Plasma membrane of most cells is not smooth. The surfaces of both small and large micropermeable cells are folded and corrugated which makes mammalian cells to have a larger membrane surface than the supposed ideal mode, that is, the smooth sphere of the same volume. Since cancer is an anthropic disease, cancer cells tend to have a larger membrane area than normal cells. Therefore, cancer cells have higher folding factor and larger radius than normal and healthy cells. On the other hand, the prevalence of breast cancer has prompted researchers to improve the treatment options raised for the disease in the past. In this paper, the impact of folding factor of the cell surface has been investigated. Considering that AFM is one of the most effective tools in performing the tests at micro- and nanoscales, it was used to determine the topography of MCF10 cells and then the resulting images and results were used to experimentally extract the folding factor of cells. By applying this factor in the Hertz, DMT and JKR contact models in the elastic and viscoelastic states, these models have been modified and the simulation of the three models shows that the simulation results are closer to the experimental results by considering the folding in the calculations. Additionally, the simulation of 3D manipulation has been done in both elastic and viscoelastic states with and without consideration of folding. Finally, the results were compared to investigate the effects of folding of the cell surface to the critical force and critical time of sliding and rolling in contact with the substrate and AFM tip in the 3D manipulation model.

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