Four separate topics have been studied under this project: (a) The head-to-tail treadmilling of subunits in actin filaments and in microtubules has been studied further. Our earlier bioenergetic analysis has been extended to take care of a three-state NTPase cycle, which is important under some experimental conditions; (b) further work has been done on the theory of binding of myosin to regulated actin; (c) as a first step in studying the structure of covalently-closed circular DNA molecules in solution, we have devised an efficient method of generating ring polymers of the freely jointed model; and (d) the structure of circular DNA molecules is being investigated using ring polymers of the freely jointed model by adding bending twisting energies to the ring.