RESUMEN
We analyze experimental motility assays of microtubules undergoing small fluctuations about a "balance point" when mixed in solution of two different kinesin motor proteins, KLP61F and Ncd. It has been proposed that the microtubule movement is due to stochastic variations in the densities of the two species of motor proteins. We test this hypothesis here by showing how it maps onto a one-dimensional random walk in a random environment. Our estimate of the amplitude of the fluctuations agrees with experimental observations. We point out that there is an initial transient in the position of the microtubule where it will typically move of order its own length. We compare the physics of this gliding assay to a recent theory of the role of antagonistic motors on restricting interpolar microtubule sliding of a cell's mitotic spindle during prometaphase. It is concluded that randomly positioned antagonistic motors can restrict relative movement of microtubules, however they do so imperfectly. A variation in motor concentrations is also analyzed and shown to lead to greater control of spindle length.