Self assembly of rectangular shapes on concentration programming and probabilistic tile assembly models.

Efficient tile sets for self assembling rectilinear shapes is of critical importance in algorithmic self assembly. A lower bound on the tile complexity of any deterministic self assembly system for an n × n square is [Formula: see text] (inferred from the Kolmogrov complexity). Deterministic self assembly systems with an optimal tile complexity have been designed for squares and related shapes in the past. However designing [Formula: see text] unique tiles specific to a shape is still an intensive task in the laboratory. On the other hand copies of a tile can be made rapidly using PCR (polymerase chain reaction) experiments. This led to the study of self assembly on tile concentration programming models. We present two major results in this paper on the concentration programming model. First we show how to self assemble rectangles with a fixed aspect ratio (α:ß), with high probability, using Θ(α + ß) tiles. This result is much stronger than the existing results by Kao et al. (Randomized self-assembly for approximate shapes, LNCS, vol 5125. Springer, Heidelberg, 2008) and Doty (Randomized self-assembly for exact shapes. In: proceedings of the 50th annual IEEE symposium on foundations of computer science (FOCS), IEEE, Atlanta. pp 85-94, 2009)-which can only self assembly squares and rely on tiles which perform binary arithmetic. On the other hand, our result is based on a technique called staircase sampling. This technique eliminates the need for sub-tiles which perform binary arithmetic, reduces the constant in the asymptotic bound, and eliminates the need for approximate frames (Kao et al. Randomized self-assembly for approximate shapes, LNCS, vol 5125. Springer, Heidelberg, 2008). Our second result applies staircase sampling on the equimolar concentration programming model (The tile complexity of linear assemblies. In: proceedings of the 36th international colloquium automata, languages and programming: Part I on ICALP '09, Springer-Verlag, pp 235-253, 2009), to self assemble rectangles (of fixed aspect ratio) with high probability. The tile complexity of our algorithm is Θ(log(n)) and is optimal on the probabilistic tile assembly model (PTAM)-n being an upper bound on the dimensions of a rectangle.

PMS5: an efficient exact algorithm for the (ℓ, d)-motif finding problem.

BACKGROUND: Motifs are patterns found in biological sequences that are vital for understanding gene function, human disease, drug design, etc. They are helpful in finding transcriptional regulatory elements, transcription factor binding sites, and so on. As a result, the problem of identifying motifs is very crucial in biology. RESULTS: Many facets of the motif search problem have been identified in the literature. One of them is (ℓ, d)-motif search (or Planted Motif Search (PMS)). The PMS problem has been well investigated and shown to be NP-hard. Any algorithm for PMS that always finds all the (ℓ, d)-motifs on a given input set is called an exact algorithm. In this paper we focus on exact algorithms only. All the known exact algorithms for PMS take exponential time in some of the underlying parameters in the worst case scenario. But it does not mean that we cannot design exact algorithms for solving practical instances within a reasonable amount of time. In this paper, we propose a fast algorithm that can solve the well-known challenging instances of PMS: (21, 8) and (23, 9). No prior exact algorithm could solve these instances. In particular, our proposed algorithm takes about 10 hours on the challenging instance (21, 8) and about 54 hours on the challenging instance (23, 9). The algorithm has been run on a single 2.4GHz PC with 3GB RAM. The implementation of PMS5 is freely available on the web at http://www.pms.engr.uconn.edu/downloads/PMS5.zip. CONCLUSIONS: We present an efficient algorithm PMS5 that uses some novel ideas and combines them with well-known algorithm PMS1 and PMSPrune. PMS5 can tackle the large challenging instances (21, 8) and (23, 9). Therefore, we hope that PMS5 will help biologists discover longer motifs in the futures.

A computational tool for identifying minimotifs in protein-protein interactions and improving the accuracy of minimotif predictions.

Protein-protein interactions are important to understanding cell functions; however, our theoretical understanding is limited. There is a general discontinuity between the well-accepted physical and chemical forces that drive protein-protein interactions and the large collections of identified protein-protein interactions in various databases. Minimotifs are short functional peptide sequences that provide a basis to bridge this gap in knowledge. However, there is no systematic way to study minimotifs in the context of protein-protein interactions or vice versa. Here we have engineered a set of algorithms that can be used to identify minimotifs in known protein-protein interactions and implemented this for use by scientists in Minimotif Miner. By globally testing these algorithms on verified data and on 100 individual proteins as test cases, we demonstrate the utility of these new computation tools. This tool also can be used to reduce false-positive predictions in the discovery of novel minimotifs. The statistical significance of these algorithms is demonstrated by an ROC analysis (P = 0.001).

