# Migration of the 3T3 Cell with a Lamellipodium on Various Stiffness Substrates--Tensegrity Model
## 4 Discussion  
It was hypothesized here that the cell's motion is guided by the cell's probing of the substrate's stiffness and the selection of the direction that will lead to the region of the higher substrate stiffness. From the principle of conservation of energy, the cell preferred to be in the lowest possible energetic state. Experiments revealed that the cells usually probe their environment by lamellipodial extensions [55, 56]. This action guides their movement to accord to the substrate stiffness [57]. The results of the current  
Figure 8: Predicted movement of a cell along the substrate with the stiffness distribution as shown in Figure 4.  
Figure 7: Elastic energy of the cell adherent to the substrate as a function of the stiffness. Inset shows a stiffness range between 0.1 and 1000 N/m.  
analysis, utilizing the tensegrity model for the cytoskeleton with a lamellipodia, show that with the substrate stiffness increase, the adherent cell internal elastic strain energy decreases. This is the reason for the cell's movement to the more rigid area of the substrate. It was shown [14; 27] that the mechanical interaction between the substrate and cell adjusts the morphology and migration of the cell. [PERSON] and [PERSON] [39] modeled the influence of the substrate stiffness on a cell's morphology and migration. The model showed that the internal elastic strain energy of the cell was affected by intracellular and extracellular forces and led to changes in the cell's morphology and migration activity. The result being that the increase in the substrate's stiffness leads to the lower internal elastic energy state of cell. The experiments presented here confirm the results of the possible cell's movement utilizing the tensegrity model. The similar experimental results were presented in the study of 3T3 cells while culturing them on flexible polyacrylamide sheets [13]. By controlling the material concentrations, the regions with different stiffness on the same substrate sheet were created. It was shown that the cell's migration rate increased when the cell crossed the boundary between the low and higher stiffness area. Thus, the cells preferred to migrate in the direction of the stiffer region. This experiment supports the results calculated on the basis of the tensegrity model of the cell.  
Mapping the migration of a cell on a substrate with the varying stiffness (Figure 4) can help in predicting the cell's movement along the surface with varying stiffness (Figure 8). The proposed procedure may be useful in the prediction of the directional movement of the cell. Since it has been verified that a cell's movement is the function of internal strain energy, mapping the cell's movement should be possible as long as the substrate's stiffness is known.  
The simulation results support the evidence that the cell migration is guided by the substrate stiffness since it leads to the minimization of the internal elastic energy of a cell. The cell's migration is guided by a multifaceted interplay of physical and chemical signals, including substrate stiffness.