Mucus is a fluid that protects animals against pathogens while promoting interactions with commensal microbes. Changes in the diffusivity of particles in mucus alter viruses’ infectivity, the efficiency of bacterial pathogens to invade a host, and the effectivity of drug delivery. Multiple physicochemical properties modulate the diffusion of microscopic particles in mucus, but their combined effect is unclear. Here, we analyzed the impact of particle size, charge, chemistry, anomalous diffusion exponent, and mucus composition in the diffusivity of particles from 106 published experiments. We used a time window sampling of one second to define a consistent, effective diffusion across experiments. The effective diffusion spanned seven orders of magnitude from 10−5 to 102 µm2/s. The anomalous exponent was the strongest predictor among all variables tested. It displayed an exponential relationship with the effective diffusion that explained 90% of the empirical data variance. We showed that the relationship and dominance of the anomalous diffusion exponent resulted from a general mathematical relationship obtained from first-principles for any subdiffusion mechanism. Our derivation demonstrated that the generalized diffusion coefficient is not a measurable physical quantity and must be replaced by the length and time scales associated with the underlying mobility mechanisms. This led us to a fundamental reformulation of the classic subdiffusion equation, which calls for a reinterpretation of anomalous diffusion in physical systems. We also discussed how our results impact the characterization of microscopic particle diffusion in mucus and other hydrogels.

Mucus is a complex fluid that coats multiple organs in animals. Various physicochemical properties can alter the diffusion of microscopic particles in mucus, impacting drug delivery, virus infection, and disease development. The simultaneous effect of these physicochemical properties in particle diffusion, however, remains elusive. Here, we analyzed 106 published experiments to identify the most dominant factors controlling particle diffusion in mucus. The effective diffusion—defined using a one-second sampling time window across experiments—spanned seven orders of magnitude, from 10–5 to 102 μm2/s. Univariate and multivariate statistical analyses identified the anomalous exponent (the logarithmic slope of the mean-squared displacement) as the strongest predictor of effective diffusion, revealing an exponential relationship that explained 89% of the variance. A theoretical scaling analysis revealed that a stronger correlation of the anomalous exponent over the generalized diffusion constant occurs for sampling times two orders of magnitude larger than the characteristic molecular (or local) displacement time. This result predicts that at these timescales, the molecular properties controlling the anomalous exponent, like particle–mucus unbinding times or the particle to mesh size ratio, would be the most relevant physicochemical factors involved in passive microrheology of particles in mucus. Our findings contrast with the fact that only one-third of the studies measured the anomalous exponent, and most experiments did not report the associated molecular properties predicted to dominate the motion of particles in mucus. The theoretical foundation of our work can be extrapolated to other systems, providing a guide to identify dominant molecular mechanisms regulating the mobility of particles in mucus and other polymeric fluids.

Classical microwave circuit theory is incapable of representing some phenomena at the quantum level. To include quantum statistical effects when treating microwave networks, various theoretical treatments can be employed such as quantum input-output network (QION) theory and SLH theory. However, these require a reformulation of classical microwave theory. To make these topics comprehensible to an electrical engineer, we demonstrate some underpinnings of microwave quantum optics in terms of microwave engineering. For instance, we equate traveling-wave phasors in a transmission line (V + 0) directly to bosonic field operators. Furthermore, we extend QION to include a state-space representation and a transfer function for a single port quantum network. This serves as a case study to highlight how microwave methodologies can be applied in open quantum systems. Although the same conclusion could be found from a full SLH theory treatment, our method was derived directly from first principles of QION.

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