Sarc chondrosarcoma cell line. Confirming the mathematical model.

<p><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0162553#pone.0162553.e014" target="_blank">Model (10)</a> was simulated with parameters fixed as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0162553#pone.0162553.t001" target="_blank">Table 1</a>, obtained with 2 × 10⁴ cells/well, and varying the initial cell density <i>u</i>₀. In (a) and (b) numerical data of migration curves were compared with experimental Cell Index respectively in the case of 3 × 10⁴ and 4 × 10⁴ initial cell number. MSE value on the Cell Index was estimated in MSE_migr = 0.0077 and MSE_migr = 0.0183, respectively in (a) and (b).</p

Schematic representation of a well of the CIM-plate.

<p>An upper and a lower chamber are separated by a permeable membrane Γ_M. In the migration assay in presence of chemoattractant, cells are placed in the upper chamber, and the chemoattractant is added in the lower chamber (directional migration). When measuring the basal migration experiment the well contains only cells (in the upper chamber) and a serum-free medium. In the mathematical formulation the spatial <i>x</i>−<i>axis</i> is oriented from the top to the bottom.</p

Initial data and parameters of the mathematical model.

<p>Initial data and parameters of the mathematical model.</p

Sensitivity analysis for the parameters of the mathematical model.

<p>Sensitivity analysis for the parameters of the mathematical model.</p

Numerical simulations on Sarc, HT1080, and A375 cell lines.

<p>For each cell line, panels on the left (a),(c),(e) show the basal migration in absence of chemoattractant. Numerical curves (blue) were compared with experimental data (red). Panels on the right (b),(d),(f) show the migration curves. The simulated values of Cell Index (blue) were compared with experiments (green). Here and in the following figures the experimental curves were obtained as the average of at least three experiments in quadruplicate (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0162553#pone.0162553.s002" target="_blank">S2 Fig</a>). About the MSE value on the Cell Index, defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0162553#pone.0162553.e022" target="_blank">Eq (15)</a>, we estimated, respectively, the following values: panels (a)-(b) MSE_basal = 0.0376 and MSE_migr = 0.0052; panels (c)-(d) MSE_basal = 0.0166 and MSE_migr = 0.0068; panels (e)-(f) MSE_basal = 0.0083 and MSE_migr = 0.0054.</p