Methods

Monoclonal Antibody Systemic Concentration

The mean peak serum concentration of SIL following the first dose of SIL 11 mg kg-1 IV in patients with multicentric Castleman’s disease was derived from the mean steady-state maximum concentration (Cmax) of 322 μg mL-1 divided by the accumulation ratio (1.7), or 195 μg mL-1 [23]. A dissociation equilibrium binding constant (Kd) for SIL has been reported as 15 pM [24].
The mean peak serum concentration of TCZ following the first dose of TCZ 8 mg kg-1 in patients with cytokine release syndrome (CRS) during chimeric antigen receptor T-cell (CAR-T) treatment is 99.5 μg mL-1 [25]. A Kd for TCZ has been reported as 1240 pM [26].

Monoclonal Antibody Concentration in the Lung

Biodistribution mechanisms and data for therapeutic monoclonal antibodies were taken from published literature [27]. Specifically, distribution to the lung has been studied in the context of respiratory syncytial virus (RSV), where anti-RSV antibodies have been developed. BALF concentrations have been quantified in studies in cynomolgus monkeys relative to serum concentrations, and suggest extremely low BALF:Serum concentration ratios of 0.1-0.2%.
For the purpose of these calculations, an optimistic BALF:Serum concentration ratio of 0.2% was used. Applying this ratio to peak SIL and TCZ serum concentrations, peak BALF concentrations are then 2690 pM and 1370 pM, respectively.

IL-6 and sIL-6R Concentration in the Lung

Measurements of IL-6 and sIL-6R concentrations in normal subjects, patients at-risk for ARDS, and subjects experiencing ARDS were obtained from the literature [5]. In this study, patients with sepsis or trauma who were at risk for ARDS and patients with ARDS (all cause) were identified by prospective screening of all patients admitted to the Medical and Surgical intensive care unit in a three-year period. These patients would correspond to patients on the World Health Organization Ordinal Scale for Clinical Improvement of 3 (hospitalized with mild disease, no oxygen requirement) to 7 (hospitalized with severe disease, ventilated plus additional organ support) [R&D Blueprint COVID-19 Therapeutic Trial Synopsis Draft Feb 18, 2020]. Vital signs, including physiologic parameters of hypoxemia (expressed as partial pressure of oxygen (PaO2) to fraction of expired oxygen (FIO2) ratio, tidal volume, and static lung compliance), were measured daily but not reported. Patients were not stratified by mild, moderate or severe ARDS, and the oxygen requirements of individual patients were not reported.
For the purpose of the present analysis, with respect to IL-6 and sIL-6R concentrations, normal levels, levels in at-risk subjects on Day 1, and levels in ARDS subjects on Day 1 were extracted (median, 25th, 75th percentiles) and analyzed as log-normal distributions. N=300 subjects were simulated from these lognormal distributions. The degree of variability reported in Park et.al. exceed 100% for both IL-6 and sIL-6R in the at-risk and ARDS population, so between-patient variability is an important consideration. The following table reports summaries of virtual subject values, as well as the calculated IL‑6:sIL-6R complex using the formula [IL-6:sIL6R] = [IL-6]*[sIL-6R] Kd-1 and assuming the reported values in Park et.al. are free IL-6 and free sIL-6R (Table 1).
Notably the induction level of IL-6 and sIL-6R in ARDS relative to normal is 370-fold and 4.88-fold, respectively. Given a reported Kd value for sIL-6R to IL-6 of 5500 pM, binding is not favored and the free moiety forms predominate over the complex IL-6:sIL-6R (CR). The induced IL-6:sIL-6R complex level in ARDS relative to normal is 1810-fold. While out-of-scope for this analysis, affinity for the IL-6:sIL-6R complex for gp130 is in the range of 10 pM, so the predicted increase in available IL-6:sIL-6R complex should be understood in that context.

Binding Constant Selection

A review of the literature provided estimates for binding constants for SIL:IL-6 complex and TCZ:IL-6R complex. These values represented data across clinical and nonclinical studies, and modeling from clinical and nonclinical species. Binding constants for use in our model were set at the median value encountered, or 15 pM for SIL:IL-6 (Kd_SC in Figure 2) and 1241 pM for TCZ:sIL-6R (Kd_TR in Figure 2).

Binding Models