Zones of low entropy in genomic sequences

AlcoR: alignment-free simulation, mapping, and visualization of low-complexity regions in biological data

BACKGROUND

Low-complexity data analysis is the area that addresses the search and quantification of regions in sequences of elements that contain low-complexity or repetitive elements. For example, these can be tandem repeats, inverted repeats, homopolymer tails, GC-biased regions, similar genes, and hairpins, among many others. Identifying these regions is crucial because of their association with regulatory and structural characteristics. Moreover, their identification provides positional and quantity information where standard assembly methodologies face significant difficulties because of substantial higher depth coverage (mountains), ambiguous read mapping, or where sequencing or reconstruction defects may occur. However, the capability to distinguish low-complexity regions (LCRs) in genomic and proteomic sequences is a challenge that depends on the model's ability to find them automatically. Low-complexity patterns can be implicit through specific or combined sources, such as algorithmic or probabilistic, and recurring to different spatial distances-namely, local, medium, or distant associations.

FINDINGS

This article addresses the challenge of automatically modeling and distinguishing LCRs, providing a new method and tool (AlcoR) for efficient and accurate segmentation and visualization of these regions in genomic and proteomic sequences. The method enables the use of models with different memories, providing the ability to distinguish local from distant low-complexity patterns. The method is reference and alignment free, providing additional methodologies for testing, including a highly flexible simulation method for generating biological sequences (DNA or protein) with different complexity levels, sequence masking, and a visualization tool for automatic computation of the LCR maps into an ideogram style. We provide illustrative demonstrations using synthetic, nearly synthetic, and natural sequences showing the high efficiency and accuracy of AlcoR. As large-scale results, we use AlcoR to unprecedentedly provide a whole-chromosome low-complexity map of a recent complete human genome and the haplotype-resolved chromosome pairs of a heterozygous diploid African cassava cultivar.

CONCLUSIONS

The AlcoR method provides the ability of fast sequence characterization through data complexity analysis, ideally for scenarios entangling the presence of new or unknown sequences. AlcoR is implemented in C language using multithreading to increase the computational speed, is flexible for multiple applications, and does not contain external dependencies. The tool accepts any sequence in FASTA format. The source code is freely provided at https://github.com/cobilab/alcor.

Informational laws of genome structures

In recent years, the analysis of genomes by means of strings of length k occurring in the genomes, called k-mers, has provided important insights into the basic mechanisms and design principles of genome structures. In the present study, we focus on the proper choice of the value of k for applying information theoretic concepts that express intrinsic aspects of genomes. The value k = lg2(n), where n is the genome length, is determined to be the best choice in the definition of some genomic informational indexes that are studied and computed for seventy genomes. These indexes, which are based on information entropies and on suitable comparisons with random genomes, suggest five informational laws, to which all of the considered genomes obey. Moreover, an informational genome complexity measure is proposed, which is a generalized logistic map that balances entropic and anti-entropic components of genomes and is related to their evolutionary dynamics. Finally, applications to computational synthetic biology are briefly outlined.

DNA entropy reveals a significant difference in complexity between housekeeping and tissue specific gene promoters

BACKGROUND

The complexity of DNA can be quantified using estimates of entropy. Variation in DNA complexity is expected between the promoters of genes with different transcriptional mechanisms; namely housekeeping (HK) and tissue specific (TS). The former are transcribed constitutively to maintain general cellular functions, and the latter are transcribed in restricted tissue and cells types for specific molecular events. It is known that promoter features in the human genome are related to tissue specificity, but this has been difficult to quantify on a genomic scale. If entropy effectively quantifies DNA complexity, calculating the entropies of HK and TS gene promoters as profiles may reveal significant differences.

RESULTS

Entropy profiles were calculated for a total dataset of 12,003 human gene promoters and for 501 housekeeping (HK) and 587 tissue specific (TS) human gene promoters. The mean profiles show the TS promoters have a significantly lower entropy (p<2.2e-16) than HK gene promoters. The entropy distributions for the 3 datasets show that promoter entropies could be used to identify novel HK genes.

CONCLUSION

Functional features comprise DNA sequence patterns that are non-random and hence they have lower entropies. The lower entropy of TS gene promoters can be explained by a higher density of positive and negative regulatory elements, required for genes with complex spatial and temporary expression.

