Growing Bayesian network models of gene networks from seed genes

MOTIVATION: For the last few years, Bayesian networks (BNs) have received increasing attention from the computational biology community as models of gene networks, though learning them from gene-expression data is problematic. Most gene-expression databases contain measurements for thousands of genes, but the existing algorithms for learning BNs from data do not scale to such high-dimensional databases. This means that the user has to decide in advance which genes are included in the learning process, typically no more than a few hundreds, and which genes are excluded from it. This is not a trivial decision. We propose an alternative approach to overcome this problem. RESULTS: We propose a new algorithm for learning BN models of gene networks from gene-expression data. Our algorithm receives a seed gene S and a positive integer R from the user, and returns a BN for the genes that depend on S such that less than R other genes mediate the dependency. Our algorithm grows the BN, which initially only contains S, by repeating the following step R + 1 times and, then, pruning some genes; find the parents and children of all the genes in the BN and add them to it. Intuitively, our algorithm provides the user with a window of radius R around S to look at the BN model of a gene network without having to exclude any gene in advance. We prove that our algorithm is correct under the faithfulness assumption. We evaluate our algorithm on simulated and biological data (Rosetta compendium) with satisfactory results.     

Seeded tree alignment

The optimal transformation of one tree into another by means of elementary edit operations is an important algorithmic problem that has several interesting applications to computational biology. Here we introduce a constrained form of this problem in which a partial mapping of a set of nodes (the "seeds") in one tree to a corresponding set of nodes in the other tree is given, and present efficient algorithms for both ordered and unordered trees. Whereas ordered tree matching based on seeded nodes has applications in pattern matching of RNA structures, unordered tree matching based on seeded nodes has applications in co-speciation and phylogeny reconciliation. The latter involves the solution of the planar tanglegram layout problem, for which a polynomial-time algorithm is given here.     

Determination of optimal vaccination strategies using an orbital stability threshold from periodically driven systems

We analyse a periodically driven SIR epidemic model for childhood related diseases, where the contact rate and vaccination rate parameters are considered periodic. The aim is to define optimal vaccination strategies for control of childhood related infections. Stability analysis of the uninfected solution is the tool for setting up the control function. The optimal solutions are sought within a set of susceptible population profiles. Our analysis reveals that periodic vaccination strategy hardly contributes to the stability of the uninfected solution if the human residence time (life span) is much larger than the contact rate period. However, if the human residence time and the contact rate periods match, we observe some positive effect of periodic vaccination. Such a vaccination strategy would be useful in the developing world, where human life spans are shorter, or basically in the case of vaccination of livestock or small animals whose life-spans are relatively shorter.     

Fast optimal genome tiling with applications to microarray design and homology search.

In this paper, we consider several variations of the following basic tiling problem: given a sequence of real numbers with two size-bound parameters, we want to find a set of tiles of maximum total weight such that each tiles satisfies the size bounds. A solution to this problem is important to a number of computational biology applications such as selecting genomic DNA fragments for PCR-based amplicon microarrays and performing homology searches with long sequence queries. Our goal is to design efficient algorithms with linear or near-linear time and space in the normal range of parameter values for these problems. For this purpose, we first discuss the solution to a basic online interval maximum problem via a sliding-window approach and show how to use this solution in a nontrivial manner for many of the tiling problems introduced. We also discuss NP-hardness results and approximation algorithms for generalizing our basic tiling problem to higher dimensions. Finally, computational results from applying our tiling algorithms to genomic sequences of five model eukaryotes are reported.     

ESPRIT-Tree: hierarchical clustering analysis of millions of 16S rRNA pyrosequences in quasilinear computational time

Taxonomy-independent analysis plays an essential role in microbial community analysis. Hierarchical clustering is one of the most widely employed approaches to finding operational taxonomic units, the basis for many downstream analyses. Most existing algorithms have quadratic space and computational complexities, and thus can be used only for small or medium-scale problems. We propose a new online learning-based algorithm that simultaneously addresses the space and computational issues of prior work. The basic idea is to partition a sequence space into a set of subspaces using a partition tree constructed using a pseudometric, then recursively refine a clustering structure in these subspaces. The technique relies on new methods for fast closest-pair searching and efficient dynamic insertion and deletion of tree nodes. To avoid exhaustive computation of pairwise distances between clusters, we represent each cluster of sequences as a probabilistic sequence, and define a set of operations to align these probabilistic sequences and compute genetic distances between them. We present analyses of space and computational complexity, and demonstrate the effectiveness of our new algorithm using a human gut microbiota data set with over one million sequences. The new algorithm exhibits a quasilinear time and space complexity comparable to greedy heuristic clustering algorithms, while achieving a similar accuracy to the standard hierarchical clustering algorithm.     

