Experimental and statistical methods for microrheological characterization of heterogeneity in human respiratory mucus mimics of health and disease progression

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.