Robust estimation of nonlinear constitutive law from static equilibrium data for modeling the mechanics of DNA

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 several biofilaments including DNA molecules. The elastic rod model predictions are however very sensitive to the model of constitutive law (material properties) of the molecule. Robust estimation of the constitutive law from experimental data and feasible molecular dynamics simulations remains a significant challenge. In this paper, we develop a two-step technique to use elastic rod model equations in combination with limited 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 describe the two-step technique to estimate the unknown constitutive law. Finally, we investigate the robustness of this technique through simulations and discuss various generalizations.