MOTIVATION: Protein-protein interaction (PPI) networks provide valuable insights into the function of biological systems. Aligning multiple PPI networks may expose relationships beyond those observable by pairwise comparisons. However, assessing the biological quality of multiple network alignments is a challenging problem. RESULTS: We propose two new measures to evaluate the quality of multiple network alignments using functional information from Gene Ontology (GO) terms. When aligning multiple real PPI networks across species, we observe that both measures are highly correlated with objective quality indicators, such as common orthologs. Additionally, our measures strongly correlate with an alignment's ability to predict novel GO annotations, which is a unique advantage over existing GO-based measures. AVAILABILITY AND IMPLEMENTATION: The scripts and the links to the raw and alignment data can be accessed at https://github.com/kimiayazdani/GO_Measures.git.

All life on Earth is related, so that some molecular interactions are common across almost all living cells, with the number of common interactions increasing as we look at more closely related species. In particular, we expect the protein–protein interaction (PPI) networks of closely related species to share high levels of similarity. This similarity may facilitate the transfer of functional knowledge between model species and human. Multiple network alignment is the process of uncovering the connection similarity between three or more networks simultaneously. Existing algorithms for multiple network alignment rely on sequence similarities to help drive the alignments, and no comprehensive study has been done to determine the most effective ways to utilize network connectivity—network topology—to drive multiple network alignment. Here, we devise and empirically test the efficacy of several measures of topological similarity between three or more networks. To evolve the alignments toward optimal, we use simulated annealing as the search algorithm since it is agnostic to the objective being optimized. We test the measures both on the partially synthetic and highly similar PPI networks from the integrated interaction database, as well as on real PPI networks from a recent BioGRID release.

The structure of protein-protein interaction (PPI) networks has been studied for over a decade. Many theoretical models have been proposed to model PPI network structure, but continuing noise and incompleteness in these networks make conclusions about their structure difficult. Using newer, larger networks from Sept. 2018 BioGRID and Jan. 2019 IID, we show the joint distribution of degree products and common neighbors has a greater impact on PPI edge connectivity than their individual distributions, and introduce two new models (CN and STICKY-CN) for PPI networks employing these features. Since graphlet-based measures are believed to be among the most discerning and sensitive network comparison tools available, we assess their overall global and local fits to PPI networks using Graphlet Kernel (GK). We fit 10 theoretical models to nine BioGRID networks and twelve Integrated Interactive Database (IID) networks and find: (1) STICKY and STICKY-CN are the overall globally best fitting models according to GK, (2) Hyperbolic Geometric Graph model is a better fit than any STICKY-based model on 4 species, (3) though STICKY-CN provides a better local fit than the STICKY model, the CN model provides the greatest local fit over most species. We conclude that the inclusion of CN into STICKY-CN makes it the best overall fit for PPI networks as it is a good fit locally and globally.