Fast Entropic Profiler: An Information Theoretic Approach for the Discovery of Patterns in Genomes

Information theory has been used for quite some time in the area of computational biology. In this paper we present a pattern discovery method, named Fast Entropic Profiler, that is based on a local entropy function that captures the importance of a region with respect to the whole genome. The local entropy function has been introduced by Vinga and Almeida in , here we discuss and improve the original formulation. We provide a linear time and linear space algorithm called Fast Entropic Profiler ( FastEP), as opposed to the original quadratic implementation. Moreover we propose an alternative normalization that can be also efficiently implemented. We show that FastEP is suitable for large genomes and for the discovery of patterns with unbounded length. FastEP is available at http://www.dei.unipd.it/~ciompin/main/FastEP.html.

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.

DNA sequences at a glance

Data summarization and triage is one of the current top challenges in visual analytics. The goal is to let users visually inspect large data sets and examine or request data with particular characteristics. The need for summarization and visual analytics is also felt when dealing with digital representations of DNA sequences. Genomic data sets are growing rapidly, making their analysis increasingly more difficult, and raising the need for new, scalable tools. For example, being able to look at very large DNA sequences while immediately identifying potentially interesting regions would provide the biologist with a flexible exploratory and analytical tool. In this paper we present a new concept, the "information profile", which provides a quantitative measure of the local complexity of a DNA sequence, independently of the direction of processing. The computation of the information profiles is computationally tractable: we show that it can be done in time proportional to the length of the sequence. We also describe a tool to compute the information profiles of a given DNA sequence, and use the genome of the fission yeast Schizosaccharomyces pombe strain 972 h(-) and five human chromosomes 22 for illustration. We show that information profiles are useful for detecting large-scale genomic regularities by visual inspection. Several discovery strategies are possible, including the standalone analysis of single sequences, the comparative analysis of sequences from individuals from the same species, and the comparative analysis of sequences from different organisms. The comparison scale can be varied, allowing the users to zoom-in on specific details, or obtain a broad overview of a long segment. Software applications have been made available for non-commercial use at http://bioinformatics.ua.pt/software/dna-at-glance.

Topological entropy of DNA sequences

MOTIVATION

Topological entropy has been one of the most difficult to implement of all the entropy-theoretic notions. This is primarily due to finite sample effects and high-dimensionality problems. In particular, topological entropy has been implemented in previous literature to conclude that entropy of exons is higher than of introns, thus implying that exons are more 'random' than introns.

RESULTS

We define a new approximation to topological entropy free from the aforementioned difficulties. We compute its expected value and apply this definition to the intron and exon regions of the human genome to observe that as expected, the entropy of introns are significantly higher than that of exons. We also find that introns are less random than expected: their entropy is lower than the computed expected value. We also observe the perplexing phenomena that introns on chromosome Y have atypically low and bimodal entropy, possibly corresponding to random sequences (high entropy) and sequences that posses hidden structure or function (low entropy).

AVAILABILITY

A Mathematica implementation is available at http://www.math.psu.edu/koslicki/entropy.nb

CONTACT

koslicki@math.psu.edu

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A visual framework for sequence analysis using n-grams and spectral rearrangement

MOTIVATION

Protein sequences are often composed of regions that have distinct evolutionary histories as a consequence of domain shuffling, recombination or gene conversion. New approaches are required to discover, visualize and analyze these sequence regions and thus enable a better understanding of protein evolution.

RESULTS

Here, we have developed an alignment-free and visual approach to analyze sequence relationships. We use the number of shared n-grams between sequences as a measure of sequence similarity and rearrange the resulting affinity matrix applying a spectral technique. Heat maps of the affinity matrix are employed to identify and visualize clusters of related sequences or outliers, while n-gram-based dot plots and conservation profiles allow detailed analysis of similarities among selected sequences. Using this approach, we have identified signatures of domain shuffling in an otherwise poorly characterized family, and homology clusters in another. We conclude that this approach may be generally useful as a framework to analyze related, but highly divergent protein sequences. It is particularly useful as a fast method to study sequence relationships prior to much more time-consuming multiple sequence alignment and phylogenetic analysis.

