A model for the intrinsic limit of cancer therapy: Duality of treatment-induced cell death and treatment-induced stemness

Abstract

Intratumor cellular heterogeneity and non-genetic cell plasticity in tumors pose a recently recognized challenge to cancer treatment. Because of the dispersion of initial cell states within a clonal tumor cell population, a perturbation imparted by a cytocidal drug only kills a fraction of cells. Due to dynamic instability of cellular states the cells not killed are pushed by the treatment into a variety of functional states, including a “stem-like state” that confers resistance to treatment and regenerative capacity. This immanent stress-induced stemness competes against cell death in response to the same perturbation and may explain the near-inevitable recurrence after any treatment. This double-edged-sword mechanism of treatment complements the selection of preexisting resistant cells in explaining post-treatment progression. Unlike selection, the induction of a resistant state has not been systematically analyzed as an immanent cause of relapse. Here, we present a generic elementary model and analytical examination of this intrinsic limitation to therapy. We show how the relative proclivity towards cell death versus transition into a stem-like state, as a function of drug dose, establishes either a window of opportunity for containing tumors or the inevitability of progression following therapy. The model considers measurable cell behaviors independent of specific molecular pathways and provides a new theoretical framework for optimizing therapy dosing and scheduling as cancer treatment paradigms move from “maximal tolerated dose,” which may promote therapy induced-stemness, to repeated “minimally effective doses” (as in adaptive therapies), which contain the tumor and avoid therapy-induced progression.

Fano factors in determining certain types of gene autoregulation

“…Notice that we can have h n > h n−1 for some n and h n ′ < h n ′ −1 for some other n ′ , meaning that positive autoregulation and negative autoregulation can both exist for the same gene, but occur at different expression levels. Such non-monotonicity in regulating gene expression often appear in reality [1].…”

“…There are some known methods that overcome the above obstacles, and there are also some possible solutions that might appear in the future. (1) The dependency can be solved by better measurements for isolated cells that do not affect each other. In fact, the relationship between autoregulation and cell-cell interaction has been studied [46].…”

Finding meaningful and workable applied mathematics problems in science

“…For researchers in mathematics, communication and collaboration with experimental biologists might not be smooth at the beginning, since the thinking modes are different. I also participated in other projects on population dynamics [1,23,6,36].…”

Three facets of mathematical cancer biology research

“…Many studies build models for cancer cells living in a free environment [28]. Some other studies consider the effect of nutrients [25] and drugs [3].…”

“…Due to such phenomena, we have to introduce more complicated mechanisms. One possible approach is to assume that at higher drug doses, the killing rate does not further increase, but the drug-induced transition rate from the sensitive state to the resistant state still increases [3]. Therefore, when we increase the drug dose, the treatment effect first increases, since the killing rate increases.…”