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.

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.

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.

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.

Measuring Topological Constraint Relaxation in Ring-Linear Polymer Blends.

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}.

Molecular Characterization of Polymer Networks.

Polymer networks are complex systems consisting of molecular components. Whereas the properties of the individual components are typically well understood by most chemists, translating that chemical insight into polymer networks themselves is limited by the statistical and poorly defined nature of network structures. As a result, it is challenging, if not currently impossible, to extrapolate from the molecular behavior of components to the full range of performance and properties of the entire polymer network. Polymer networks therefore present an unrealized, important, and interdisciplinary opportunity to exert molecular-level, chemical control on material macroscopic properties. A barrier to sophisticated molecular approaches to polymer networks is that the techniques for characterizing the molecular structure of networks are often unfamiliar to many scientists. Here, we present a critical overview of the current characterization techniques available to understand the relation between the molecular properties and the resulting performance and behavior of polymer networks, in the absence of added fillers. We highlight the methods available to characterize the chemistry and molecular-level properties of individual polymer strands and junctions, the gelation process by which strands form networks, the structure of the resulting network, and the dynamics and mechanics of the final material. The purpose is not to serve as a detailed manual for conducting these measurements but rather to unify the underlying principles, point out remaining challenges, and provide a concise overview by which chemists can plan characterization strategies that suit their research objectives. Because polymer networks cannot often be sufficiently characterized with a single method, strategic combinations of multiple techniques are typically required for their molecular characterization.

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).

Surface patterning of nanoparticles with polymer patches.

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.

Single-Event Spectroscopy and Unravelling Kinetics of Covalent Domains Based on Cyclobutane Mechanophores.

Mechanochemical reactions that lead to an increase in polymer contour length have the potential to serve as covalent synthetic mimics of the mechanical unfolding of noncovalent "stored length" domains in structural proteins. Here we report the force-dependent kinetics of stored length release in a family of covalent domain polymers based on cis-1,2-substituted cyclobutane mechanophores. The stored length is determined by the size (n) of a fused ring in an [n.2.0] bicyclic architecture, and it can be made sufficiently large (>3 nm per event) that individual unravelling events are resolved in both constant-velocity and constant-force single-molecule force spectroscopy (SMFS) experiments. Replacing a methylene in the pulling attachment with a phenyl group drops the force necessary to achieve rate constants of 1 s-1 from ca. 1970 pN (dialkyl handles) to 630 pN (diaryl handles), and the substituent effect is attributed to a combination of electronic stabilization and mechanical leverage effects. In contrast, the kinetics are negligibly perturbed by changes in the amount of stored length. The independent control of unravelling force and extension holds promise as a probe of molecular behavior in polymer networks and for optimizing the behaviors of materials made from covalent domain polymers.

Mechanism Dictates Mechanics: A Molecular Substituent Effect in the Macroscopic Fracture of a Covalent Polymer Network.

The fracture of rubbery polymer networks involves a series of molecular events, beginning with conformational changes along the polymer backbone and culminating with a chain scission reaction. Here, we report covalent polymer gels in which the macroscopic fracture "reaction" is controlled by mechanophores embedded within mechanically active network strands. We synthesized poly(ethylene glycol) (PEG) gels through the end-linking of azide-terminated tetra-arm PEG (Mn = 5 kDa) with bis-alkyne linkers. Networks were formed under identical conditions, except that the bis-alkyne was varied to include either a cis-diaryl (1) or cis-dialkyl (2) linked cyclobutane mechanophore that acts as a mechanochemical "weak link" through a force-coupled cycloreversion. A control network featuring a bis-alkyne without cyclobutane (3) was also synthesized. The networks show the same linear elasticity (G' = 23-24 kPa, 0.1-100 Hz) and equilibrium mass swelling ratios (Q = 10-11 in tetrahydrofuran), but they exhibit tearing energies that span a factor of 8 (3.4 J, 10.6, and 27.1 J·m-2 for networks with 1, 2, and 3, respectively). The difference in fracture energy is well-aligned with the force-coupled scission kinetics of the mechanophores observed in single-molecule force spectroscopy experiments, implicating local resonance stabilization of a diradical transition state in the cycloreversion of 1 as a key determinant of the relative ease with which its network is torn. The connection between macroscopic fracture and a small-molecule reaction mechanism suggests opportunities for molecular understanding and optimization of polymer network behavior.

Nonlinear rheometry of entangled polymeric rings and ring-linear blends.

