Topological entropy of DNA sequences

Machine learning classification of archaea and bacteria identifies novel predictive genomic features

BACKGROUND

Archaea and Bacteria are distinct domains of life that are adapted to a variety of ecological niches. Several genome-based methods have been developed for their accurate classification, yet many aspects of the specific genomic features that determine these differences are not fully understood. In this study, we used publicly available whole-genome sequences from bacteria ( N = 2546 ) and archaea ( N = 109 ). From these, a set of genomic features (nucleotide frequencies and proportions, coding sequences (CDS), non-coding, ribosomal and transfer RNA genes (ncRNA, rRNA, tRNA), Chargaff's, topological entropy and Shannon's entropy scores) was extracted and used as input data to develop machine learning models for the classification of archaea and bacteria.

RESULTS

The classification accuracy ranged from 0.993 (Random Forest) to 0.998 (Neural Networks). Over the four models, only 11 examples were misclassified, especially those belonging to the minority class (Archaea). From variable importance, tRNA topological and Shannon's entropy, nucleotide frequencies in tRNA, rRNA and ncRNA, CDS, tRNA and rRNA Chargaff's scores have emerged as the top discriminating factors. In particular, tRNA entropy (both topological and Shannon's) was the most important genomic feature for classification, pointing at the complex interactions between the genetic code, tRNAs and the translational machinery.

CONCLUSIONS

tRNA, rRNA and ncRNA genes emerged as the key genomic elements that underpin the classification of archaea and bacteria. In particular, higher nucleotide diversity was found in tRNA from bacteria compared to archaea. The analysis of the few classification errors reflects the complex phylogenetic relationships between bacteria, archaea and eukaryotes.

Entropy-Driven, Integrative Bioinformatics Approaches Reveal the Recent Transmission of the Monkeypox Virus from Nigeria to Multiple Non-African Countries

Monkeypox virus (mpox) has currently affected multiple countries around the globe. This study aims to analyze how the virus spread globally. The study uses entropy-driven bioinformatics in five directions to analyze the 60 full-length complete genomes of mpox. We analyzed the topological entropy distribution of the genomes, principal component analysis (PCA), the dissimilarity matrix, entropy-driven phylogenetics, and genome clustering. The topological entropy distribution showed genome positional entropy. We found five clusters of the mpox genomes through the two PCA, while the three PCA elucidated the clustering events in 3D space. The clustering of genomes was further confirmed through the dissimilarity matrix and phylogenetic analysis which showed the bigger size of Cluster 1 and size similarity between Clusters 2 and 4 as well as Clusters 3 and 5. It corroborated with the phylogenetics of the genomes, where Cluster 1 showed clear segregation from the other four clusters. Finally, the study concluded that the spreading of the mpox is likely to have originated from African countries to the rest of the non-African countries. Overall, the spreading and distribution of the mpox will shed light on its evolution and pathogenicity of the mpox and help to adopt preventive measures to stop the spreading of the virus.

Detecting tipping points of complex diseases by network information entropy

The progression of complex diseases often involves abrupt and non-linear changes characterized by sudden shifts that trigger critical transformations. Identifying these critical states or tipping points is crucial for understanding disease progression and developing effective interventions. To address this challenge, we have developed a model-free method named Network Information Entropy of Edges (NIEE). Leveraging dynamic network biomarkers, sample-specific networks, and information entropy theories, NIEE can detect critical states or tipping points in diverse data types, including bulk, single-sample expression data. By applying NIEE to real disease datasets, we successfully identified critical predisease stages and tipping points before disease onset. Our findings underscore NIEE's potential to enhance comprehension of complex disease development.

