Cancer progression determined by cancer stem cells: the dynamics of growth and therapy.

L. BENÍTEZ; C.A. CONDAT; L. BARBERIS

Cusco

Congreso; X SOLABIMA; 2017

Sociedad Latinoamericana de Biología Matemática

We investigate the hypothesis that cancer growth is mediated by cancer stem cells  as a driving mechanism for the tumor progression. Cancer stem cells would be pathological versions of normal stem cells.Cancer stem cells may not necessarily constitute a minor component of the tumor. In high-grade tumors from patients, an increased pool of cancer stem cells may underlie their aggressive behavior.   Experimentally it is observed that tumor spheroids, in vitro cultures  of cancer cells , not always contain cancer stem cells. But growth curves for just cancer cells and just cancer stem cells cultures,  as the ones shown in the figure at right, also can be measured.        When cancer stem cells divide, with a rate $r_S$, there are three possible outcomes:         1) Replication, with probability p_r gives two cancer stem cells.        2) Symmetric division, with probability p_s, gives two cancer cells.        3) Asymmetric  division, with probability p_a, where the original cancer stem cell becomes a cancer cell  and give birth to another cancer cell.      There are several hypothesis on the differentiation probabilities for the reproduction of cancer stem cells, among them:  1) The asymmetric division just change the time scale thus p_a similar to 0.       2) The symmetric division rarely occurs, i.e. p_s similar to 0.      Also cancer stem cells are uniquely capable of recapitulating the tumor and are assumed to be highly resistant to radio and chemotherapy.