Data Compression Concepts and Algorithms and their Applications to Bioinformatics

The Resolved Mutual Information Function as a Structural Fingerprint of Biomolecular Sequences for Interpretable Machine Learning Classifiers

In the present article we propose the application of variants of the mutual information function as characteristic fingerprints of biomolecular sequences for classification analysis. In particular, we consider the resolved mutual information functions based on Shannon-, Rényi-, and Tsallis-entropy. In combination with interpretable machine learning classifier models based on generalized learning vector quantization, a powerful methodology for sequence classification is achieved which allows substantial knowledge extraction in addition to the high classification ability due to the model-inherent robustness. Any potential (slightly) inferior performance of the used classifier is compensated by the additional knowledge provided by interpretable models. This knowledge may assist the user in the analysis and understanding of the used data and considered task. After theoretical justification of the concepts, we demonstrate the approach for various example data sets covering different areas in biomolecular sequence analysis.

AC2: An Efficient Protein Sequence Compression Tool Using Artificial Neural Networks and Cache-Hash Models

Recently, the scientific community has witnessed a substantial increase in the generation of protein sequence data, triggering emergent challenges of increasing importance, namely efficient storage and improved data analysis. For both applications, data compression is a straightforward solution. However, in the literature, the number of specific protein sequence compressors is relatively low. Moreover, these specialized compressors marginally improve the compression ratio over the best general-purpose compressors. In this paper, we present AC2, a new lossless data compressor for protein (or amino acid) sequences. AC2 uses a neural network to mix experts with a stacked generalization approach and individual cache-hash memory models to the highest-context orders. Compared to the previous compressor (AC), we show gains of 2–9% and 6–7% in reference-free and reference-based modes, respectively. These gains come at the cost of three times slower computations. AC2 also improves memory usage against AC, with requirements about seven times lower, without being affected by the sequences’ input size. As an analysis application, we use AC2 to measure the similarity between each SARS-CoV-2 protein sequence with each viral protein sequence from the whole UniProt database. The results consistently show higher similarity to the pangolin coronavirus, followed by the bat and human coronaviruses, contributing with critical results to a current controversial subject. AC2 is available for free download under GPLv3 license.

Causal discovery using compression-complexity measures

Causal inference is one of the most fundamental problems across all domains of science. We address the problem of inferring a causal direction from two observed discrete symbolic sequences X and Y. We present a framework which relies on lossless compressors for inferring context-free grammars (CFGs) from sequence pairs and quantifies the extent to which the grammar inferred from one sequence compresses the other sequence. We infer X causes Y if the grammar inferred from X better compresses Y than in the other direction. To put this notion to practice, we propose three models that use the Compression-Complexity Measures (CCMs) - Lempel-Ziv (LZ) complexity and Effort-To-Compress (ETC) to infer CFGs and discover causal directions without demanding temporal structures. We evaluate these models on synthetic and real-world benchmarks and empirically observe performances competitive with current state-of-the-art methods. Lastly, we present two unique applications of the proposed models for causal inference directly from pairs of genome sequences belonging to the SARS-CoV-2 virus. Using numerous sequences, we show that our models capture causal information exchanged between genome sequence pairs, presenting novel opportunities for addressing key issues in sequence analysis to investigate the evolution of virulence and pathogenicity in future applications.

Vertical lossless genomic data compression tools for assembled genomes: A systematic literature review

The recent decrease in cost and time to sequence and assemble of complete genomes created an increased demand for data storage. As a consequence, several strategies for assembled biological data compression were created. Vertical compression tools implement strategies that take advantage of the high level of similarity between multiple assembled genomic sequences for better compression results. However, current reviews on vertical compression do not compare the execution flow of each tool, which is constituted by phases of preprocessing, transformation, and data encoding. We performed a systematic literature review to identify and compare existing tools for vertical compression of assembled genomic sequences. The review was centered on PubMed and Scopus, in which 45726 distinct papers were considered. Next, 32 papers were selected according to the following criteria: to present a lossless vertical compression tool; to use the information contained in other sequences for the compression; to be able to manipulate genomic sequences in FASTA format; and no need prior knowledge. Although we extracted performance compression results, they were not compared as the tools did not use a standardized evaluation protocol. Thus, we conclude that there's a lack of definition of an evaluation protocol that must be applied by each tool.

