Mouth breathing, dry air, and low water permeation promote inflammation, and activate neural pathways, by osmotic stresses acting on airway lining mucus

Respiratory disease and breathing abnormalities worsen with dehydration of the upper airways. We find that humidification of inhaled air occurs by evaporation of water over mucus lining the upper airways in such a way as to deliver an osmotic force on mucus, displacing it towards the epithelium. This displacement thins the periciliary layer of water beneath mucus while thickening topical water that is partially condensed from humid air on exhalation. With the rapid mouth breathing of dry air, this condensation layer, not previously reported while common to transpiring hydrogels in nature, can deliver an osmotic compressive force of up to around 100 cm H2O on underlying cilia, promoting adenosine triphosphate secretion and activating neural pathways. We derive expressions for the evolution of the thickness of the condensation layer, and its impact on cough frequency, inflammatory marker secretion, cilia beat frequency and respiratory droplet generation. We compare our predictions with human clinical data from multiple published sources and highlight the damaging impact of mouth breathing, dry, dirty air and high minute volume on upper airway function. We predict the hypertonic (or hypotonic) saline mass required to reduce (or amplify) dysfunction by restoration (or deterioration) of the structure of ciliated and condensation water layers in the upper airways and compare these predictions with published human clinical data. Preserving water balance in the upper airways appears critical in light of contemporary respiratory health challenges posed by the breathing of dirty and dry air.

the airway epithelium notably in the upper airways by way of the transmission of osmotic pressure differential arising from water flow through airway mucus. We note in the following that the magnitude of these mass-transfer-delivered stresses relative to heat and momentum stresses is such that, at least in the context of the breathing of warm (30 C) air in well-hydrated airways, airway water evaporation can be understood to leading order purely in mass transfer terms.
The mass evaporative flux of water (Qe) (kg/s) from the air/water interface over airway lining fluid and into airway lumen can be approximated per airway compartment (nose and trachea) of area A by the Penman Equation (MacArthur 1990) where xs is the mass water per mass dry air at saturated conditions, x the value at actual air conditions, and the evaporation rate constant Ke (kg/m 2 /h) per compartment (MacArthur 1990) including constant quiescent and convective evaporation contributions, the latter growing linearly with average compartmental air velocity ua (m/s). We assume relatively quiescent conditions over the majority of surface area within the nose in that principal air flow occurs in the narrow air passage of the middle or inferior meatus, and an average velocity on inhalation in the trachea of around 1 m/s, dictated by the jet of air that forms on inhalation within the larynx (characteristic peak air velocity ~ 3 m/s), and that differentiates the tracheal evaporative mass transport conditions from the nose. The evaporation rate constant for the nose compartment follows as KE ~ 0.007 kg/m 2 /s, while for the tracheal compartment KE ~ 0.01 kg/m 2 /s. Standard humidity tables give xs = 0.02 in the nose and tracheal compartments (ρ=1.225 kg/m 3 ), while x=0.002 at 10% RH and x=0.01 at 60% RH. This yields a total predicted average mass evaporative loss of water from the nose ranging from Qe ~ 2 mg/s (10%RH) to Qe ~ 1mg/s (60% RH), and in the trachea from Qe ~ 1.2 mg/s (10%RH) to Qe ~ 0.6 mg/s (60% RH). Assuming full condensation of super saturated water on exhalation at external air RH of 10% we estimate (see Tables 1 and 2) ~ 16.7 mg water condenses over the 220 cm 2 ALF surface in the upper airways, leading to a condensation layer thickness of ~ 1 µm. Over many inhalations and exhalations, a mean time-averaged osmotic flow rate of water through the mucus and the underlying epithelium can be determined by balancing this osmotic flux with time-averaged rate of evaporative water loss to the inhaled air.

