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Many biological processes involve transport and organization of inclusions in thin fluid interfaces. A key aspect of these assemblies is the active dissipative stresses applied from the inclusions to the fluid interface, resulting in long-range active interfacial flows. We study the effect of these active flows on the self-organization of rod-like inclusions in the interface. Specifically, we consider a di- lute suspension of Brownian rods of length L, embedded in a thin fluid interface of 2D viscosity ηm and surrounded on both sides with 3D fluid domains of viscosity ηf . The momentum transfer from the interfacial flows to the surrounding fluids occurs over length l0 = ηm/ηf , known as Saffman- Delbru ̈ck length. We use zeroth, first and second moments of Smoluchowski equation to obtain the conservation equations for concentration, polar order and nematic order fields, and use linear stability analysis and continuum simulations to study the dynamic variations of these fields as a function of L/l0, the ratio of active to thermal stresses, and the dimensionless self-propulsion velocity of the embedded particles. We find that at sufficiently large activities, the suspensions of active extensile stress (pusher) with no directed motion undergo a finite wavelength nematic ordering, with the length of the ordered domains decreasing with increasing L/l0. The ordering transition is hindered with further increases in L/l0. In contrast, the suspensions with active contractile stress (puller) remain uniform with variations of activity. We notice that the self-propulsion velocity results in significant concentration fluctuations and changes in the size of the order domains that depend on L/l0. Our re- search highlights the role of hydrodynamic interactions in the self-organization of active inclusions on biological interfaces. 

Human respiratory mucus (HRM) is extremely soft, compelling passive microrheology for linear viscoelastic characterization. We focus this study on the use of passive microrheology to characterize HRM heterogeneity, a phenomenon in normal HRM that becomes extreme during cystic fibrosis (CF) disease. Specifically, a fraction of the mucin polymers comprising HRM phase-separate into insoluble structures, called flakes, dispersed in mucin-depleted solution. We first reconstitute HRM samples to the MUC5B:MUC5AC mucin ratios consistent with normal and CF clinical samples, which we show recapitulate progressive flake formation and heterogeneity. We then employ passive particle tracking with 200 nm and 1 μm diameter beads in each reconstituted sample. To robustly analyze the tracking data, we introduce statistical denoising methods for low signal-to-noise tracking data within flakes, tested and verified using model-generated synthetic data. These statistical methods provide a fractional Brownian motion classifier of all successfully denoised, tracked beads in flakes and the dilute solution. From the ensemble of classifier data, per bead diameter and mucus sample, we then employ clustering methods to learn and infer multiple levels of heterogeneity: (i) tracked bead data within vs. outside flakes and (ii) within-flake data buried within or distinguishable from the experimental noise floor. Simulated data consistent with experimental data (within and outside flakes) are used to explore form(s) of the generalized Stokes–Einstein relation (GSER) that recover the dynamic moduli of homogeneous and heterogeneous truth sets of purely flakelike, dilute solution, and mixture samples. The appropriate form of GSER is applied to experimental data to show (i) flakes are heterogeneous with gel and sol domains; (ii) dilute solutions are heterogeneous with only sol domains; and (iii) flake and dilute solution properties vary with probe diameter. 

Abstract We develop the first molecular dynamics model of airway mucus based on the detailed physical properties and chemical structure of the predominant gel‐forming mucin MUC5B. Our airway mucus model leverages the LAMMPS open‐source code [https://lammps.sandia.gov], based on the statistical physics of polymers, from single molecules to networks. On top of the LAMMPS platform, the chemical structure of MUC5B is used to superimpose proximity‐based, noncovalent, transient interactions within and between the specific domains of MUC5B polymers. We explore feasible ranges of hydrophobic and electrostatic interaction strengths between MUC5B domains with 9 nm spatial and 1 ns temporal resolution. Our goal here is to propose and test a mechanistic hypothesis for a striking clinical observation with respect to airway mucus: a 10‐fold increase in nonswellable, dense structures called flakes during progression of cystic fibrosis disease. Among the myriad possible effects that might promote self‐organization of MUC5B networks into flake structures, we hypothesize and confirm that the clinically confirmed increase in mucin concentration, from 1.5 to 5 mg/ml, alone is sufficient to drive the structure changes observed with scanning electron microscopy images from experimental samples. We postprocess the LAMMPS simulated data sets at 1.5 and 5 mg/ml, both to image the structure transition and compare with scanning electron micrographs and to show that the 3.33‐fold increase in concentration induces closer proximity of interacting electrostatic and hydrophobic domains, thereby amplifying the proximity‐based strength of the interactions.