CGBayesNets: Conditional Gaussian Bayesian Network Learning and Inference with Mixed Discrete and Continuous Data

Bayesian Networks (BN) have been a popular predictive modeling formalism in bioinformatics, but their application in modern genomics has been slowed by an inability to cleanly handle domains with mixed discrete and continuous variables. Existing free BN software packages either discretize continuous variables, which can lead to information loss, or do not include inference routines, which makes prediction with the BN impossible. We present CGBayesNets, a BN package focused around prediction of a clinical phenotype from mixed discrete and continuous variables, which fills these gaps. CGBayesNets implements Bayesian likelihood and inference algorithms for the conditional Gaussian Bayesian network (CGBNs) formalism, one appropriate for predicting an outcome of interest from, e.g., multimodal genomic data. We provide four different network learning algorithms, each making a different tradeoff between computational cost and network likelihood. CGBayesNets provides a full suite of functions for model exploration and verification, including cross validation, bootstrapping, and AUC manipulation. We highlight several results obtained previously with CGBayesNets, including predictive models of wood properties from tree genomics, leukemia subtype classification from mixed genomic data, and robust prediction of intensive care unit mortality outcomes from metabolomic profiles. We also provide detailed example analysis on public metabolomic and gene expression datasets. CGBayesNets is implemented in MATLAB and available as MATLAB source code, under an Open Source license and anonymous download at http://www.cgbayesnets.com.

This is a PLOS Computational Biology Software Article

     

Accelerated likelihood surface exploration: the likelihood ratchet

The existence of multiple likelihood maxima necessitates algorithms that explore a large part of the tree space. However, because of computational constraints, stepwise addition-based tree-searching methods do not allow for this exploration in reasonable time. Here, I present an algorithm that increases the speed at which the likelihood landscape can be explored. The iterative algorithm combines the computational speed of distance-based tree construction methods to arrive at approximations of the global optimum with the accuracy of optimality criterion based branch-swapping methods to improve on the result of the starting tree. The algorithm moves between local optima by iteratively perturbing the tree landscape through a process of reweighting randomly drawn samples of the underlying sequence data set. Tests on simulated and real data sets demonstrated that the optimal solution obtained using stepwise addition-based heuristic searches was found faster using the algorithm presented here. Tests on a previously published data set that established the presence of tree islands under maximum likelihood demonstrated that the algorithm identifies the same tree islands in a shorter amount of time than that needed using stepwise addition. The algorithm can be readily applied using standard software for phylogenetic inference.     

Using Grid technology for computationally intensive applied bioinformatics analyses

For several applications and algorithms used in applied bioinformatics, a bottle neck in terms of computational time may arise when scaled up to facilitate analyses of large datasets and databases. Re-codification, algorithm modification or sacrifices in sensitivity and accuracy may be necessary to accommodate for limited computational capacity of single work stations. Grid computing offers an alternative model for solving massive computational problems by parallel execution of existing algorithms and software implementations. We present the implementation of a Grid-aware model for solving computationally intensive bioinformatic analyses exemplified by a blastp sliding window algorithm for whole proteome sequence similarity analysis, and evaluate the performance in comparison with a local cluster and a single workstation. Our strategy involves temporary installations of the BLAST executable and databases on remote nodes at submission, accommodating for dynamic Grid environments as it avoids the need of predefined runtime environments (preinstalled software and databases at specific Grid-nodes). Importantly, the implementation is generic where the BLAST executable can be replaced by other software tools to facilitate analyses suitable for parallelisation. This model should be of general interest in applied bioinformatics. Scripts and procedures are freely available from the authors.     

Influence of prior knowledge in constraint-based learning of gene regulatory networks

Constraint-based structure learning algorithms generally perform well on sparse graphs. Although sparsity is not uncommon, there are some domains where the underlying graph can have some dense regions; one of these domains is gene regulatory networks, which is the main motivation to undertake the study described in this paper. We propose a new constraint-based algorithm that can both increase the quality of output and decrease the computational requirements for learning the structure of gene regulatory networks. The algorithm is based on and extends the PC algorithm. Two different types of information are derived from the prior knowledge; one is the probability of existence of edges, and the other is the nodes that seem to be dependent on a large number of nodes compared to other nodes in the graph. Also a new method based on Gene Ontology for gene regulatory network validation is proposed. We demonstrate the applicability and effectiveness of the proposed algorithms on both synthetic and real data sets.     

Reconstruction of ancestral genomic sequences using likelihood.

