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Biological cells in soft materials can be modeled as anisotropic force contraction dipoles. The corresponding elastic interaction potentials are long ranged (approximately 1/r3 with distance r) and depend sensitively on elastic constants, geometry, and cellular orientations. On elastic substrates, the elastic interaction is similar to that of electric quadrupoles in two dimensions and for dense systems leads to aggregation with herringbone order on a cellular scale. Free and clamped surfaces of samples of finite size introduce attractive and repulsive corrections, respectively, which vary on the macroscopic scale. Our theory predicts cell reorientation on stretched elastic substrates.
Schwarz et al. (Fri,) studied this question.