Estimation of Nonlinear Three-dimensional Constitutive Law for DNA Molecules

TL;DR

This paper develops a method to estimate the nonlinear, sequence-dependent constitutive law of DNA molecules by combining elastic rod models with experimental or simulation data, addressing a key challenge in understanding DNA mechanics.

Contribution

The paper introduces a novel two-step technique to identify the nonlinear constitutive law of DNA using state-space modeling and limited data, improving modeling accuracy.

Findings

The method successfully estimates nonlinear constitutive laws from limited data.

The approach demonstrates robustness through simulation studies.

It enables better understanding of DNA deformation mechanics.

Abstract

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.