In this thesis, we study the physics of the pulled polymer loops motivated by a biological problem of chromosome alignment during meiosis in fission yeast. During prophase I of meiotic fission yeast, the chromosomes form a loop structure by binding their telomeres to the Spindle Pole Body (SPB). SPB nucleates the growth of microtubules in the cytoplasm. Molecular motors attached to the cell membrane can exert the force on the microtubules and thus pull the whole nucleus. The nucleus performs oscillatory motion from one to the other end of the elongated zygote cell. Experimental evidence suggests that these oscillations facilitate homologous chromosome alignment which is required for the gene recombination. Our goal is to understand the physical mechanism of this alignment. We thus propose a model of pulled polymer loops to represent the chromosomal motion during oscillations. Using a freely-jointed bead-rod model for the pulled polymer loop, we solve the equilibrium statistics of the polymer configurations both in 1D and 3D. In 1D, we find a peculiar mapping of the bead-rod system to a system of particles on a lattice. Utilizing the wealth of tools of the particle system, we solve exactly the 1D stationary measure and map it back to the polymer system. To address the looping geometry, the Brownian Bridge technique is employed. The mean and variance of beads position along the loop are discussed in detail both in 1D and 3D. We then can calculate the three-dimensional statistics of the distance between corresponding beads from a pair of loops in order to discuss the pairing problem of homologous chromosomes. The steady-state shape of a three-dimensional pulled polymer loop is quantified using the descriptors based on the gyration tensor. Beyond the steady state statistics, the relaxation dynamics of the pinned polymer loop in a constant external force field is discussed. In 1D we show the mapping of polymer dynamics to the well-known Asymmetric Simple Exclusion Process (ASEP) model. Our pinned polymer loop is mapped to a half-filled ASEP with reflecting boundaries. We solve the ASEP model exactly by using the generalized Bethe ansatz method. Thus with the help of the ASEP theory, the relaxation time of the polymer problem can be calculated analytically. To test our theoretical predictions, extensive simulations are performed. We find that our theory of relaxation time fit very well to the relaxation time of a 3D polymer in the direction of the external force field. Finally, we discuss the relevance of our findings to the problem of chromosome alignment in fission yeast.

In this thesis, we study the physics of the pulled polymer loops motivated by a biological problem of chromosome alignment during meiosis in fission yeast. During prophase I of meiotic fission yeast, the chromosomes form a loop structure by binding their telomeres to the Spindle Pole Body (SPB). SPB nucleates the growth of microtubules in the cytoplasm. Molecular motors attached to the cell membrane can exert the force on the microtubules and thus pull the whole nucleus. The nucleus performs oscillatory motion from one to the other end of the elongated zygote cell. Experimental evidence suggests that these oscillations facilitate homologous chromosome alignment which is required for the gene recombination. Our goal is to understand the physical mechanism of this alignment. We thus propose a model of pulled polymer loops to represent the chromosomal motion during oscillations. Using a freely-jointed bead-rod model for the pulled polymer loop, we solve the equilibrium statistics of the polymer configurations both in 1D and 3D. In 1D, we find a peculiar mapping of the bead-rod system to a system of particles on a lattice. Utilizing the wealth of tools of the particle system, we solve exactly the 1D stationary measure and map it back to the polymer system. To address the looping geometry, the Brownian Bridge technique is employed. The mean and variance of beads position along the loop are discussed in detail both in 1D and 3D. We then can calculate the three-dimensional statistics of the distance between corresponding beads from a pair of loops in order to discuss the pairing problem of homologous chromosomes. The steady-state shape of a three-dimensional pulled polymer loop is quantified using the descriptors based on the gyration tensor. Beyond the steady state statistics, the relaxation dynamics of the pinned polymer loop in a constant external force field is discussed. In 1D we show the mapping of polymer dynamics to the well-known Asymmetric Simple Exclusion Process (ASEP) model. Our pinned polymer loop is mapped to a half-filled ASEP with reflecting boundaries. We solve the ASEP model exactly by using the generalized Bethe ansatz method. Thus with the help of the ASEP theory, the relaxation time of the polymer problem can be calculated analytically. To test our theoretical predictions, extensive simulations are performed. We find that our theory of relaxation time fit very well to the relaxation time of a 3D polymer in the direction of the external force field. Finally, we discuss the relevance of our findings to the problem of chromosome alignment in fission yeast.