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Computational Model for Cell Migration in Three-Dimensional Matrices

Muhammad H. Zaman ^* , Roger D. Kamm  , Paul Matsudaira ^*   and Douglas A. Lauffenburger  

^* Whitehead Institute for Biomedical Research, Biological Engineering Division, Department of Mechanical Engineering, and Department of Biology, Massachusetts Institute of Technology, Cambridge, Massachusetts

Correspondence: Address reprint requests to Muhammad H. Zaman, Whitehead Institute, 9 Cambridge Center, Cambridge, MA 02142. E-mail: mhzaman{at}mit.edu.

Although computational models for cell migration on two-dimensional (2D) substrata have described how various molecular and cellular properties and physiochemical processes are integrated to accomplish cell locomotion, the same issues, along with certain new ones, might contribute differently to a model for migration within three-dimensional (3D) matrices. To address this more complicated situation, we have developed a computational model for cell migration in 3D matrices using a force-based dynamics approach. This model determines an overall locomotion velocity vector, comprising speed and direction, for individual cells based on internally generated forces transmitted into external traction forces and considering a timescale during which multiple attachment and detachment events are integrated. Key parameters characterize cell and matrix properties, including cell/matrix adhesion and mechanical and steric properties of the matrix; critical underlying molecular properties are incorporated explicitly or implicitly. Model predictions agree well with experimental results for the limiting case of migration on 2D substrata as well as with recent experiments in 3D natural tissues and synthetic gels. Certain predicted features such as biphasic behavior of speed with density of matrix ligands for 3D migration are qualitatively similar to their 2D counterparts, but new effects generally absent in 2D systems, such as effects due to matrix sterics and mechanics, are now predicted to arise in many 3D situations. As one particular sample manifestation of these effects, the optimal levels of cell receptor expression and matrix ligand density yielding maximal migration are dependent on matrix mechanical compliance.

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