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The formation of tight tumor clusters affects the efficacy of cell cycle inhibitors: a hybrid model study

Significance Statement
Rigorous mathematical modeling and comprehensive computer simulations are able to test differences in cell responses to individual inhibitors of the cell cycle phases; and to delineate the extent to which combined inhibitors effect individual cells in the tumor cluster. In this paper, the inhibitors of cyclin-dependent kinases, CDK1 and CDK2, were considered, since they are known to regulate passage through the G2/M and G1 checkpoints of the cell cycle, respectively. Our computational results indicated that when the cells form tight multicellular spheroids, they are likely to be arrested in the G1 phase due to contact inhibition; and, in turn, these cells may not be responsive to CDK1 and CDK2 inhibition. Whilst the overall tumor cluster may appear to be growth-arrested, the individual cells will re-enter the cell cycle once the space become available (for example, due to death of the inhibited cells), and may lead to tumor recurrence. Our simulations showed also that the effects of each inhibitor separately and in combination cannot be distinguished by inspecting the usually collected experimental data, such as the population-doubling curves or the patterns of growing cells from the colony assay. However, the spatial distribution of different cell cycle phases, such as those showed in the figure above, provide quantification of the effects of each kind of inhibition.

Figure legend
Distribution of cell-cycle phases within the tight clusters of tumor cells exposed to CDK1 or CDK2 inhibitors. Clinical solid tumors are composed of clusters of cells that either actively progress through their cell cycle or are arrested at a specific cell-cycle checkpoint (G1, G2 or G2/M). If the cell clusters are tight, the distribution of cell-cycle phases may be affected by cell-cell contact inhibition mechanisms, and thus efficacy of drugs that inhibit progression through the cell-cycle checkpoints may be diminished. Two tight tumor cell cluster exposed to CDK1 inhibitor (left) and CDK2 inhibitor (right) are shown; cell-cycle phases are represented by colors: G1-red; S-green; G2-blue; M-black.


he formation of tight tumor clusters affects the efficacy of cell cycle inhibitors







Journal Reference

Kim M1, Reed D2, Rejniak KA3.

J Theor Biol. 2014 Jul 7;352:31-50.

1Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA. Electronic address: [email protected] and

2Sarcoma Program, Chemical Biology and Molecular Medicine, Adolescent and Young Adult Oncology Program, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA. and

3Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA; Department of Oncologic Sciences, College of Medicine, University of South Florida, Tampa, FL, USA. Electronic address: [email protected]



 Cyclin-dependent kinases (CDKs) are vital in regulating cell cycle progression, and, thus, in highly proliferating tumor cells CDK inhibitors are gaining interest as potential anticancer agents. Clonogenic assay experiments are frequently used to determine drug efficacy against the survival and proliferation of cancer cells. While the anticancer mechanisms of drugs are usually described at the intracellular single-cell level, the experimental measurements are sampled from the entire cancer cell population. This approach may lead to discrepancies between the experimental observations and theoretical explanations of anticipated drug mechanisms. To determine how individual cell responses to drugs that inhibit CDKs affect the growth of cancer cell populations, we developed a spatially explicit hybrid agent-based model. In this model, each cell is equipped with internal cell cycleregulation mechanisms, but it is also able to interact physically with its neighbors. We model cell cycle progression, focusing on the G1 and G2/Mcell cycle checkpoints, as well as on related essential components, such as CDK1, CDK2, cell size, and DNA damage. We present detailed studies of how the emergent properties (e.g., cluster formation) of an entire cell population depend on altered physical and physiological parameters. We analyze the effects of CDK1 and CKD2 inhibitors on population growth, time-dependent changes in cell cycle distributions, and the dynamic evolution of spatial cell patterns. We show that cell cycle inhibitors that cause cell arrest at different cell cycle phases are not necessarily synergistically super-additive. Finally, we demonstrate that the physical aspects of cell population growth, such as the formation of tight cell clusters versus dispersed colonies, alter the efficacy of cell cycle inhibitors, both in 2D and 3D simulations. This finding may have implications for interpreting the treatment efficacy results of in vitro experiments, in which treatment is applied before the cells can grow to produce clusters, especially because in vivo tumors, in contrast, form large masses before they are detected and treated.

Copyright © 2014 The Authors. Published by Elsevier Ltd.. All rights reserved.

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