Active Elasticity and Interactions of Cells in Gels

S. A. Safran

Dept. Materials and Interfaces, Weizmann Institute of Science

Mechanical forces acting externally on entire tissues, or generated internally by the contractile activity of individual cells within a tissue, play an important regulatory role in many physiological processes, including: bone and muscle growth and wound healing. Understanding the response of single cells in artificial substrates to mechanical loadings, and their behavior as a collective, is important not only for basic biological science but also for the rational design of artificial tissues. Individual cells possess specific mechanisms that enable them to sense and respond to changes in their mechanical environment. By pulling on their environment cells sense rigidity gradients, boundaries and strain. Many cell types respond to these signals by actively adjusting cell polarity. On a macroscopic level, the forces generated by a collection of cells in a tissue significantly alter the overall elastic response of the system. We predict the response of cells in a three dimensional elastic medium to externally applied strain fields. The cells are modeled as polarizable elastic force dipoles that can change their orientation in response to the local elastic stress. We model the ensemble of cells by an extension of the treatment of dielectric response of polar molecules. We introduce the elastic analogy of the frequency-dependant dielectric function of the medium that allows us to predict the average cell polarization and orientational order, the effective material constants, and the dynamical response to time-varying cyclic loadings.