SUMMARY: BLAST creates local sequence alignments by first building a database of small k-letter sub-sequences called k-mers. Identical k-mers from different regions provide 'seeds' for longer local alignments. This seed-and-extend heuristic makes BLAST extremely fast and has led to its almost exclusive use despite the existence of more accurate, but slower, algorithms. In this paper, we introduce the Basic Local Alignment for Networks Tool (BLANT). BLANT is the analog of BLAST, but for networks: given an input graph, it samples small, induced, k-node sub-graphs called k-graphlets. Graphlets have been used to classify networks, quantify structure, align networks both locally and globally, identify topology-function relationships and build taxonomic trees without the use of sequences. Given an input network, BLANT produces millions of graphlet samples in seconds-orders of magnitude faster than existing methods. BLANT offers sampled graphlets in various forms: distributions of graphlets or their orbits; graphlet degree or graphlet orbit degree vectors, the latter being compatible with ORCA; or an index to be used as the basis for seed-and-extend local alignments. We demonstrate BLANT's usefelness by using its indexing mode to find functional similarity between yeast and human PPI networks. AVAILABILITY AND IMPLEMENTATION: BLANT is written in C and is available at https://github.com/waynebhayes/BLANT/releases. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Motivation: Gene Ontology (GO) terms are frequently used to score alignments between protein-protein interaction (PPI) networks. Methods exist to measure GO similarity between proteins in isolation, but proteins in a network alignment are not isolated: each pairing is dependent on every other via the alignment itself. Existing measures fail to take into account the frequency of GO terms across networks, instead imposing arbitrary rules on when to allow GO terms. Results: Here we develop NetGO, a new measure that naturally weighs infrequent, informative GO terms more heavily than frequent, less informative GO terms, without arbitrary cutoffs, instead downweighting GO terms according to their frequency in the networks being aligned. This is a global measure applicable only to alignments, independent of pairwise GO measures, in the same sense that the edge-based EC or S3 scores are global measures of topological similarity independent of pairwise topological similarities. We demonstrate the superiority of NetGO in alignments of predetermined quality and show that NetGO correlates with alignment quality better than any existing GO-based alignment measures. We also demonstrate that NetGO provides a measure of taxonomic similarity between species, consistent with existing taxonomic measuresa feature not shared with existing GObased network alignment measures. Finally, we re-score alignments produced by almost a dozen aligners from a previous study and show that NetGO does a better job at separating good alignments from bad ones. Availability and implementation: Available as part of SANA. Contact: [email protected]. Supplementary information: Supplementary data are available at Bioinformatics online.

SUMMARY: Every alignment algorithm consists of two orthogonal components: an objective function M measuring the quality of an alignment, and a search algorithm that explores the space of alignments looking for ones scoring well according to M . We introduce a new search algorithm called SANA (Simulated Annealing Network Aligner) and apply it to protein-protein interaction networks using S 3 as the topological measure. Compared against 12 recent algorithms, SANA produces 5-10 times as many correct node pairings as the others when the correct answer is known. We expose an anti-correlation in many existing aligners between their ability to produce good topological vs. functional similarity scores, whereas SANA usually outscores other methods in both measures. If given the perfect objective function encoding the identity mapping, SANA quickly converges to the perfect solution while many other algorithms falter. We observe that when aligning networks with a known mapping and optimizing only S 3 , SANA creates alignments that are not perfect and yet whose S 3 scores match that of the perfect alignment. We call this phenomenon saturation of the topological score . Saturation implies that a measure's correlation with alignment correctness falters before the perfect alignment is reached. This, combined with SANA's ability to produce the perfect alignment if given the perfect objective function, suggests that better objective functions may lead to dramatically better alignments. We conclude that future work should focus on finding better objective functions, and offer SANA as the search algorithm of choice. AVAILABILITY AND IMPLEMENTATION: Software available at http://sana.ics.uci.edu . CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Borders are important as they demarcate developing tissue into distinct functional units. A key challenge is the discovery of mechanisms that can convert morphogen gradients into tissue borders. While mechanisms that produce ultrasensitive cellular responses provide a solution, how extracellular morphogens drive such mechanisms remains poorly understood. Here, we show how Bone Morphogenetic Protein (BMP) and Fibroblast Growth Factor (FGF) pathways interact to generate ultrasensitivity and borders in the dorsal telencephalon. BMP and FGF signaling manipulations in explants produced border defects suggestive of cross inhibition within single cells, which was confirmed in dissociated cultures. Using mathematical modeling, we designed experiments that ruled out alternative cross inhibition mechanisms and identified a cross-inhibitory positive feedback (CIPF) mechanism, or "toggle switch", which acts upstream of transcriptional targets in dorsal telencephalic cells. CIPF explained several cellular phenomena important for border formation such as threshold tuning, ultrasensitivity, and hysteresis. CIPF explicitly links graded morphogen signaling in the telencephalon to switch-like cellular responses and has the ability to form multiple borders and scale pattern to size. These benefits may apply to other developmental systems.

