Figure 2
where: S and T are the free concentrations of SIL and TCZ in BALF, respectively; C and R are the free concentrations of IL-6 cytokine and sIL-6R, respectively; SC is the concentration of SIL:IL-6 complex; TR is the concentration of TCZ:sIL-6R; CR is the concentration of sIL-6R bound to IL-6. Kd_SC, Kd_TR and Kd_CR are the equilibrium dissocation binding constants for SIL:IL-6, TCZ:sIL-6R and IL-6:sIL-6R, respectively.
CR is the complex that (presumably) signals though the ubiquitously expressed gp130 receptor.
In stoichiometric form:
These reactions were implemented as a system of ordinary differential equations (ODEs). Initial conditions of IL-6 (C ) and sIL-6R (R ) were given from the BALF concentration data in normal, pre-ARDS and ARDS subjects from the above table. IL-6:sIL-6R (CR ) was calculated, as above. Binding constants are given for SIL:IL-6 (SC ) of 15 pM, IL‑6:sIL‑6R (CR ) of 5500 and TCZ:sIL-6R (TR ) of 1241.
Solving the resulting equilibrium equations may be possible, but these authors opted instead to simply simulate from the (dynamic) ordinary-differential equations out to steady-state. Off-rates were set 0.1 s-1 for each reaction, so on-rates were derived kon=koff Kd-1. Although the off-rate is much more rapid than is typical for antibodies, the simulations were run out to steady-state so this assumption plays no role in the simulation results. Simulations at off-rate values of 0.01 and 0.01 s-1 were performed to confirm similar results at equilibrium (time >> koff-1.) Should an analytical solution to the equilibrium equations be derived, the results would be expected to match these.
The model solutions for C (IL-6), R (sIL-6R) and CR (IL-6:sIL-6R complex) at binding equilibrium were produced for each synthetic subject.