An Estimation Method of a Constitutive-law for the Rod Model of DNA using Discrete-Structure Simulations

The continuum-rod model has emerged as an efficient tool to describe the long-length-scale structural-deformations of DNA which are critical to understanding the nature of many biological processes such as gene expression. However, a significant challenge in continuum-mechanics-based modeling of DNA is to estimate its constitutive law, which follows from its interatomic bond-stiffness. Experiments and all-atom molecular dynamics (MD) simulations have suggested that the constitutive law is nonlinear and non-homogeneous (sequence-dependent) along the length of DNA. In this paper, we present an estimation method and a validation study using discrete-structure simulations. We consider a simple cantilever-rod with an artificially constructed, discrete lattice-structure which gives rise to a constitutive law. Large deformations are then simulated. An effective constitutive-law is estimated from these deformations using inverse methods. Finally, we test the estimated law by employing it in the continuum rod-model and comparing the simulation results with those of discrete-structure simulations under a different cantilever loading-conditions.