Fig 1.
Schematic diagram of the cellular and molecular processes considered in the mathematical model.
A: stem cell division (this figure was adapted from Fig. 1 in [24] B: IL-6 binding dynamics.
Table 1.
List of model variables.
Fig 2.
The probability of stem cell self-renewal, PS, as a function of stem cell number.
Table 2.
Parameter values taken from the literature and their sources.
Fig 3.
A: Data for tumor growth. B: Data for stem cell percentage. This data plot was redrawn from Figs 1B and 1C in [8], where they generated tumor xenografts by transplanting primary human cancer stem-like cells in SCID mice without human endothelial cells.
Table 3.
Parameter values obtained using IL-6+/+ data for primary tumor cells.
Table 4.
Variables related to anti-IL-6R treatment model.
Fig 4.
Time profiles of TCZ in plasma.
The best fit of Is(t) (solid line) defined by Eq 23 is plotted together with experimental data (dots) from an in vivo study [53] of TCZ (and a PH-dependent binding variant of TCZ) in normal mice.
Table 5.
Pharmacokinetic parameter values for the PK-model with i.v. injection.
Fig 5.
Numerical simulations of pre-treatment tumor growth, CSC percentage, and IL-6R fractional occupancy.
A: Best fit of the mathematical model prediction of tumor volume over time to the IL-6+/+ data for primary tumors implanted without human endothelial cells in [8]. The green curve in (A) shows the special case in which the tumor cells are not producing IL-6, ρ = 0. B: Comparison of the experimentally measured percentage of CSCs in primary tumors (brown), the experimentally measured percentage of CSCs on day 121 for tumors grown in IL-6 +/+ mice (blue), and the mathematical model prediction percentage of CSCs on day 121 (red). C: Model prediction of the temporal changes in the fractional occupancy of IL-6 receptors on CSCs, ϕS. D: Model prediction of the stem cell percentage over time.
Fig 6.
Model prediction of the temporal changes in the factional occupancy of IL-6 receptors on CSCs, ϕS, as the IL-6 secretion rate by tumor cells, ρ, varies from its baseline value (ρ = 7 × 10−7 fmol/cell/day) to the value that leads to 90% fractional occupancy (5.35 × 10−6 fmol/cell/day).
Fig 7.
PRCC values for the parameters using the tumor volume as the output of interest.
Fig 8.
PRCC values for the parameters using the percentage of cancer stem cells as the output of interest.
Fig 9.
IL-6R sensitivity/PRCC values for the parameters using the fractional occupancy of IL-6R on CSCs as the output of interest.
Fig 10.
Numerical simulations of TCZ treatment.
A: The amount of TCZ within the tumor during 7 weeks of treatment. B: Model predictions of tumor volume vs. time after treatment with TCZ. 1mg/kg or 5 mg/kg of TCZ is administered weekly when tumor reaches 125 mm3.
Fig 11.
IL-6R occupancy post-treatment.
A: Model prediction of the fraction of IL-6 receptors on CSCs over time that are occupied by IL-6, ϕS, for the control case (no treatment, blue), 1 mg/kg TCZ (red), and 5 mg/kg TCZ (yellow). B: Model prediction of the fraction of IL-6 receptors on CSCs over time that are occupied by TCZ, ϕI, for doses of 1 mg/kg TCZ (blue), and 5 mg/kg TCZ (red).
Fig 12.
TCZ impact on CSC death, self-renewal, and percentage.
Model predictions of the temporal impact of administering 1mg/kg or 5mg/kg of TCZ on the A: death rate of CSCs, B: probability of CSC self-renewal and C: percentage of CSCs within the tumor. As mentioned in the Section 2.2, these predictions are based on training the model with data from [8] were primary tumor cells were transplanted into IL6 +/+ mice without the addition of human endothelial cells.
Fig 13.
Impact of the amplification factor, Ain and the differentiated cell death rate, δD on tumor growth.
Model predictions of the tumor volume vs. time for the control cases as well as for treatment with 1 or 5 mg/kg TCZ when A: the amplification factor, Ain, is slightly increased from its baseline value and when C: the differentiated cell death rate, δD is slightly decreased from baseline. Model predictions of the CSC percentage vs time for the control cases as well as for treatment with 1 or 5 mg/kg TCZ when B: the amplification factor, Ain, is slightly increased and when D: the differentiated cell death rate, δD is slightly decreased (D).
Fig 14.
Model predictions of the tumor volume vs. time for the control case (no treatment) as well as for treatment with 1 mg/kg TCZ administered every 7, 14, 21 and 28 days. The line shows the first day of the final dose for each treatment schedule.