Simulations of polymer translocation

Transport of molecules across membranes is an essential mechanism for life processes. These molecules are often long, and the pores in the membranes are too narrow for the molecules to pass through as a single unit. In such circumstances, the molecules have to squeeze --- i.e., translocate --- themselves through the pores. DNA, RNA and proteins are such naturally occuring long molecules in a variety of biological processes. Understandably, the process of translocation has been an active topic of current research: not only because it is a cornerstone of many biological processes, but also due to its relevance for practical applications. Translocation is a complicated process in living organisms --- the presence of chaperone molecules, pH, chemical potential gradients, and assisting molecular motors strongly influence its dynamics. Consequently, the translocation process has been empirically studied in great variety in biological literature. Study of translocation as a biophysical process is more recent. Herein, the polymer is simplified to a sequentially connected string of N monomers as it passes through a narrow pore on a membrane. The quantities of interest are the typical time scale for the polymer to leave a confining cell (the ``escape of a polymer from a vesicle'' time scale), and the typical time scale the polymer spends in the pore (the ``dwell'' time scale) as a function of N and other parameters like membrane thickness, membrane adsorption, electrochemical potential gradient, etc. Our research is focused on computer simulations of translocation. Since our main interest is in the scaling properties, we use a highly simplified description of the translocation process. The polymer is described as a self-avoiding walk on a lattice, and its dynamics consists of single-monomer jumps from one lattice site to another neighboring one. Since we have a very efficient program to simulate such polymer dynamics, which we decribe in Chapter 2, we can perform long simulations in which long polymers creep through tiny pores. In Chapter 3 we study pore blockage times for a translocating polymer of length N, driven by a field E across te pore. In three dimensions we find that the typical time the pore remains blocked during a translocation event scales as ~N^{1.37}/E We show that the scaling behavior stems from the polymer dynamics at the immediate vicinity of the pore --- in particular, the memory effects in the polymer chain tension imbalance across the pore. Chapter 4 studies the unbiased translocation of a polymer with length N, surrounded by equally long polymers, through a narrow pore in a membrane. We show that in dense polymeric systems a relaxation time exists that scales as N^{2.65}, much longer than the Rouse time ~N^2. If the polymers are well entangled, we find that the mean dwell times scales as N^{3.3}, while for shorter, less entangled polymers, we measure dwell times scaling as N^{2.7}. In Chapter 5 we study the translocation of an RNA molecule, pulled through a nanopore by an optical tweezer, as a method to determine its secondary structure. The resolution with which the elements of the secondary structure can be determined is limited by thermal fluctuations, ruling out single-nucleotide resolution under normal experimental conditions.