In this report, we examine how the cell can selectively stabilize anchored filaments and suppress spontaneous filament assembly. Because microtubules and actin filaments have an organized distribution in cells, the cell must have a mechanism for suppressing spontaneous and random polymerization. Though the mechanism for suppressing spontaneous polymerization is unknown, an unusual property of these filaments has been demonstrated recently, i.e., under steady-stae conditions, in vitro actin filaments and microtubules can exhibit a flux of subunits through the polymers called "treadmilling." In vivo, however, most, if not all, of these polymers are attached at one end to specific structures and treadmilling should not occur. The function of treadmilling in vivo is, therefore, unclear at present. However, as shown here, the same physicochemical property of coupling assembly to ATP or GTP hydrolysis that leads to treadmilling in vitro can act to selectively stabilize anchored polymers in vivo. I show here that the theory of treadmilling implies that the concentration of subunits necessary for assembly of the nonanchored polymer will in general be higher than the concentration necessary for the assembly of polymers anchored with a specific polarity. This disparity in the monomer concentrations required for assembly can lead to a selective stabilization of anchored polymers and complete suppression of spontaneous polymerization at apparent equilibrium in vivo. It is possible, therefore, that the phenomenon of treadmilling is an in vitro manifestation of a mechanism designed to use ATP or GTP hydrolysis to control the spatial organization of filaments in the cell.