Statistical analysis of synonymous and stop codons in pseudo-random and real sequences as a function of GC content

Knowledge of the frequencies of synonymous triplets in protein-coding and non-coding DNA stretches can be used in gene finding. These frequencies depend on the GC content of the genome or parts of it. An example of interest is provided by stop codons. This is relevant for the definition of Open Reading Frames. A generic case is provided by pseudo-random sequences, especially when they code for complex proteins or when they are non-coding and not subject to selection pressure. Here, we calculate, for such sequences and for all 25 known genetic codes, the frequency of each amino acid and stop codon based on their set of codons and as a function of GC content. The amino acids can be classified into five groups according to the GC content where their expected frequency reaches its maximum. We determine the overall Shannon information based on groups of synonymous codons and show that it becomes maximum at a percent GC of 43.3% (for the standard code). This is in line with the observation that in most fungi, plants, and animals, this genomic parameter is in the range from 35 to 50%. By analysing natural sequences, we show that there is a clear bias for triplets corresponding to stop codons near the 5'- and 3'-splice sites in the introns of various clades.

The Intransitive Logic of Directed Cycles and Flipons Enhances the Evolution of Molecular Computers by Augmenting the Kolmogorov Complexity of Genomes

Cell responses are usually viewed as transitive events with fixed inputs and outputs that are regulated by feedback loops. In contrast, directed cycles (DCs) have all nodes connected, and the flow is in a single direction. Consequently, DCs can regenerate themselves and implement intransitive logic. DCs are able to couple unrelated chemical reactions to each edge. The output depends upon which node is used as input. DCs can also undergo selection to minimize the loss of thermodynamic entropy while maximizing the gain of information entropy. The intransitive logic underlying DCs enhances their programmability and impacts their evolution. The natural selection of DCs favors the persistence, adaptability, and self-awareness of living organisms and does not depend solely on changes to coding sequences. Rather, the process can be RNA-directed. I use flipons, nucleic acid sequences that change conformation under physiological conditions, as a simple example and then describe more complex DCs. Flipons are often encoded by repeats and greatly increase the Kolmogorov complexity of genomes by adopting alternative structures. Other DCs allow cells to regenerate, recalibrate, reset, repair, and rewrite themselves, going far beyond the capabilities of current computational devices. Unlike Turing machines, cells are not designed to halt but rather to regenerate.

Machine Learning Algorithms Highlight tRNA Information Content and Chargaff’s Second Parity Rule Score as Important Features in Discriminating Probiotics from Non-Probiotics

Simple Summary

Probiotics are a group of beneficial microorganisms that are symbionts of the human gut microbiome. The identification of new probiotics is therefore of paramount importance from both public health and commercial perspectives. In this study, we show for the first time that Artificial Intelligence algorithms can identify novel probiotics and also discriminate them from pathogenic organisms in the human gut. We were also able to determine the information content within tRNA sequences as the key genomic features capable of characterizing probiotics.

Abstract

Probiotic bacteria are microorganisms with beneficial effects on human health and are currently used in numerous food supplements. However, no selection process is able to effectively distinguish probiotics from non-probiotic organisms on the basis of their genomic characteristics. In the current study, four Machine Learning algorithms were employed to accurately identify probiotic bacteria based on their DNA characteristics. Although the prediction accuracies of all algorithms were excellent, the Neural Network returned the highest scores in all the evaluation metrics, managing to discriminate probiotics from non-probiotics with an accuracy greater than 90%. Interestingly, our analysis also highlighted the information content of the tRNA sequences as the most important feature in distinguishing the two groups of organisms probably because tRNAs have regulatory functions and might have allowed probiotics to evolve faster in the human gut environment. Through the methodology presented here, it was also possible to identify seven promising new probiotics that have a higher information content in their tRNA sequences compared to non-probiotics. In conclusion, we prove for the first time that Machine Learning methods can discriminate human probiotic from non-probiotic organisms underlining information within tRNA sequences as the most important genomic feature in distinguishing them.

