Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect

Abstract

Most models of cancer cell population expansion assume exponential growth kinetics at low cell densities, with deviations to account for observed slowing of growth rate only at higher densities due to limited resources such as space and nutrients. However, recent preclinical and clinical observations of tumor initiation or recurrence indicate the presence of tumor growth kinetics in which growth rates scale positively with cell numbers. These observations are analogous to the cooperative behavior of species in an ecosystem described by the ecological principle of the Allee effect. In preclinical and clinical models, however, tumor growth data are limited by the lower limit of detection (i.e., a measurable lesion) and confounding variables, such as tumor microenvironment, and immune responses may cause and mask deviations from exponential growth models. In this work, we present alternative growth models to investigate the presence of an Allee effect in cancer cells seeded at low cell densities in a controlled in vitro setting. We propose a stochastic modeling framework to disentangle expected deviations due to small population size stochastic effects from cooperative growth and use the moment approach for stochastic parameter estimation to calibrate the observed growth trajectories. We validate the framework on simulated data and apply this approach to longitudinal cell proliferation data of BT-474 luminal B breast cancer cells. We find that cell population growth kinetics are best described by a model structure that considers the Allee effect, in that the birth rate of tumor cells increases with cell number in the regime of small population size. This indicates a potentially critical role of cooperative behavior among tumor cells at low cell densities with relevance to early stage growth patterns of emerging and relapsed tumors.

Eradicating Metastatic Cancer and the Eco-Evolutionary Dynamics of Anthropocene Extinctions

“…As generally seen in background extinctions, an identical perturbation may result in entirely different outcomes in small populations compared to large groups of the same species (17). This is due to the vulnerability of small populations to stochastic changes in birth and death rates (17), decreased cellular heterogeneity, and Allee effects that adversely affect small populations (19,22).…”

“…Of these, there are three important factors for cancer treatment: (i) demographic stochasticity (which arises from the probabilistic nature of birth and death at the level of individual cells); (ii) population heterogeneity (which is related to variation in vital rates among individual cells); and (iii) the Allee or "aggregation" effects (which are the benefits each cancer cells gains during therapy because it is a member of a group; refs. [18][19][20][21][22]. How and to what extent each of these factors shape extinction risk will likely change during the course of treatment.…”

Modeling How Heterogeneity in Cell Cycle Length Affects Cancer Cell Growth Dynamics in Response to Treatment

“…As can be seen, recurrence is highly probable in the heterogeneous populations when initialized with normal distribution. Note that other mechanisms, like the Allee effect ( 19 , 20 ), might play a critical role at these extremely low densities of recurrence, probably prohibiting the growth of these populations in real settings. The spatiotemporal evolution of the tumor population indicatively for the initially normal distribution of phenotypes can be seen in the Video SV2 for random death probability equal to 0.4.…”

Genome analysis of the monoclonal marbled crayfish reveals genetic separation over a short evolutionary timescale

“…The logistic population growth model is described by and the population size at time point ti+1- ti, where the maximum number of individuals was set to N max = 192,000 (SE = 34.98%) for the current population. The growth with strong Allee effect described by where parameter A was chosen according to an established Allee threshold 56 of −3.1.…”