In what ways do the forces generated locally by cells affect other cells in their environment?  

Mechanical forces exerted by cells not only feedback on the morphology and internal structure of each cell individually, but may also impact other cells in the surroundings. These, generally long-ranged elastic interactions are thought to play an important role in the orientation and self-assembly of cells to form organized tissue structures. We develop tools based on generic considerations of force balance to predict how cells actively self-assemble and orient to form organized tissue structures by virtue of the forces they exert on the matrix and their response to these forces. Our models take into account the active forces exerted by the cells, the elastic resisting forces of the environment, as well as the feedback mechanisms that modulate cell activity. This results in a complicated self-consistency problem to solve for the force generation and self-assembly of cells in the medium. Interestingly, because elastic interactions are long-ranged, some aspects of cell-cell elastic interactions may be understood by analogy to other systems with long-ranged interactions such as electrical dipoles in a dielectric. The slide below shows how a theory for the active susceptibility of cells to externally applied forces was developed by analogy to the theory of polar dielectrics developed by Lars Onsager in the 30's.  To read more on this interesting analogy see the references below. 

In addition, we develop computer simulations and approximate analytical theory to study the self-assembly properties of ensembles of elastically interacting cells. One interesting prediction of our analysis is the regulation of cellular self-assembly behavior by the rigidity of the surrounding extracellular matrix. We predict how the surroundings' rigidity may alter the propensity of cells to aggregate, disperse or form interesting phases depending on their density and inherent stochastic nature. 

1. Zemel, A, IB Bischofs, and SA SAFRAN. 2006. “Active Elasticity Of Gels With Contractile Cells.” Physical Review Letters 97. APS: 128103.
2. Zemel, A, and SA SAFRAN. 2007. “Active Self-Polarization Of Contractile Cells In Asymmetrically Shaped Domains.” Physical Review E 76. APS: 021905.