## 4 Discussion
The choice of model parameter values for which the experimental observations could be reproduced suggest that negatively and moderately positively charged substrates promote cell-material adhesion after a longer time for growth (24 h). In the case of cells seeded on a highly positively charged substrate, the choice of model parameter values suggests that the forces due to cell cortical tension dominate the forces due to cell-substrate adhesion. As a result, cells decrease their cross-sectional area but retain their initial, higher circularity value. The model also shows that the circularity value of cells placed on a moderately positively charged substrate is more dispersed than in the case of cells placed on highly positively charged surface, as also observed in experiments. Taken together, our analysis indirectly suggests that the charge of the substrate exerts an influence on the cell mechanical properties, causing a transition in the mechanical behavior of the cells from a fluid-like to a more solid-like state. The measured changes in cell shape and actin cytoskeleton could be explained by the following ideas: [PERSON] et al. [34] reported that in the presence of highly positive surface charges, the membrane integrity was compromised; i.e., the membranes displayed holes. This could be attributed to the incomplete formation of small membrane vesicles around the high charges, as described before for dendrimer structures by [PERSON] et al. [73]. It might be possible that the high charges increase the cortical membrane tension, as suggested by the model. For micrometer-sized pillar structures, it is known that osteoblasts try to phagocytize them [74]. Since nanoparticles with highly positive surface charges are commonly used for drug delivery due to their strong interaction with the membrane's proteoglycans, it could be speculated that the cells also try to take up the interfering high surface charges of biomaterials, resulting in clustered actin filaments. As for the reduced cell viability on highly positively charged material coatings [34], a great cytotoxicity has been also described for these nanoparticles [75]. A question still open involves exactly how negative and positive charges at the material interface affect the actin filament growth. Here, further in vitro experiments with Cytochalasin D causing the disruption of actin filaments and inhibition of actin polymerization could be helpful. In the study by [PERSON] et al. [67], the application of 1 uM Cytochalasin D to cells on Ti surfaces induced a decrease in cell area after 3 h compared with the untreated control. Controversially, the cells were able to overcome this decrease on PPAAm in most parts. The authors suggested a more membrane-driven cell spreading. However, the substrate-generated electric fields apparently play a role and regulate intracellular signaling pathways, subsequently influencing the actin dynamics. It could be potentially interesting to investigate the Rho signaling pathways, as changes in the balance of the Rho protein family activity are known to be sufficient to achieve rearrangements in the actin cytoskeleton and thus link the cell shape and function [59; 76]. Lamellipodia are induced via Rac, filopodia are induced via Cdc42, and actin stress fibers are induced via Rho [59; 77]. As [PERSON] et al. [78] indicated, the integrin downstream signaling of RhoA/ ROCK plays a major role in the recognition of microtopographies and hence, the adaption of actin filaments to a surface by osteoblasts. The authors revealed an attenuated actin clustering on pillar structures by the inhibition of ROCK (Rho-associated kinase). In this study, surface charges were shown to profoundly affect the organization of the actin cytoskeleton and the resulting cell shape. Highly positive surface charges caused a significant decline in cell area and actin filament number and length, which underlines the importance of an intact actin cytoskeleton for changes in cell shape during the spreading process.