AVAILABILITY

A software implementation (MOSAIC) of the framework described here can be downloaded from http://bioinformatics.org.au/mosaic/

CONTACT

m.ragan@uq.edu.au

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Entropic Profiler - detection of conservation in genomes using information theory

Background

In the last decades, with the successive availability of whole genome sequences, many research efforts have been made to mathematically model DNA. Entropic Profiles (EP) were proposed recently as a new measure of continuous entropy of genome sequences. EP represent local information plots related to DNA randomness and are based on information theory and statistical concepts. They express the weighed relative abundance of motifs for each position in genomes. Their study is very relevant because under or over-representation segments are often associated with significant biological meaning.

Findings

The Entropic Profiler application here presented is a new tool designed to detect and extract under and over-represented DNA segments in genomes by using EP. It allows its computation in a very efficient way by recurring to improved algorithms and data structures, which include modified suffix trees. Available through a web interface and as downloadable source code, it allows to study positions and to search for motifs inside the whole sequence or within a specified range. DNA sequences can be entered from different sources, including FASTA files, pre-loaded examples or resuming a previously saved work. Besides the EP value plots, p-values and z-scores for each motif are also computed, along with the Chaos Game Representation of the sequence.

Conclusion

EP are directly related with the statistical significance of motifs and can be considered as a new method to extract and classify significant regions in genomes and estimate local scales in DNA. The present implementation establishes an efficient and useful tool for whole genome analysis.

Local Renyi entropic profiles of DNA sequences

Background

In a recent report the authors presented a new measure of continuous entropy for DNA sequences, which allows the estimation of their randomness level. The definition therein explored was based on the Rényi entropy of probability density estimation (pdf) using the Parzen's window method and applied to Chaos Game Representation/Universal Sequence Maps (CGR/USM). Subsequent work proposed a fractal pdf kernel as a more exact solution for the iterated map representation. This report extends the concepts of continuous entropy by defining DNA sequence entropic profiles using the new pdf estimations to refine the density estimation of motifs.

Results

The new methodology enables two results. On the one hand it shows that the entropic profiles are directly related with the statistical significance of motifs, allowing the study of under and over-representation of segments. On the other hand, by spanning the parameters of the kernel function it is possible to extract important information about the scale of each conserved DNA region. The computational applications, developed in Matlab m-code, the corresponding binary executables and additional material and examples are made publicly available at .

Conclusion

The ability to detect local conservation from a scale-independent representation of symbolic sequences is particularly relevant for biological applications where conserved motifs occur in multiple, overlapping scales, with significant future applications in the recognition of foreign genomic material and inference of motif structures.

A fast and symmetric DUST implementation to mask low-complexity DNA sequences

The DUST module has been used within BLAST for many years to mask low-complexity sequences. In this paper, we present a new implementation of the DUST module that uses the same function to assign a complexity score to a sequence, but uses a different rule by which high-scoring sequences are masked. The new rule masks every nucleotide masked by the old rule and occasionally masks more. The new masking rule corrects two related deficiencies with the old rule. First, the new rule is symmetric with respect to reversing the sequence. Second, the new rule is not context sensitive; the decision to mask a subsequence does not depend on what sequences flank it. The new implementation is at least four times faster than the old on the human genome. We show that both the percentage of additional bases masked and the effect on MegaBLAST outputs are very small.

Information capacity of nucleotide sequences and its applications

The information capacity of nucleotide sequences is defined through the specific entropy of frequency dictionary of a sequence determined with respect to another one containing the most probable continuations of shorter strings. This measure distinguishes a sequence both from a random one, and from ordered entity. A comparison of sequences based on their information capacity is studied. An order within the genetic entities is found at the length scale ranged from 3 to 8. Some other applications of the developed methodology to genetics, bioinformatics, and molecular biology are discussed.

