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Ribosome recycling, the disassembly of the posttermination complex after each round of protein synthesis, is an essential step in mRNA translation, but its mechanism has remained obscure. In eubacteria, recycling is catalyzed by RRF (ribosome recycling factor) and EF-G (elongation factor G). By using cryo-electron microscopy, we have obtained two density maps, one of the RRF bound posttermination complex and one of the 50S subunit bound with both EF-G and RRF. Comparing the two maps, we found domain I of RRF to be in the same orientation, while domain II in the EF-G-containing 50S subunit is extensively rotated (approximately 60 degrees) compared to its orientation in the 70S complex. Mapping the 50S conformation of RRF onto the 70S posttermination complex suggests that it can disrupt the intersubunit bridges B2a and B3, and thus effect a separation of the two subunits. These observations provide the structural basis for the mechanism by which the posttermination complex is split into subunits by the joint action of RRF and EF-G.

Abstract. In this paper we propose and develop an iterative method to calculate a limiting probability distribution vector of a transition probability tensor P arising from a higher-order Markov chain. In the model, the computation of such limiting probability distribution vector x can be formulated as a Z-eigenvalue problem Px m−1 = x associated with the eigenvalue 1 of P where all the entries of x are required to be non-negative and its summation must be equal to one. This is an analog of the matrix case for a limiting probability vector of a transition probability matrix arising from the first order Markov chain. We show that if P is a transition probability tensor, then solutions of this Z-eigenvalue problem exist. When P is irreducible, all the entries of solutions are positive. With some suitable conditions of P, the limiting probability distribution vector is even unique. Under the same uniqueness assumption, the linear convergence of the iterative method can be established. Numerical examples are presented to illustrate the theoretical results of the proposed model and the iterative method.

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