  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.
