Our group uses clonal growth models to simulate the cellular transformation data resulting from the in vivo and in vitro exposure of organisms to chemical mixtures. Exposure chemicals have include hexachlorobenene and PCB126, and complex mixtures, such as benzo[a]pyrene + marine diesel fuel.
One basic model used in clonal growth modeling is the two-stage carcinogenesis model developed
by Moolgavkar-Venzon-Knudson (MVK). In this model, a susceptible cell is at one of three states:
normal, initiated, and malignant. A normal or initiated cell is subjected to
division into two susceptible cells without mutation (event 1), death/differentiation
(event 2), division into two susceptible cells with one mutated (event 3), or no change.
A malignant is committed to develop into a tumor in a fixed time. A clonal growth model
describes the processes of Normal cell -> Initiated cell and the growth of initiated cells;
the mutation of initiated cells is not considered.
The MVK model, as well as more complex models (three stage and multistage), have been implemented in computer simulation programs in our laboratory.
The figure below is an example of the predictive capability of clonal growth models we have developed for in vivo systems. This example was taken from an exposure study involving a mixture of hexachlorobenzene + PCB.
Experimentally derived data are shown as symbols and model simulations are shown as curves for this time-course medium-term pharmacokinetics/liver foci bioassay. The panels in the figure refer to the following conditions:
For each index, 20 runs of simulations are shown to illustrate the
stochasticity of the clonal growth model. The low dose is hexachlorobenzene
0.03 mmol/kg + PCB 126 0.01 µmol/kg and the high dose is hexachlorobenzene
0.1 mmol/kg + PCB 126 0.03 µmol/kg. The mixture was given through daily oral gavage,
7 days/week. The arrows indicate when the partial hepatectomy (PH) was performed.
The model was coded and run in Advanced Continuous Simulation Language (ACSL).
In the following plot is an example of the predictive capability of clonal growth models we have developed for in vitro systems. This example was taken from an study involving transformed immortalized human epidermal keratinocytes exposed to various complex chemical mixtures.
Shown is the transformation of N (normal) cells to A (initiated) cells, as quantified by cloning efficiency.
Cloning efficiency is the fraction of A cells in the total population.
The graph depicts 123 simulation runs, and anchorage independent growth (AIG)
data of DMSO vehicle control RHEK cells
from three chronic study experiments. Multiple simulation results are due to the
randomization of sub-cultured cells.
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