Uch as human keratinocytes [26, 86], embryo fibroblasts [27], human retinal pigment epithelial cells [87] and fish epidermal cells [40]. A single cell embedded within a uniform EF will be ionized and charged. Therefore the electrical force experienced by this individual cell can be obtained by FEF ?E O ?S EF ?0?where E is uniform dcEF strength and O(E) stands for the surface charge density of the cell. eEF is a unit vector in the direction of the dcEF toward the cathode or anode, depending on the cell type. The time course of the translocation response during exposing a cell to a dcEF demonstrates that the cell velocity versus translocation varies depending on the dcEF strength. Experiments of Nishimura et al. [26] on human keratinocytes indicate that the net migration velocity raises by increase the dcEF strength to about 100 mV/mm while further increase the dcEF strength does not affect the cell net migration velocity. Since the Ca2+ influx into intracellularPLOS ONE | DOI:10.1371/journal.pone.Vercirnon custom synthesis 0122094 March 30,7 /3D Num. Model of Cell Morphology during Mig. in Multi-Signaling Sub.may play a role in this process [25, 26, 28, 88?0], it is thought that the imposed dcEF regulates the concentration of intracellular Ca2+. Therefore, it can be deduced that the cell surface charge is directly proportional to the imposed dcEF strength [25, 26]. Consequently, we assume a linear relationship between the cell surface charge and the applied dcEF strength as 8 > Osatur E < E Esatur ?1?O ??Esatur > : Osatur E > Esatur where Osatur is the saturation value of the surface charge and Esatur is the maximum dcEF strength that causes Ca2+ influx into intracellular.Deformation and reorientation of the cellSolid line in Fig 2 shows a spherical cell configuration which is initially considered. It is assumed that the cell first exerts mechano-sensing forces on the membrane to probe its surrounding micro-environment which is named mechano-sensing process. Thus, the cell internal strain at each finite element node of the cell membrane along ei can be calculated by cell ?ei : i : ei T ?2?Fig 2. Calculation of the cell reorientation. a- A initially spherical cell (solid line) is deformed (dashed line) during mechano-sensing process. emech is mechanotaxis reorientation of the cell. b- A cell is reoriented due to exposing to chemotaxis, thermotaxis and electrotaxis where ech, eth and eEF denote the unit vector in the direction of each cue, respectively. The coefficients mech, ch, and th are effective factors of mechanotactic, ZM241385 site chemotactic and thermotactic trac cues, respectively. Fnet is the magnitude of the net traction force, Fprot is the random protrusion force, FEF represents the electrical force that is exerted by dcEF and Fdrag stands for drag force. epol represents the net polarisation direction of a cell in a multi-signaling environment. doi:10.1371/journal.pone.0122094.gPLOS ONE | DOI:10.1371/journal.pone.0122094 March 30,8 /3D Num. Model of Cell Morphology during Mig. in Multi-Signaling Sub.where i is the strain tensor of ith node located on cell membrane due to mechanosensing process. A cell exerts contraction forces towards its centroid compressing itself so that the cell internal deformation, cell, created by these forces on each finite element node of the cell membrane is negative. Hence, according to Equations 1 and 2 nodes with a less internal deformation experience a higher internal stress and traction force. Therefore, the net traction forces, Ftra.Uch as human keratinocytes [26, 86], embryo fibroblasts [27], human retinal pigment epithelial cells [87] and fish epidermal cells [40]. A single cell embedded within a uniform EF will be ionized and charged. Therefore the electrical force experienced by this individual cell can be obtained by FEF ?E O ?S EF ?0?where E is uniform dcEF strength and O(E) stands for the surface charge density of the cell. eEF is a unit vector in the direction of the dcEF toward the cathode or anode, depending on the cell type. The time course of the translocation response during exposing a cell to a dcEF demonstrates that the cell velocity versus translocation varies depending on the dcEF strength. Experiments of Nishimura et al. [26] on human keratinocytes indicate that the net migration velocity raises by increase the dcEF strength to about 100 mV/mm while further increase the dcEF strength does not affect the cell net migration velocity. Since the Ca2+ influx into intracellularPLOS ONE | DOI:10.1371/journal.pone.0122094 March 30,7 /3D Num. Model of Cell Morphology during Mig. in Multi-Signaling Sub.may play a role in this process [25, 26, 28, 88?0], it is thought that the imposed dcEF regulates the concentration of intracellular Ca2+. Therefore, it can be deduced that the cell surface charge is directly proportional to the imposed dcEF strength [25, 26]. Consequently, we assume a linear relationship between the cell surface charge and the applied dcEF strength as 8 > Osatur E < E Esatur ?1?O ??Esatur > : Osatur E > Esatur where Osatur is the saturation value of the surface charge and Esatur is the maximum dcEF strength that causes Ca2+ influx into intracellular.Deformation and reorientation of the cellSolid line in Fig 2 shows a spherical cell configuration which is initially considered. It is assumed that the cell first exerts mechano-sensing forces on the membrane to probe its surrounding micro-environment which is named mechano-sensing process. Thus, the cell internal strain at each finite element node of the cell membrane along ei can be calculated by cell ?ei : i : ei T ?2?Fig 2. Calculation of the cell reorientation. a- A initially spherical cell (solid line) is deformed (dashed line) during mechano-sensing process. emech is mechanotaxis reorientation of the cell. b- A cell is reoriented due to exposing to chemotaxis, thermotaxis and electrotaxis where ech, eth and eEF denote the unit vector in the direction of each cue, respectively. The coefficients mech, ch, and th are effective factors of mechanotactic, chemotactic and thermotactic trac cues, respectively. Fnet is the magnitude of the net traction force, Fprot is the random protrusion force, FEF represents the electrical force that is exerted by dcEF and Fdrag stands for drag force. epol represents the net polarisation direction of a cell in a multi-signaling environment. doi:10.1371/journal.pone.0122094.gPLOS ONE | DOI:10.1371/journal.pone.0122094 March 30,8 /3D Num. Model of Cell Morphology during Mig. in Multi-Signaling Sub.where i is the strain tensor of ith node located on cell membrane due to mechanosensing process. A cell exerts contraction forces towards its centroid compressing itself so that the cell internal deformation, cell, created by these forces on each finite element node of the cell membrane is negative. Hence, according to Equations 1 and 2 nodes with a less internal deformation experience a higher internal stress and traction force. Therefore, the net traction forces, Ftra.