Biological cells sense and respond to physical forces, which can shape and guide their behavior. Cells can also actively generate forces, to probe and deform materials in their surrounding environment. These dynamic interactions between clusters of cells and their environment are critical to an immense range of activities including early development and cancer progression. In recent years there has been a growing interest to uncover what drives cells to escape from growing clusters, either independently or in collective streams. However, a thorough understanding of the biophysics governing such activity is lacking. To address these issues, a novel computational and experimental framework will be developed to investigate how the interplay between cellular forces, adhesion, and environmental physics drive cells to proliferate, escape, and invade distant regions of the body. The new tools proposed will impact many areas in biology, including normal and abnormal tissue development, wound healing, and tissue regeneration. The innovative mathematical models and methods will advance computing in biology as well as other fields of science such as bioengineering and biotechnology.

Current mathematical models cannot predict why cells invade from a proliferative cluster and migrate either independently or as collective strands, which determines the metastatic risk of invading cells during cancer progression. This problem will be addressed through a novel multi-scale framework that integrates computational models of highly non- linear matrix mechanics, force-mediated cell signaling, and active cell contractility. Such an approach will provide a new understanding of the mechanisms by which matrix properties promote or discourage cell invasion, and why cells tend to either move collectively or act alone. In particular, the critical role of cell-mediated matrix remodeling, long range force transmission, and epithelial-to-mesenchymal transitions (EMT) will be uncovered. The kinetics of cell invasion requires the formation of protrusions, assembly and dissolution of adhesions, and remodeling of contractile actomyosin fibers. These stochastic processes will be modelled using Kinetic Monte Carlo methods, that will explicitly account for fluctuations in the cell’s response to its environment. Additionally, a novel multi-scale bio-chemo-mechanical model of tissue growth will be developed to predict formation of arbitrarily shaped cell clusters and to quantify how complex patterns of cells emerge from such clusters. This research will lead to a paradigm shift in the mathematical modelling of cell invasion by explicitly including signalling, non-linear matrix mechanics and the two-way recursive dialog between cells and the matrix.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
Application #
Program Officer
Zhilan Feng
Project Start
Project End
Budget Start
Budget End
Support Year
Fiscal Year
Total Cost
Indirect Cost
University of California Irvine
United States
Zip Code