MOTIVATION: Genome sequencing technologies reveal a huge amount of genomic sequences. Neural network-based methods can be prime candidates for retrieving insights from these sequences because of their applicability to large and diverse datasets. However, the highly variable lengths of genome sequences severely impair the presentation of sequences as input to the neural network. Genetic variations further complicate tasks that involve sequence comparison or alignment. RESULTS: Inspired by the theory and applications of "spaced seeds," we propose a graph representation of genome sequences called "gapped pattern graph." These graphs can be transformed through a Graph Convolutional Network to form lower-dimensional embeddings for downstream tasks. On the basis of the gapped pattern graphs, we implemented a neural network model and demonstrated its performance on diverse tasks involving microbe and mammalian genome data. Our method consistently outperformed all the other state-of-the-art methods across various metrics on all tasks, especially for the sequences with limited homology to the training data. In addition, our model was able to identify distinct gapped pattern signatures from the sequences. AVAILABILITY AND IMPLEMENTATION: The framework is available at https://github.com/deepomicslab/GCNFrame.

BACKGROUND: Distance functions are fundamental for evaluating the differences between gene expression profiles. Such a function would output a low value if the profiles are strongly correlated-either negatively or positively-and vice versa. One popular distance function is the absolute correlation distance, [Formula: see text], where [Formula: see text] is similarity measure, such as Pearson or Spearman correlation. However, the absolute correlation distance fails to fulfill the triangle inequality, which would have guaranteed better performance at vector quantization, allowed fast data localization, as well as accelerated data clustering. RESULTS: In this work, we propose [Formula: see text] as an alternative. We prove that [Formula: see text] satisfies the triangle inequality when [Formula: see text] represents Pearson correlation, Spearman correlation, or Cosine similarity. We show [Formula: see text] to be better than [Formula: see text], another variant of [Formula: see text] that satisfies the triangle inequality, both analytically as well as experimentally. We empirically compared [Formula: see text] with [Formula: see text] in gene clustering and sample clustering experiment by real-world biological data. The two distances performed similarly in both gene clustering and sample clustering in hierarchical clustering and PAM (partitioning around medoids) clustering. However, [Formula: see text] demonstrated more robust clustering. According to the bootstrap experiment, [Formula: see text] generated more robust sample pair partition more frequently (P-value [Formula: see text]). The statistics on the time a class "dissolved" also support the advantage of [Formula: see text] in robustness. CONCLUSION: [Formula: see text], as a variant of absolute correlation distance, satisfies the triangle inequality and is capable for more robust clustering.

Correction: BMC Bioinformatics (2023) 24:40 https://doi.org/10.1186/s12859-023-05161-y Following publication of the original article [1], it was reported that the article entitled “On triangle inequalities of correlation-based distances for gene expression profiles” was published in the regular issue of this journal instead of in the supplement issue. The details of the supplement in which this article ought to have been published are given below: This article has been published as part of BMC Bioinformatics Volume 23 Supplement 3, 2022: Selected articles from the International Conference on Intelligent Biology and Medicine (ICIBM 2021): bioinformatics. The full contents of the supplement are available online at https://bmcbioinformatics.biomedcentral.com/articles/supplements/volume-23-supplement-3. The publisher apologizes for any inconvenience caused. © 2023, The Author(s).

Heterozygosity has long plagued genome assembly. A wealth of sophisticated algorithms and procedures have been introduced for their treatment in genome assembly. In this paper, we propose a method called Hank (Heterozygosity assimilation through normalized k-mers) for this purpose. The method eliminates heterozygosity from reads by modifying the k-mers in heterozygous regions to increase their coverages to the levels of those in homozygous regions. When evaluated on simulated Illumina data at levels of heterozygosity from 0.1% to 2.0%, Hank was able to remove 80~96% of the heterozygosity. We also examined the effects of the corrections on de novo genome assembly using SOAPdenovo2, ALLPATH-LG and Platanus. All three methods improved in performance using the treated k-mers (we do not include these assembly results in this manuscript due to space constraint).