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 shear stress growth coefficient, steady-state shear viscosity, and first and second normal stress differences are obtained and discussed as functions of shear rate as well as molecular parameters (molar mass, blend composition and decreasing molar mass of linear component in 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 shear rate. Universal scaling of strain at overshoot and fractional overshoot (ratio of maximum to 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 behaviour 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 N 2 is negative and its absolute value stays below that of N 1 , as for linear polymers, the ratio -N 2 /N 1 is unambiguously larger for rings compared to linear polymer solutions with the same number of entanglements (almost by factor of two), in agreement with recent non-equilibrium molecular dynamics simulations. Further, -N 2 exhibits slightly weaker shear rate dependence compared to N 1 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 behaviour. 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 conforms the interlocking scenario of rings and their important role in mechanically reinforcing linear matrices.

Roles of mucus adhesion and cohesion in cough clearance.

Clearance of intrapulmonary mucus by the high-velocity airflow generated by cough is the major rescue clearance mechanism in subjects with mucoobstructive diseases and failed cilial-dependent mucus clearance, e.g., subjects with cystic fibrosis (CF) or chronic obstructive pulmonary disease (COPD). Previous studies have investigated the mechanical forces generated at airway surfaces by cough but have not considered the effects of mucus biophysical properties on cough efficacy. Theoretically, mucus can be cleared by cough from the lung by an adhesive failure, i.e., breaking mucus-cell surface adhesive bonds and/or by cohesive failure, i.e., directly fracturing mucus. Utilizing peel-testing technologies, mucus-epithelial surface adhesive and mucus cohesive strengths were measured. Because both mucus concentration and pH have been reported to alter mucus biophysical properties in disease, the effects of mucus concentration and pH on adhesion and cohesion were compared. Both adhesive and cohesive strengths depended on mucus concentration, but neither on physiologically relevant changes in pH nor bicarbonate concentration. Mucus from bronchial epithelial cultures and patient sputum samples exhibited similar adhesive and cohesive properties. Notably, the magnitudes of both adhesive and cohesive strength exhibited similar velocity and concentration dependencies, suggesting that viscous dissipation of energy within mucus during cough determines the efficiency of cough clearance of diseased, hyperconcentrated, mucus. Calculations of airflow-induced shear forces on airway mucus related to mucus concentration predicted substantially reduced cough clearance in small versus large airways. Studies designed to improve cough clearance in subjects with mucoobstructive diseases identified reductions of mucus concentration and viscous dissipation as key therapeutic strategies.

Topological Linking Drives Anomalous Thickening of Ring Polymers in Weak Extensional Flows.

Molecular dynamics simulations confirm recent extensional flow experiments showing ring polymer melts exhibit strong extension-rate thickening of the viscosity at Weissenberg numbers Wi≪1. Thickening coincides with the extreme elongation of a minority population of rings that grows with Wi. The large susceptibility of some rings to extend is due to a flow-driven formation of topological links that connect multiple rings into supramolecular chains. Links form spontaneously with a longer delay at lower Wi and are pulled tight and stabilized by the flow. Once linked, these composite objects experience larger drag forces than individual rings, driving their strong elongation. The fraction of linked rings depends nonmonotonically on Wi, increasing to a maximum when Wi∼1 before rapidly decreasing when the strain rate approaches 1/τ_{e}.

Single-stranded nucleic acid elasticity arises from internal electrostatic tension.

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.

Motion microscopy for visualizing and quantifying small motions.

Although the human visual system is remarkable at perceiving and interpreting motions, it has limited sensitivity, and we cannot see motions that are smaller than some threshold. Although difficult to visualize, tiny motions below this threshold are important and can reveal physical mechanisms, or be precursors to large motions in the case of mechanical failure. Here, we present a "motion microscope," a computational tool that quantifies tiny motions in videos and then visualizes them by producing a new video in which the motions are made large enough to see. Three scientific visualizations are shown, spanning macroscopic to nanoscopic length scales. They are the resonant vibrations of a bridge demonstrating simultaneous spatial and temporal modal analysis, micrometer vibrations of a metamaterial demonstrating wave propagation through an elastic matrix with embedded resonating units, and nanometer motions of an extracellular tissue found in the inner ear demonstrating a mechanism of frequency separation in hearing. In these instances, the motion microscope uncovers hidden dynamics over a variety of length scales, leading to the discovery of previously unknown phenomena.

Helicoidal Patterning of Nanorods with Polymer Ligands.

