Process; (ii) the study of the cell configurations is limited to elliptical modes. In addition, numerical model presented by Han et al. [49] predicts the spatiotemporal dynamics of cell behavior in presence of mechanical and chemical cues on 2D substrates. Considering constant cell shape, they assume that the formation of a new adhesion regulates the reactivation of the assembly of fiber stress within a cell and defines the spatial distribution of traction forces. Their findings indicates that the strain energy is produced by the traction forces which arise due to a cyclic relationship between the formation of a new adhesion in the front and the release of old adhesion at the rear. Altogether, although, available models provide significant insights about cell behavior, they include several main drawbacks: (i) most of the present models incorporate signals received by the cell with mechanics of actin polymerization, myosin contraction and adhesion dynamics but do not deal with the traction forces exerted by the cell during cell movement [57?0]; (ii) some of available models simply simulate cell migration with constant cell configuration [57, 61]; (iii) models considering cell morphology only concentrate on the dynamics of cellular shapes which are not easily applicable for temporal and spatial investigation of cell shape changes coupled with cell movement [52, 62?5]; (iv) models predicting cell morphology are restricted to a few rigid cellular configurations [52, 62]; (v) some of existent models overlook mechanotactic process of cell migration [17, 50, 51] which is inseparable from cell-matrix interaction [12]. Apart from this shortages, most of the models FT011 web dealing with cell migration and cell shape changes are developed in 2D [17, 52, 55, 57?0] that according to the comprehensive experimental investigations of Hakkinen et al. [63], in many concepts cell behavior, ICG-001 biological activity particularly as for cell morphology, on 2D substrates strongly differs from that within 3D substrates.PLOS ONE | DOI:10.1371/journal.pone.0122094 March 30,3 /3D Num. Model of Cell Morphology during Mig. in Multi-Signaling Sub.However in many viewpoints, 2D models improve our notions on cell motility and cellular configuration. Above all shortcomings mentioned before, to our knowledge, there is no comprehensive model to investigate cell shapes changes during cell-matrix interactions within multi-signaling environments (mechano-chemo-thermo-electrotaxis). We have previously developed a 3D numerical model of cell migration within a 3D multisignaling matrix with constant cell configuration [66, 67]. In addition, a novel mechanotactic 3D model of cell morphology is recently presented by the same authors [68]. The objective of the present work is to extend previously presented models [66?8] to investigate cell shape changes during cell migration in a 3D multi-signaling micro-environment. The model takes into account the fundamental feature of cell shape changes associated in cell migration in consequence of cell-matrix interaction. It relies on equilibrium of forces acting on cell body which is able to predict key spatial and temporal features of cell such as cell shape changes accompanied with migration, traction force exerted by the cell and cell velocity in the presence of multiple stimuli. Some of the results match with findings of experimental studies while some others provide new insights for performing more efficient experimental investigations.Model description Transmission of.Process; (ii) the study of the cell configurations is limited to elliptical modes. In addition, numerical model presented by Han et al. [49] predicts the spatiotemporal dynamics of cell behavior in presence of mechanical and chemical cues on 2D substrates. Considering constant cell shape, they assume that the formation of a new adhesion regulates the reactivation of the assembly of fiber stress within a cell and defines the spatial distribution of traction forces. Their findings indicates that the strain energy is produced by the traction forces which arise due to a cyclic relationship between the formation of a new adhesion in the front and the release of old adhesion at the rear. Altogether, although, available models provide significant insights about cell behavior, they include several main drawbacks: (i) most of the present models incorporate signals received by the cell with mechanics of actin polymerization, myosin contraction and adhesion dynamics but do not deal with the traction forces exerted by the cell during cell movement [57?0]; (ii) some of available models simply simulate cell migration with constant cell configuration [57, 61]; (iii) models considering cell morphology only concentrate on the dynamics of cellular shapes which are not easily applicable for temporal and spatial investigation of cell shape changes coupled with cell movement [52, 62?5]; (iv) models predicting cell morphology are restricted to a few rigid cellular configurations [52, 62]; (v) some of existent models overlook mechanotactic process of cell migration [17, 50, 51] which is inseparable from cell-matrix interaction [12]. Apart from this shortages, most of the models dealing with cell migration and cell shape changes are developed in 2D [17, 52, 55, 57?0] that according to the comprehensive experimental investigations of Hakkinen et al. [63], in many concepts cell behavior, particularly as for cell morphology, on 2D substrates strongly differs from that within 3D substrates.PLOS ONE | DOI:10.1371/journal.pone.0122094 March 30,3 /3D Num. Model of Cell Morphology during Mig. in Multi-Signaling Sub.However in many viewpoints, 2D models improve our notions on cell motility and cellular configuration. Above all shortcomings mentioned before, to our knowledge, there is no comprehensive model to investigate cell shapes changes during cell-matrix interactions within multi-signaling environments (mechano-chemo-thermo-electrotaxis). We have previously developed a 3D numerical model of cell migration within a 3D multisignaling matrix with constant cell configuration [66, 67]. In addition, a novel mechanotactic 3D model of cell morphology is recently presented by the same authors [68]. The objective of the present work is to extend previously presented models [66?8] to investigate cell shape changes during cell migration in a 3D multi-signaling micro-environment. The model takes into account the fundamental feature of cell shape changes associated in cell migration in consequence of cell-matrix interaction. It relies on equilibrium of forces acting on cell body which is able to predict key spatial and temporal features of cell such as cell shape changes accompanied with migration, traction force exerted by the cell and cell velocity in the presence of multiple stimuli. Some of the results match with findings of experimental studies while some others provide new insights for performing more efficient experimental investigations.Model description Transmission of.