Storage Space Allocation Strategy for Digital Data with Message Importance

This paper mainly focuses on the problem of lossy compression storage based on the data value that represents the subjective assessment of users when the storage size is still not enough after the conventional lossless data compression. To this end, we transform this problem to an optimization, which pursues the least importance-weighted reconstruction error in data reconstruction within limited total storage size, where the importance is adopted to characterize the data value from the viewpoint of users. Based on it, this paper puts forward an optimal allocation strategy in the storage of digital data by the exponential distortion measurement, which can make rational use of all the storage space. In fact, the theoretical results show that it is a kind of restrictive water-filling. It also characterizes the trade-off between the relative weighted reconstruction error and the available storage size. Consequently, if a relatively small part of total data value is allowed to lose, this strategy will improve the performance of data compression. Furthermore, this paper also presents that both the users’ preferences and the special characteristics of data distribution can trigger the small-probability event scenarios where only a fraction of data can cover the vast majority of users’ interests. Whether it is for one of the reasons above, the data with highly clustered message importance is beneficial to compression storage. In contrast, from the perspective of optimal storage space allocation based on data value, the data with a uniform information distribution is incompressible, which is consistent with that in the information theory.

Algorithms designed for compressed-gene-data transformation among gene banks with different references

Background

With the reduction of gene sequencing cost and demand for emerging technologies such as precision medical treatment and deep learning in genome, it is an era of gene data outbreaks today. How to store, transmit and analyze these data has become a hotspot in the current research. Now the compression algorithm based on reference is widely used due to its high compression ratio. There exists a big problem that the data from different gene banks can’t merge directly and share information efficiently, because these data are usually compressed with different references. The traditional workflow is decompression-and-recompression, which is too simple and time-consuming. We should improve it and speed it up.

Results

In this paper, we focus on this problem and propose a set of transformation algorithms to cope with it. We will 1) analyze some different compression algorithms to find the similarities and the differences among all of them, 2) come up with a naïve method named TDM for data transformation between difference gene banks and finally 3) optimize former method TDM and propose the method named TPI and the method named TGI. A number of experiment result proved that the three algorithms we proposed are an order of magnitude faster than traditional decompression-and-recompression workflow.

Conclusions

Firstly, the three algorithms we proposed all have good performance in terms of time. Secondly, they have their own different advantages faced with different dataset or situations. TDM and TPI are more suitable for small-scale gene data transformation, while TGI is more suitable for large-scale gene data transformation.

Sequence Factorization with Multiple References

The success of high-throughput sequencing has lead to an increasing number of projects which sequence large populations of a species. Storage and analysis of sequence data is a key challenge in these projects, because of the sheer size of the datasets. Compression is one simple technology to deal with this challenge. Referential factorization and compression schemes, which store only the differences between input sequence and a reference sequence, gained lots of interest in this field. Highly-similar sequences, e.g., Human genomes, can be compressed with a compression ratio of 1,000:1 and more, up to two orders of magnitude better than with standard compression techniques. Recently, it was shown that the compression against multiple references from the same species can boost the compression ratio up to 4,000:1. However, a detailed analysis of using multiple references is lacking, e.g., for main memory consumption and optimality. In this paper, we describe one key technique for the referential compression against multiple references: The factorization of sequences. Based on the notion of an optimal factorization, we propose optimization heuristics and identify parameter settings which greatly influence 1) the size of the factorization, 2) the time for factorization, and 3) the required amount of main memory. We evaluate a total of 30 setups with a varying number of references on data from three different species. Our results show a wide range of factorization sizes (optimal to an overhead of up to 300%), factorization speed (0.01 MB/s to more than 600 MB/s), and main memory usage (few dozen MB to dozens of GB). Based on our evaluation, we identify the best configurations for common use cases. Our evaluation shows that multi-reference factorization is much better than single-reference factorization.

Conditional entropy in variation-adjusted windows detects selection signatures associated with expression quantitative trait loci (eQTLs)

BACKGROUND

Over the past 50,000 years, shifts in human-environmental or human-human interactions shaped genetic differences within and among human populations, including variants under positive selection. Shaped by environmental factors, such variants influence the genetics of modern health, disease, and treatment outcome. Because evolutionary processes tend to act on gene regulation, we test whether regulatory variants are under positive selection. We introduce a new approach to enhance detection of genetic markers undergoing positive selection, using conditional entropy to capture recent local selection signals.

