Simulation studies of biopolymers under spatial and topological constraints
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The translocation of a biopolymer through a narrow pore exists in universal cellular processes, such as the translocations of nascent proteins through ribosome and the degradation of protein by ATP-dependent proteases. However, the molecular details of these translocation processes remain unclear. Using computer simulations we study the translocations of a ubiquitin-like protein into a pore. It shows that the mechanism of co-translocational unfolding of proteins through pores depends on the pore diameter, the magnitude of pulling force and on whether the force is applied at the N- or the C-terminus. Translocation dynamics depends on whether or not polymer reversal is likely to occur during translocation. Although it is of interest to compare the timescale of polymer translocation and reversal, there are currently no theories available to estimate the timescale of polymer reversal inside a pore. With computer simulations and approximate theories, we show how the polymer reversal depends on the pore size, r, and the chain length, N. We find that one-dimensional transition state theory (TST) using the polymer extension along the pore axis as a reaction coordinate adequately predicts the exponentially strong dependence of the reversal rate on r and N. Additionally, we find that the transmission factor (the ratio of the exact rate and the TST rate) has a much weaker power law dependence on r and N. Finite-size effects are observed even for chains with several hundred monomers. If metastable states are separated by high energy-barriers, transitions between them will be rare events. Instead of calculating the relative energy by studying those transitions, we can calculate absolute free energy separately to compare their relative stability. We proposed a method for calculating absolute free energy from Monte Carlo or molecular dynamics data. Additionally, the diffusion of a knot in a tensioned polymer is studied using simulations and it can be modeled as a one-dimensional free diffusion problem. The diffusion coefficient is determined by the number of monomers involved in a knot and its tension dependence shows a maximum due to two dominating factors: the friction from solvents and “local friction” from interactions among monomers in a compact knot.