Lenore J. Cowen

Compact routing with minimum stretch

We present the first universal compact routing algorithm with maximum stretch bounded by 3 that uses sublinear space at every vertex. The algorithm uses local routing tables of size O(n2/3log4/3n) and achieves paths that are most 3 times the length of the shortest path distances for all nodes in an arbitrary weighted undirected network. This answers an open question of Gavoille and Gengler who showed that any universal compact routing algorithm with maximum stretch strictly less than 3 must use ?(n) local space at some vertex.

Matt: Local Flexibility Aids Protein Multiple Structure Alignment

Even when there is agreement on what measure a protein multiple structure alignment should be optimizing, finding the optimal alignment is computationally prohibitive. One approach used by many previous methods is aligned fragment pair chaining, where short structural fragments from all the proteins are aligned against each other optimally, and the final alignment chains these together in geometrically consistent ways. Ye and Godzik have recently suggested that adding geometric flexibility may help better model protein structures in a variety of contexts. We introduce the program Matt (Multiple Alignment with Translations and Twists), an aligned fragment pair chaining algorithm that, in intermediate steps, allows local flexibility between fragments: small translations and rotations are temporarily allowed to bring sets of aligned fragments closer, even if they are physically impossible under rigid body transformations. After a dynamic programming assembly guided by these “bent” alignments, geometric consistency is restored in the final step before the alignment is output. Matt is tested against other recent multiple protein structure alignment programs on the popular Homstrad and SABmark benchmark datasets. Matts global performance is competitive with the other programs on Homstrad, but outperforms the other programs on SABmark, a benchmark of multiple structure alignments of proteins with more distant homology. On both datasets, Matt demonstrates an ability to better align the ends of α-helices and β-strands, an important characteristic of any structure alignment program intended to help construct a structural template library for threading approaches to the inverse protein-folding problem. The related question of whether Matt alignments can be used to distinguish distantly homologous structure pairs from pairs of proteins that are not homologous is also considered. For this purpose, a p-value score based on the length of the common core and average root mean squared deviation (RMSD) of Matt alignments is shown to largely separate decoys from homologous protein structures in the SABmark benchmark dataset. We postulate that Matts strong performance comes from its ability to model proteins in different conformational states and, perhaps even more important, its ability to model backbone distortions in more distantly related proteins.

betawrap: Successful prediction of parallel β-helices from primary sequence reveals an association with many microbial pathogens

The amino acid sequence rules that specify β-sheet structure in proteins remain obscure. A subclass of β-sheet proteins, parallel β-helices, represent a processive folding of the chain into an elongated topologically simpler fold than globular β-sheets. In this paper, we present a computational approach that predicts the right-handed parallel β-helix supersecondary structural motif in primary amino acid sequences by using β-strand interactions learned from non-β-helix structures. A program called BETAWRAP (http://theory.lcs.mit.edu/betawrap) implements this method and recognizes each of the seven known parallel β-helix families, when trained on the known parallel β-helices from outside that family. BETAWRAP identifies 2,448 sequences among 595,890 screened from the National Center for Biotechnology Information (NCBI; http://www.ncbi.nlm.nih.gov/) nonredundant protein database as likely parallel β-helices. It identifies surprisingly many bacterial and fungal protein sequences that play a role in human infectious disease; these include toxins, virulence factors, adhesins, and surface proteins of Chlamydia, Helicobacteria, Bordetella, Leishmania, Borrelia, Rickettsia, Neisseria, and Bacillus anthracis. Also unexpected was the rarity of the parallel β-helix fold and its predicted sequences among higher eukaryotes. The computational method introduced here can be called a three-dimensional dynamic profile method because it generates interstrand pairwise correlations from a processive sequence wrap. Such methods may be applicable to recognizing other beta structures for which strand topology and profiles of residue accessibility are well conserved.

Defective coloring revisited

A graph is (k, d)-colorable if one can color the vertices with k colors such that no vertex is adjacent to more than d vertices of its same color. In this paper we investigate the existence of such colorings in surfaces and the complexity of coloring problems. It is shown that a toroidal graph is (3, 2)- and (5, 1)-colorable, and that a graph of genus γ is (χγ/(d + 1) + 4, d)-colorable, where χγ is the maximum chromatic number of a graph embeddable on the surface of genus γ. It is shown that the (2, k)-coloring, for k ≥ 1, and the (3, 1)-coloring problems are NP-complete even for planar graphs. In general graphs (k, d)-coloring is NP-complete for k ≥ 3, d ≥ 0. The tightness is considered. Also, generalizations to defects of several algorithms for approximate (proper) coloring are presented.