RESULTS

We use conditional logistic regression to compare our Adjusted Haplotype Conditional Entropy (H|H) measure of positive selection to existing positive selection measures. H|H and existing measures were applied to published regulatory variants acting in cis (cis-eQTLs), with conditional logistic regression testing whether regulatory variants undergo stronger positive selection than the surrounding gene. These cis-eQTLs were drawn from six independent studies of genotype and RNA expression. The conditional logistic regression shows that, overall, H|H is substantially more powerful than existing positive-selection methods in identifying cis-eQTLs against other Single Nucleotide Polymorphisms (SNPs) in the same genes. When broken down by Gene Ontology, H|H predictions are particularly strong in some biological process categories, where regulatory variants are under strong positive selection compared to the bulk of the gene, distinct from those GO categories under overall positive selection. . However, cis-eQTLs in a second group of genes lack positive selection signatures detectable by H|H, consistent with ancient short haplotypes compared to the surrounding gene (for example, in innate immunity GO:0042742); under such other modes of selection, H|H would not be expected to be a strong predictor.. These conditional logistic regression models are adjusted for Minor allele frequency(MAF); otherwise, ascertainment bias is a huge factor in all eQTL data sets. Relationships between Gene Ontology categories, positive selection and eQTL specificity were replicated with H|H in a single larger data set. Our measure, Adjusted Haplotype Conditional Entropy (H|H), was essential in generating all of the results above because it: 1) is a stronger overall predictor for eQTLs than comparable existing approaches, and 2) shows low sequential auto-correlation, overcoming problems with convergence of these conditional regression statistical models.

CONCLUSIONS

Our new method, H|H, provides a consistently more robust signal associated with cis-eQTLs compared to existing methods. We interpret this to indicate that some cis-eQTLs are under positive selection compared to their surrounding genes. Conditional entropy indicative of a selective sweep is an especially strong predictor of eQTLs for genes in several biological processes of medical interest. Where conditional entropy is a weak or negative predictor of eQTLs, such as innate immune genes, this would be consistent with balancing selection acting on such eQTLs over long time periods. Different measures of selection may be needed for variant prioritization under other modes of evolutionary selection.

Information theory applications for biological sequence analysis

Information theory (IT) addresses the analysis of communication systems and has been widely applied in molecular biology. In particular, alignment-free sequence analysis and comparison greatly benefited from concepts derived from IT, such as entropy and mutual information. This review covers several aspects of IT applications, ranging from genome global analysis and comparison, including block-entropy estimation and resolution-free metrics based on iterative maps, to local analysis, comprising the classification of motifs, prediction of transcription factor binding sites and sequence characterization based on linguistic complexity and entropic profiles. IT has also been applied to high-level correlations that combine DNA, RNA or protein features with sequence-independent properties, such as gene mapping and phenotype analysis, and has also provided models based on communication systems theory to describe information transmission channels at the cell level and also during evolutionary processes. While not exhaustive, this review attempts to categorize existing methods and to indicate their relation with broader transversal topics such as genomic signatures, data compression and complexity, time series analysis and phylogenetic classification, providing a resource for future developments in this promising area.

Using weighted entropy to rank chemicals in quantitative high-throughput screening experiments

Quantitative high-throughput screening (qHTS) experiments can simultaneously produce concentration-response profiles for thousands of chemicals. In a typical qHTS study, a large chemical library is subjected to a primary screen to identify candidate hits for secondary screening, validation studies, or prediction modeling. Different algorithms, usually based on the Hill equation logistic model, have been used to classify compounds as active or inactive (or inconclusive). However, observed concentration-response activity relationships may not adequately fit a sigmoidal curve. Furthermore, it is unclear how to prioritize chemicals for follow-up studies given the large uncertainties that often accompany parameter estimates from nonlinear models. Weighted Shannon entropy can address these concerns by ranking compounds according to profile-specific statistics derived from estimates of the probability mass distribution of response at the tested concentration levels. This strategy can be used to rank all tested chemicals in the absence of a prespecified model structure, or the approach can complement existing activity call algorithms by ranking the returned candidate hits. The weighted entropy approach was evaluated here using data simulated from the Hill equation model. The procedure was then applied to a chemical genomics profiling data set interrogating compounds for androgen receptor agonist activity.

