  Long length-scale structural deformations of DNA play a central role in many
biological processes including gene expression. The elastic rod model, which
uses a continuum approximation, has emerged as a viable tool to model
deformations of DNA molecules. The elastic rod model predictions are however
very sensitive to the constitutive law (material properties) of the molecule,
which in turn, vary along the molecules length according to its base-pair
sequence. Identification of the nonlinear sequence-dependent constitutive law
from experimental data and feasible molecular dynamics simulations remains a
significant challenge. In this paper, we develop techniques to use elastic rod
model equations in combination with limited experimental measurements or
high-fidelity molecular dynamics simulation data to estimate the nonlinear
constitutive law governing DNA molecules. We first cast the elastic rod model
equations in state-space form and express the effect of the unknown
constitutive law as an unknown input to the system. We then develop a two-step
technique to estimate the unknown constitutive law. We discuss various
generalizations and investigate the robustness of this technique through
simulations.
