Abstract
Individual cells exhibit specific proliferative responses to changes in microenvironmental conditions. Whether such potential is constrained by the cell density throughout the growth process is however unclear. Here, we identify a theoretical framework that captures how the information encoded in the initial density of cancer cell populations impacts their growth profile. By following the growth of hundreds of populations of cancer cells, we found that the time they need to adapt to the environment decreases as the initial cell density increases. Moreover, the population growth rate shows a maximum at intermediate initial densities. With the support of a mathematical model, we show that the observed interdependence of adaptation time and growth rate is significantly at odds both with standard logistic growth models and with the Monod-like function that governs the dependence of the growth rate on nutrient levels. Our results (i) uncover and quantify a previously unnoticed heterogeneity in the growth dynamics of cancer cell populations; (ii) unveil how population growth may be affected by single-cell adaptation times; (iii) contribute to our understanding of the clinically-observed dependence of the primary and metastatic tumor take rates on the initial density of implanted cancer cells.
Highlights
Approaches the carrying capacity of the m edium[1,20]
Following adaptation (“lag phase”), every population entered a regime of exponential growth (“log phase”) with a roughly constant rate up to the maximum attainable, at which point the concentration of cells saturated
Despite the variability uncovered in recent years in the behaviour of single cells within a population[34,35], it is not unreasonable to expect that different populations of the same cells grown in identical media will display similar growth characteristics due essentially to the fact that different single-cell features will be averaged out in large enough populations
Summary
Approaches the carrying capacity of the m edium[1,20]. Other types of behaviours, especially positive correlations between the growth rate and N0 , may have different origins. It is known that randomness in cellular reproduction events can propagate to macroscopic p arameters[21,22,23] If such heterogeneities are putatively averaged out in large inocula, they may become relevant when the initial cell density is small and/or when the performance of the population is driven by single cells having extreme behaviours. We found that the average growth rates of the populations has a striking non-monotonic dependence on N0 , with a plateau at small N0 , the theoretically expected logistic decrease at large N0 , and a marked maximum at intermediate values. Implications of our results, both for cancer biology and for theoretical approaches, are discussed in the final part of this article
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