Modeling Differentiation Therapy for Cancer-Stem-Cell-Driven Tumors

JERÓNIMO FOTINÓS; BARBERIS, LUCAS; CARLOS A. CONDAT

Bilbao

Congreso; 13th International Conference, Dynamical Systems Applied to Biology and Natural Sciences (DSABNS); 2022

Basque Center for Applied Mathematics

Many solid tumors have been found to be driven by chemo- and radiotherapy-resistant cancer stem cells (CSCs). A possible therapeutic avenue in these cases consists of using a differentiating agent (DA) to force the differentiation of the CSCs and then applying conventional therapeutic courses to eliminate the differentiated cancer cells (DCCs). To describe the effects of a DA that reprograms cancer stem cells into DCCs, we adapt a differential equation model developed to investigate tumorspheres, which are assumed to be formed by two jointly evolving cancer cell subpopulations, CSCs and DCCs. We analyze the mathematical properties of the model, finding the equilibria and their stability. We also present numerical solutions and phase diagrams to describe the system evolution and the therapy effects, characterizing the DA strength by a parameter adif . To obtain realistic predictions, we choose the other model parameters to be those determined previously from fits to various experimental datasets ([1, 2, 3]).In the case of a tumor that exhibits intraspecific competition and interspecific cooperation between the subpopulations ([1]), low adif values lead to their stable coexistence, with the final tumor size decreasing with adif , but there is a critical value above which the end state does not contain any stem cells. For growth on a hard substrate ([2]), the CSCs cooperate, and the tumor grows without limits for small doses of the DA (low adif ). The main effect of the therapy is to delay growth, but if exceeds a critical threshold, the tumor reaches a state formed solely by DCCs. We also studied the consequences of modifying the therapy starting time. In summary, our model shows how the effects of a differentiation therapy depend critically not only on the dosage and timing of the drug application but also on the tumor nature and its environment.References[1] Barberis, L., Benítez, L., Condat, C.A. (2021). Elucidating the role played by cancer stem cells in cancer growth. Revista de Modelamiento Matemático de Sistemas Biológicos 1: 48-54.[2] Benítez, L., Barberis, L., Condat, C.A. (2019). Modeling tumorspheres reveals cancer stem cell niche building and plasticity. Physica A 533(121906): 1-11. https: //doi.org/10.1016/j.physa.2019.121906[3] Benítez, L., Barberis, L., Vellón, L., Condat, C.A. (2021). Understanding the influence of substrate when growing tumorspheres. BMC Cancer 21(276): 1-11.https://doi.org/10.1186/s12885-021-07918-1[4] Chen, Y-Ch., Patrick N., Ingram, P.N., Fouladdel, S., McDermott, S.P., Azizi, E., Wicha, M.S., Yoon, E. (2016). High-throughput single-cell derived sphere formation for cancer stem-like cell identification and analysis. Scientific Reports 6(27301): 1-12. https://doi.org/10.1038/srep27301[5] Wang, J., Liu. X., Jiang, Z., Li, L., Cui, Z., Gao, Y., Kong, D., Liu, X. (2016). A novel method to limit breast cancer stem cells in states of quiescence, proliferation or differentiation: use of gel stress in combination with stem cell growth factors. Oncology Letters 12(2): 1355-1360. https://doi.org/10.3892/ol.2016.