Prediction of Intrinsically Disordered Proteins Using Machine Learning Based on Low Complexity Methods

Prediction of intrinsic disordered proteins is a hot area in the field of bio-information. Due to the high cost of evaluating the disordered regions of protein sequences using experimental methods, we used a low-complexity prediction scheme. Sequence complexity is used in this scheme to calculate five features for each residue of the protein sequence, including the Shannon entropy, the Topo-logical entropy, the Permutation entropy and the weighted average values of two propensities. Particularly, this is the first time that permutation entropy has been applied to the field of protein sequencing. In addition, in the data preprocessing stage, an appropriately sized sliding window and a comprehensive oversampling scheme can be used to improve the prediction performance of our scheme, and two ensemble learning algorithms are also used to verify the prediction results before and after. The results show that adding permutation entropy improves the performance of the prediction algorithm, in which the MCC value can be improved from the original 0.465 to 0.526 in our scheme, proving its universality. Finally, we compare the simulation results of our scheme with those of some existing schemes to demonstrate its effectiveness.

A fractal scaling analysis of the SARS-CoV-2 genome sequence

An approach based on fractal scaling analysis to characterize the organization of the SARS-CoV-2 genome sequence was used. The method is based on the detrended fluctuation analysis (DFA) implemented on a sliding window scheme to detect variations of long-range correlations over the genome sequence regions. The nucleotides sequence is mapped in a numerical sequence by using four different assignation rules: amino-keto, purine-pyrimidine, hydrogen-bond and hydrophobicity patterns. The originally reported sequence from Wuhan isolates (Wuhan Hu-1) was considered as a reference to contrast the structure of the 2002-2004 SARS-CoV-1 strain. Long-range correlations, quantified in terms of a scaling exponent, depended on both the mapping rule and the sequence region. Deviations from randomness were attributed to serial correlations or anti-correlations, which can be ascribed to ordered regions of the genome sequence. It was found that the Wuhan Hu-1 sequence was more random than the SARS-CoV-1 sequence, which suggests that the SARS-CoV-2 possesses a more efficient genomic structure for replication and infection. In general, the virus isolated in the early 2020 months showed slight correlation differences with the Wuhan Hu-1 sequence. However, early isolates from India and Italy presented visible differences that led to a more ordered sequence organization. It is apparent that the increased sequence order, particularly in the spike region, endowed some early variants with a more efficient mechanism to spreading, replicating and infecting. Overall, the results showed that the DFA provides a suitable framework to assess long-term correlations hidden in the internal organization of the SARS-CoV-2 genome sequence.

Large-scale k-mer-based analysis of the informational properties of genomes, comparative genomics and taxonomy

Information theoretic approaches are ubiquitous and effective in a wide variety of bioinformatics applications. In comparative genomics, alignment-free methods, based on short DNA words, or k-mers, are particularly powerful. We evaluated the utility of varying k-mer lengths for genome comparisons by analyzing their sequence space coverage of 5805 genomes in the KEGG GENOME database. In subsequent analyses on four k-mer lengths spanning the relevant range (11, 21, 31, 41), hierarchical clustering of 1634 genus-level representative genomes using pairwise 21- and 31-mer Jaccard similarities best recapitulated a phylogenetic/taxonomic tree of life with clear boundaries for superkingdom domains and high subtree similarity for named taxons at lower levels (family through phylum). By analyzing ~14.2M prokaryotic genome comparisons by their lowest-common-ancestor taxon levels, we detected many potential misclassification errors in a curated database, further demonstrating the need for wide-scale adoption of quantitative taxonomic classifications based on whole-genome similarity.

Information Entropy in Chemistry: An Overview

Basic applications of the information entropy concept to chemical objects are reviewed. These applications deal with quantifying chemical and electronic structures of molecules, signal processing, structural studies on crystals, and molecular ensembles. Recent advances in the mentioned areas make information entropy a central concept in interdisciplinary studies on digitalizing chemical reactions, chemico-information synthesis, crystal engineering, as well as digitally rethinking basic notions of structural chemistry in terms of informatics.

