Computational Study of Proteolysis-Driven Single Cell Migration in a Three-Dimensional Matrix

Abstract

Cell migration is a fundamental process that is crucial to a variety of physiological events. While traditional approaches have focused on two-dimensional (2D) systems, recent efforts have shifted to studying migration in three-dimensional (3D) matrices. A major distinction that has emerged is the increased importance of cell-matrix interactions in 3D environments. In particular, cell motility in 3D matrices is more dependent on matrix metalloproteinases (MMPs) to degrade steric obstacles than in 2D systems. In this study, we implement the effects of MMP-mediated proteolysis in a force-based computational model of 3D migration, testing two matrix ligand-MMP relationships that have been observed experimentally: linear and log-linear. The model for both scenarios predicts maximal motility at intermediate matrix ligand and MMP levels, with the linear case providing more physiologically compelling results. Recent experimental results suggesting MMP influence on integrin expression are also integrated into the model. While the biphasic behavior is retained, with MMP-integrin feedback peak cell speed is observed in a low ligand, high MMP regime instead of at intermediate ligand and MMP levels for both ligand-MMP relationships. The simulation provides insight into the expanding role of cell-matrix interactions in cell migration in 3D environments and has implications for cancer research.

Computational Model for Migration of a Cell Cluster in Three-Dimensional Matrices

“…This model builds upon earlier work, 14,25 extending the models developed for a single cell to a new body, a cluster composed of five cells. As stated previously, while there are a number of studies on invasion, there is not much information in the literature corresponding to studies on cell cluster motion in a 3D environment.…”

“…For the case where the Reynolds number is very small (what is known as ''creeping flow'') and the geometry is simple, the body drag can be computed. This was the case in previous models, 14,25 where the drag force had been calculated through the Einstein-Stokes equation since a single cell was being modeled as a sphere. In general for ''creeping flow'', the drag coefficient if proportional to …”

“…The traction force for each cell occurs due to the cytoskeletal contractile forces exerted against the adhesion sites; it is a function of the force per ligand complex and a parameter defined as adhesivity (b). A more thorough description of this force can be found in the work by Zaman et al 14,25 It is important to note that adhesivity is taken to be different in the front and the back of the cell based on the number of receptors present, as shown by Eqs. (2) and (3):…”

Computational Model to Probe Cellular Mechanics during Epithelial-Mesenchymal Transition

“…In recent years, numerous models for single cell migration have emerged and shown success in reproducing cell morphology, directionality, persistence and velocity, as a function of cellular and environmental properties [Zaman et al, 2005;Harjanto and Zaman, 2010]. Contrary to single cell motion, our understanding of collective cell motion is largely qualitative.…”

“…A force-based dynamics approach, similar to previously developed models [Zaman et al, 2005;Harjanto and Zaman, 2010;Vargas and Zaman, 2011], was used to define motion of the cells. Each time step simulates the motion of each cell over 30 s, during which all forces acting on the cell are summed.…”