Before revision:  We present a complete analytical formulation of this problem, in the case of a single fixed target and for arbitrary cell size. We derive a set of Green's functions for the microtubule dynamics and an associated set of first passage quantities. An implicit analytical expression for the probability distribution of the search time is then obtained , with appropriate boundary conditions at the outer cell membrane. We extract the conditions of optimized search from our formalism. Our results are in qualitative and semi-quantitative agreement with known experimental results for different cell types{\it   .
After revision:  Although the entire cell cycle can be up to 24 hours long, the mitotic phase typically takes only less than an hour. How does the cell keep the duration of mitosis within this limit? Previous theoretical studies have suggested that the chromosome search and capture is optimized by tuning the microtubule dynamic parameters to minimize the search time. In this paper, we examine this conjecture. We compute the mean search time for a single target by microtubules from a single nucleating site, using a systematic and rigorous theoretical approach, for arbitrary kinetic parameters. The result is extended to multiple targets and nucleating sites by physical arguments. Estimates of mitotic time scales are then obtained for different cells using experimental data. In yeast and mammalian cells, the observed changes in microtubule kinetics between interphase and mitosis are beneficial in reducing the search time. In{\it .