MOTIVATION: A factory in a metabolic network specifies how to produce target molecules from source compounds through biochemical reactions, properly accounting for reaction stoichiometry to conserve or not deplete intermediate metabolites. While finding factories is a fundamental problem in systems biology, available methods do not consider the number of reactions used, nor address negative regulation. METHODS: We introduce the new problem of finding optimal factories that use the fewest reactions, for the first time incorporating both first- and second-order negative regulation. We model this problem with directed hypergraphs, prove it is NP-complete, solve it via mixed-integer linear programming, and accommodate second-order negative regulation by an iterative approach that generates next-best factories. RESULTS: This optimization-based approach is remarkably fast in practice, typically finding optimal factories in a few seconds, even for metabolic networks involving tens of thousands of reactions and metabolites, as demonstrated through comprehensive experiments across all instances from standard reaction databases. AVAILABILITY AND IMPLEMENTATION: Source code for an implementation of our new method for optimal factories with negative regulation in a new tool called Odinn, together with all datasets, is available free for non-commercial use at http://odinn.cs.arizona.edu.

Cell signaling pathways, which are a series of reactions that start at receptors and end at transcription factors, are basic to systems biology. Properly modeling the reactions in such pathways requires directed hypergraphs, where an edge is now directed between two sets of vertices. Inferring a pathway by the most parsimonious series of reactions then corresponds to finding a shortest hyperpath in a directed hypergraph, which is NP-complete. The state of the art for shortest hyperpaths in cell-signaling hypergraphs solves a mixed-integer linear program to find an optimal hyperpath that is restricted to be acyclic, and offers no efficiency guarantees. We present for the first time a heuristic for general shortest hyperpaths that properly handles cycles, and is guaranteed to be efficient. Its accuracy is demonstrated through exhaustive experiments on all instances from the standard NCI-PID and Reactome pathway databases, which show the heuristic finds a hyperpath that matches the state-of-the-art mixed-integer linear program on over 99% of all instances that are acyclic. On instances where only cyclic hyperpaths exist, the heuristic surpasses the state-of-the-art, which finds no solution; on every such cyclic instance, enumerating all possible hyperpaths shows that the solution found by the heuristic is in fact optimal.

MOTIVATION: Protein secondary structure prediction is a fundamental precursor to many bioinformatics tasks. Nearly all state-of-the-art tools when computing their secondary structure prediction do not explicitly leverage the vast number of proteins whose structure is known. Leveraging this additional information in a so-called template-based method has the potential to significantly boost prediction accuracy. METHOD: We present a new hybrid approach to secondary structure prediction that gains the advantages of both template- and non-template-based methods. Our core template-based method is an algorithmic approach that uses metric-space nearest neighbor search over a template database of fixed-length amino acid words to determine estimated class-membership probabilities for each residue in the protein. These probabilities are then input to a dynamic programming algorithm that finds a physically valid maximum-likelihood prediction for the entire protein. Our hybrid approach exploits a novel accuracy estimator for our core method, which estimates the unknown true accuracy of its prediction, to discern when to switch between template- and non-template-based methods. RESULTS: On challenging CASP benchmarks, the resulting hybrid approach boosts the state-of-the-art Q8 accuracy by more than 2-10%, and Q3 accuracy by more than 1-3%, yielding the most accurate method currently available for both 3- and 8-state secondary structure prediction. AVAILABILITY AND IMPLEMENTATION: A preliminary implementation in a new tool we call Nnessy is available free for non-commercial use at http://nnessy.cs.arizona.edu.

Summary Measuring execution time is one of the most used performance evaluation techniques in computer science research. Inaccurate measurements cannot be used for a fair performance comparison between programs. Despite the prevalence of its use, the intrinsic variability in the time measurement makes it hard to obtain repeatable and accurate timing results of a program running on an operating system. We propose a novel execution time measurement protocol (termed EMP) for measuring the execution time of a compute‐bound program on Linux, while minimizing that measurement's variability. During the development of execution time measurement protocol, we identified several factors that disturb execution time measurement. We introduce successive refinements to the protocol by addressing each of these factors, in concert, reducing variability by more than an order of magnitude. We also introduce a new visualization technique, what we term ‘dual‐execution scatter plot’ that highlights infrequent, long‐running daemons, differentiating them from frequent and/or short‐running daemons. Our empirical results show that the proposed protocol successfully achieves three major aspects—precision, accuracy, and scalability—in execution time measurement that can work for open‐source and proprietary software. Copyright © 2017 John Wiley & Sons, Ltd.

