Thermodynamic equilibrium dose-response models for MERS-CoV infection reveal a potential protective role of human lung mucus but not for SARS-CoV-2

Abstract

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and Middle East respiratory syndrome coronavirus (MERS-CoV) infect the human respiratory tract. A prototype thermodynamic equilibrium model is presented here for the probability of the virions getting through the mucus barrier and infecting epithelial cells based on the binding affinity (K_mucin) of the virions to mucin molecules in the mucus and parameters for binding and infection of the epithelial cell. Both MERS-CoV and SARS-CoV-2 bind strongly to their cellular receptors, DDP4 and ACE2, respectively, and infect very efficiently both bronchus and lung ex vivo cell cultures which are not protected by a mucus barrier. According to the model, mucin binding could reduce the infectivity for MERS-CoV compared to SARS-CoV-2 by at least 100-fold depending on the magnitude of K_mucin. Specifically K_mucin values up to 10⁶ M^-1 have little protective effect and thus the mucus barrier would not remove SARS-CoV-2 which does not bind to sialic acids (SA) and hence would have a very low K_mucin. Depending on the viability of individual virions, the ID₅₀ for SARS-CoV-2 is estimated to be ~500 virions (viral RNA genomic copies) representing 1 to 2 pfu. In contrast MERS-CoV binds both SA and human mucin and a K_mucin of 5 × 10⁹ M^-1 as reported for lectins would mop up 99.83% of the virus according to the model with the ID₅₀ for MERS-CoV estimated to be ~295,000 virions (viral RNA genomic copies) representing 819 pfu. This could in part explain why MERS-CoV is poorly transmitted from human to human compared to SARS-CoV-2. Some coronaviruses use an esterase to escape the mucin, although MERS-CoV does not. Instead, it is shown here that "clustering" of virions into single aerosol particles as recently reported for rotavirus in extracellular vesicles could provide a co-operative mechanism whereby MERS-CoV could theoretically overcome the mucin barrier locally and a small proportion of 10 μm diameter aerosol particles could contain ~70 virions based on reported maximum levels in saliva. Although recent evidence suggests SARS-CoV-2 initiates infection in the nasal epithelium, the thermodynamic equilibrium models presented here could complement published approaches for modelling the physical entry of pathogens to the lung based on the fate and transport of the pathogen particles (as for anthrax spores) to develop a dose-response model for aerosol exposure to respiratory viruses. This would enable the infectivity through aerosols to be defined based on molecular parameters as well as physical parameters. The role of the spike proteins of MERS-CoV and SARS-CoV-2 binding to SA and heparan sulphate, respectively, may be to aid non-specific attachment to the host cell. It is proposed that a high K_mucin is the cost for subsequent binding of MERS-CoV to SAs on the cell surface to partially overcome the unfavourable entropy of immobilisation as the virus adopts the correct orientation for spike protein interactions with its protein cellular receptor DPP4.

Keywords: Dose-response; Infection; Mucin; Risk; SARS-CoV-2.

Fig. 1

Pathway from virus exposure to infection of cell.

Fig. 2

The fraction, F_v, of free virus in mucus calculated by the difference equation approach decreases with increasing magnitude of the association constant, K_mucin, for binding of virus to mucin and is strongly affected by the local virus to mucin molecule ratio which is set to 2:1 (dash-dotted line), 1:1 (dashed line), 1:2 (dotted line) and <0.1:1 (solid line). The solid line is also represented by Eq. 8 for fully dispersed virus with [Muc_free] = 1.18 × 10⁻⁷ M. In a) the y-axis is linear to visualise the effect for the 2:1 virus:mucin ratio. In b) the y-axis is logarithm transformed to visualise small fractions of F_v as the virus becomes more dispersed in the mucus.

Fig. 3

The major proportion of virions is predicted to be bound to host cells in the human lung when K_{a_virus_T} > ~10¹⁴ M⁻¹. Fraction, F_c, of virus dose of 1,000 virions predicted to be bound to host cells as a function of K_{a_virus_T} for the human lung (solid line, C_total = 1.2 × 10⁹ cells in 0.025 dm³ of lung lining fluid, [C_total] = 8.0 × 10⁻¹⁴ M); human intestine (dashed line, C_total = 4.15 × 10⁸ cells in 0.314 dm³ of gut contents, [C_total] = 2.2 × 10⁻¹⁵ M) and mosquito midgut (dotted line, C_total = 1 × 10³ cells in 10⁻⁶ dm³ of midgut contents, [C_total] = 1.7 × 10⁻¹⁵ M) as calculated by the difference equation approach (Gale 2018).

Fig. 4

Prototype dose-response models according to Equation 5 for respiratory coronavirus virion exposure with F_trans = 1, p_pfu = 0.0028, F_c = 1 and p_cell = 0.5. F_v values calculated with Equation 8 using [Muc_free] ~ [Muc_total] = 1.18 × 10⁻⁷ M assuming K_mucin values of 10³ M⁻¹ (dashed line), 10⁶ M⁻¹ (solid line), 10⁹ M⁻¹ (dash-dot line), and 10¹² M⁻¹ (dotted line) to represent N_m = 1, 2, 3, and 4 spike protein/mucin SA contacts, respectively, of K_{d_mucin} = 10⁻³ M (Eq. 9). Also K_mucin = 5 × 10⁹ M⁻¹ (dash-dot-dot line) as for the lectin soy bean agglutinin binding to porcine submaxillary mucin (Dam and Brewer 2010). Squares represent proportion of mice which died after intranasal challenge of mouse hepatitis coronavirus (open) or SARS-CoV (filled) from Watanabe et al. (2010) assuming 1 pfu = 360 virions or genomic copies. In b) the y-axis is logarithm transformed to visualise risks from low doses of dispersed virus.

Fig. 5

Dose-response for respiratory coronavirus virion exposure varies between individuals depending on MUC5B concentration in the mucus (Table 4) according to Equation 5 (with F_trans = 1, p_pfu = 0.0028, F_c = 1 and p_cell = 0.5) for SARS-CoV-2 fully dispersed in lung mucus with K_mucin = 10¹⁰ M⁻¹ and F_v values calculated with Equation 8 using [Muc_free] ~ [Muc_total] = 0.2 × 10⁻⁷ M (dotted line), 1.08 × 10⁻⁷ M (solid line) and 3.0 × 10⁻⁷ M (dash-dot line).