Osmotic Pressure Acting on Airway Mucus
In its fully hydrated state, human airway mucus is a relatively permeable hydrogel with solids content of around 5% by weight, able to slow the movement of viruses, pathogens, and airborne particles of any kind, and immobilize particles of around 500 nm and larger (Walji 2010, Shuster et al 2013. Smaller size particles are also hindered in their movements, while in ways influenced by surface interactions with mucins, such that particles as small as 20 nm in diameter have been observed to be hindered in their diffusion relative to pure water (Walji 2010). Similar surface interactions also retard the movement of ions within mucus, albeit to weaker degree.
On the breathing of typical dirty air (PM 2.5 = 20 µg/m 3 and PM 0.1 = 20 µg/m 3 ) mucus in the upper airways becomes populated with deposited inhaled airborne particles. In dehydrating circumstances, this coverage naturally increases. Ultra-fine particles are known to predominately deposit in the upper airways on inhalation owing to Brownian motion (Cohen et al 1990). Assuming 50% of ultra-fine particle deposition in the trachea with an average diameter of ~ 20 nm, tidal breathing of air at tidal volume of 500 cm 3 , 15 breaths per minute, upper airway mean mucus residence (clearance) times of either 2 hours (fully hydrated, cilia moving in the trachea at a rate of around 1 mm/min) or 24 hours (relatively dehydrated), it follows that between 10 µg to ~ 100 µg of ultra-fine particle mass exists over the surface of the tracheal airway lining fluid after an hour or so of breathing air with PM 0.1 equal to 20 µg/m 3 . Similar and even greater masses of the larger particles (PM 2.5 and PM 10.0) will deposit in the trachea as well, recognizing that tracheal deposition of airborne particles is maximal for mass median particle diameters of ~ 10 µm owing to inertial impaction (Darquenne 2020). All of these particles will initially land on the surface of the mucus, and diffuse into the hydrogel with restricted movement conditioned by particle nature. Some of the larger particles will become trapped in the hydrogel, and this entrapment will reorient the smaller particles on their random walk through the hydrogel. Assuming a similar order of magnitude mass of PM 2.5 particles in the tracheal airway lining fluid, and given these particles are unable to penetrate far into the mucus, therefore tending to remain in or near the condensation layer, it is possible to estimate the concentration of particulate mass in comparison to the concentration of mucus solids. Concentrating the 100 µg particulate mass in the 1 µm this condensation layer with 60 cm 2 of tracheal surface area gives a solids mass fraction of 0.6 -in comparison to the 0.05 solids mass fraction of hydrated mucus.
Such particle coverage likely fouls the hydrogel, potentially retarding the movement of other, smaller particles, while decreasing overall water permeability of the mucus.
To characterize osmotic water flow in across airway mucus barriers, and begin to estimate impact of deposited airborne particle fouling, we modeled mucus as a porous medium with infinitely long cylindrical pores (i.e., the radius of the pores, R, much smaller than the length of the pores or the mucus thickness, L ~ 23 µm). Each pore is identical to the other, and of an approximate radius ~ 250 nm in hydrated and clean mucus, while with deposited particle clogging may be of a smaller effective radius. Steady-state diffusion of molecular and particulate osmolytes through the pores of the mucus gel leads to a steady mass flow of water (Qm) in the opposite direction of the concentration gradient determined by (Anderson & Malone 1974) where ρ is the mass density of water, and A the area of the upper airway compartment, with the osmotic pressure difference on either side of the membrane owing to concentration differences of osmolytically active molecules (i) in solution and Brownian particles (p). Here, Rg is the molar gas constant (8.315 J/K-mol), Tk the temperature ( o K), k the Boltzmann constant (1.381 x 10 -23 J/K) and, ΔC the concentration difference of all osmotic solutes across the mucus layer (ΔC=CC-CPCL). The hydraulic membrane coefficient can be expressed as (Anderson & Malone 1974) with ε the porosity of the membrane (0.95), µ = 0.01 g-s/cm, L = 23 µm. The particle/solute reflection coefficient through the porous hydrogel can be expressed per particle by representing the degree to which solutes are prevented from entering the pores of the hydrogel, where is the partition coefficient in the mucus membrane, and the ratio of osmolyte size to pore size. In the case where a is much smaller than R, as with salt ions or ultrafine particles, reflection can still occur owing to wall interactions with the solute. Values of V far smaller than 1 reflect an essentially irreversible attraction between the solute and the mucus elements as ion association with charged mucin surfaces.