While the multiple sequence alignment output by an aligner strongly depends on the parameter values used for the alignment scoring function (such as the choice of gap penalties and substitution scores), most users rely on the single default parameter setting provided by the aligner. A different parameter setting, however, might yield a much higher-quality alignment for the specific set of input sequences. The problem of picking a good choice of parameter values for specific input sequences is called parameter advising. A parameter advisor has two ingredients: (i) a set of parameter choices to select from, and (ii) an estimator that provides an estimate of the accuracy of the alignment computed by the aligner using a parameter choice. The parameter advisor picks the parameter choice from the set whose resulting alignment has highest estimated accuracy. In this paper, we consider for the first time the problem of learning the optimal set of parameter choices for a parameter advisor that uses a given accuracy estimator. The optimal set is one that maximizes the expected true accuracy of the resulting parameter advisor, averaged over a collection of training data. While we prove that learning an optimal set for an advisor is NP-complete, we show there is a natural approximation algorithm for this problem, and prove a tight bound on its approximation ratio. Experiments with an implementation of this approximation algorithm on biological benchmarks, using various accuracy estimators from the literature, show it finds sets for advisors that are surprisingly close to optimal. Furthermore, the resulting parameter advisors are significantly more accurate in practice than simply aligning with a single default parameter choice.

While the multiple sequence alignment output by an aligner strongly depends on the parameter values used for its alignment scoring function (i.e. choice of gap penalties and substitution scores), most users rely on the single default parameter setting. A different parameter setting, however, might yield a much higher-quality alignment for a specific set of input sequences. The problem of picking a good choice of parameter values for a given set of input sequences is called parameter advising. A parameter advisor has two ingredients: (i) a set of parameter choices to select from, and (ii) an estimator that estimates the accuracy of a computed alignment; the parameter advisor then picks the parameter choice from the set whose resulting alignment has highest estimated accuracy. Our estimator Facet ( F eature-based Ac curacy E s t imator) is a linear combination of real-valued feature functions of an alignment. We assume the feature functions are given as well as the universe of parameter choices from which the advisor's set is drawn. For this scenario we define the problem of learning an optimal advisor by finding the best possible parameter set for a collection of training data of reference alignments. Learning optimal advisor sets is NP-complete [ 1 ]. For the advisor sets problem, we develop a greedy ℓ k -approximation algorithm that finds near optimal sets of size at most k given an optimal solution of size ℓ

When aligning biological sequences, the choice of parameter values for the alignment scoring function is critical. Small changes in gap penalties, for example, can yield radically different alignments. A rigorous way to compute parameter values that are appropriate for aligning biological sequences is through inverse parametric sequence alignment. Given a collection of examples of biologically correct alignments, this is the problem of finding parameter values that make the scores of the example alignments close to those of optimal alignments for their sequences. We extend prior work on inverse parametric alignment to partial examples, which contain regions where the alignment is left unspecified, and to an improved formulation based on minimizing the average error between the score of an example and the score of an optimal alignment. Experiments on benchmark biological alignments show we can find parameters that generalize across protein families and that boost the accuracy of multiple sequence alignment by as much as 25 percent.

Software watermarking is a tool used to combat software piracy by embedding identifying information into a program. Most existing proposals for software watermarking have the shortcoming that the mark can be destroyed via fairly straightforward semantics-preserving code transformations. This paper introduces path-based watermarking, a new approach to software watermarking based on the dynamic branching behavior of programs. The advantage of this technique is that error-correcting and tamper-proofing techniques can be used to make path-based watermarks resilient against a wide variety of attacks. Experimental results, using both Java bytecode and IA-32 native code, indicate that even relatively large watermarks can be embedded into programs at modest cost.

A basic computational problem that arises in both the construction and local-search phases of the best heuristics for multiple sequence alignment is that of aligning the columns of two multiple alignments. When the scoring function is the sum-of-pairs objective and induced pairwise alignments are evaluated using linear gap-costs, we call this problem Aligning Alignments. While seemingly a straightforward extension of two-sequence alignment, we prove it is actually NP-complete. As explained in the paper, this provides the first demonstration that minimizing linear gap-costs, in the context of multiple sequence alignment, is inherently hard.We also develop an exact algorithm for Aligning Alignments that is remarkably efficient in practice, both in time and space. Even though the problem is NP-complete, computational experiments on both biological and simulated data show we can compute optimal alignments for all benchmark instances in two standard datasets, and solve very-large random instances with highly-gapped sequences.

