Computer simulations and theory of protein translocation

The translocation of proteins through pores is central to many biological phenomena, such as mitochondrial protein import, protein degradation, and delivery of protein toxins to their cytosolic targets. Because proteins typically have to pass through constrictions that are too narrow to accommodate folded structures, translocation must be coupled to protein unfolding. The simplest model that accounts for such co-translocational unfolding assumes that both translocation and unfolding are accomplished by pulling on the end of the polypeptide chain mechanically. In this Account, we describe theoretical studies and computer simulations of this model and discuss how the time scales of translocation depend on the pulling force and on the protein structure. Computationally, this is a difficult problem because biologically or experimentally relevant time scales of translocation are typically orders of magnitude slower than those accessible by fully atomistic simulations. For this reason, we explore one-dimensional free energy landscapes along suitably defined translocation coordinates and discuss various approaches to their computation. We argue that the free energy landscape of translocation is often bumpy because confinement partitions the protein's configuration space into distinct basins of attraction separated by large entropic barriers. Favorable protein-pore interactions and nonnative interactions within the protein further contribute to the complexity. Computer simulations and simple scaling estimates show that forces of just 2-6 pN are often sufficient to ensure transport of unstructured polypeptides, whereas much higher forces are typically needed to translocate folded protein domains. The unfolding mechanisms found from simulations of translocation are different from those observed in the much better understood case of atomic force microscopy (AFM) pulling studies, in which proteins are unraveled by stretching them between their N- and C-termini. In contrast to AFM experiments, single-molecule experimental studies of protein translocation have just started to emerge. We describe one example of a collaborative study, in which dwell times of beta-hairpin-forming peptides inside the alpha-hemolysin pore were both measured experimentally and estimated using computer simulations. Analysis of the simulated trajectories has explained the experimental finding that more stable hairpins take, on the average, longer to traverse the pore. Despite the insight we have gained, the general relationship between the structure of proteins and their resistance to mechanically driven co-translocational unfolding remains poorly understood. Future theoretical progress likely will be made in conjunction with single-molecule experiments and will require realistic models to account for specific protein-pore interactions and for solvent effects.