Universal sequence map (USM) of arbitrary discrete sequences

BACKGROUND: For over a decade the idea of representing biological sequences in a continuous coordinate space has maintained its appeal but not been fully realized. The basic idea is that any sequence of symbols may define trajectories in the continuous space conserving all its statistical properties. Ideally, such a representation would allow scale independent sequence analysis – without the context of fixed memory length. A simple example would consist on being able to infer the homology between two sequences solely by comparing the coordinates of any two homologous units. RESULTS: We have successfully identified such an iterative function for bijective mappingψ of discrete sequences into objects of continuous state space that enable scale-independent sequence analysis. The technique, named Universal Sequence Mapping (USM), is applicable to sequences with an arbitrary length and arbitrary number of unique units and generates a representation where map distance estimates sequence similarity. The novel USM procedure is based on earlier work by these and other authors on the properties of Chaos Game Representation (CGR). The latter enables the representation of 4 unit type sequences (like DNA) as an order free Markov Chain transition table. The properties of USM are illustrated with test data and can be verified for other data by using the accompanying web-based tool:http://bioinformatics.musc.edu/~jonas/usm/. CONCLUSIONS: USM is shown to enable a statistical mechanics approach to sequence analysis. The scale independent representation frees sequence analysis from the need to assume a memory length in the investigation of syntactic rules

Computing distribution of scale independent motifs in biological sequences

The use of Chaos Game Representation (CGR) or its generalization, Universal Sequence Maps (USM), to describe the distribution of biological sequences has been found objectionable because of the fractal structure of that coordinate system. Consequently, the investigation of distribution of symbolic motifs at multiple scales is hampered by an inexact association between distance and sequence dissimilarity. A solution to this problem could unleash the use of iterative maps as phase-state representation of sequences where its statistical properties can be conveniently investigated. In this study a family of kernel density functions is described that accommodates the fractal nature of iterative function representations of symbolic sequences and, consequently, enables the exact investigation of sequence motifs of arbitrary lengths in that scale-independent representation. Furthermore, the proposed kernel density includes both Markovian succession and currently used alignment-free sequence dissimilarity metrics as special solutions. Therefore, the fractal kernel described is in fact a generalization that provides a common framework for a diverse suite of sequence analysis techniques

Fractal MapReduce decomposition of sequence alignment

This work was supported in part by the Center for Clinical and Translational Sciences of the University of Alabama at Birmingham under contract no. 5UL1 RR025777-03 from NIH National Center for Research Resources, by the National Cancer Institute grant 1U24CA143883-01, by the European Union FP7 PNEUMOPATH (HEALTH F3 2009 222983).Background: The dramatic fall in the cost of genomic sequencing, and the increasing convenience of distributed cloud computing resources, positions the MapReduce coding pattern as a cornerstone of scalable bioinformatics algorithm development. In some cases an algorithm will find a natural distribution via use of map functions to process vectorized components, followed by a reduce of aggregate intermediate results. However, for some data analysis procedures such as sequence analysis, a more fundamental reformulation may be required. Results: In this report we describe a solution to sequence comparison that can be thoroughly decomposed into multiple rounds of map and reduce operations. The route taken makes use of iterated maps, a fractal analysis technique, that has been found to provide a "alignment-free" solution to sequence analysis and comparison. That is, a solution that does not require dynamic programming, relying on a numeric Chaos Game Representation (CGR) data structure. This claim is demonstrated in this report by calculating the length of the longest similar segment by inspecting only the USM coordinates of two analogous units: with no resort to dynamic programming. Conclusions: The procedure described is an attempt at extreme decomposition and parallelization of sequence alignment in anticipation of a volume of genomic sequence data that cannot be met by current algorithmic frameworks. The solution found is delivered with a browser-based application (webApp), highlighting the browser's emergence as an environment for high performance distributed computing. Availability: Public distribution of accompanying software library with open source and version control at http://usm.github.com. Also available as a webApp through Google Chrome's WebStore http://chrome.google.com/webstore: search with "usm".publishersversionpublishe

Biological sequences as pictures – a generic two dimensional solution for iterated maps

<p>Abstract</p> <p>Background</p> <p>Representing symbolic sequences graphically using iterated maps has enjoyed an enduring popularity since it was first proposed in Jeffrey 1990 as chaos game representation (CGR). The usefulness of this representation goes beyond the convenience of a scale independent representation. It provides a variable memory length representation of transition. This includes the representation of succession with non-integer order, which comes with the promise of generalizing Markovian formalisms. The original proposal targeted genomic sequences only but since then several generalizations have been proposed, many specifically designed to handle protein data.</p> <p>Results</p> <p>The challenge of a general solution is that of deriving a bijective transformation of symbolic sequences into bi-dimensional planes. More specifically, it requires the regular fractal nesting of polygons. A first attempt at a general solution was proposed by Fiser 1994 by using non-overlapping circles that contain the polygons. This was used as a starting point to identify a more efficient solution where the encapsulating circles can overlap without the same happening for the sequence maps which are circumscribed to fractal polygon domains.</p> <p>Conclusion</p> <p>We identified the optimal inscribed packing solution for iterated maps of any Biological sequence, indeed of any symbolic sequence. The new solution maintains the prized bijective mapping property and includes the Sierpinski triangle and the CGR square as particular solutions of the more encompassing formulation.</p

