Both cases the ultimate cell elongation and CMI are greater that all previous studied cases.Cell shape change in Multi-signalling substrateFinally, to simultaneously evaluate the effect of different stimuli on cell shape change during cell migration, we have designed 30 different cases through which different thermotaxis and chemotaxis effective factors as well as different EF strengths are applied. The maximum cell elongation, elong, and CMI versus the combination of stimuli, which occur in the intermediate area of the substrate, are summarized in Figs 15 and 16, respectively. Our findings indicate that the increase of each stimulus effect increases both the cell elongation and CMI. Obviously, Figs 15 and 16 illustrate that the rate of changes in the cell elongation and CMI is greater in the di�m rection of the electrotactic axis (E.O) than that of other cues (mchmechth ), indicating dominant role m of electrotaxis. Moreover, increasing the EF strength more than the saturation value does not remarkably affect the cell elongation and CMI. It should be mentioned that, generally, the greater the cell elongation and CMI the less cell random movement. The dominant role of the WP1066 site electrotaxis on cell directional movement is already discussed in the previous work in which a constant spherical cell shape was considered [67].ConclusionsIn this study, our objective is to qualitatively characterize cell shape changes correlated with cell migration in the ABT-737 chemical information presence of multiple signals. Therefore, previously developed models of cell migration with constant spherical cell shape [67, 69] and mechanotactic effect on cell morphology [68] are here extended. The present 3D model is developed base on force equilibrium on cell body using finite element discrete methodology. This model allows predicting the cell behavior when it is surrounded by different micro-environmental cues. The results obtainedPLOS ONE | DOI:10.1371/journal.pone.0122094 March 30,23 /3D Num. Model of Cell Morphology during Mig. in Multi-Signaling Sub.Fig 14. Cell elongation, elong (left axis), and CMI (right axis) versus the cell centroid translocation in the presence of electotaxis as well as mechanotaxis. a- E = 10 mV/mm and b- E = 100 mV/mm. The cell elongation and CMI reaches a maximum amount sooner than previous cases and are aproximately constant until the cell reaches the cathode pole. The cell elongation and CMI decrease when the cell reaches the surface on which the cathode pole is located but they never diminish less than those of other stimuli. However, in the case of higher EF strength the cell elongation and CMI again increase. The cell elongation and CMI are maximum in this case compared to the other previous cases. doi:10.1371/journal.pone.0122094.ghere are qualitatively consistent with those of corresponding experimental works reported in the literature [13, 19, 20, 26, 96, 106]. In absence of external stimuli, the cell elongates along the stiffness gradient and migrates towards the surface of maximum stiffness. Although the cell may randomly extend different pseudopods, it retracts those pseudopods in subsequent steps and maintains its body in determinated distance from the surface of maximum elastic modulus, due to its unconstrained state. This is observed in the previous works of cell migration with a constant spherical shape as wellPLOS ONE | DOI:10.1371/journal.pone.0122094 March 30,24 /3D Num. Model of Cell Morphology during Mig. in Multi-Signaling Sub.Fig 15. Variat.Both cases the ultimate cell elongation and CMI are greater that all previous studied cases.Cell shape change in Multi-signalling substrateFinally, to simultaneously evaluate the effect of different stimuli on cell shape change during cell migration, we have designed 30 different cases through which different thermotaxis and chemotaxis effective factors as well as different EF strengths are applied. The maximum cell elongation, elong, and CMI versus the combination of stimuli, which occur in the intermediate area of the substrate, are summarized in Figs 15 and 16, respectively. Our findings indicate that the increase of each stimulus effect increases both the cell elongation and CMI. Obviously, Figs 15 and 16 illustrate that the rate of changes in the cell elongation and CMI is greater in the di�m rection of the electrotactic axis (E.O) than that of other cues (mchmechth ), indicating dominant role m of electrotaxis. Moreover, increasing the EF strength more than the saturation value does not remarkably affect the cell elongation and CMI. It should be mentioned that, generally, the greater the cell elongation and CMI the less cell random movement. The dominant role of the electrotaxis on cell directional movement is already discussed in the previous work in which a constant spherical cell shape was considered [67].ConclusionsIn this study, our objective is to qualitatively characterize cell shape changes correlated with cell migration in the presence of multiple signals. Therefore, previously developed models of cell migration with constant spherical cell shape [67, 69] and mechanotactic effect on cell morphology [68] are here extended. The present 3D model is developed base on force equilibrium on cell body using finite element discrete methodology. This model allows predicting the cell behavior when it is surrounded by different micro-environmental cues. The results obtainedPLOS ONE | DOI:10.1371/journal.pone.0122094 March 30,23 /3D Num. Model of Cell Morphology during Mig. in Multi-Signaling Sub.Fig 14. Cell elongation, elong (left axis), and CMI (right axis) versus the cell centroid translocation in the presence of electotaxis as well as mechanotaxis. a- E = 10 mV/mm and b- E = 100 mV/mm. The cell elongation and CMI reaches a maximum amount sooner than previous cases and are aproximately constant until the cell reaches the cathode pole. The cell elongation and CMI decrease when the cell reaches the surface on which the cathode pole is located but they never diminish less than those of other stimuli. However, in the case of higher EF strength the cell elongation and CMI again increase. The cell elongation and CMI are maximum in this case compared to the other previous cases. doi:10.1371/journal.pone.0122094.ghere are qualitatively consistent with those of corresponding experimental works reported in the literature [13, 19, 20, 26, 96, 106]. In absence of external stimuli, the cell elongates along the stiffness gradient and migrates towards the surface of maximum stiffness. Although the cell may randomly extend different pseudopods, it retracts those pseudopods in subsequent steps and maintains its body in determinated distance from the surface of maximum elastic modulus, due to its unconstrained state. This is observed in the previous works of cell migration with a constant spherical shape as wellPLOS ONE | DOI:10.1371/journal.pone.0122094 March 30,24 /3D Num. Model of Cell Morphology during Mig. in Multi-Signaling Sub.Fig 15. Variat.