Mechanistic Pharmacokinetic/Pharmacodynamic Model of Sunitinib and Dopamine in MCF-7/Adr Xenografts: Linking Cellular Heterogeneity to Tumour Burden

Abstract

The self-renewal and differentiation of cancer stem-like cells (CSCs) leads to cellular heterogeneity, causing one of the greatest challenges in cancer therapy. Growing evidence suggests that CSC-targeting therapy enhances the effect of concomitant antitumour therapy. To gain an in-depth understanding of this enhanced effect, the kinetic profile of estimated CSC frequency (the fraction of CSCs in tumour) was evaluated for in vivo characterization of cellular heterogeneity using sunitinib and dopamine as a paradigm combination therapy. Female MCF-7/Adr xenografted Balb/c nude mice were treated with sunitinib (p.o., 20 mg/kg) and dopamine (i.p., 50 mg/kg), alone or in combination. Estimated CSC frequency and tumour size were measured over time. Mechanistic PK/PD modelling was performed to quantitatively describe the relationship between drug concentration, estimated CSC frequency and tumour size. Sunitinib reduced tumour size by inducing apoptosis of differentiated tumour cells (DTCs) and enriched CSCs by stimulating its proliferation. Dopamine exhibited anti-CSC effects by suppressing the capacity of CSCs and inducing its differentiation. Simulation and animal studies indicated that concurrent administration was superior to sequential administration under current experimental conditions. Alongside tumour size, the current study provides mechanistic insights into the estimation of CSC frequency as an indicator for cellular heterogeneity. This forms the conceptual basis for in vivo characterization of other combination therapies in preclinical cancer studies.

Appendices

Appendices

Existing Knowledge

Here, we summarise the existing knowledge of CSC theory and the related pharmacological activities of dopamine and sunitinib. All information was incorporated into a mechanistic model that described the sunitinib/dopamine combination in the treatment of drug-resistant breast cancer:

• 1) The cancer stem-like cells (CSCs) and the differentiated tumour cells (DTCs) own the capacity of converting to the other one [1].

• 2) The size of CSCs is much smaller than DTCs [38].

• 3) The DTC population grow more aggressively and mainly contribute to the tumour bulk [39].

• 4) The CSC population cycle very slowly and eventually reach the steady state during the evolution of tumour [23, 40].

• 5) Dopamine can eradicate CSCs [7].

• 6) Sunitinib is a multi-targeted receptor tyrosine kinase inhibitor (TKI) with anti-angiogenic and antitumour activities [9, 10].

• 7) Sunitinib enriches the CSC population within the tumour [11,12,13].

Derivation of the Equation for Tumour Volume

In this study, the tumour volume is approximated by the sum of volumes of different cancel cells. As the tumour mainly consists of two representative cell subpopulations (i.e. CSCs and DTCs), the tumour volumes at time 0 (Eq. A1) and t (Eq. A2) are derived:

$$ {V}_0={CSC}_0\cdotp {V}_{s- CSC}+{DTC}_0\cdotp {V}_{s- DTC} $$

(A1)

$$ V(t)= CSC(t)\cdotp {V}_{s- CSC}+ DTC(t)\cdotp {V}_{s- DTC} $$

(A2)

Here, V₀ and V(t) represent the tumour volume at time 0 and t. CSC(t) and DTC(t) denote the amount of CSCs or DTCs at time t, respectively. V_{s − CSC} and V_{s − DTC} represent the volume of a single cell of CSC or DTC, respectively.

Re-organizing the Eqs. A1 and A2 yields the expression of tumour volume at time t related to the tumour volume at time 0 (Eq. A3):

$$ V(t)={V}_0\cdotp \frac{CSC(t)\cdotp {V}_{s- CSC}+ DTC(t)\cdotp {V}_{s- DTC}}{CSC_0\cdotp {V}_{s- CSC}+{DTC}_0\cdotp {V}_{s- DTC}} $$

(A3)

Dividing the numerator and denominator by V_{s − DTC} yields Eq. A4:

$$ V(t)={V}_0\cdotp \frac{CSC(t)\cdotp Ratio+ DTC(t)}{CSC_0\cdotp Ratio+{DTC}_0} $$

(A4)

Here, Ratio represents the volume ratio of a single CSC to a single DTC.

Since the exact amount of initial tumour cells is unknown, the initial amount of total tumour cells is assumed to be 100 (arbitrary units). From our experiments, the average estimated CSC frequency before the first drug administration is 1.55%. Thus, the initial amount of CSCs (CSC₀) is 1.55 units, and the initial amount of DTCs (DTC₀) is 98.45 units. In addition, it is known that the size of CSCs is much smaller than DTCs (Existing knowledge 2), indicating that the volume ratio of a single CSC to a single DTC (Ratio) is much smaller than 1. Therefore, the product of CSC₀ and Ratio (CSC₀ ∙ Ratio) is much smaller than DTC₀. Thus, Eq. A4 can be reduced into Eq. A5.

$$ V(t)={V}_0\cdotp \frac{CSC(t)\cdotp Ratio+ DTC(t)}{DTC_0} $$

(A5)

It is known that the DTC population grow more aggressively and mainly contribute to the tumour bulk (Existing knowledge 3), indicating that DTC(t) is much larger than CSC(t). Furthermore, Ratio is much smaller than 1 (Existing knowledge 2). Hence, the product of CSC(t) and Ratio is much smaller than DTC(t). Thus, Eq. A5 can be reduced into the final expression of tumour volume (Eq. A6):

$$ V(t)={V}_0\cdotp \frac{DTC(t)}{DTC_0} $$

(A6)