A viscoelastic-stochastic model of cell adhesion considering matrix morphology and medium viscoelasticity

Quantitative investigation of the adhesive behavior between cells and the extracellular matrix (ECM) through molecular bonds is essential for cell culture and bio-medical engineering in vitro. Cell adhesion is a complex multi-scale behavior that includes temporal and spatial scales. However, the influence of the cell and matrix creep effect and the complex spatial morphology characteristics of the matrix on the cell adhesion mechanism is unclear. In the present study, an idealized theoretical model has been considered, where the adhesion of cells and the matrix is simplified into a planar strain problem of homogeneous viscoelastic half-spaces. Furthermore, a new viscoelastic-stochastic model that considers the morphological characteristics of the matrix, the viscoelasticity of the cell and the viscoelasticity of the substrate was developed under the action of a constant external force. The model characterizes the matrix topographical features by fractal dimension (FD), interprets the effects of FD and medium viscoelasticity on the molecular bond force and the receptor-ligand bond re-association rate and reveals a new mechanism for the stable adhesion of molecular bond clusters by Monte Carlo simulation. Based on this model, it was identified that the temporal and spatial distribution of molecular bond force was affected by the matrix FD and the lifetime and stability of the molecular bond cluster could be significantly improved by tuning the FD. At the same time, the viscoelastic creep effect of the cell and matrix increased the re-association rate of open bonds and could expand the window of stable adhesion more flexibly.