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:
- S + C <– Kd_SC –> SC where Kd_SC=S*C
SC-1
- T + R <– Kd_TR –> TR where Kd_TR=T*R
TR-1
- C + R <– Kd_CR –> CR where Kd_CR=C*R
CR-1
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.