Stress, strain, and mechanotransduction in cells

It is widely accepted that numerous cell types respond to mechanical stimuli, yet there is no general agreement as to whether particular cells respond directly to stress, strain, strain-rate, strain-energy, or other mechanical quantities. By recalling the definitions of the mathematical (not physical) concepts of stress and strain, it is suggested herein that cells cannot respond directly to these continuum metrics or to quantities derived from them--mechanistic models will need to be based on more fundamental quantities, as, for example, inter-atomic forces or conformational changes of the appropriate molecules. Nonetheless, the concepts of stress and strain should continue to play an important role in mechanobiology, both in the identification of empirical correlations and in the development of phenomenological constitutive models, each of which can contribute to our basic understanding as well as help in the design of future experiments and some clinical interventions. It is important to remember, therefore, that empirical correlations and most constitutive relations in continuum mechanics do not seek to model the actual physics--rather, their utility is in their predictive capability, which is often achieved via different relations in terms of different metrics for the same material under different conditions. Hence, with regard to quantifying cellular responses to mechanical stimuli, we must delineate between the identification of fundamental mechanisms and the formulation of phenomenological correlations, the latter of which only requires convenient metrics that need not be unique or physical.