FRESCO: Referential compression of highly similar sequences

In many applications, sets of similar texts or sequences are of high importance. Prominent examples are revision histories of documents or genomic sequences. Modern high-throughput sequencing technologies are able to generate DNA sequences at an ever-increasing rate. In parallel to the decreasing experimental time and cost necessary to produce DNA sequences, computational requirements for analysis and storage of the sequences are steeply increasing. Compression is a key technology to deal with this challenge. Recently, referential compression schemes, storing only the differences between a to-be-compressed input and a known reference sequence, gained a lot of interest in this field. In this paper, we propose a general open-source framework to compress large amounts of biological sequence data called Framework for REferential Sequence COmpression (FRESCO). Our basic compression algorithm is shown to be one to two orders of magnitudes faster than comparable related work, while achieving similar compression ratios. We also propose several techniques to further increase compression ratios, while still retaining the advantage in speed: 1) selecting a good reference sequence; and 2) rewriting a reference sequence to allow for better compression. In addition,we propose a new way of further boosting the compression ratios by applying referential compression to already referentially compressed files (second-order compression). This technique allows for compression ratios way beyond state of the art, for instance,4,000:1 and higher for human genomes. We evaluate our algorithms on a large data set from three different species (more than 1,000 genomes, more than 3 TB) and on a collection of versions of Wikipedia pages. Our results show that real-time compression of highly similar sequences at high compression ratios is possible on modern hardware.

Adaptive efficient compression of genomes

Modern high-throughput sequencing technologies are able to generate DNA sequences at an ever increasing rate. In parallel to the decreasing experimental time and cost necessary to produce DNA sequences, computational requirements for analysis and storage of the sequences are steeply increasing. Compression is a key technology to deal with this challenge. Recently, referential compression schemes, storing only the differences between a to-be-compressed input and a known reference sequence, gained a lot of interest in this field. However, memory requirements of the current algorithms are high and run times often are slow. In this paper, we propose an adaptive, parallel and highly efficient referential sequence compression method which allows fine-tuning of the trade-off between required memory and compression speed. When using 12 MB of memory, our method is for human genomes on-par with the best previous algorithms in terms of compression ratio (400:1) and compression speed. In contrast, it compresses a complete human genome in just 11 seconds when provided with 9 GB of main memory, which is almost three times faster than the best competitor while using less main memory.

Communication theory and multicellular biology

In this Perspective, we propose that communication theory--a field of mathematics concerned with the problems of signal transmission, reception and processing--provides a new quantitative lens for investigating multicellular biology, ancient and modern. What underpins the cohesive organisation and collective behaviour of multicellular ecosystems such as microbial colonies and communities (microbiomes) and multicellular organisms such as plants and animals, whether built of simple tissue layers (sponges) or of complex differentiated cells arranged in tissues and organs (members of the 35 or so phyla of the subkingdom Metazoa)? How do mammalian tissues and organs develop, maintain their architecture, become subverted in disease, and decline with age? How did single-celled organisms coalesce to produce many-celled forms that evolved and diversified into the varied multicellular organisms in existence today? Some answers can be found in the blueprints or recipes encoded in (epi)genomes, yet others lie in the generic physical properties of biological matter such as the ability of cell aggregates to attain a certain complexity in size, shape, and pattern. We suggest that Lasswell's maxim "Who says what to whom in what channel with what effect" provides a foundation for understanding not only the emergence and evolution of multicellularity, but also the assembly and sculpting of multicellular ecosystems and many-celled structures, whether of natural or human-engineered origin. We explore how the abstraction of communication theory as an organising principle for multicellular biology could be realised. We highlight the inherent ability of communication theory to be blind to molecular and/or genetic mechanisms. We describe selected applications that analyse the physics of communication and use energy efficiency as a central tenet. Whilst communication theory has and could contribute to understanding a myriad of problems in biology, investigations of multicellular biology could, in turn, lead to advances in communication theory, especially in the still immature field of network information theory.