Signaling environment. doi:10.1371/journal.pone.0122094.g136,161 nodes while the cell is represented by 643 elements. The calculation time is about one minute for each time step in which each step corresponds to approximately 10 minutes of real cell-matrix interaction [68]. Initially the cell is assumed to have a spherical shape as shown in Fig 2a. In Table 1, the properties of the matrix and the cell are enumerated. For each simulation it is of interest to quantify the cell shape. Therefore, two parameters are calculated to quantify the cell shape changes during cell migration in 3D multi-signaling matrix: Cell Morphological Index (CMI) CMI ??S ?Sin ?3?where Sin denotes the initial area of cell membrane (spherical cell shape); and the cellPLOS ONE | DOI:10.1371/journal.pone.0122094 March 30,12 /3D Num. Model of Cell Morphology during Mig. in Multi-Signaling Sub.Table 1. 3D matrix and cell properties. Symbol r Kpas Kact max min max kf = kb nf = nb E Description Poisson ratio Viscosity Cell radius ABT-737 mechanism of action Stiffness of microtubules Stiffness of myosin II Maximum strain of the cell Minimum strain of the cell Maximum contractile stress exerted by actin-myosin machinery Binding constant at the rear and at the front of the cell Number of available receptors at the rear and at the front of the cell Concentration of the ligands at the rear and at the front of the cell Order of surface charge density of the cell Range of applied electric field Value 0.3 1000 Pa 20 m 2.8 kPa 2 kPa 0.09 -0.09 0.1 kPa 108 mol-1 105 10-5 mol 10-4 C/m2 0?00 mV/ mm Ref. [97, 98] [75, 97] [99] [100] [100] [69, 83] [69, 83] [101, 102] [75] [75] [75] [24] [25, 30]doi:10.1371/journal.pone.0122094.telongation elong ?1 ?pffiffiffiffiffiffiffiffiffiffiffiffiffi lmin lmed lmax ?4?Here the second term of the equation represents the ratio of the geometric mean over the cell length. elong is a representative value of cell elongation. It is calculated to evaluate a spherical cell shape versus an elongated cell configuration according to the experimental work of Lee et al [96]. According to Equation 24, elong = 0 for a spherical cell configuration, in contrast for a highly elongated cell, elong ‘ 1. This means that the cell length in one direction is much higher than that of other two mutual perpendicular directions. On the other hand, CMI is another parameter to show how the cell surface area changes during cell migration. In our cases study, we assume that the cell initially has a spherical shape (CMI = 1). This value goes to increase while cell migrates. Therefore, although there is no direct relation between elong and CMI, they may follow the same trend during cell migration. So, both parameters are minimum for a spherical cell shape and maximum for an elongated cell shape. These variables are probed versus cell position (the cell centroid translocation) in each step to see how the cell elongation and surface area change during cell migration in presence of different GrazoprevirMedChemExpress Grazoprevir stimuli. In addition, the cellular random alignment in a 3D matrix with a cue gradient (stiffness, thermal and/or chemical gradients) or dcEF can be assessed by the angle between the net polarisation direction of the cell and the imposed gradient direction or EF direction, . Therefore, the Random Index (RI) can be described byN XcosyiRI ?i??5?Nwhere N represents the number of time steps during which the cell elongation does not change considerably (the cell reaches steady state). RI = -1 indicates totally random alig.Signaling environment. doi:10.1371/journal.pone.0122094.g136,161 nodes while the cell is represented by 643 elements. The calculation time is about one minute for each time step in which each step corresponds to approximately 10 minutes of real cell-matrix interaction [68]. Initially the cell is assumed to have a spherical shape as shown in Fig 2a. In Table 1, the properties of the matrix and the cell are enumerated. For each simulation it is of interest to quantify the cell shape. Therefore, two parameters are calculated to quantify the cell shape changes during cell migration in 3D multi-signaling matrix: Cell Morphological Index (CMI) CMI ??S ?Sin ?3?where Sin denotes the initial area of cell membrane (spherical cell shape); and the cellPLOS ONE | DOI:10.1371/journal.pone.0122094 March 30,12 /3D Num. Model of Cell Morphology during Mig. in Multi-Signaling Sub.Table 1. 3D matrix and cell properties. Symbol r Kpas Kact max min max kf = kb nf = nb E Description Poisson ratio Viscosity Cell radius Stiffness of microtubules Stiffness of myosin II Maximum strain of the cell Minimum strain of the cell Maximum contractile stress exerted by actin-myosin machinery Binding constant at the rear and at the front of the cell Number of available receptors at the rear and at the front of the cell Concentration of the ligands at the rear and at the front of the cell Order of surface charge density of the cell Range of applied electric field Value 0.3 1000 Pa 20 m 2.8 kPa 2 kPa 0.09 -0.09 0.1 kPa 108 mol-1 105 10-5 mol 10-4 C/m2 0?00 mV/ mm Ref. [97, 98] [75, 97] [99] [100] [100] [69, 83] [69, 83] [101, 102] [75] [75] [75] [24] [25, 30]doi:10.1371/journal.pone.0122094.telongation elong ?1 ?pffiffiffiffiffiffiffiffiffiffiffiffiffi lmin lmed lmax ?4?Here the second term of the equation represents the ratio of the geometric mean over the cell length. elong is a representative value of cell elongation. It is calculated to evaluate a spherical cell shape versus an elongated cell configuration according to the experimental work of Lee et al [96]. According to Equation 24, elong = 0 for a spherical cell configuration, in contrast for a highly elongated cell, elong ‘ 1. This means that the cell length in one direction is much higher than that of other two mutual perpendicular directions. On the other hand, CMI is another parameter to show how the cell surface area changes during cell migration. In our cases study, we assume that the cell initially has a spherical shape (CMI = 1). This value goes to increase while cell migrates. Therefore, although there is no direct relation between elong and CMI, they may follow the same trend during cell migration. So, both parameters are minimum for a spherical cell shape and maximum for an elongated cell shape. These variables are probed versus cell position (the cell centroid translocation) in each step to see how the cell elongation and surface area change during cell migration in presence of different stimuli. In addition, the cellular random alignment in a 3D matrix with a cue gradient (stiffness, thermal and/or chemical gradients) or dcEF can be assessed by the angle between the net polarisation direction of the cell and the imposed gradient direction or EF direction, . Therefore, the Random Index (RI) can be described byN XcosyiRI ?i??5?Nwhere N represents the number of time steps during which the cell elongation does not change considerably (the cell reaches steady state). RI = -1 indicates totally random alig.