Chiral packing of ligands on the surface of nanoparticles (NPs) is of fundamental and practical importance, as it determines how NPs interact with each other and with the molecular world. Herein, for gold nanorods (NRs) capped with end-grafted nonchiral polymer ligands, we show a new mechanism of chiral surface patterning. Under poor solvency conditions, a smooth polymer layer segregates into helicoidally organized surface-pinned micelles (patches). The helicoidal morphology is dictated by the polymer grafting density and the ratio of the polymer ligand length to nanorod radius. Outside this specific parameter space, a range of polymer surface structures was observed, including random, shish-kebab, and hybrid patches, as well as a smooth polymer layer. We characterize polymer surface morphology by theoretical and experimental state diagrams. The helicoidally organized polymer patches on the NR surface can be used as a template for the helicoidal organization of other NPs, masked synthesis on the NR surface, as well as the exploration of new NP self-assembly modes.

Nanorheology of Entangled Polymer Melts.

We use molecular simulations to probe the local viscoelasticity of an entangled polymer melt by tracking the motion of embedded nonsticky nanoparticles (NPs). As in conventional microrheology, the generalized Stokes-Einstein relation is employed to extract an effective stress relaxation function G_{GSE}(t) from the mean square displacement of NPs. G_{GSE}(t) for different NP diameters d are compared with the stress relaxation function G(t) of a pure polymer melt. The deviation of G_{GSE}(t) from G(t) reflects the incomplete coupling between NPs and the dynamic modes of the melt. For linear polymers, a plateau in G_{GSE}(t) emerges as d exceeds the entanglement mesh size a and approaches the entanglement plateau in G(t) for a pure melt with increasing d. For ring polymers, as d increases towards the spanning size R of ring polymers, G_{GSE}(t) approaches G(t) of the ring melt with no entanglement plateau.

Solvent-free, supersoft and superelastic bottlebrush melts and networks.

Polymer gels are the only viable class of synthetic materials with a Young's modulus below 100 kPa conforming to biological applications, yet those gel properties require a solvent fraction. The presence of a solvent can lead to phase separation, evaporation and leakage on deformation, diminishing gel elasticity and eliciting inflammatory responses in any surrounding tissues. Here, we report solvent-free, supersoft and superelastic polymer melts and networks prepared from bottlebrush macromolecules. The brush-like architecture expands the diameter of the polymer chains, diluting their entanglements without markedly increasing stiffness. This adjustable interplay between chain diameter and stiffness makes it possible to tailor the network's elastic modulus and extensibility without the complications associated with a swollen gel. The bottlebrush melts and elastomers exhibit an unprecedented combination of low modulus (∼100 Pa), high strain at break (∼1,000%), and extraordinary elasticity, properties that are on par with those of designer gels.

A Rheological Study of the Association and Dynamics of MUC5AC Gels.

The details of how a mucus hydrogel forms from its primary structural component, mucin polymers, remain incompletely resolved. To explore this, we use a combination of macrorheology and single-particle tracking to investigate the bulk and microscopic mechanical properties of reconstituted MUC5AC mucin gels. We find that analyses of thermal fluctuations on the length scale of the micrometer-sized particles are not predictive of the linear viscoelastic response of the mucin gels, and that taken together, the results from both techniques help to provide complementary insight into the structure of the network. In particular, we show that macroscopic stiffening of MUC5AC gels can be brought about in different ways by targeting specific associations within the network using environmental triggers such as modifications to the pH, surfactant, and salt concentration. Our work may be important for understanding how environmental factors, including pathogens and therapeutic agents, alter the mechanical properties of fully constituted mucus.

Flory theory of randomly branched polymers.

Randomly branched polymer chains (or trees) are a classical subject of polymer physics with connections to the theory of magnetic systems, percolation and critical phenomena. More recently, the model has been reconsidered for RNA, supercoiled DNA and the crumpling of topologically-constrained polymers. While solvable in the ideal case, little is known exactly about randomly branched polymers with volume interactions. Flory theory provides a simple, unifying description for a wide range of branched systems, including isolated trees in good and θ-solvent, and tree melts. In particular, the approach provides a common framework for the description of randomly branched polymers with quenched connectivity and for randomly branching polymers with annealed connectivity. Here we review the Flory theory for interacting trees in the asymptotic limit of very large polymerization degree for good solvent, θ-solutions and melts, and report its predictions for annealed connectivity in θ-solvents. We compare the predictions of Flory theory for randomly branched polymers to a wide range of available analytical and numerical results and conclude that they are qualitatively excellent and quantitatively good in most cases.