Relative Salt & Particle Osmotic Mucus Stress Contributions
To assess the relative importance of small particles and salt ions to the overall osmotic pressure force acting on mucus it is instructive to estimate the salt osmotic pressure from Eq (4) as ΔΠ ~ 8.315 J/K-mol x 310 K x 0.3 osmoles/L or ~ 760,000 Pascals (Newton/m 2 ). Comparing this to the particle osmotic pressure acting in the very thin layer of water over mucus (the number of resident particles of 20 nm average diameter will be ~ 3 x 10 12 or a condensation layer concentration of ~ 1/2 x 10 21 /m 3 assuming a 24 h clearance time) i.e., ΔΠ ~ 1.381 x 10 -23 J/K x 310 K x 10 22 /m 3 or ~ 20 Pascals (Newton/m 2 ) reveals salt ions to be the predominant contributor to osmotic stress on mucus in the airways. Both salt and particle contributions are overwhelmingly larger than predicted epithelial stress contributions (~ 1 Pa or less) of heat and momentum transfer owing to water evaporative and air flow stresses during normal tidal breathing (Wu et al 2015(Wu et al , 2018).
An estimate of the water permeability of mucus can therefore be determined from Eq (3) and using Eq (8) for the ion reflection coefficient with V ~(a/R) (using a ~ 0.25 nm and R ~ 250 nm gives σ ~ 10 -6 ) -note this value is approximately the same as the one deduced from Eq. (6) assuming merely steric hindrance as the two expressions become identical for very small λ -In conventional units we estimate the mucus water permeability to have a value of 2.4 x 10 -2 m/s (= σ PmRgTk / vw where vw = 18.14 x 10 -6 m 3 /mol is the molar volume of water). Particle fouling of mucus (or any increase in solids content of mucus by particle fouling or dehydration) might render small particles a factor in the mucus permeability in two obvious ways. Deposited particles might reduce Pm by increasing steric hindrance. They might also be anticipated to increase the reflection coefficient. Recalling the 5 orders of magnitude difference in salt versus particle concentrations on the breathing of typical particle-laden air, the reflection coefficient would need to increase from 10 -6 by one to three orders of magnitude -and the water permeability reduce by two to four orders of magnitude -for particles themselves to be direct and decisive contributors to the overall osmotic stress on the mucus, and in this case mucus is so impermeable to water that excessive dehydration of the upper airways is bound to occur.

Displacement of the Mucus Membrane
Displacement of mucus into the PCL by way of the osmotic stress accompanying water evaporation can be quantified by application of Newton's first law on the mucus mass Mm, yielding where um = Qm/ρA is the velocity of the mucus hydrogel toward or away from the epithelium, t is time, and lPCL is the thickness of the PCL. In steady-state conditions To further understand mucus displacement it is important to determine the degree to which water that evaporates from the upper airways is drawn from within the airway lining fluid by osmosis or is supplied by condensation on exhalation. Condensation rate in the upper airways on exhalation (Qc) relates to evaporation rate on inhalation (Qe) by the relative humidity of the exhaled air from beyond the carina (RHexh) The simplifying assumption that the relative humidity at the carina on inhalation RHinh is maintained into the airways up to the airway generation where full saturation occurs RHexhcan be stated as or Here Vsat is the air volume from the carina to the airway generation where saturation occurs, and Vexh is the total volume of exhaled air -i.e., 1/2 liter in our example. The airway condensation factor expresses the fractional degree to which evaporation from the upper airways is supplied by water drawn from the ALF versus water that has been condensed from lung air, the 0.66 factor reflecting that full consideration of heat and mass transfer (Haut et al 2021) indicates ~ 33% of water that is evaporated on inhalation is condensed on exhalation. Variations in χ from the average 33% replenishment of the condensation layer by exhaled air, i.e. are attributable to the degree to which exhaled air is less than fully saturated with water.
The displacement of the mucus membrane on inhalation by the amount dPCL as indicated in Eq (9) is reversed on exhalation, so that the membrane vibrates with respect to the underlying layer of water. The mean displacement of the mucus membrane toward the epithelium many identical breath cycles is driven by the net time-averaged movement of water Qm through the mucus following inhalation and exhalation, i.e., the difference between the rate of condensation and exhalation This relationship allows the time-averaged displacement of the mucus membrane to be estimated where total inhalation and exhalation times are identical, T=Tinh=Texh. Mass conservation between the condensation layer, mucus layer, PCL and epithelium necessitates Here the over bar connotes time average and the (transcellular and paracellular) epithelial (epith) transport characteristics mirror those of the mucus itself. The osmotic pressure imbalances (ignoring particle effects) across the membrane and epithelium are related to the ion concentration differences produced by evaporation of water by where * denotes the surrounding tissues and cellular mass. We assume the hydration state of the tissues surrounding the airways to be relatively constant over the course of the breathing, such that the time averaged concentration of salt ions in the surrounding tissues is a constant C* We also assume the mean time-steady state concentration of salt ions in the ALF is regulated by the epithelium to be constant, and that the mucus is undeformed (meaning a conservation of mass of osmotic solutes in the mucus), such that the total mass of salt ions is and It follows that where Note that with the value determined above for σmPm ~ 10 -10 m 2 s/kg (equal to a mucus water permeability in conventional units ~ 10 -2 m/s) and with σepithPepith ~ 10 -12 m 2 s/kg (given experimentally reported epithelial water permeabilities ~ 10 -4 m/s) it follows that From the above we have In normal hydrated airways the membrane and epithelial permeation rates are relatively large, meaning they contribute in healthy circumstances only a minor amount to Eq. (24). Thus Eq.
(24) reduces in normal circumstances to

