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Titanium surface treated with titanium oxide nanotubes was used in manystudies to quantify the effect of surface topography on cell fate. However, thepredicted optimal diameter of nanotubes considerably differs among studies. Wepropose a model that explain cell adhesion to nanostructured surface byconsidering deformation energy of cell protrusions into titanium nanotubes andadhesion to surface. The optimal surface topology is defined as a geometry thatgives membrane a minimum energy shape. A dimensionless parameter, the cellinteraction index, was proposed to describe interplay between the cell membranebending, intrinsic curvature and strength of cell adhesion. Model simulationshow that optimal nanotube diameter ranging from 20 nm to 100 nm (cellinteraction index between 0.2 and 1, respectively) is feasible within certainrange of parameters describing adhesion and bending energy. The resultsindicates a possibility to tune the topology of nanostructural surface in orderto enhance proliferation and differentation of cells mechanically compatiblewith given surface geometry while suppress the growth of other mechanicallyincompatible cells.

Optimal surface topography for cell adhesion is driven by cell membrane mechanics