds, however, tension, f b, 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 f ch increases while f b 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 f b is dominant over a wide range of network deformations and brush grafting densities.

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.

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.

An equilibrium statistical mechanical theory for the formation of reversible networks in two-component solutions of associative polymers is presented to account for the phase behavior due to hydrogen bonding, metal–ligand, electrostatic, or other pairwise heterotypic associative interactions. We derive explicit analytical expressions for the binding statistics, gelation condition, and free energy, in which we consider polymers of types A and B with many associating groups per chain and consider only A–B association between the groups. The free energy is approximated at the mean-field level, considering overlapping polymer chains with an ideal gas of "stickers" capable of intermolecular association. It is shown that the number of associations is maximized at stoichiometric conditions between A and B associative groups. Accordingly, homogeneous networks are most easily formed near stoichiometric conditions between A and B associative groups, resulting in a re-entrant sol–gel–sol transition as the overall composition is altered. Association and reversible network formation are found to be accompanied by a tendency for phase separation. These results demonstrate that reversibly associating polymers have a large parameter space in terms of molecular design, binding energy, and mixture compositions. Our predictions are expected to be useful in the rational design of interacting polymer mixtures and the formation of reversible networks.

We present a modified Lake–Thomas theory that accounts for the molecular details of network connectivity upon crack propagation in polymer networks. This theory includes not only the energy stored in the breaking network strands (bridging strands) but also the energy stored in the tree-like structure of the strands connecting the bridging strands to the network continuum, which remains intact as the crack propagates. The energy stored in each of the generations of this tree depends nonmonotonically on the generation index due to the nonlinear elasticity of the stretched network strands. Further, the energy required to break a single bridging strand is not necessarily dominated by the energy stored in the bridging strand itself but in the higher generations of the tree. We describe the effect of mechanophores with stored length on the energy stored in the tree-like structure. In comparison with the “strong” mechanophores that can only be activated in the bridging strand, “weak” mechanophores that can be activated both in the bridging strand and in other generations could provide more energy dissipation due to their larger contribution to higher generations of the tree.

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.