Minimotif miner 2nd release: a database and web system for motif search.

Minimotif Miner (MnM) consists of a minimotif database and a web-based application that enables prediction of motif-based functions in user-supplied protein queries. We have revised MnM by expanding the database more than 10-fold to approximately 5000 motifs and standardized the motif function definitions. The web-application user interface has been redeveloped with new features including improved navigation, screencast-driven help, support for alias names and expanded SNP analysis. A sample analysis of prion shows how MnM 2 can be used. Weblink: http://mnm.engr.uconn.edu, weblink for version 1 is http://sms.engr.uconn.edu.

Efficient parallel and out of core algorithms for constructing large bi-directed de Bruijn graphs.

BACKGROUND: Assembling genomic sequences from a set of overlapping reads is one of the most fundamental problems in computational biology. Algorithms addressing the assembly problem fall into two broad categories - based on the data structures which they employ. The first class uses an overlap/string graph and the second type uses a de Bruijn graph. However with the recent advances in short read sequencing technology, de Bruijn graph based algorithms seem to play a vital role in practice. Efficient algorithms for building these massive de Bruijn graphs are very essential in large sequencing projects based on short reads. In an earlier work, an O(n/p) time parallel algorithm has been given for this problem. Here n is the size of the input and p is the number of processors. This algorithm enumerates all possible bi-directed edges which can overlap with a node and ends up generating Θ(nΣ) messages (Σ being the size of the alphabet). RESULTS: In this paper we present a Θ(n/p) time parallel algorithm with a communication complexity that is equal to that of parallel sorting and is not sensitive to Σ. The generality of our algorithm makes it very easy to extend it even to the out-of-core model and in this case it has an optimal I/O complexity of Θ(nlog(n/B)Blog(M/B)) (M being the main memory size and B being the size of the disk block). We demonstrate the scalability of our parallel algorithm on a SGI/Altix computer. A comparison of our algorithm with the previous approaches reveals that our algorithm is faster--both asymptotically and practically. We demonstrate the scalability of our sequential out-of-core algorithm by comparing it with the algorithm used by VELVET to build the bi-directed de Bruijn graph. Our experiments reveal that our algorithm can build the graph with a constant amount of memory, which clearly outperforms VELVET. We also provide efficient algorithms for the bi-directed chain compaction problem. CONCLUSIONS: The bi-directed de Bruijn graph is a fundamental data structure for any sequence assembly program based on Eulerian approach. Our algorithms for constructing Bi-directed de Bruijn graphs are efficient in parallel and out of core settings. These algorithms can be used in building large scale bi-directed de Bruijn graphs. Furthermore, our algorithms do not employ any all-to-all communications in a parallel setting and perform better than the prior algorithms. Finally our out-of-core algorithm is extremely memory efficient and can replace the existing graph construction algorithm in VELVET.

MimoSA: a system for minimotif annotation.

BACKGROUND: Minimotifs are short peptide sequences within one protein, which are recognized by other proteins or molecules. While there are now several minimotif databases, they are incomplete. There are reports of many minimotifs in the primary literature, which have yet to be annotated, while entirely novel minimotifs continue to be published on a weekly basis. Our recently proposed function and sequence syntax for minimotifs enables us to build a general tool that will facilitate structured annotation and management of minimotif data from the biomedical literature. RESULTS: We have built the MimoSA application for minimotif annotation. The application supports management of the Minimotif Miner database, literature tracking, and annotation of new minimotifs. MimoSA enables the visualization, organization, selection and editing functions of minimotifs and their attributes in the MnM database. For the literature components, Mimosa provides paper status tracking and scoring of papers for annotation through a freely available machine learning approach, which is based on word correlation. The paper scoring algorithm is also available as a separate program, TextMine. Form-driven annotation of minimotif attributes enables entry of new minimotifs into the MnM database. Several supporting features increase the efficiency of annotation. The layered architecture of MimoSA allows for extensibility by separating the functions of paper scoring, minimotif visualization, and database management. MimoSA is readily adaptable to other annotation efforts that manually curate literature into a MySQL database. CONCLUSIONS: MimoSA is an extensible application that facilitates minimotif annotation and integrates with the Minimotif Miner database. We have built MimoSA as an application that integrates dynamic abstract scoring with a high performance relational model of minimotif syntax. MimoSA's TextMine, an efficient paper-scoring algorithm, can be used to dynamically rank papers with respect to context.

