Order independent structural alignment of circularly permuted proteins

Circular permutation connects the N and C termini of a protein and concurrently cleaves elsewhere in the chain, providing an important mechanism for generating novel protein fold and functions. However, their in genomes is unknown because current detection methods can miss many occurances, mistaking random repeats as circular permutation. Here we develop a method for detecting circularly permuted proteins from structural comparison. Sequence order independent alignment of protein structures can be regarded as a special case of the maximum-weight independent set problem, which is known to be computationally hard. We develop an efficient approximation algorithm by repeatedly solving relaxations of an appropriate intermediate integer programming formulation, we show that the approximation ratio is much better then the theoretical worst case ratio of $r = 1/4$. Circularly permuted proteins reported in literature can be identified rapidly with our method, while they escape the detection by publicly available servers for structural alignment.Comment: 5 pages, 3 figures, Accepted by IEEE-EMBS 2004 Conference Proceeding

Steiner Problem in Multistage Computer Networks

Multistage computer networks are popular in parallel architectures and communication applications. We consider the message communication problem for the two types of multistage networks: one popular for parallel architectures and the other popular for communication networks. A subset of the problem can be equated to the Steiner tree problem for multistage graphs. Inherent complexities of the problem is shown and polynomial-time heuristics are developed. Performance of these heuristics is evaluated using analytical as well as simulation results. 1 Introduction Multistage interconnection networks (MINs) are popular among parallel architecture and/or communication network topologies. An N \Theta log 2 N element MIN consists of log 2 N stages of N elements each. A common pictorial view of an N \Theta log 2 N MIN is to collect N elements in a stage (vertically) and arrange log 2 N + 1 such stages horizontally one after the other. MINs offer a good balance between network cost and performa..