Modeling Helps Understand the Influence of Substrate on Tumorsphere Growth

Tumorspheres, cellular spheroids formed by clonal proliferation from established cell lines or tumor tissue, are experimental systems used to investigate diverse features of cancer. They may be especially useful to ascertain the effects of cancer stem cells on neoplastic development. Here we use a recently developed model that considers the interactions between cell subpopulations [L. Benitez et al, Physica A 533, 121906 (2019)] to interpret the results of experiments probing the influence of substrate hardness on tumorsphere growth [Wang et al, Oncol. Lett. 12, 1355 (2016)]. These authors cultured breast cancer stem cells on soft and hard matrix surfaces using stem cell growth factors, observing that the number of cancer stem cells increased continuously, albeit in different ways. They also cultured the cancer stem cells on hard agar in the absence of growth factors (the “control” experiment). In this case the spheroids grew faster, even if the stem cell number remained stationary. Fitting our model results to the data corresponding to the use of growth factors, we found that interspecific interactions between cells in different populations always promoted growth via a positive feedback loop. These interactions enhanced the stem cell doubling rate in what appears to be a frustrated attempt to reach the equilibrium fractions corresponding to the cancer stem cell niche. Moreover, if growth proceeded on soft agar, intraspecific interactions were always inhibitory, as we should expect from their competition for nutrients, but on hard agar the interactions between differentiated cells were strongly inhibitory while those between stem cells were collaborative. Experimental evidence also suggests that the hard substrate induces a large fraction of asymmetric stem cell divisions and the likelihood of plasticity processes, two features that appear to be absent in the case of the soft substrate. In the absence of stem cell growth factors, the barrier to differentiation is broken: although the stem cell number was conserved, overall growth was faster than in the other two cases. The interactions accelerate the effective growth rate of the differentiated cell fraction. Our interpretation of the results points to the centrality of the concept of stem cell niche and helps us to understand the relation between substrate stiffness and the dynamics of stem-cell fueled tumor growth.