A challenging task in computational biology is the reconstruction of genomic sequences of extinct ancestors, given the phylogenetic tree and the sequences at the leafs. This task is best solved by calculating the most likely estimate of the ancestral sequences, along with the most likely edge lengths. We deal with this problem and also the variant in which the phylogenetic tree in addition to the ancestral sequences need to be estimated. The latter problem is known to be NP-hard, while the computational complexity of the former is unknown. Currently, all algorithms for solving these problems are heuristics without performance guarantees. The biological importance of these problems calls for developing better algorithms with guarantees of finding either optimal or approximate solutions.We develop approximation, fix parameter tractable (FPT), and fast heuristic algorithms for two variants of the problem; when the phylogenetic tree is known and when it is unknown. The approximation algorithm guarantees a solution with a log-likelihood ratio of 2 relative to the optimal solution. The FPT has a running time which is polynomial in the length of the sequences and exponential in the number of taxa. This makes it useful for calculating the optimal solution for small trees. Moreover, we combine the approximation algorithm and the FPT into an algorithm with arbitrary good approximation guarantee (PTAS). We tested our algorithms on both synthetic and biological data. In particular, we used the FPT for computing the most likely ancestral mitochondrial genomes of hominidae (the great apes), thereby answering an interesting biological question. Moreover, we show how the approximation algorithms find good solutions for reconstructing the ancestral genomes for a set of lentiviruses (relatives of HIV). Supplementary material of this work is available at www.nada.kth.se/~isaac/publications/aml/aml.html.     

Computational assignment of protein backbone NMR peaks by efficient bounding and filtering

NMR resonance assignment is one of the key steps in solving an NMR protein structure. The assignment process links resonance peaks to individual residues of the target protein sequence, providing the prerequisite for establishing intra- and inter-residue spatial relationships between atoms. The assignment process is tedious and time-consuming, which could take many weeks. Though there exist a number of computer programs to assist the assignment process, many NMR labs are still doing the assignments manually to ensure quality. This paper presents a new computational method based on the combination of a suite of algorithms for automating the assignment process, particularly the process of backbone resonance peak assignment. We formulate the assignment problem as a constrained weighted bipartite matching problem. While the problem, in the most general situation, is NP-hard, we present an efficient solution based on a branch-and-bound algorithm with effective bounding techniques using two recently introduced approximation algorithms. We also devise a greedy filtering algorithm for reducing the search space. Our experimental results on 70 instances of (pseudo) real NMR data derived from 14 proteins demonstrate that the new solution runs much faster than a recently introduced (exhaustive) two-layer algorithm and recovers more correct peak assignments than the two-layer algorithm. Our result demonstrates that integrating different algorithms can achieve a good tradeoff between backbone assignment accuracy and computation time.     

The k partition-distance problem

Many applications of data partitioning (clustering) have been well studied in bioinformatics. Consider, for instance, a set N of organisms (elements) based on DNA marker data. A partition divides all elements in N into two or more disjoint clusters that cover all elements, where a cluster contains a non-empty subset of N. Different partitioning algorithms may produce different partitions. To compute the distance and find the consensus partition (also called consensus clustering) between two or more partitions are important and interesting problems that arise frequently in bioinformatics and data mining, in which different distance functions may be considered in different partition algorithms. In this article, we discuss the k partition-distance problem. Given a set of elements N with k partitions of N, the k partition-distance problem is to delete the minimum number of elements from each partition such that all remaining partitions become identical. This problem is NP-complete for general k?>?2 partitions, and no algorithms are known at present. We design the first known heuristic and approximation algorithms with performance ratios 2 to solve the k partition-distance problem in O(k?·?ρ?·?|N|) time, where ρ is the maximum number of clusters of these k partitions and |N| is the number of elements in N. We also present the first known exact algorithm in O(??·?2(?)·k(2)?·?|N|(2)) time, where ? is the partition-distance of the optimal solution for this problem. Performances of our exact and approximation algorithms in testing the random data with actual sets of organisms based on DNA markers are compared and discussed. Experimental results reveal that our algorithms can improve the computational speed of the exact algorithm for the two partition-distance problem in practice if the maximum number of elements per cluster is less than ρ. From both theoretical and computational points of view, our solutions are at most twice the partition-distance of the optimal solution. A website offering the interactive service of solving the k partition-distance problem using our and previous algorithms is available (see http://mail.tmue.edu.tw/~yhchen/KPDP.html).     

