Modeling structural deformations of DNA molecules using identification techniques

Dynamics of long-length-scale structural deformations of DNA molecules play a central role in many biological processes including gene expression. The elastic rod model, which uses a continuum approximation, has emerged as an efficient tool to model the deformations of DNA molecules. Although the general form of the elastic rod model can be derived from first principles, it is impractical to derive the constitutive law representing the material properties from first principles. However, the accuracy of elastic rod predictions depend strongly on the constitutive law, which follows from the atomistic structure of the DNA molecule and is known to be nonlinear and vary along the length according to the base-pair sequence of the DNA. 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 dynamic experimental measurements or high-fidelity molecular dynamics simulation data to estimate the nonlinear sequence-dependent 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 illustrate these ideas through a simple example.