A global metagenomic map of urban microbiomes and antimicrobial resistance

We present a global atlas of 4,728 metagenomic samples from mass-transit systems in 60 cities over 3 years, representing the first systematic, worldwide catalog of the urban microbial ecosystem. This atlas provides an annotated, geospatial profile of microbial strains, functional characteristics, antimicrobial resistance (AMR) markers, and genetic elements, including 10,928 viruses, 1,302 bacteria, 2 archaea, and 838,532 CRISPR arrays not found in reference databases. We identified 4,246 known species of urban microorganisms and a consistent set of 31 species found in 97% of samples that were distinct from human commensal organisms. Profiles of AMR genes varied widely in type and density across cities. Cities showed distinct microbial taxonomic signatures that were driven by climate and geographic differences. These results constitute a high-resolution global metagenomic atlas that enables discovery of organisms and genes, highlights potential public health and forensic applications, and provides a culture-independent view of AMR burden in cities.

Single-cell transcriptional landscapes reveal HIV-1-driven aberrant host gene transcription as a potential therapeutic target

Understanding HIV-1-host interactions can identify the cellular environment supporting HIV-1 reactivation and mechanisms of clonal expansion. We developed HIV-1 SortSeq to isolate rare HIV-1-infected cells from virally suppressed, HIV-1-infected individuals upon early latency reversal. Single-cell transcriptome analysis of HIV-1 SortSeq⁺ cells revealed enrichment of nonsense-mediated RNA decay and viral transcription pathways. HIV-1 SortSeq⁺ cells up-regulated cellular factors that can support HIV-1 transcription (IMPDH1 and JAK1) or promote cellular survival (IL2 and IKBKB). HIV-1-host RNA landscape analysis at the integration site revealed that HIV-1 drives high aberrant host gene transcription downstream, but not upstream, of the integration site through HIV-1-to-host aberrant splicing, in which HIV-1 RNA splices into the host RNA and aberrantly drives host RNA transcription. HIV-1-induced aberrant transcription was driven by the HIV-1 promoter as shown by CRISPR-dCas9-mediated HIV-1-specific activation and could be suppressed by CRISPR-dCas9-mediated inhibition of HIV-1 5' long terminal repeat. Overall, we identified cellular factors supporting HIV-1 reactivation and HIV-1-driven aberrant host gene transcription as potential therapeutic targets to disrupt HIV-1 persistence.

IIMLP: integrated information-entropy-based method for LncRNA prediction

BACKGROUND

The prediction of long non-coding RNA (lncRNA) has attracted great attention from researchers, as more and more evidence indicate that various complex human diseases are closely related to lncRNAs. In the era of bio-med big data, in addition to the prediction of lncRNAs by biological experimental methods, many computational methods based on machine learning have been proposed to make better use of the sequence resources of lncRNAs.

RESULTS

We developed the lncRNA prediction method by integrating information-entropy-based features and machine learning algorithms. We calculate generalized topological entropy and generate 6 novel features for lncRNA sequences. By employing these 6 features and other features such as open reading frame, we apply supporting vector machine, XGBoost and random forest algorithms to distinguish human lncRNAs. We compare our method with the one which has more K-mer features and results show that our method has higher area under the curve up to 99.7905%.

CONCLUSIONS

We develop an accurate and efficient method which has novel information entropy features to analyze and classify lncRNAs. Our method is also extendable for research on the other functional elements in DNA sequences.

Uncovering patterns of the evolution of genomic sequence entropy and complexity

The lack of consensus concerning the biological meaning of entropy and complexity of genomes and the different ways to assess these data hamper conclusions concerning what are the causes of genomic entropy variation among species. This study aims to evaluate the entropy and complexity of genomic sequences of several species without using homologies to assess relationships among these variables and non-molecular data (e.g., the number of individuals) to seek a trigger of interspecific genomic entropy variation. The results indicate a relationship among genomic entropy, genome size, genomic complexity, and the number of individuals: species with a small number of individuals harbors large genome, and hence, low entropy but a higher complexity. We defined that the complexity of a genome relies on the entropy of each DNA segment within genome. Then, the entropy and complexity of a genome reflects its organization solely. Exons of vertebrates harbor smaller entropies than non-exon regions (likely by the repeats that accumulated from duplications), whereas other taxonomic groups do not present this pattern. Our findings suggest that small initial population might have defined current genomic entropy and complexity: actual genomes are less complex than ancestral ones. Besides, our data disagree with the relationship between phenotype and genomic entropies previously established. Finally, by establishing the relationship between genomic entropy/complexity with the number of individuals and genome size, under an evolutive perspective, ideas concerning the genomic variability may emerge.

Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics

The Thermodynamic Formalism provides a rigorous mathematical framework for studying quantitative and qualitative aspects of dynamical systems. At its core, there is a variational principle that corresponds, in its simplest form, to the Maximum Entropy principle. It is used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of science. In particular, it has been fruitful and influential in neurosciences. In this article, we review how the Thermodynamic Formalism can be exploited in the field of theoretical neuroscience, as a conceptual and operational tool, in order to link the dynamics of interacting neurons and the statistics of action potentials from either experimental data or mathematical models. We comment on perspectives and open problems in theoretical neuroscience that could be addressed within this formalism.

A model of k-mer surprisal to quantify local sequence information content surrounding splice regions

Molecular sequences carry information. Analysis of sequence conservation between homologous loci is a proven approach with which to explore the information content of molecular sequences. This is often done using multiple sequence alignments to support comparisons between homologous loci. These methods therefore rely on sufficient underlying sequence similarity with which to construct a representative alignment. Here we describe a method using a formal metric of information, surprisal, to analyse biological sub-sequences without alignment constraints. We applied our model to the genomes of five different species to reveal similar patterns across a panel of eukaryotes. As the surprisal of a sub-sequence is inversely proportional to its occurrence within the genome, the optimal size of the sub-sequences was selected for each species under consideration. With the model optimized, we found a strong correlation between surprisal and CG dinucleotide usage. The utility of our model was tested by examining the sequences of genes known to undergo splicing. We demonstrate that our model can identify biological features of interest such as known donor and acceptor sites. Analysis across all annotated coding exon junctions in Homo sapiens reveals the information content of coding exons to be greater than the surrounding intron regions, a consequence of increased suppression of the CG dinucleotide in intronic space. Sequences within coding regions proximal to exon junctions exhibited novel patterns within DNA and coding mRNA that are not a function of the encoded amino acid sequence. Our findings are consistent with the presence of secondary information encoding features such as DNA and RNA binding sites, multiplexed through the coding sequence and independent of the information required to define the corresponding amino-acid sequence. We conclude that surprisal provides a complementary methodology with which to locate regions of interest in the genome, particularly in situations that lack an appropriate multiple sequence alignment.

Integrated entropy-based approach for analyzing exons and introns in DNA sequences

BACKGROUND

Numerous essential algorithms and methods, including entropy-based quantitative methods, have been developed to analyze complex DNA sequences since the last decade. Exons and introns are the most notable components of DNA and their identification and prediction are always the focus of state-of-the-art research.

RESULTS

In this study, we designed an integrated entropy-based analysis approach, which involves modified topological entropy calculation, genomic signal processing (GSP) method and singular value decomposition (SVD), to investigate exons and introns in DNA sequences. We optimized and implemented the topological entropy and the generalized topological entropy to calculate the complexity of DNA sequences, highlighting the characteristics of repetition sequences. By comparing digitalizing entropy values of exons and introns, we observed that they are significantly different. After we converted DNA data to numerical topological entropy value, we applied SVD method to effectively investigate exon and intron regions on a single gene sequence. Additionally, several genes across five species are used for exon predictions.

CONCLUSIONS

Our approach not only helps to explore the complexity of DNA sequence and its functional elements, but also provides an entropy-based GSP method to analyze exon and intron regions. Our work is feasible across different species and extendable to analyze other components in both coding and noncoding region of DNA sequences.

