Mathematical Modeling of Melanoma Cell Migration with an Elastic Continuum Model for the Evaluation of the Influence of Tumor Necrosis Factor-Alpha on Migration

Abstract

An elastic continuum mathematical model was implemented to study collective C8161 melanoma cell migration during a “scratch wound” assay, in control and under the influence of the proinflammatory cytokine tumour necrosis factor-alpha (TNF-α). The model has four constants: force that results from lamellipod formation (F), adhesion constant between cells and extracellular matrix (ECM) (b), cell layer elasticity modulus (k), and growth rate (ρ). A nonlinear regression routine was used to obtain the parameters of the model with data from an experiment made with C8161 melanoma cells, with and without TNF-α. Coefficient of determination for both situations was R2=0.89 and R2=0.92, respectively. The parameters values obtained were similar to the ones found in the literature. However, the adhesion constant value decreased with the introduction of TNF-α, which is not in accordance with expected since the presence of TNF-α is associated with an increased expression of integrins that would promote an enhanced adhesion among cells. The model was used in a study relating to the adhesion constant and cell migration, and the results suggested that cell migration decreases with higher adhesion, which is also not in accordance with expected. These differences would not occur if it was considered that TNF-α increases the elasticity modulus of the cell layer.