## 4 Discussion
Similar to this cell behavior on highly positively charged surfaces, studies with respect to surface topography as an external stimulus demonstrated phenotypic changes of actin organization such as clustering of the actin filaments, which in turn resulted in functional changes in the cell [45; 68]. Osteoblasts with a reorganization of the actin cytoskeleton on pillar [40] and groove structures [40; 69] exhibited a decreased cell area after 24 h as well. In addition, the cell edge height is lower on moderately positively charged PPAAm compared with negatively charged borosilicate glass after 1 h. Since we measured the sum of both cleft and cell height at the cell edge, we cannot directly compare with work addressing the cleft only. However, our results are compatible with reported cleft thicknesses of about 60 nm, as measured by metal-induced energy transfer [70] and about 40 nm by interferometric photo-activated localization microscopy [71]. Interestingly, after 3 h, there is no significant difference in cell edge height on PPAAm and glass. However, taking into account regions of peripheral ruffles, we observe a higher average cell edge height on glass. This indicates that either the region of peripheral ruffles is higher on glass i.e., specifically at the edges, the cell is not well attached to the substrate, or that if the edges fold back, they fold back further, leading to longer peripheral ruffles and therefore higher edge heights. In the initial phase of adhesion, physicochemical interactions dominate over the slow cellular responses requiring biosynthesis. The difference in \(\zeta\)-potentials of material surface (\(-60\) mV for glass and +7 mV for PPAAm [34]) and cell surface (for MG-63 osteoblasts \(-16\) mV [15]) amounts to \(\approx\)(\(-60\) mV) \(-\) (\(-16\) mV) \(=\)\(-44\) mV for glass and to \(\approx\)(+7 mV) \(-\) (\(-16\) mV) \(=\) +23 mV for PPAAm substrates. Thus, electric fields or Coulomb forces, if not fully screened by the double layer, would be stronger with respect to the glass substrate. The interaction of medium or ECM protein with the surface might be of relevance. Due to its amine content, protein tends to exhibit slightly positive \(\zeta\)-potentials. Upon adsorption on a surface, the delicate protein folding will be least disturbed or best preserved on surfaces exhibiting low \(\zeta\)-potentials in terms of absolute value [72] e.g., \(-1\) mV or +1 mV (just immobilizing, hardly deforming). Hence, probably just the difference to the \(\zeta\)-potential of the cell membrane is decisive. It is conceivable that cells prefer sites with adsorbed intact protein or with weak field gradients, leaving their ECM protein structure largely intact. Otherwise, MG-63 cells exhibit negative charges on their outer surface due to their hyaluron coat; this is responsible for the cells' attachment on positively charged material surfaces via electrostatic forces [42]. To further study the changes in the shape of single cells placed on charged substrates, we adopted a vertex-based model originally developed to investigate cell shape changes in confluent tissues. The model shows that different cell shapes, characterized by cell area and circularity, as observed in experiments, arise due to changes in cell mechanical properties, such as area elastic modulus governing cell area compressibility, bond tension due to actomyosin contractility, and mechanics of cell-substrate adhesion. Here, we used the knowledge of the well-known rigidity transition studied in vertex models for confluent tissues to understand cell shape changes due to intracellular actin cytoskeleton remodeling on differently charged surfaces. On negatively and moderately positively charged substrates, cell shape change is associated with a drop in the value of cell circularity but no significant change in the cell area.