Significance of Knotted Structures for Function of Proteins and Nucleic Acids
Poster Session I
11 – POS
Board 11
Mapping Consitutive Law of Biological Filaments from MD Simulations
Sachin Goyal
.
University of California, Merced, USA.
Dynamics of bending and twisting deformations of biological filaments such as DNA play a
central role in their biological functions. For example, looping of DNA is an important step in
gene regulatory mechanisms, which is often mediated by protein binding. Continuum models
such as elastic rod have evolved as efficient computational tools to simulate the nonlinear
dynamics of large twisting and bending of biological filaments. However, a major roadblock to
this approach is the inaccurate modeling of the constitutive law, which captures the restoring
effects in the bending and torsional deformations of the filament in question and which depends
on the filament’s atomistic-level structure. Traditional models assume a linear constitutive law
and experimental measurements focus on the estimation of just a handful of stiffness parameters
such as bending and torsional stiffness. Only recently the focus has shifted to examining the
dependence of the stiffness parameters on the base-pair sequence. We are developing a
methodology to map non-linear constitutive laws directly from molecular dynamics (MD)
simulations without any a priori assumptions of its functional form. The methodology employs a
two-step technique using an inverse rod model. Step one estimates the curvature and twist along
with internal restoring moments and forces at every cross-section in the deformed states of the
filament obtained from MD simulations. Step two fits a constitutive law through the estimated
data using function-fitting. We have validated the approach with proof-of-concept results, and
have also analyzed its robustness by adding noise in the data.
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