  We study the compression and extension dynamics of a DNA-like polymer
interacting with non-DNA binding and DNA-binding proteins, by means of computer
simulations. The geometry we consider is inspired by recent experiments probing
the compressional elasticity of the bacterial nucleoid (DNA plus associated
proteins), where DNA is confined into a cylindrical container and subjected to
the action of a "piston" - a spherical bead to which an external force is
applied. We quantify the effect of steric interactions (excluded volume) on the
force-extension curves as the polymer is compressed. We find that
non-DNA-binding proteins, even at low densities, exert an osmotic force which
can be a lot larger than the entropic force exerted by the compressed DNA. The
trends we observe are qualitatively robust with respect to changes in protein
size, and are similar for neutral and charged proteins (and DNA). We also
quantify the dynamics of DNA expansion following removal of the "piston": while
the expansion is well fitted by power laws, the apparent exponent depends on
protein concentration, and protein-DNA interaction in a significant way. We
further highlight an interesting kinetic process which we observe during the
expansion of DNA interacting with DNA-binding proteins when the interaction
strength is intermediate: the proteins bind while the DNA is packaged by the
compression force, but they "pop-off" one-by-one as the force is removed,
leading to a slow unzipping kinetics. Finally, we quantify the importance of
supercoiling, which is an important feature of bacterial DNA in vivo.