Near-Linear Time Construction of Sparse Neighborhood Covers

This paper introduces a near-linear time sequential algorithm for constructing a sparse neighborhood cover. This implies analogous improvements (from quadratic to near-linear time) for any problem whose solution relies on network decompositions, including small edge cuts in planar graphs, approximate shortest paths, and weight- and distance-preserving graph spanners. In particular, an O(log n) approximation to the k-shortest paths problem on an n-vertex, E-edge graph is obtained that runs in

Compact roundtrip routing in directed networks

\soh{n + E + k}

BETASCAN: Probable β-amyloids Identified by Pairwise Probabilistic Analysis

time.

Compact routing with name independence

The first sublinear average space universal compact routing schemes for directed networks are presented. For each integer k ≥ 1, they use O(k log n)size addresses; O(kn1/(k+1))-sized routing tables on average at each node; and achieve roundtrip routes of stretch at most 2k+1 - 1 in any (weighted) directed network. We also present universal compact roundtrip routing schemes with the stronger requirement that they use sublinear maximum space at every node. These schemes also use O(k log n) size addresses and achieve roundtrip routes of stretch at most 2k+ 1 -1 in any (weighted) directed network, and they bound the maximum sized table at each node by O(kn(3k+1)/(2ċ3k)).

Fast Distributed Network Decompositions and Covers

Amyloids and prion proteins are clinically and biologically important β-structures, whose supersecondary structures are difficult to determine by standard experimental or computational means. In addition, significant conformational heterogeneity is known or suspected to exist in many amyloid fibrils. Recent work has indicated the utility of pairwise probabilistic statistics in β-structure prediction. We develop here a new strategy for β-structure prediction, emphasizing the determination of β-strands and pairs of β-strands as fundamental units of β-structure. Our program, BETASCAN, calculates likelihood scores for potential β-strands and strand-pairs based on correlations observed in parallel β-sheets. The program then determines the strands and pairs with the greatest local likelihood for all of the sequences potential β-structures. BETASCAN suggests multiple alternate folding patterns and assigns relative a priori probabilities based solely on amino acid sequence, probability tables, and pre-chosen parameters. The algorithm compares favorably with the results of previous algorithms (BETAPRO, PASTA, SALSA, TANGO, and Zyggregator) in β-structure prediction and amyloid propensity prediction. Accurate prediction is demonstrated for experimentally determined amyloid β-structures, for a set of known β-aggregates, and for the parallel β-strands of β-helices, amyloid-like globular proteins. BETASCAN is able both to detect β-strands with higher sensitivity and to detect the edges of β-strands in a richly β-like sequence. For two proteins (Aβ and Het-s), there exist multiple sets of experimental data implying contradictory structures; BETASCAN is able to detect each competing structure as a potential structure variant. The ability to correlate multiple alternate β-structures to experiment opens the possibility of computational investigation of prion strains and structural heterogeneity of amyloid. BETASCAN is publicly accessible on the Web at http://betascan.csail.mit.edu.

The distinguishing number of the hypercube

This paper is concerned with compact routing in the name independent model first introduced by Awerbuch et al. [1] for adaptive routing in dynamic networks. A compact routing scheme that uses local routing tables of size <i>Õ(n^1/2)</i>, <i>O(log² n)</i>-sized packet headers, and stretch bounded by 5 is obtained. Alternative schemes reduce the packet header size to <i>O(log n)</i> at cost of either increasing the stretch to 7, or increasing the table size to <i>Õ(n^2/3)</i>. For smaller table-size requirements, the ideas in these schemes are generalized to a scheme that uses <i>O(log² n)</i>-sized headers, <i>Õ(k²n^2/k)</i>-sized tables, and achieves a stretch of <i>min[1 + (k-1)(2^k/2-2), 16k²+4k ]</i>, improving the best previously-known name-independent scheme due to Awerbuch and Peleg [3].