Table 2 List of differential equations for the recycling model.

From: Mathematical modeling of drug-induced receptor internalization in the HER2-positive SKBR3 breast cancer cell-line

\(\frac{d}{dt}\)Nm = kprod − kact · Nm · T + kdiss · \({{\rm{N}}}_{m}^{T}-{k}_{{\rm{int}}}\) · Nm + krec · Ni − kon · A · Nm + koff · N\({m}^{A}\)

\(\frac{d}{dt}\,\)Ni = kdiss · N\({i}^{T}\) + kint · Nm − krec · Ni − kdeg · Ni + koff · N\({i}^{A}\)

\(\frac{d}{dt}\,\)N\({m}^{T}\) = kact · Nm · T − kdiss · \({{\rm{N}}}_{m}^{T}-{k}_{{\rm{int}},{\rm{T}}}\) · N\({m}^{T}\) + krec,T · \({{\rm{N}}}_{i}^{T}-{k}_{{\rm{on}}}\) · A · N\({m}^{T}\) + koff · N\({m}^{T,A}\)

\(\frac{d}{dt}\,\)N\({i}^{T}\) = −kdiss · N\({i}^{T}\) + kint,T · \({{\rm{N}}}_{m}^{T}-{k}_{{\rm{rec}},{\rm{T}}}\) · \({{\rm{N}}}_{i}^{T}-{k}_{{\rm{\deg }},{\rm{T}}}\) · N\({i}^{T}\) + koff · N\({i}^{T,A}\)

\(\frac{d}{dt}\,\)N\({m}^{A}\) = −kact · N\({m}^{A}\) · T + kdiss · \({{\rm{N}}}_{m}^{T,A}-{k}_{{\rm{int}}}\) · N\({m}^{A}\) + krec · N\({i}^{A}\) + kon · A · Nm − koff · N\({m}^{A}\)

\(\frac{d}{dt}\,\)N\({m}^{T,A}\) = kact · N\({m}^{A}\) · T − kdiss · \({{\rm{N}}}_{m}^{T,A}-{k}_{{\rm{int}},{\rm{T}}}\) · N\({m}^{T,A}\) + krec,T · N\({i}^{T,A}\) + kon · A · \({{\rm{N}}}_{m}^{T}-{k}_{{\rm{off}}}\) · N\({m}^{T,A}\)

\(\frac{d}{dt}\,\)N\({i}^{A}\) = kdiss · N\({i}^{T,A}\) + kint · \({{\rm{N}}}_{m}^{A}-{k}_{{\rm{rec}}}\) · \({{\rm{N}}}_{i}^{A}-{k}_{{\rm{\deg }}}\) · \({{\rm{N}}}_{i}^{A}-{k}_{{\rm{off}}}\) · N\({i}^{A}\)

\(\frac{d}{dt}\,\)N\({i}^{T,A}\) = −kdiss · N\({i}^{T,A}\) + kint,T · \({{\rm{N}}}_{m}^{T,A}-{k}_{{\rm{rec}},{\rm{T}}}\) · \({{\rm{N}}}_{i}^{T,A}-{k}_{{\rm{\deg }},{\rm{T}}}\) · \({{\rm{N}}}_{i}^{T,A}-{k}_{{\rm{off}}}\) · N\({i}^{T,A}\)

\(\frac{d}{dt}\,\)T = −kact · N\({m}^{A}\) · T + kdiss · \({{\rm{N}}}_{m}^{T,A}-{k}_{{\rm{act}}}\) · Nm · T + kdiss · N\({m}^{T}\)

\(\frac{d}{dt}\,\)A = −kon · A · Nm + koff · \({{\rm{N}}}_{m}^{A}-{k}_{{\rm{on}}}\) · A · N\({m}^{T}\) + koff · N\({m}^{T,A}\)

  1. The HER2 receptor N is labeled with suffix m or i indicating its location either on the membrane or internal. Bound Trastuzumab T or Affibody A are indicated by the superscripts T and A.
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