A Multicompartment Mathematical Model of Cancer Stem Cell-Driven Tumor Growth Dynamics

Abstract

Tumors are appreciated to be an intrinsically heterogeneous population of cells with varying proliferation capacities and tumorigenic potentials. As a central tenet of the so-called cancer stem cell hypothesis, most cancer cells have only a limited lifespan and thus cannot initiate or re-initiate tumors. Longevity and clonogenicity are properties unique to the subpopulation of cancer stem cells. To understand the implications of the population structure suggested by this hypothesis - a hierarchy consisting of cancer stem cells and progeny non-stem cancer cells which experience a reduction in their remaining proliferation capacity per division - we set out to develop a mathematical model for the development of the aggregate population. We show that overall tumor progression rate during the exponential growth phase is identical to the growth rate of the cancer stem cell compartment. Tumors with identical stem cell proportions, however, can have different growth rates, dependent on the proliferation kinetics of all participating cell populations. Analysis of the model revealed that the proliferation potential of non-stem cancer cells is likely to be small to reproduce biologic observations. Furthermore, a single compartment of non-stem cancer cell population may adequately represent population growth dynamics only when the compartment proliferation rate is scaled with the generational hierarchy depth.

Heritable tumor cell division rate heterogeneity induces clonal dominance

“…In line with our explanation for the massive clone loss, increasing the probability of symmetric CSC division strongly reduced clone loss ( Fig 3E). Increasing the initial percentage of stem cells had a less pronounced effect on clone loss ( Fig 3E), which fits with the observation in [28] that the proportion of CSCs in the population will become constant in the long term and does not depend on the initial percentage of CSCs. Altogether, increasing the probability of a symmetric CSC to 1 and the initial CSC percentage to 100% did not lead to clone loss matching that observed experimentally.…”

“…We fine-tuned the parameters of the CSC growth model such that the population growth rate is consistent with the 19 hour doubling time reported by Porter et al [13]. For this we exploited the analytical solution of the CSC model elegantly derived by Weekes et al [28]. This solution predicts that the population of cells initially grows, and then develops according to one of three growth regimes determined by β = (p 1 − p 3 )r CSC .…”

An agent-based model of cancer stem cell initiated avascular tumour growth and metastasis: the effect of seeding frequency and location

“…In several studies, Enderling and co-workers have modelled stem cell originated tumour growth [35][36][37][38]. The models focus on the conditions for dormancy [36] as a function of rate of migration [35], directed migration tumour immune response [37] and hierarchical growth dynamics [39]. There are many types of computational models and each has its own strengths and weaknesses [40].…”

Exponential Growth of GlioblastomaIn VivoDriven by Rapidly Dividing and Outwardly Migrating Cancer Stem Cells

“…A key consequence of this hierarchical cellular organization of the tumor is that the exponential growth rate of the tumor mass is equal to the symmetric division rate of the BTSCs (Supplementary Theory) [39]; the proliferation, differentiation and death parameters of TPCs and DTCs have no impact on the long-term growth of the tumor mass because they lack the ability to self-renew. Moreover, we find that during the exponential growth phase the relative proportions of BTSCs, TPCs and DTCs remain constant; these fractions are governed by all proliferation and death rates of the various subpopulations (Supplementary Theory).…”