A Mathematical Model of Cell Confluency In Vitro

Cellular and molecular biologists often perform cellular assays to obtain a better understanding of how cells work. However, in order to obtain a measurable response by the end of an experiment, the cells must reach an ideal cell confluency. Prior to conducting the cellular assays, range-finding experiments need to be conducted to determine an initial plating density that will result in this ideal confluency, which can be costly. To help alleviate this common issue, a mathematical model was developed that describes the dynamics of the cell population used in these experiments. To develop the model, images of cells from different three-day experiments were analyzed in Photoshop®, giving a measure of cell count and confluency (the percentage of surface area covered by cells). The cell count data were then fitted into an exponential growth model and were correlated to the cell confluency to obtain a relationship between the two. The resulting mathematical model was then evaluated with data from an independent experiment. Overall, the exponential growth model provided a reasonable and robust prediction of the cell confluency, though improvements to the model can be made with a larger dataset. The approach used to develop this model can be adapted to generate similar models of different cell-lines, which will reduce the number of preliminary range-finding experiments. Reducing the number of these preliminary experiments can save valuable time and experimental resources needed to conduct studies using cellular assays.