Accurately identifying gene regulatory network serves an important task in understanding in vivo biological activities. The inference of such network is often accomplished through the use of gene expression data. Some methods further predict the regulatory directions in the network by using the location of eQTL single nucleotide polymorphisms, or through gene knock out/down experiments; regrettably, these additional data are not always available, especially for the samples deriving from human tissues. In this paper, we propose Context Based Dependency Network (CBDN), a method that is able to infer gene regulatory networks, complete with the regulatory directions, from only gene expression data. CBDN applies directed data processing inequality (DDPI) to distinguish between direct and transitive relationship between genes. In our experiments with simulated and real data, CBDN outperforms the current state-of-the-art approaches. When used to identify important regulators in a network, CBDN 1. correctly identified TYROBP in the network related to Alzheimer's disease; 2. predicted potential important regulators ZNF329 and RB1 for human brain tumors.

The Local/Global Alignment (Zemla, 2003), or LGA, is a popular method for the comparison of protein structures. One of the two components of LGA requires us to compute the longest common contiguous segments between two protein structures. That is, given two structures A = (a1, ... ,a(n)) and B = (b1, ... ,b(n)) where a(k), b(k) ∈ ℝ(3), we are to find, among all the segments f = (a(i), ... ,a(j)) and g = (b(i), ... ,b(j)) that fulfill a certain criterion regarding their similarity, those of the maximum length. We consider the following criteria: (1) the root mean squared deviation (RMSD) between f and g is to be within a given t ∈ ℝ; (2) f and g can be superposed such that for each k, i ≤ k ≤ j, ||a(k) - b(k)|| ≤ t for a given t ∈ ℝ. We give an algorithm of O(n log n + nl) time complexity when the first requirement applies, where l is the maximum length of the segments fulfilling the criterion. We show an FPTAS which, for any ϵ ∈ ℝ, finds a segment of length at least l, but of RMSD up to (1 + ϵ)t, in O(n log n + n/ϵ) time. We propose an FPTAS which for any given ϵ ∈ R, finds all the segments f and g of the maximum length which can be superposed such that for each k, i ≤ k ≤ j, ||a(k) - b(k)|| ≤ (1 + ϵ)t, thus fulfilling the second requirement approximately. The algorithm has a time complexity of O(n log(2) n/ϵ(5)) when consecutive points in A are separated by the same distance (which is the case with protein structures). These worst-case runtime complexities are verified using C++ implementations of the algorithms, which we have made available at http://alcs.sourceforge.net/.

BACKGROUND: Ab initio protein structure prediction methods generate numerous structural candidates, which are referred to as decoys. The decoy with the most number of neighbors of up to a threshold distance is typically identified as the most representative decoy. However, the clustering of decoys needed for this criterion involves computations with runtimes that are at best quadratic in the number of decoys. As a result currently there is no tool that is designed to exactly cluster very large numbers of decoys, thus creating a bottleneck in the analysis. RESULTS: Using three strategies aimed at enhancing performance (proximate decoys organization, preliminary screening via lower and upper bounds, outliers filtering) we designed and implemented a software tool for clustering decoys called Calibur. We show empirical results indicating the effectiveness of each of the strategies employed. The strategies are further fine-tuned according to their effectiveness.Calibur demonstrated the ability to scale well with respect to increases in the number of decoys. For a sample size of approximately 30 thousand decoys, Calibur completed the analysis in one third of the time required when the strategies are not used.For practical use Calibur is able to automatically discover from the input decoys a suitable threshold distance for clustering. Several methods for this discovery are implemented in Calibur, where by default a very fast one is used. Using the default method Calibur reported relatively good decoys in our tests. CONCLUSIONS: Calibur's ability to handle very large protein decoy sets makes it a useful tool for clustering decoys in ab initio protein structure prediction. As the number of decoys generated in these methods increases, we believe Calibur will come in important for progress in the field.