MOTIVATION: Large amounts of biological network data exist for many species. Analogous to sequence comparison, network comparison aims to provide biological insight. Graphlet-based methods are proving to be useful in this respect. Recently some doubt has arisen concerning the applicability of graphlet-based measures to low edge density networks-in particular that the methods are 'unstable'-and further that no existing network model matches the structure found in real biological networks. RESULTS: We demonstrate that it is the model networks themselves that are 'unstable' at low edge density and that graphlet-based measures correctly reflect this instability. Furthermore, while model network topology is unstable at low edge density, biological network topology is stable. In particular, one must distinguish between average density and local density. While model networks of low average edge densities also have low local edge density, that is not the case with protein-protein interaction (PPI) networks: real PPI networks have low average edge density, but high local edge densities, and hence, they (and thus graphlet-based measures) are stable on these networks. Finally, we use a recently devised non-parametric statistical test to demonstrate that PPI networks of many species are well-fit by several models not previously tested. In addition, we model several viral PPI networks for the first time and demonstrate an exceptionally good fit between the data and theoretical models.

We describe a system that builds quantitative structural descriptions of spiral galaxies. This enables translation of sky survey images into data needed to help address fundamental astrophysical questions such as the origin of spiral structure - a phenomenon that has eluded full theoretical description despite 150 years of study. The difficulty of automated measurement is underscored by the fact that, to date, only manually-guided efforts (such as the citizen science project Galaxy Zoo) have been able to extract structural information about spiral galaxies. An automated approach is needed to eliminate measurement subjectivity and handle the otherwise-overwhelming image quantities (up to billions of images) from near-future surveys. Our approach automatically describes spiral galaxy structure as a set of arcs fit to pixel clusters, precisely characterizing spiral arm segment arrangement while retaining the flexibility needed to accommodate the observed wide variety of spiral galaxy structure. The largest existing quantitative measurements were manually-guided and encompassed fewer than 100 galaxies, while we have already applied our method to nearly 30,000 galaxies. Our output is consistent with previous information, both quantitatively over small existing samples, and qualitatively with human classifications.

BACKGROUND: Recent advancements in experimental biotechnology have produced large amounts of protein-protein interaction (PPI) data. The topology of PPI networks is believed to have a strong link to their function. Hence, the abundance of PPI data for many organisms stimulates the development of computational techniques for the modeling, comparison, alignment, and clustering of networks. In addition, finding representative models for PPI networks will improve our understanding of the cell just as a model of gravity has helped us understand planetary motion. To decide if a model is representative, we need quantitative comparisons of model networks to real ones. However, exact network comparison is computationally intractable and therefore several heuristics have been used instead. Some of these heuristics are easily computable "network properties," such as the degree distribution, or the clustering coefficient. An important special case of network comparison is the network alignment problem. Analogous to sequence alignment, this problem asks to find the "best" mapping between regions in two networks. It is expected that network alignment might have as strong an impact on our understanding of biology as sequence alignment has had. Topology-based clustering of nodes in PPI networks is another example of an important network analysis problem that can uncover relationships between interaction patterns and phenotype. RESULTS: We introduce the GraphCrunch 2 software tool, which addresses these problems. It is a significant extension of GraphCrunch which implements the most popular random network models and compares them with the data networks with respect to many network properties. Also, GraphCrunch 2 implements the GRAph ALigner algorithm ("GRAAL") for purely topological network alignment. GRAAL can align any pair of networks and exposes large, dense, contiguous regions of topological and functional similarities far larger than any other existing tool. Finally, GraphCruch 2 implements an algorithm for clustering nodes within a network based solely on their topological similarities. Using GraphCrunch 2, we demonstrate that eukaryotic and viral PPI networks may belong to different graph model families and show that topology-based clustering can reveal important functional similarities between proteins within yeast and human PPI networks. CONCLUSIONS: GraphCrunch 2 is a software tool that implements the latest research on biological network analysis. It parallelizes computationally intensive tasks to fully utilize the potential of modern multi-core CPUs. It is open-source and freely available for research use. It runs under the Windows and Linux platforms.

