  Negatively charged DNA can be compacted by positively charged dendrimers and
the degree of compaction is a delicate balance between the strength of the
electrostatic interaction and the elasticity of DNA. We report various elastic
properties of short double stranded DNA (dsDNA) and the effect of dendrimer
binding using fully atomistic molecular dynamics and numerical simulations. In
equilibrium at room temperature, the contour length distribution P(L) and
end-to-end distance distribution P(R) are nearly Gaussian, the former gives an
estimate of the stretch modulus {\gamma}_1 of dsDNA in quantitative agreement
with the literature value. The bend angle distribution P({\theta}) of the dsDNA
also has a Gaussian form and allows to extract a persistence length, L_p of 43
nm. When the dsDNA is compacted by positively charged dendrimer, the stretch
modulus stays invariant but the effective bending rigidity estimated from the
end-to-end distance distribution decreases dramatically due to backbone charge
neutralization of dsDNA by dendrimer. We support our observations with
numerical solutions of the worm-like-chain (WLC) model as well as using
non-equilibrium dsDNA stretching simulations. These results are helpful in
understanding the dsDNA elasticity at short length scales as well as how the
elasticity is modulated when dsDNA binds to a charged object such as a
dendrimer or protein.
