Protein dynamics: An approach based on the Cauchy–Born rule

• We suggest a tensor description of protein dynamics.
• We determine the driving force from a discrete system.
• The model represents well constrained dynamics such as protein translocation.

We propose a continuum model for the description of the dynamics of isolated macromolecules. A second-rank tensor describes the macromolecular shape. We identify the action occurring along the molecular dynamics by imposing power equivalence between the discrete and continuum schemes, on the basis of a pertinet expression of the Cauchy–Born rule. We compare molecular dynamics stretching simulations with the continuum model starting from discrete toy schemes, going on with increasing complexity, and ending with the analysis of the Ubiquitin protein. We show that the proposed model is appropriate for the analysis of constrained dynamics of interest in laboratory experiments, such as protein mechanical unfolding driven by atomic-force microscopy.