Multi-stranded helices are widespread in nature. The interplay of polymeric properties with biological function is seldom discussed. This study probes analogies between structural and mechanical properties of collagen and DNA. We modeled collagen with Eulerian rotational and translational parameters of adjacent rungs in the triple-helix ladder and developed statistical potentials by extracting the dispersion of the parameters from a database of atomic-resolution structures. The resulting elastic model provides a common quantitative way to describe collagen deformations upon interacting with integrins or matrix metalloproteinase and DNA deformations upon protein binding. On a larger scale, deformations in Type I collagen vary with a periodicity consistent with the D-periodic banding of higher-order fibers assemblies. This indicates that morphologies of natural higher-order collagen packing might be rooted in the characteristic deformation patterns.