We present a novel, online algorithm for exact summation of a stream of floating-point numbers. By “online” we mean that the algorithm needs to see only one input at a time, and can take an arbitrary length input stream of such inputs while requiring only constant memory. By “exact” we mean that the sum of the internal array of our algorithm is exactly equal to the sum of all the inputs, and the returned result is the correctly-rounded sum. The proof of correctness is valid for all inputs (including nonnormalized numbers but modulo intermediate overflow), and is independent of the number of summands or the condition number of the sum. The algorithm asymptotically needs only 5 FLOPs per summand, and due to instruction-level parallelism runs only about 2--3 times slower than the obvious, fast-but-dumb “ordinary recursive summation” loop when the number of summands is greater than 10,000. Thus, to our knowledge, it is the fastest, most accurate, and most memory efficient among known algorithms. Indeed, it is difficult to see how a faster algorithm or one requiring significantly fewer FLOPs could exist without hardware improvements. An application for a large number of summands is provided.

The quest for reliable integration of initial value problems (IVPs) for ordinary differential equations (ODEs) is a long-standing problem in numerical analysis. At one end of the reliability spectrum are fixed stepsize methods implemented using standard floating point, where the onus lies entirely with the user to ensure the stepsize chosen is adequate for the desired accuracy. At the other end of the reliability spectrum are rigorous interval-based methods, that can provide provably correct bounds on the error of a numerical solution. This rigour comes at a price, however: interval methods are generally two to three orders of magnitude more expensive than fixed stepsize floating-point methods. Along the spectrum between these two extremes lie various methods of different expense that estimate and control some measure of the local errors and adjust the stepsize accordingly. In this article, we continue previous investigations into a class of interpolants for use in Runge-Kutta methods that have a defect function whose qualitative behavior is asymptotically independent of the problem being integrated. In particular the point, in a step, where the maximum defect occurs as h → 0 is known a priori. This property allows the defect to be monitored and controlled in an efficient and robust manner even for modestly large stepsizes. Our interpolants also have a defect with the highest possible order given the constraints imposed by the order of the underlying discrete formula. We demonstrate the approach on three Runge-Kutta methods of orders 5, 6, and 8, and provide Fortran and preliminary Matlab interfaces to these three new integrators. We also consider how sensitive such methods are to roundoff errors. Numerical results for four problems on a range of accuracy requests are presented.

MOTIVATION: Comparison of nucleic acid and protein sequences is a fundamental tool of modern bioinformatics. A dominant method of such string matching is the 'seed-and-extend' approach, in which occurrences of short subsequences called 'seeds' are used to search for potentially longer matches in a large database of sequences. Each such potential match is then checked to see if it extends beyond the seed. To be effective, the seed-and-extend approach needs to catalogue seeds from virtually every substring in the database of search strings. Projects such as mammalian genome assemblies and large-scale protein matching, however, have such large sequence databases that the resulting list of seeds cannot be stored in RAM on a single computer. This significantly slows the matching process. RESULTS: We present a simple and elegant method in which only a small fraction of seeds, called 'minimizers', needs to be stored. Using minimizers can speed up string-matching computations by a large factor while missing only a small fraction of the matches found using all seeds.

It is well known that the Ethernet medium access control protocol can cause significant short-term unfairness through a mechanism known as the Capture Effect, and that this unfairness condition is worst in heavily loaded Ethernets with a small number of active nodes. Recently, Ramakrishnan and Yang proposed Capture Avoidance Binary Exponential Backoff (CABEB) to provide 1-packet-per-turn round robin service in the important special case of a 2-node collision domain. In this paper, we introduce an equal time round-robin scheme, in which only one node needs to be modified. In our scheme, the modified node maintains a local copy of the attempts counter of the other node. It uses this information to trigger switching its medium access policy between the two extremes of aggressively persistent and completely passive. As a result, the modified node can control the actions of the other node in such a way that both enjoy fair, low delay, round-robin access to the shared channel. 1 Introductio...