  Time-dependent Hamiltonian dynamics is derived for a curve (molecular strand)
in $\mathbb{R}^3$ that experiences both nonlocal (for example, electrostatic)
and elastic interactions. The dynamical equations in the symmetry-reduced
variables are written on the dual of the semidirect-product Lie algebra $so(3)
\circledS (\mathbb{R}^3\oplus\mathbb{R}^3\oplus\mathbb{R}^3\oplus\mathbb{R}^3)$
with three 2-cocycles. We also demonstrate that the nonlocal interaction
produces an interesting new term deriving from the coadjoint action of the Lie
group SO(3) on its Lie algebra $so(3)$. The new filament equations are written
in conservative form by using the corresponding coadjoint actions.
