Continuum mechanical model of a cell traction force assay

The reorganization of fibrillar protein networks in the extracellular matrix (ECM) of soft tissue or in reconstituted collagen gels by connective tissue cells is dramatic manifestation of cell traction forces, cytoplasmic forces transmitted by cell protrusions to the matrix fibers. Traction forces are fundamental to cell spreading and motility and are operative in the structuring and remodeling of tissue during development and wound repair. Current assays used to characterize these forces often measure compaction of a disk of cell-populated collagen gel simply in terms of rate or extent. This type of analysis is dependent on assay properties not reflective of the intrinsic force generating ability of the cells such as the initial cell concentration, the initial collagen concentration, and the geometry of the gel. Thus, there is a clear need to identify an objective index of traction force which reflects the intrinsic cell-fiber mechanical interaction. Here we propose such an index for this force using a continuum approach in which the interactive processes of cell migration and matrix deformation are modeled by expressions for cell and matrix conservation coupled to the mechanical force balance for the cell-gel composite. The equations are formulated and solved for an adaptation of the fibroblast-populated collagen lattice (FPCL) assay in which cells are initially dispersed in a microsphere of collagen gel. The solution of the nonlinear system of partial differential equations (parameterized on the traction parameter of the theory) is then compared to compaction data for the microsphere assay.