Algorithms for the design of maximum hydropathic complementarity molecules

In this article, we address the problem of designing a string with optimal complementarity properties with respect to another given string according to a given criterion. The motivation comes from a drug design application, in which the complementarity between two sequences (proteins) is measured according to the values of the hydropathic coefficients associated with the sequence elements (amino acids). We present heuristic and exact optimization algorithms, and we report on some computational experiments on amino peptides taken from Semaphorin and human Interleukin-1β, which have already been investigated in the literature using heuristic algorithms. With our techniques, we proved the optimality of a known solution for Semaphorin-3A, and we discovered several other optimal and near-optimal solutions in a short computing time; we also found in fractions of a second an optimal solution for human interleukin-1β, whose complementary value is one order of magnitude better than previously known ones. The source code of a prototype C++ implementation of our algorithms is freely available for noncommercial use on the web. As a main result, we showed that in this context mathematical programming methods are more successful than heuristics, such as simulated annealing. Our algorithm unfolds its potential, especially when different measures could be used for scoring peptides, and is able to provide not only a single optimal solution, but a ranking of provable good ones; this ranking can then be used by biologists as a starting basis for further refinements, simulations, or in vitro experiments.     

A Family of Algorithms for Computing Consensus about Node State from Network Data

Biological and social networks are composed of heterogeneous nodes that contribute differentially to network structure and function. A number of algorithms have been developed to measure this variation. These algorithms have proven useful for applications that require assigning scores to individual nodes–from ranking websites to determining critical species in ecosystems–yet the mechanistic basis for why they produce good rankings remains poorly understood. We show that a unifying property of these algorithms is that they quantify consensus in the network about a node''s state or capacity to perform a function. The algorithms capture consensus by either taking into account the number of a target node''s direct connections, and, when the edges are weighted, the uniformity of its weighted in-degree distribution (breadth), or by measuring net flow into a target node (depth). Using data from communication, social, and biological networks we find that that how an algorithm measures consensus–through breadth or depth– impacts its ability to correctly score nodes. We also observe variation in sensitivity to source biases in interaction/adjacency matrices: errors arising from systematic error at the node level or direct manipulation of network connectivity by nodes. Our results indicate that the breadth algorithms, which are derived from information theory, correctly score nodes (assessed using independent data) and are robust to errors. However, in cases where nodes “form opinions” about other nodes using indirect information, like reputation, depth algorithms, like Eigenvector Centrality, are required. One caveat is that Eigenvector Centrality is not robust to error unless the network is transitive or assortative. In these cases the network structure allows the depth algorithms to effectively capture breadth as well as depth. Finally, we discuss the algorithms'' cognitive and computational demands. This is an important consideration in systems in which individuals use the collective opinions of others to make decisions.     

Identification of copy number variants from exome sequence data

Background

With advances in next generation sequencing technologies and genomic capture techniques, exome sequencing has become a cost-effective approach for mutation detection in genetic diseases. However, computational prediction of copy number variants (CNVs) from exome sequence data is a challenging task. Whilst numerous programs are available, they have different sensitivities, and have low sensitivity to detect smaller CNVs (1–4 exons). Additionally, exonic CNV discovery using standard aCGH has limitations due to the low probe density over exonic regions. The goal of our study was to develop a protocol to detect exonic CNVs (including shorter CNVs that cover 1–4 exons), combining computational prediction algorithms and a high-resolution custom CGH array.

Results

We used six published CNV prediction programs (ExomeCNV, CONTRA, ExomeCopy, ExomeDepth, CoNIFER, XHMM) and an in-house modification to ExomeCopy and ExomeDepth (ExCopyDepth) for computational CNV prediction on 30 exomes from the 1000 genomes project and 9 exomes from primary immunodeficiency patients. CNV predictions were tested using a custom CGH array designed to capture all exons (exaCGH). After this validation, we next evaluated the computational prediction of shorter CNVs. ExomeCopy and the in-house modified algorithm, ExCopyDepth, showed the highest capability in detecting shorter CNVs. Finally, the performance of each computational program was assessed by calculating the sensitivity and false positive rate.

Conclusions

In this paper, we assessed the ability of 6 computational programs to predict CNVs, focussing on short (1–4 exon) CNVs. We also tested these predictions using a custom array targeting exons. Based on these results, we propose a protocol to identify and confirm shorter exonic CNVs combining computational prediction algorithms and custom aCGH experiments.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2164-15-661) contains supplementary material, which is available to authorized users.     

Parameter estimation for stiff equations of biosystems using radial basis function networks

Background  

The modeling of dynamic systems requires estimating kinetic parameters from experimentally measured time-courses. Conventional global optimization methods used for parameter estimation, e.g. genetic algorithms (GA), consume enormous computational time because they require iterative numerical integrations for differential equations. When the target model is stiff, the computational time for reaching a solution increases further.     