Border length minimization problem on a square array.

Protein/peptide microarrays are rapidly gaining momentum in the diagnosis of cancer. High-density and high-throughput peptide arrays are being extensively used to detect tumor biomarkers, examine kinase activity, identify antibodies having low serum titers, and locate antibody signatures. Improving the yield of microarray fabrication involves solving a hard combinatorial optimization problem called the border length minimization problem (BLMP). An important question that remained open for the past 7 years is if the BLMP is tractable or not. We settle this open problem by proving that the BLMP is [Formula: see text]-hard. We also present a hierarchical refinement algorithm that can refine any heuristic solution for the BLMP and prove that the TSP+1-threading heuristic is an O(N)-approximation.

Secondary structure, a missing component of sequence-based minimotif definitions.

Minimotifs are short contiguous segments of proteins that have a known biological function. The hundreds of thousands of minimotifs discovered thus far are an important part of the theoretical understanding of the specificity of protein-protein interactions, posttranslational modifications, and signal transduction that occur in cells. However, a longstanding problem is that the different abstractions of the sequence definitions do not accurately capture the specificity, despite decades of effort by many labs. We present evidence that structure is an essential component of minimotif specificity, yet is not used in minimotif definitions. Our analysis of several known minimotifs as case studies, analysis of occurrences of minimotifs in structured and disordered regions of proteins, and review of the literature support a new model for minimotif definitions that includes sequence, structure, and function.

Efficient Out of Core Sorting Algorithms for the Parallel Disks Model.

In this paper we present efficient algorithms for sorting on the Parallel Disks Model (PDM). Numerous asymptotically optimal algorithms have been proposed in the literature. However many of these merge based algorithms have large underlying constants in the time bounds, because they suffer from the lack of read parallelism on PDM. The irregular consumption of the runs during the merge affects the read parallelism and contributes to the increased sorting time. In this paper we first introduce a novel idea called the dirty sequence accumulation that improves the read parallelism. Secondly, we show analytically that this idea can reduce the number of parallel I/O's required to sort the input close to the lower bound of [Formula: see text]. We experimentally verify our dirty sequence idea with the standard R-Way merge and show that our idea can reduce the number of parallel I/Os to sort on PDM significantly.

AN EFFICIENT ALGORITHM FOR CHINESE POSTMAN WALK ON BI-DIRECTED DE BRUIJN GRAPHS.

Sequence assembly from short reads is an important problem in biology. It is known that solving the sequence assembly problem exactly on a bi-directed de Bruijn graph or a string graph is intractable. However, finding a shortest double stranded DNA string (SDDNA) containing all the k-long words in the reads seems to be a good heuristic to get close to the original genome. This problem is equivalent to finding a cyclic Chinese Postman (CP) walk on the underlying unweighted bi-directed de Bruijn graph built from the reads. The Chinese Postman walk Problem (CPP) is solved by reducing it to a general bi-directed flow on this graph which runs in O(|E|2 log2(|V|)) time. In this paper we show that the cyclic CPP on bi-directed graphs can be solved without reducing it to bi-directed flow. We present a Θ(p(|V| + |E|) log(|V|) + (dmaxp)3) time algorithm to solve the cyclic CPP on a weighted bi-directed de Bruijn graph, where p = max{|{υ∣din(υ) - dout(υ) > 0}|, |{υ∣din(υ) - dout(υ) < 0}|} and dmax = max{∣din(υ) - dout(υ)}. Our algorithm performs asymptotically better than the bi-directed flow algorithm when the number of imbalanced nodes p is much less than the nodes in the bi-directed graph. From our experimental results on various datasets, we have noticed that the value of p/|V| lies between 0.08% and 0.13% with 95% probability. Many practical bi-directed de Bruijn graphs do not have cyclic CP walks. In such cases it is not clear how the bi-directed flow can be useful in identifying contigs. Our algorithm can handle such situations and identify maximal bi-directed sub-graphs that have CP walks. A Θ(p(|V| + |E|)) time heuristic algorithm based on these ideas has been implemented for the SDDNA problem. This algorithm was tested on short reads from a plant genome and achieves an approximation ratio of at most 1.0134. We also present a Θ((|V| + |E|) log(V)) time algorithm for the single source shortest path problem on bi-directed de Bruijn graphs, which may be of independent interest.