Seminarium "Modeling of Complex Systems"

If we tie a knot on a piece of a rope and then pull it through a narrow hole, the knot tightens, and can block the opening. We argue that a similar phenomenon can take place in microworld, during thetransport of knotted proteins through the pores in cellular membranes. The radius of gyration of the tight knot is about 7-8 Angstrom for a trefoil, whereas the radius of the narrowest constriction of e.g. the mitochondrial pores are about 6 Angstrom, which means that the knot is a shade too large to squeeze through the pore opening. We show how such topological traps might be prevented by using a pulling protocol of a repetitive, on-off character. During the off-force period some stored length is inserted into the knotted core, and the knot loosens, thus escaping the tightened configuration. Subsequently, during the next on-force period the protein makes another attempt at the translocation. Since the probability of getting trapped in each of n successive tries rapidly decreases with n, repetitive trying always leads to a final success. Importantly, such a repetitive pulling is biologically relevant, since molecular import motors are ATP-hydrolysis driven and thus cyclic in character. Finally, we analyze the dependence of the translocation rate on force period and magnitude and show that there exists an optimum range of these parameters which lead to the most efficient translocation.