Cell organization in soft media due to active mechanosensing

I. B. Bischofs and U. S. Schwarz*
Max Planck Institute of Colloids and Interfaces, 14424 Potsdam, Germany
Communicated by Tom C. Lubensky, University of Pennsylvania, Philadelphia, PA, June 10, 2003 (received for review January 21, 2003)

Until recently, biologists have considered an adherent cell’s physiological function to be the main influence on its mechanical activity. Scientists suggest a new theory: adherent cells orient themselves in their environments to maximize effective stiffness. This theory relies on fairly complex mathematical equations whose derivations were far from trivial. Before constructing any formulas, scientists had to find a way to calculate the stress and strain on a cell due to its surroundings. They then tried to measure how much work a cell must do on its surroundings to build up a certain force at its point of contact. They came up with a complicated integral calculating the work, where minimum work corresponded to the cell sensing maximum stiffness. Note that they are not implying that cells actually execute this minimal work; rather, the effectiveness of the measurement lies in allowing them to compare different values of work in different elastic environments. Thus, they can see the varying degrees of effectiveness in extracting information through mechanosensing.
The results showed that cells interacting with homogeneous external strains orient themselves with the direction of stretch. Specifically, experiments with fibroblasts on elastic substrates and collagen gels support this orientation corresponding to minimal work. The scientist’s model also agrees with preexisting results regarding the mechanical activity of cells on boundaries. They also investigated cooperative effects of cells. Their work-minimizing model suggested that two neighboring cells would completely align their dipoles to maximize stiffness. This agrees with experimental results where strings of cells align themselves parallel to the external strain. Thus, this paper proposed various mathematical formulas for calculating the work done by various types of cells. Then, with the equations, found the orientations of the cells that minimized the work. Then, the paper compared these predictions with previously found experimental results. The consistent agreement between the predictions and experimental results provides a strong case supporting the validity of the optimization principle of cells in soft media.
I chose to read and summarize this article because of its substantial mathematical and physical content. I think work is a fascinating physical phenomenon. When I glossed over the articles, all the integrals and equations for work in this paper sparked my interest. I wanted to understand what the formulas represented biologically. Explaining biological phenomena with the tools in math and physics is, in my opinion, a very precise and beautiful way of understanding why cells behave the ways they do. This paper, in particular, is important because it presents a theory to describe previously observed experimental results on cell orientation. Understanding why cells orient themselves in a certain way is so much more exciting, to me, than just learning how they orient themselves. With math and physics, we have found ways to deepen our understandings of observed phenomena.