Improved Prediction of Regulatory Element Using Hybrid Abelian Complexity Features with DNA Sequences

Deciphering the code of cis-regulatory element (CRE) is one of the core issues of current biology. As an important category of CRE, enhancers play crucial roles in gene transcriptional regulations in a distant manner. Further, the disruption of an enhancer can cause abnormal transcription and, thus, trigger human diseases, which means that its accurate identification is currently of broad interest. Here, we introduce an innovative concept, i.e., abelian complexity function (ACF), which is a more complex extension of the classic subword complexity function, for a new coding of DNA sequences. After feature selection by an upper bound estimation and integration with DNA composition features, we developed an enhancer prediction model with hybrid abelian complexity features (HACF). Compared with existing methods, HACF shows consistently superior performance on three sources of enhancer datasets. We tested the generalization ability of HACF by scanning human chromosome 22 to validate previously reported super-enhancers. Meanwhile, we identified novel candidate enhancers which have supports from enhancer-related ENCODE ChIP-seq signals. In summary, HACF improves current enhancer prediction and may be beneficial for further prioritization of functional noncoding variants.

A new model for ancient DNA decay based on paleogenomic meta-analysis

The persistence of DNA over archaeological and paleontological timescales in diverse environments has led to a revolutionary body of paleogenomic research, yet the dynamics of DNA degradation are still poorly understood. We analyzed 185 paleogenomic datasets and compared DNA survival with environmental variables and sample ages. We find cytosine deamination follows a conventional thermal age model, but we find no correlation between DNA fragmentation and sample age over the timespans analyzed, even when controlling for environmental variables. We propose a model for ancient DNA decay wherein fragmentation rapidly reaches a threshold, then subsequently slows. The observed loss of DNA over time may be due to a bulk diffusion process in many cases, highlighting the importance of tissues and environments creating effectively closed systems for DNA preservation. This model of DNA degradation is largely based on mammal bone samples due to published genomic dataset availability. Continued refinement to the model to reflect diverse biological systems and tissue types will further improve our understanding of ancient DNA breakdown dynamics.

Equalizing the information amounts of protein and mRNA by information theory

Based on the Shannon's information communication theory, information amount of the entire length of a polymeric macromolecule can be calculated in bits through adding the entropies of each building block. Proteins, DNA and RNA are such macromolecules. When only the building blocks' variation is considered as the source of entropy, there is seemingly lower information in case of the protein if this approach is applied directly on a protein of specific size and the coding sequence size of the mRNA corresponding to the particular length of the protein. This decrease in the information amount seems contradictory but this apparent conflict is resolved by considering the conformational variations in proteins as a new variable in the calculation and balancing the approximated entropy of the coding part of the mRNA and the protein. Probabilities can change therefore we also assigned hypothetical probabilities to the conformational states, which represent the uneven distribution as the time spent in one conformation, providing the probability of the presence in either or one of the possible conformations. Results that are obtained by using hypothetical probabilities are in line with the experimental values of variations in the conformational-state of protein populations. This equalization approach has further biological relevance that it compensates for the degeneracy in the codon usage during protein translation and it leads to the conclusion that the alphabet size for the protein is rather optimal for the proper protein functioning within the thermodynamic milieu of the cell. The findings were also discussed in relation to the codon bias and have implications in relation to the codon evolution concept. Eventually, this work brings the fields of protein structural studies and molecular protein translation processes together with a novel approach.

