208 B. Miraglio et al.
The negative feedback of T4Bon TSH production mediated exclusively by
D 2 (as illustrated in Fig. 1 ) is highlighted inTSHsynthandTSHdestr. Indeed,
T3Pitcan only be obtained through deiodination of T4Bby D 2 (rulesPitsynth
andPitdestr).
Activation and metabolism of TH.The activation of blood TH is handled by D 1
and D 2. Their equilibria and their impact on the system are handled thanks to
the following rules:
D (^1) synth:Ω⇒D 1 when(XD1=ε) boost(T3B=ε)
D (^1) destr:D 1 ⇒Ωwhen(XD1>ε∨(D 1 =θ∧T3B>ε))
D (^2) synth:Ω⇒D 2 when(T3B<θ∧XD2=ε) boost(T3B=ε)
D (^2) destr:D 2 ⇒Ωwhen(T3B=θ∨XD2>ε∨(D 2 =θ∧T3B>ε))
Irecycling:T4B⇒IB when(D 1 >ε)
THactivation:T4B⇒T3B when(D 1 =θ∨D 2 >ε) boost(D 2 =θ)
Both D 1 and D 2 levels are induced by a lack of T3Bin the system. On the
contrary, D 2 levels are reduced by an excess of T3B. On top of that, the presence
of exogenous disruptors such as XD1or XD2alters D 1 and D 2 levels.
As the vast majority of sulfated TH is composed of T4B,Irecyclingmodels
accurately the preponderant recycling role of D 1 .D 1 also intervenes marginally
in T4Bdeiodation, as shown inTHactivation, where D 1 needs to be at levelθ
to satisfy thewhenstatement. As for D 2 , the enzyme acts essentially on T4B
deiodation in T3B, as shown by bothwhenandbooststatements ofTHactivation.
The metabolism of TH is mainly provided by D 3 and Detox. The rules involv-
ing these entities are:
D (^3) synth:Ω⇒D 3 when(T3B>ε) boost(T3B=θ)
D (^3) destr:D 3 ⇒Ωwhen(T3B=ε∨(D 3 =θ∧T3B<θ))
Detoxsynth:Ω⇒Detox boost(XHep>ε)
Detoxdestr:Detox⇒Ωwhen(Detox =θ∧XHep=ε)
T (^3) destr:T3B⇒Ωwhen(D 3 =θ∨Detox =θ∨(T3B=θ∧D 3 >ε))
T (^4) destr:T4B⇒Ωwhen(D 3 =θ∨Detox =θ∨(T4B=θ∧D 3 >ε))
The regulation of D 3 levels is symmetrical to D 2 regulation, as T3Bis an
inducer of D 3 levels. The case of Detoxis interesting: since we are only interested
in an excessive activity of the hepatic detoxifying enzymes, the set of admissible
levels of this entity is{Δ, θ}. An excess of Detox is only triggered by the presence
of XHep, as seen inDetoxsynthandDetoxdestr.
Furthermore, thewhenstatements of rulesT (^3) destrandT (^4) destrreflects two
important notions on the metabolism of T3Band T4B:
- An excess of D 3 or Detox is enough to decrease the levels of both TH.
- If TH are in excess, the presence of D 3 is enough to restore normal TH levels.
It is capital to note that when both levels of D 3 and TH are normal, D 3 does
not trigger the decrease of TH levels.
The set of all these rules allows to generate the system dynamics. It is then
possible to constrain these dynamics thanks to biological observations expressed