One of the key open problems in large-scale DNA sequence assembly is the correct reconstruction of sequences that contain repeats. A long repeat can confound a sequence assembler into falsely overlaying fragments that sample its copies, effectively compressing out the repeat in the reconstructed sequence. We call the task of correcting this compression by separating the overlaid fragments into the distinct copies they sample, the repeat separation problem. We present a rigorous formulation of repeat separation in the general setting without prior knowledge of consensus sequences of repeats or their number of copies. Our formulation decomposes the task into a series of four subproblems, and we design probabilistic tests or combinatorial algorithms that solve each subproblem. The core subproblem separates repeats using the so-called k-median problem in combinatorial optimization, which we solve using integer linear-programming. Experiments with an implementation show we can separate fragments that are overlaid at 10 times the coverage with very few mistakes in a few seconds of computation, even when the sequencing error rate and the error rate between copies are identical. To our knowledge this is the first rigorous and fully general approach to separating repeats that directly addresses the problem.

We present a new method for reconstructing the distances between probes in physical maps of chromosomes constructed by hybridizing pairs of clones under the so-called sampling-without-replacement protocol. In this protocol, which is simple, inexpensive, and has been used to successfully map several organisms, equal-length clones are hybridized against a clone-subset called the probes. The probes are chosen by a sequential process that is designed to generate a pairwise-nonoverlapping subset of the clones. We derive a likelihood function on probe spacings and orders for this protocol under a natural model of hybridization error, and describe how to reconstruct the most likely spacing for a given order under this objective using continuous optimization. The approach is tested on simulated data and real data from chromosome VI of Aspergillus nidulans. On simulated data we recover the true order and close to the true spacing; on the real data, for which the true order and spacing is unknown, we recover a probe order differing significantly from the published one. To our knowledge this is the first practical approach for computing a globally-optimal maximum-likelihood reconstruction of interprobe distances from clone-probe hybridization data.

We introduce a new combinatorial formulation of chromosome physical-mapping by the sampling-without-replacement protocol.In this protocol, which is simple, inexpensive, and has been used to successfully map several organisms, equal-length clones are hybridized against a subset of the clones called probes, which are designed to form a maximal nonoverlapping clone-subset.The output of the protocol is the clone-probe hybridization matrix H.The problem of finding a maximum-likelihood reconstruction of the order of the probes along the chromosome in the presence of false positive and negative hybridization error is equivalent to finding the minimum number of entries of H to change to zeros so that the resulting matrix has at most 2 ones per row, and the consecutive-ones property across rows.This combinatorial problem, which we call 2-Consecutive-Ones Mapping, has a concise integer linear-prograniming formulation, to which we apply techniques from polyhedral combinatorics.The formulation is unique in that it does not explicitly represent the probe permutation, and in contrast to prior linear-programming approaches, the number of variables is small: in practice, linear in the number of clones.We derive a large class of facet-defining inequalities for the 2-consecutive-ones polytope that we call the augmented k- degree inequalities, and we show that the basic k-degree class can be efficiently separated using bipartite matchings.Computational results with an implementation of the resulting branch-and-cut algorithm applied to both simulated and real data from the complete genome of Aspergillus nidulans show that we can solve many problems to provable optimality and find maps of higher quality than previously possible.

A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridiz;c tion experiments between unique probes and clones of chromosome fragments in the presence of error.Alizadeh, Karp, Weisser and Zweig (AKWZ94] first considered a maximumlikelihood model of the problem that is equivalent to finding an o&ring of the probes that minimizes a weighted sum of errors, and developed several effective heuristics.We show that by exploiting information about the endprobes of clones, this model can be formulated as a weighted Betweenness Problem.Thii affords the signiicant advautage of allowing the well-developed tools of integer lmearprogramming aud branch-and-cut algorithms to be brought to bear on physical mapping, enabling us for the first time to solve small mapping instances to optima&y even in the presence of high error.We also show that by combining the optimal solution of many small overlapping Betweenness Problems, one can effectively screen errors from larger instances, and solve the edited instance to optimality as a Hamming-Distance Traveling Salesman Problem.This suggests a new combined approach to physical map construction.

We consider a branch-and-cut approach for solving the multiple sequence alignment problem, which is a central problem in computational biology. We propose a general model for this problem in which arbitrary gap costs are allowed. An interesting aspect of our approach is that the three (exponentially large) classes of natural valid inequalities that we consider turn out to be both facet-defining for the convex hull of integer solutions and separable in polynomial time. Both the proofs that these classes of valid inequalities are facet-defining and the description of the separation algorithms are far from trivial. Experimental results on several benchmark instances show that our method outperforms the best tools developed so far, in that it produces alignments that are better from a biological point of view. A noteworthy outcome of the results is the effectiveness of using branch-and-cut with only a carefully-selected subset of the variables as a heuristic.