Genome-Wide Prediction of DNA Methylation Using DNA Composition and Sequence Complexity in Human

DNA methylation plays a significant role in transcriptional regulation by repressing activity. Change of the DNA methylation level is an important factor affecting the expression of target genes and downstream phenotypes. Because current experimental technologies can only assay a small proportion of CpG sites in the human genome, it is urgent to develop reliable computational models for predicting genome-wide DNA methylation. Here, we proposed a novel algorithm that accurately extracted sequence complexity features (seven features) and developed a support-vector-machine-based prediction model with integration of the reported DNA composition features (trinucleotide frequency and GC content, 65 features) by utilizing the methylation profiles of embryonic stem cells in human. The prediction results from 22 human chromosomes with size-varied windows showed that the 600-bp window achieved the best average accuracy of 94.7%. Moreover, comparisons with two existing methods further showed the superiority of our model, and cross-species predictions on mouse data also demonstrated that our model has certain generalization ability. Finally, a statistical test of the experimental data and the predicted data on functional regions annotated by ChromHMM found that six out of 10 regions were consistent, which implies reliable prediction of unassayed CpG sites. Accordingly, we believe that our novel model will be useful and reliable in predicting DNA methylation.

Gene essentiality prediction based on fractal features and machine learning

Predicting bacterial essential genes using only fractal features.

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.

Symbolic extensions applied to multiscale structure of genomes

A genome of a living organism consists of a long string of symbols over a finite alphabet carrying critical information for the organism. This includes its ability to control post natal growth, homeostasis, adaptation to changes in the surrounding environment, or to biochemically respond at the cellular level to various specific regulatory signals. In this sense, a genome represents a symbolic encoding of a highly organized system of information whose functioning may be revealed as a natural multilayer structure in terms of complexity and prominence. In this paper we use the mathematical theory of symbolic extensions as a framework to shed light onto how this multilayer organization is reflected in the symbolic coding of the genome. The distribution of data in an element of a standard symbolic extension of a dynamical system has a specific form: the symbolic sequence is divided into several subsequences (which we call layers) encoding the dynamics on various "scales". We propose that a similar structure resides within the genomes, building our analogy on some of the most recent findings in the field of regulation of genomic DNA functioning.

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.

A generalized topological entropy for analyzing the complexity of DNA sequences

Topological entropy is one of the most difficult entropies to be used to analyze the DNA sequences, due to the finite sample and high-dimensionality problems. In order to overcome these problems, a generalized topological entropy is introduced. The relationship between the topological entropy and the generalized topological entropy is compared, which shows the topological entropy is a special case of the generalized entropy. As an application the generalized topological entropy in introns, exons and promoter regions was computed, respectively. The results indicate that the entropy of introns is higher than that of exons, and the entropy of the exons is higher than that of the promoter regions for each chromosome, which suggest that DNA sequence of the promoter regions is more regular than the exons and introns.

Coding sequence density estimation via topological pressure

We give a new approach to coding sequence (CDS) density estimation in genomic analysis based on the topological pressure, which we develop from a well known concept in ergodic theory. Topological pressure measures the 'weighted information content' of a finite word, and incorporates 64 parameters which can be interpreted as a choice of weight for each nucleotide triplet. We train the parameters so that the topological pressure fits the observed coding sequence density on the human genome, and use this to give ab initio predictions of CDS density over windows of size around 66,000 bp on the genomes of Mus Musculus, Rhesus Macaque and Drososphilia Melanogaster. While the differences between these genomes are too great to expect that training on the human genome could predict, for example, the exact locations of genes, we demonstrate that our method gives reasonable estimates for the 'coarse scale' problem of predicting CDS density. Inspired again by ergodic theory, the weightings of the nucleotide triplets obtained from our training procedure are used to define a probability distribution on finite sequences, which can be used to distinguish between intron and exon sequences from the human genome of lengths between 750 and 5,000 bp. At the end of the paper, we explain the theoretical underpinning for our approach, which is the theory of Thermodynamic Formalism from the dynamical systems literature. Mathematica and MATLAB implementations of our method are available at http://sourceforge.net/projects/topologicalpres/ .

Structural complexity of DNA sequence

In modern bioinformatics, finding an efficient way to allocate sequence fragments with biological functions is an important issue. This paper presents a structural approach based on context-free grammars extracted from original DNA or protein sequences. This approach is radically different from all those statistical methods. Furthermore, this approach is compared with a topological entropy-based method for consistency and difference of the complexity results.