Algorithm for haplotype inference via galled-tree networks with simple galls.

The problem of determining haplotypes from genotypes has gained considerable prominence in the research community. Here the focus is on determining sets of SNP values on individual chromosomes since such information captures the genetic causes of diseases. The most efficient algorithmic tool for haplotyping is based on perfect phylogenetic trees. A drawback of this method is that it cannot be applied in situations when the data contains homoplasies (multiple mutations of the same character) or recombinations. Recently, Song et al. ( 2005 ) studied the two cases: haplotyping via imperfect phylogenies with a single homoplasy and via galled-tree networks with one gall. In Gupta et al. ( 2010 ), we have shown that the haplotyping via galled-tree networks is NP-hard, even if we restrict to the case when every gall contains at most 3 mutations. We present a polynomial algorithm for haplotyping via galled-tree networks with simple galls (each having two mutations) for genotype matrices which satisfy a natural condition which is implied by presence of at least one 1 in each column that contains a 2. In the end, we give the experimental results comparing our algorithm with PHASE on simulated data.

Prediction of 492 human protein kinase substrate specificities.

BACKGROUND: Complex intracellular signaling networks monitor diverse environmental inputs to evoke appropriate and coordinated effector responses. Defective signal transduction underlies many pathologies, including cancer, diabetes, autoimmunity and about 400 other human diseases. Therefore, there is high impetus to define the composition and architecture of cellular communications networks in humans. The major components of intracellular signaling networks are protein kinases and protein phosphatases, which catalyze the reversible phosphorylation of proteins. Here, we have focused on identification of kinase-substrate interactions through prediction of the phosphorylation site specificity from knowledge of the primary amino acid sequence of the catalytic domain of each kinase. RESULTS: The presented method predicts 488 different kinase catalytic domain substrate specificity matrices in 478 typical and 4 atypical human kinases that rely on both positive and negative determinants for scoring individual phosphosites for their suitability as kinase substrates. This represents a marked advancement over existing methods such as those used in NetPhorest (179 kinases in 76 groups) and NetworKIN (123 kinases), which consider only positive determinants for kinase substrate prediction. Comparison of our predicted matrices with experimentally-derived matrices from about 9,000 known kinase-phosphosite substrate pairs revealed a high degree of concordance with the established preferences of about 150 well studied protein kinases. Furthermore for many of the better known kinases, the predicted optimal phosphosite sequences were more accurate than the consensus phosphosite sequences inferred by simple alignment of the phosphosites of known kinase substrates. CONCLUSIONS: Application of this improved kinase substrate prediction algorithm to the primary structures of over 23, 000 proteins encoded by the human genome has permitted the identification of about 650, 000 putative phosphosites, which are posted on the open source PhosphoNET website (http://www.phosphonet.ca).

Haplotype inferring via galled-tree networks is NP-complete.

The problem of determining haplotypes from genotypes has gained considerable prominence in the research community since the beginning of the HapMap project. Here the focus is on determining the sets of SNP values of individual chromosomes (haplotypes), since such information better captures the genetic causes of diseases. One of the main algorithmic tools for haplotyping is based on the assumption that the evolutionary history for the original haplotypes satisfies perfect phylogeny. This tool can be applied only on individual blocks of chromosomes, in which it is assumed that recombinations do not happen. However, exact determination of blocks is usually not possible. It would be desirable to develop a method for haplotyping which can account for recombinations, and thus can be applied on multiblock sections of chromosomes. A natural candidate for such a method is haplotyping via phylogenetic networks (which model recombinations) or their simplified version: galled-tree networks. However, even haplotyping via galled-tree networks appears hard, as the efficient algorithms exist only for very special cases: the galled-tree network has either a single gall or only small galls with two mutations each. Building on our previous results, we show that, in general, haplotyping via galled-tree networks is NP-complete, and it remains NP-complete when galls are allowed to have at most k mutations, for any k ≥ 3.

Two lower bounds for self-assemblies at temperature 1.

Using the Tile Assembly Model proposed by Rothemund and Winfree, we give two lower bounds on the minimum number of tile types needed to uniquely assemble a shape at temperature 1 under a natural assumption that there are no binding domain mismatches (any two adjacent tiles either form a bond or else both touching sides of the tiles are without glues). Rothemund and Winfree showed that uniquely assembling a full N x N square (a square where there is a bond between any two adjacent tiles) at temperature 1 requires N(2) distinct tile types, and conjectured that the minimum number of tile types needed to self-assemble an N x N square (not a full square) is 2N - 1. Our lower bounds imply that a tile system that uniquely assembles an N x N square without binding domains mismatches, requires at least 2N - 1 tile types.

An algorithm for the energy barrier problem without pseudoknots and temporary arcs.

We make two new contributions to the problem of calculating pseudoknot-free folding pathways with minimum energy barrier between pairs (Α,Β) of RNA secondary structures. Our first contribution pertains to a problem posed by Morgan and Higgs: find a min-barrier direct folding pathway for a simple energy model in which each base pair contributes -1. In a direct folding pathway, intermediate structures contain only base pairs in Α and Β and are of length |AΔB| (the size of the symmetric difference of the two structures). We show how to solve this problem exactly, using techniques for deconstructing bipartite graphs. The problem is NP-hard and so our algorithm requires exponential time in the worst case but performs quite well empirically on pairs of structures that are hundreds of nucleotides long. Our second contribution shows that for the simple energy model, repeatedly adding or removing a base pair from A U B along a pathway is not useful in minimizing the energy barrier. Two consequences of this result are that (i) the problem of determining the min-barrier pseudoknot-free folding pathway from the space of direct pathways with repeats is NP-hard and (ii) our new algorithm finds the min-barrier pathway not only from the space of direct folding pathways but in fact from the space of direct pathways with repeats.

Characterization of the existence of galled-tree networks.

In this paper, we give a complete characterization of the existence of a galled-tree network in the form of simple sufficient and necessary conditions for both root-known and root-unknown cases. As a by-product we obtain a simple algorithm for constructing galled-tree networks. We also introduce a new necessary condition for the existence of a galled-tree network similar to bi-convexity.

Structure-approximating inverse protein folding problem in the 2D HP model.

The inverse protein folding problem is that of designing an amino acid sequence which has a particular native protein fold. This problem arises in drug design where a particular structure is necessary to ensure proper protein-protein interactions. In this paper, we show that in the 2D HP model of Dill it is possible to solve this problem for a broad class of structures. These structures can be used to closely approximate any given structure. One of the most important properties of a good protein (in drug design) is its stability--the aptitude not to fold simultaneously into other structures. We show that for a number of basic structures, our sequences have a unique fold.

Inverse protein folding in 2D HP mode (extended abstract).

The inverse protein folding problem is that of designing an amino acid sequence which has a particular native protein fold. This problem arises in drug design where a particular structure is necessary to ensure proper protein-protein interactions. In this paper we show that in the 2D HP model of Dill it is possible to solve this problem for a broad class of structures. These structures can be used to closely approximate any given structure. One of the most important properties of a good protein is its stability -- the aptitude not to fold simultanously into other structures. We show that for a number of basic structures, our sequences have a unique fold.