A novel automatic procedure for identifying domains from protein atomic coordinates is presented. The procedure, termed STRUDL (STRUctural Domain Limits), does not take into account information on secondary structures and handles any number of domains made up of contiguous or non-contiguous chain segments. The core algorithm uses the Kernighan-Lin graph heuristic to partition the protein into residue sets which display minimum interactions between them. These interactions are deduced from the weighted Voronoi diagram. The generated partitions are accepted or rejected on the basis of optimized criteria, representing basic expected physical properties of structural domains. The graph heuristic approach is shown to be very effective, it approximates closely the exact solution provided by a branch and bound algorithm for a number of test proteins. In addition, the overall performance of STRUDL is assessed on a set of 787 representative proteins from the Protein Data Bank by comparison to domain definitions in the CATH protein classification. The domains assigned by STRUDL agree with the CATH assignments in at least 81% of the tested proteins. This result is comparable to that obtained previously using PUU (Holm and Sander, Proteins 1994;9:256-268), the only other available algorithm designed to identify domains with any number of non-contiguous chain segments. A detailed discussion of the structures for which our assignments differ from those in CATH brings to light some clear inconsistencies between the concept of structural domains based on minimizing inter-domain interactions and that of delimiting structural motifs that represent acceptable folding topologies or architectures. Considering both concepts as complementary and combining them in a layered approach might be the way forward. Proteins 1999;35:338-352.
Abstract. The b-clique polytope CP n b is the convex hull of the node and edge incidence vectors of all subcliques of size at most b of a complete graph on n nodes. Including the Boolean quadric polytope QP n as a special case and being closely related to the quadratic knapsack polytope, it has received considerable attention in the literature. In particular, the max-cut problem is equivalent with optimizing a linear function over QP n n . The problem of optimizing linear functions over CP n b has so far been approached via heuristic combinatorial algorithms and cutting-plane methods.We study the structure of CP n b in further detail and present a new computational approach to the linear optimization problem based on Lucena's suggestion of integrating cutting planes into a Lagrangian relaxation of an integer programming problem. In particular, we show that the separation problem for tree inequalities becomes polynomial in our Lagrangian framework. Finally, computational results are presented.
A novel automatic procedure for identifying domains from protein atomic coordinates is presented. The procedure, termed STRUDL (STRUctural Domain Limits), does not take into account information on secondary structures and handles any number of domains made up of contiguous or non-contiguous chain segments. The core algorithm uses the Kernighan-Lin graph heuristic to partition the protein into residue sets which display minimum interactions between them. These interactions are deduced from the weighted Voronoi diagram. The generated partitions are accepted or rejected on the basis of optimized criteria, representing basic expected physical properties of structural domains. The graph heuristic approach is shown to be very effective, it approximates closely the exact solution provided by a branch and bound algorithm for a number of test proteins. In addition, the overall performance of STRUDL is assessed on a set of 787 representative proteins from the Protein Data Bank by comparison to domain definitions in the CATH protein classification. The domains assigned by STRUDL agree with the CATH assignments in at least 81% of the tested proteins. This result is comparable to that obtained previously using PUU (Holm and Sander, Proteins 1994;9:256-268), the only other available algorithm designed to identify domains with any number of non-contiguous chain segments. A detailed discussion of the structures for which our assignments differ from those in CATH brings to light some clear inconsistencies between the concept of structural domains based on minimizing inter-domain interactions and that of delimiting structural motifs that represent acceptable folding topologies or architectures. Considering both concepts as complementary and combining them in a layered approach might be the way forward.
Yamnitsky and Levin proposed a variant of Khachiyan's ellopsoid method for testing feasibility of systems of linear inequalities that also runs in polynomial time but uses simpliees instead of ellipsoids. Starting with the n-simplex S and the half-space {x[arx <_ fl}, the algorithm finds a simplex SrL of small volume that encloses S c~ {xlarx < B}-We interpret SrL as a simplex obtainable by point-sliding and show that the smallest such simplex can be determined by minimizing a simple strictly convex function. We furthermore discuss some numerical results. The results suggest that the number of iterations used by our method may be considerably less than that of the standard ellipsoid method.
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