The Interrelated Thinning of the Condensation Layer and the PCL
The PCL thins in a very intuitive way. The contribution in Eq. (25) represents the net water loss to the air from the condensation layer over a full cycle of breathing. The condensation layer meanwhile generally thickens in a parallel way to the PCL, while it being sensitive to the permeation of water through the mucus and epithelial membranes.
Setting the left side of Eq (24) to zero leads to the definition of a critical epithelial permeability characterizing a condition where the airway epithelium is unable to supply the water needed to hydrate inhaled air. The condensation layer in this case disappears. At values of epithelial permeability below the critical value (above) the condensation layer thickness becomes negative, and the water/air surface begins to recede into the mucus, with the mucus drying out. A similar loss of condensation layer thickness can occur when the mucus permeability becomes vanishingly small, as on shrinkage of the mucus hydrogel (increase in solids content) during drying, acidification, and evolution of ionic composition. With low mucus permeability, the thickness of the condensation layer becomes vanishingly small, while it does not entirely disappear so long as epithelial permeation is sufficiently large.

ALF Dysfunction (Inflammatory Markers, CBF, EBP)
Quantitative estimates of airway dysfunction associated with small changes of mucus placement and ALF solute concentration relative to the fully hydrated PCL thickness and the isotonic salt ion concentration C*, can be determined by perturbation analysis, i.e., where α is a measure of dysfunction (as in the concentration of inflammatory marker in the ALF), α0 is a hydrated equilibrium value, δ is a small dimensionless parameter reflecting the force of departure from the equilibrium state, and α1, α2, and α3 are first, second and third order approximations of the variable α.
For dysfunction variables dependent on the compressive force or conformation change applied to cilia by the displacement of the mucus that occurs on dehydration, δ can be expressed as the steady-state displacement of the mucus layer relative to the thickness of fully hydrated PCL), leading to relative to a baseline value CI0 and dimensional (cm 2 /mg) inflammatory constant αI. A similar expression follows for cilia beat frequency (CBF) relative to a hydrated state CBF0 and dimensional (cm 2 /mg) CBF constant αCBF Loss of ALF volume, as occurs with inadequate permeation of mucus or epithelial layers, increases nonvolatile solute concentration in the ALF. The impact of ALF volume reduction on surfactants is to increase surfactant absorption onto the free ALF (condensation layer) surface.
Breakup of the air-water interface can occur by the shear flow of air on inhalation or exhalation over the air-water surface, a phenomenon common in nature, as in the formation of sea spray at wind speeds exceeding approximately 2 m/s (Liu et al 2021).  (Edwards et al 1991, Lucassen et al 1993. The ALF being a mixed surfactant system, with strong lung surfactants (e.g., DPPC) being produced predominantly in the alveolar region of the lungs, while also in the upper airways and undergoing transport up and down the airway tree on the exhalation and inhalation of air in the form of droplet nuclei and larger respiratory droplets. Increase in solute concentration within the ALF on the evaporation of water will increase surfactant concentration and favor absorption onto the shear-flow perturbed air-ALF surface of the strongest surfactants, such that instability and breakup of the surface of the ALF will grow with solute concentration.
Equation (31) can be used then to estimate surface breakup under the shear flow of air that occurs during inhalation. Assuming the number of droplets formed by the breakup of the condensation layer surface is proportional to the number of exhaled droplets in a clean-room environment (i.e., where all of the aerosol particles exhaled from the nose and mouth represent droplets formed within the airways), exhaled breath particles EBP on normal tidal breathing can be estimated to first-order approximation by a linear relation to condensation layer solute concentration relative to a hydrated state EBP0, with αEBP a dimensionless breakup constant

On the Temporary Regulation of the Condensation Layer by Inhaled Salty Water
Depositing a volume of hypertonic saline droplets VD on a region of the airways of total surface area A and with ALF water volume VALF alters the concentration of salt ions in the airways from C* to C+ by an amount Osmotic regulation of the ALF volume to equilibrate salt ion concentrations across the apical epithelial membrane results in a volume of water egress by osmosis Vosm of an amount Assuming the salt mass fraction in the deposited droplets and in the ALF is small compared to unity the water transport across the mucus post deposition and across the apical epithelium by osmosis largely remains above and beneath the mucus, such that the displacement of the mucus by an amount dosm in steady state can be estimated by

This gives
From the above where MD and MALF are the masses of the deposited water and ALF respectively.
Finally, Table 1 (Main Article) provides estimates of the depth of air penetration and air volume (Vsat) needed to fully saturate inhaled air -using the Weibel airway geometry (Table S1) from the main bronchi to the lower airways. While the convective evaporation contribution to Eq (2) is negligible beyond the carina, significant evaporation can still occur in the central airways even in the ideal circumstances of equatorial (30 0 C) air.