On strain and stress in living cells.

Recent theoretical simulations of amelogenesis and network formation and new, simple analyses of the basic multicellular unit (BMU) allow estimation of the order of magnitude of the strain energy density in populations of living cells in their natural environment. A similar simple calculation translates recent measurements of the force–displacement relation for contacting cells (cell–cell adhesion energy) into equivalent volume energy densities, which are formed by averaging the changes in contact energy caused by a cell׳s migration over the cell׳s volume. The rates of change of these mechanical energy densities (energy density rates) are then compared to the order of magnitude of the metabolic activity of a cell, expressed as a rate of production of metabolic energy per unit volume. The mechanical energy density rates are 4–5 orders of magnitude smaller than the metabolic energy density rate in amelogenesis or bone remodeling in the BMU, which involve modest cell migration velocities, and 2–3 orders of magnitude smaller for innervation of the gut or angiogenesis, where migration rates are among the highest for all cell types. For representative cell–cell adhesion gradients, the mechanical energy density rate is 6 orders of magnitude smaller than the metabolic energy density rate. The results call into question the validity of using simple constitutive laws to represent living cells. They also imply that cells need not migrate as inanimate objects of gradients in an energy field, but are better regarded as self-powered automata that may elect to be guided by such gradients or move otherwise. [ABSTRACT FROM AUTHOR]