Ján Maňuch

Prediction of 492 human protein kinase substrate specificities

BackgroundComplex 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.ResultsThe 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.ConclusionsApplication 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).

Linearization of ancestral multichromosomal genomes.

BackgroundRecovering the structure of ancestral genomes can be formalized in terms of properties of binary matrices such as the Consecutive-Ones Property (C1P). The Linearization Problem asks to extract, from a given binary matrix, a maximum weight subset of rows that satisfies such a property. This problem is in general intractable, and in particular if the ancestral genome is expected to contain only linear chromosomes or a unique circular chromosome. In the present work, we consider a relaxation of this problem, which allows ancestral genomes that can contain several chromosomes, each either linear or circular.ResultWe show that, when restricted to binary matrices of degree two, which correspond to adjacencies, the genomic characters used in most ancestral genome reconstruction methods, this relaxed version of the Linearization Problem is polynomially solvable using a reduction to a matching problem. This result holds in the more general case where columns have bounded multiplicity, which models possibly duplicated ancestral genes. We also prove that for matrices with rows of degrees 2 and 3, without multiplicity and without weights on the rows, the problem is NP-complete, thus tracing sharp tractability boundaries.ConclusionAs it happened for the breakpoint median problem, also used in ancestral genome reconstruction, relaxing the definition of a genome turns an intractable problem into a tractable one. The relaxation is adapted to some biological contexts, such as bacterial genomes with several replicons, possibly partially assembled. Algorithms can also be used as heuristics for hard variants. More generally, this work opens a way to better understand linearization results for ancestral genome structure inference.

On the Gapped Consecutive-Ones Property

Abstract Motivated by problems of comparative genomics and paleogenomics, we introduce the Gapped Consecutive-Ones Property Problem ( k , δ ) -C1P: given a binary matrix M and two integers k and δ, can the columns of M be permuted such that each row contains at most k sequences of 1s and no two consecutive sequences of 1s are separated by a gap of more than δ 0s. The classical C1P problem, which is known to be polynomial, is equivalent to the (1,0)-C1P Problem. We show that the ( 2 , δ ) -C1P Problem is NP-complete for δ ⩾ 2 . We conjecture that the ( k , δ ) -C1P Problem is NP-complete for k ⩾ 2 , δ ⩾ 1 , ( k , δ ) ≠ ( 2 , 1 ) . We also show that the ( k , δ ) -C1P Problem can be reduced to a graph bandwidth problem parameterized by a function of k, δ and of the maximum number s of 1s in a row of M, and hence is polytime solvable if all three parameters are constant.

The Odd-Distance Plane Graph

The vertices of the odd-distance graph are the points of the plane ℝ2. Two points are connected by an edge if their Euclidean distance is an odd integer. We prove that the chromatic number of this graph is at least five. We also prove that the odd-distance graph in ℝ2 is countably choosable, while such a graph in ℝ3 is not.

Step-Assembly with a Constant Number of Tile Types

Demaine et. al. [1] have introduced a model for staged assembly for constructing self-assembled shapes as an extension to the multiple tile model [2]. In their model the assembly proceeds in several bins and several stages with different sets of tiles and supertiles applied on each bin and in each stage. Taking advantage of all these features they showed that a constant number of tile types is sufficient to self-assemble any given shape. In this paper, we consider a simplified model of staged assembly, called the step assembly model, in which we only have one bin in each step and assembly happens by attaching tiles one by one to the growing structure as in the standard assembly model. We show that in this simplified model a constant number of tile types (24) is sufficient to assemble a large class of shapes. This class includes all shapes obtained from any shape by scaling by a factor of 2. For general shapes, we note that the tile complexity of this model has connections to the monotone connected node search number of a spanning tree of the shape.

NP-Completeness of the Direct Energy Barrier Problem without Pseudoknots

Knowledge of energy barriers between pairs of secondary structures for a given DNA or RNA molecule is useful, both in understanding RNA function in biological settings and in design of programmed molecular systems. Current heuristics are not guaranteed to find the exact energy barrier, raising the question whether the energy barrier can be calculated efficiently. In this paper, we study the computational complexity of a simple formulation of the energy barrier problem, in which each base pair contributes an energy of ? 1 and only base pairs in the initial and final structures may be used on a folding pathway from initial to final structure. We show that this problem is NP-complete.

Reachability Bounds for Chemical Reaction Networks and Strand Displacement Systems

Chemical reaction networks (CRNs) and DNA strand displacement systems (DSDs) are widely-studied and useful models of molecular programming. However, in order for some DSDs in the literature to behave in an expected manner, the initial number of copies of some reagents is required to be fixed. In this paper we show that, when multiple copies of all initial molecules are present, general types of CRNs and DSDs fail to work correctly if the length of the shortest sequence of reactions needed to produce any given molecule exceeds a threshold that grows polynomially with attributes of the system.

Tractability results for the consecutive-ones property with multiplicity

A binary matrix has the Consecutive-Ones Property (C1P) if its columns can be ordered in such a way that all 1s in each row are consecutive. We consider here a variant of the C1P where columns can appear multiple times in the ordering. Although the general problem of deciding the C1P with multiplicity is NP-complete, we present here a case of interest in comparative genomics that is tractable.

Haplotype inferring via galled-tree networks using a hypergraph covering problem for special genotype matrices

Since exact determination of haplotype blocks is usually not possible, it is desirable to develop a haplotyping method which can account for recombinations. A natural candidate for such a method is haplotyping via phylogenetic networks or their simplified version: galled-tree networks. In earlier work we characterized the existence of the galled-tree networks. Building on this, we reduce the problem of haplotype inferring via galled-tree networks to a hypergraph covering problem for genotype matrices satisfying a combinatorial condition. Our experiments on actual data show that this condition is almost always satisfied when the percentage of minor alleles for each SNP reaches at least 30%.

On Conjugacy of Languages

We say that two languages X and Y are conjugates if they satisfy the conjugacy equation XZ = ZY for some language Z. We study several problems associated with this equation. For example, we characterize all sets which are conjugated via a two-element biprex set Z, as well as all two-element sets which are conjugates. Mathematics Subject Classication. 68R15, 68Q70.