  ATP-dependent chromatin remodeling enzymes (CRE) are bio-molecular motors in
eukaryotic cells. These are driven by a chemical fuel, namely, adenosine
triphosphate (ATP). CREs actively participate in many cellular processes that
require accessibility of specific segments of DNA which are packaged as
chromatin. The basic unit of chromatin is a nucleosome where 146 bp $\sim$ 50
nm of a double stranded DNA (dsDNA) is wrapped around a spool formed by histone
proteins. The helical path of histone-DNA contact on a nucleosome is also
called "footprint". We investigate the mechanism of footprint traversal by a
CRE that translocates along the dsDNA. Our two-state model of a CRE captures
effectively two distinct chemical (or conformational) states in the
mechano-chemical cycle of each ATP-dependent CRE. We calculate the mean time of
traversal. Our predictions on the ATP-dependence of the mean traversal time can
be tested by carrying out {\it in-vitro} experiments on mono-nucleosomes.