Detecting controlling nodes of boolean regulatory networks

Boolean models of regulatory networks are assumed to be tolerant to perturbations. That qualitatively implies that each function can only depend on a few nodes. Biologically motivated constraints further show that functions found in Boolean regulatory networks belong to certain classes of functions, for example, the unate functions. It turns out that these classes have specific properties in the Fourier domain. That motivates us to study the problem of detecting controlling nodes in classes of Boolean networks using spectral techniques. We consider networks with unbalanced functions and functions of an average sensitivity less than ?k, where k is the number of controlling variables for a function. Further, we consider the class of 1-low networks which include unate networks, linear threshold networks, and networks with nested canalyzing functions. We show that the application of spectral learning algorithms leads to both better time and sample complexity for the detection of controlling nodes compared with algorithms based on exhaustive search. For a particular algorithm, we state analytical upper bounds on the number of samples needed to find the controlling nodes of the Boolean functions. Further, improved algorithms for detecting controlling nodes in large-scale unate networks are given and numerically studied.     

On divide-and-conquer strategies for parsimony analysis of large data sets: Rec-I-DCM3 versus TNT

Roshan et al. recently described a "divide-and-conquer" technique for parsimony analysis of large data sets, Rec-I-DCM3, and stated that it compares very favorably to results using the program TNT. Their technique is based on selecting subsets of taxa to create reduced data sets or subproblems, finding most-parsimonious trees for each reduced data set, recombining all parts together, and then performing global TBR swapping on the combined tree. Here, we contrast this approach to sectorial searches, a divide-and-conquer algorithm implemented in TNT. This algorithm also uses a guide tree to create subproblems, with the first-pass state sets of the nodes that join the selected sectors with the rest of the topology; this allows exact length calculations for the entire topology (that is, any solution N steps shorter than the original, for the reduced subproblem, must also be N steps shorter for the entire topology). We show here that, for sectors of similar size analyzed with the same search algorithms, subdividing data sets with sectorial searches produces better results than subdividing with Rec-I-DCM3. Roshan et al.'s claim that Rec-I-DCM3 outperforms the techniques in TNT was caused by a poor experimental design and algorithmic settings used for the runs in TNT. In particular, for finding trees at or very close to the minimum known length of the analyzed data sets, TNT clearly outperforms Rec-I-DCM3. Finally, we show that the performance of Rec-I-DCM3 is bound by the efficiency of TBR implementation for the complete data set, as this method behaves (after some number of iterations) as a technique for cyclic perturbations and improvements more than as a divide-and-conquer strategy.     

Implantable cardioverter defibrillator algorithms: status review in terms of computational cost.

In recent decades, implantable cardioverter defibrillators (ICDs) have improved substantially, becoming the treatment of choice for patients at high risk of life-threatening arrhythmias. Nevertheless, inappropriate shock therapy for non-ventricular arrhythmias is still a problem. Extending the ICD battery lifetime demands very low power consumption, which is obtained at very low microprocessor clock frequencies. Currently, some high-performance algorithms remain beyond the computational capabilities of ICDs. Future ICDs with higher computing power will permit the implementation of computationally intensive algorithms, enhancing the discrimination performance and preventing inappropriate shock therapies. An ICD algorithm status review is presented from the point of view of signal processing techniques and their computational costs. Several examples of discrimination algorithms with increasing computational cost are analyzed. Whereas some of them are already used in commercial ICDs, other algorithms cannot be implemented yet in current ICDs. A solution based on dynamic adaptation of microprocessor power consumption to meet algorithm computational requirements is proposed. This solution allows implementation of complex discrimination algorithms in ICDs without significantly increasing the power consumption.     

Suppression of experimental allergic encephalomyelitis in rats by mercuric chloride

Brown-Norway (BN) rats are uniquely susceptible to development of autoimmune phenomena and enlargement of lymph nodes and spleen after repeated injections of mercuric chloride. Despite its ability to produce autoimmunity, HgCl2 inhibited the development in BN rats of experimental allergic encephalomyelitis (EAE), another autoimmune process. The inhibition by mercury was probably due to lack of the normal absorption and granulomatous reaction to the EAE inoculum in the enlarged lymph nodes draining the inoculation site. Lewis rats did not develop enlarged nodes from HgCl2 treatment. Lewis lymph nodes absorbed the EAE inoculum abundantly and developed an extensive granulomatous reaction despite the mercury treatment, and there was only a slight inhibition of EAE. Therefore, the ability of HgCl2 to produce lymphadenopathy in BN rats may be responsible for the inability of these rats to absorb the inoculated antigen. The mercury-induced failure of absorption was manifested as an inhibition of EAE in BN rats.