Rényi continuous entropy of DNA sequences

Entropy measures of DNA sequences estimate their randomness or, inversely, their repeatability. L-block Shannon discrete entropy accounts for the empirical distribution of all length-L words and has convergence problems for finite sequences. A new entropy measure that extends Shannon's formalism is proposed. Renyi's quadratic entropy calculated with Parzen window density estimation method applied to CGR/USM continuous maps of DNA sequences constitute a novel technique to evaluate sequence global randomness without some of the former method drawbacks. The asymptotic behaviour of this new measure was analytically deduced and the calculation of entropies for several synthetic and experimental biological sequences was performed. The results obtained were compared with the distributions of the null model of randomness obtained by simulation. The biological sequences have shown a different p-value according to the kernel resolution of Parzen's method, which might indicate an unknown level of organization of their patterns. This new technique can be very useful in the study of DNA sequence complexity and provide additional tools for DNA entropy estimation. The main MATLAB applications developed and additional material are available at the webpage . Specialized functions can be obtained from the authors.

Comparison of Real Frequencies of Strings vs. the Expected Ones Reveals the Information Capacity of Macromoleculae

The information capacity of nucleotide sequences is defined through the calculation of specific entropy of their frequency dictionary. The specificentropy of the frequency dictionary is calculated against the reconstructeddictionary; this latter bears the most probable continuations of the shorterstrings. This developed measure allows to distinguish the sequences both from the randons ones, and from those with high level of (rather simple) order. Some implications of the developed methodology in the fields of genetics,bioinformatics, and molecular biology are discussed.

Genome compartimentation by a hybrid chromosome model (HXM). Application to Saccharomyces cerevisae subtelomeres

The aim of this paper is to present a new approach, called 'Hybrid Chromosome Model' (HXM), which allows both the extraction of regions of similarity between two sequences, and the compartimentation of a set of DNA sequences. The principle of the method consists in compacting a set of sequences (split into fragments of fixed length) into a 'hybrid chromosome', which results from the stacking of the whole sequence fragments. We have illustrated our approach on the 32 subtelomeres of Saccharomyces cerevisae. The compartimentation of these chromosome extremities into common regions of similarity has been carried out. The approach HXM is a fast and efficient tool for mapping entire genomes and for extracting ancient duplications within or between genomes.

Low-Complexity Regions in Plasmodium falciparum Proteins

Full-sequence data available for Plasmodium falciparumchromosomes 2 and 3 are exploited to perform a statistical analysis of the long tracts of biased amino acid composition that characterize the vast majority of P. falciparum proteins and to make a comparison with similarly defined tracts from other simple eukaryotes. When the relatively minor subset of prevalently hydrophobic segments is discarded from the set of low-complexity segments identified by current segmentation methods in P. falciparum proteins, a good correspondence is found between prevalently hydrophilic low-complexity segments and the species-specific, rapidly diverging insertions detected by multiple-alignment procedures when sequences of bona fide homologs are available. Amino acid preferences are fairly uniform in the set of hydrophilic low-complexity segments identified in the twoP. falciparum chromosomes sequenced, as well as in sequenced genes from Plasmodium berghei, but differ from those observed in Saccharomyces cerevisiae and Dictyostelium discoideum. In the two plasmodial species, amino acid frequencies do not correlate with properties such as hydrophilicity, small volume, or flexibility, which might be expected to characterize residues involved in nonglobular domains but do correlate with A-richness in codons. An effect of phenotypic selection versus neutral drift, however, is suggested by the predominance of asparagine over lysine.

Low-complexity regions in Plasmodium falciparum proteins

Full-sequence data available for Plasmodium falciparum chromosomes 2 and 3 are exploited to perform a statistical analysis of the long tracts of biased amino acid composition that characterize the vast majority of P. falciparum proteins and to make a comparison with similarly defined tracts from other simple eukaryotes. When the relatively minor subset of prevalently hydrophobic segments is discarded from the set of low-complexity segments identified by current segmentation methods in P. falciparum proteins, a good correspondence is found between prevalently hydrophilic low-complexity segments and the species-specific, rapidly diverging insertions detected by multiple-alignment procedures when sequences of bona fide homologs are available. Amino acid preferences are fairly uniform in the set of hydrophilic low-complexity segments identified in the two P. falciparum chromosomes sequenced, as well as in sequenced genes from Plasmodium berghei, but differ from those observed in Saccharomyces cerevisiae and Dictyostelium discoideum. In the two plasmodial species, amino acid frequencies do not correlate with properties such as hydrophilicity, small volume, or flexibility, which might be expected to characterize residues involved in nonglobular domains but do correlate with A-richness in codons. An effect of phenotypic selection versus neutral drift, however, is suggested by the predominance of asparagine over lysine.