Multi-level dynamic modeling in biological systems : application of hybrid Petri nets to network simulation

The recent progress in the high-throughput experimental technologies allows the reconstruction of many biological networks and to evaluate changes in proteins, genes and metabolites levels in different conditions. On the other hand, computational models, when complemented with regulatory information, can be used to predict the phenotype of an organism under different genetic and environmental conditions. These computational methods can be used for example to identify molecular targets capable of inactivating a bacterium and to understand its virulence factors. This work proposes a hybrid metabolic-regulatory Petri net approach that is based on the combination of approximate enzyme-kinetic rate laws and Petri nets. A prototypic network model is used as a test-case to illustrate the application of these concepts in Systems Biology.This work was partially supported by post-doctoral grant by Fundacao para a Ciencia e a Tecnologia (FCT) (SFRH/BPD/80784/2011), project PneumoSyS - A Systems Biology approach to the role of pneumococcal carbon metabolism in colonization and invasive disease (FCT contract: PTDC/SAU-MII/100964/2008) and by FCT (INESC-ID multiannual funding) through the PIDDAC program funds

Pattern matching through Chaos Game Representation: bridging numerical and discrete data structures for biological sequence analysis

This work was partially supported by FCT through the PIDDAC Program funds (INESC-ID multiannual funding) and under grant PEst-OE/EEI/LA0008/2011 (IT multiannual funding). In addition, it was also partially funded by projects HIVCONTROL (PTDC/EEA-CRO/100128/2008, S. Vinga, PI), TAGS (PTDC/EIA-EIA/112283/2009) and NEUROCLINOMICS (PTDC/EIA-EIA/111239/2009) from FCT (Portugal).Background: Chaos Game Representation (CGR) is an iterated function that bijectively maps discrete sequences into a continuous domain. As a result, discrete sequences can be object of statistical and topological analyses otherwise reserved to numerical systems. Characteristically, CGR coordinates of substrings sharing an L-long suffix will be located within 2(-L) distance of each other. In the two decades since its original proposal, CGR has been generalized beyond its original focus on genomic sequences and has been successfully applied to a wide range of problems in bioinformatics. This report explores the possibility that it can be further extended to approach algorithms that rely on discrete, graph-based representations. Results: The exploratory analysis described here consisted of selecting foundational string problems and refactoring them using CGR-based algorithms. We found that CGR can take the role of suffix trees and emulate sophisticated string algorithms, efficiently solving exact and approximate string matching problems such as finding all palindromes and tandem repeats, and matching with mismatches. The common feature of these problems is that they use longest common extension (LCE) queries as subtasks of their procedures, which we show to have a constant time solution with CGR. Additionally, we show that CGR can be used as a rolling hash function within the Rabin-Karp algorithm. Conclusions: The analysis of biological sequences relies on algorithmic foundations facing mounting challenges, both logistic (performance) and analytical (lack of unifying mathematical framework). CGR is found to provide the latter and to promise the former: graph-based data structures for sequence analysis operations are entailed by numerical-based data structures produced by CGR maps, providing a unifying analytical framework for a diversity of pattern matching problems.publishersversionpublishe

Pattern matching through Chaos Game Representation: bridging numerical and discrete data structures for biological sequence analysis

BACKGROUND: Chaos Game Representation (CGR) is an iterated function that bijectively maps discrete sequences into a continuous domain. As a result, discrete sequences can be object of statistical and topological analyses otherwise reserved to numerical systems. Characteristically, CGR coordinates of substrings sharing an L-long suffix will be located within 2(-L )distance of each other. In the two decades since its original proposal, CGR has been generalized beyond its original focus on genomic sequences and has been successfully applied to a wide range of problems in bioinformatics. This report explores the possibility that it can be further extended to approach algorithms that rely on discrete, graph-based representations. RESULTS: The exploratory analysis described here consisted of selecting foundational string problems and refactoring them using CGR-based algorithms. We found that CGR can take the role of suffix trees and emulate sophisticated string algorithms, efficiently solving exact and approximate string matching problems such as finding all palindromes and tandem repeats, and matching with mismatches. The common feature of these problems is that they use longest common extension (LCE) queries as subtasks of their procedures, which we show to have a constant time solution with CGR. Additionally, we show that CGR can be used as a rolling hash function within the Rabin-Karp algorithm. CONCLUSIONS: The analysis of biological sequences relies on algorithmic foundations facing mounting challenges, both logistic (performance) and analytical (lack of unifying mathematical framework). CGR is found to provide the latter and to promise the former: graph-based data structures for sequence analysis operations are entailed by numerical-based data structures produced by CGR maps, providing a unifying analytical framework for a diversity of pattern matching problems

Local Renyi entropic profiles of DNA sequences

<p>Abstract</p> <p>Background</p> <p>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.</p> <p>Results</p> <p>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 <url>http://kdbio.inesc-id.pt/~svinga/ep/</url>.</p> <p>Conclusion</p> <p>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.</p

Time-Lagged Correlation Analysis of Shellfish Toxicity Reveals Predictive Links to Adjacent Areas, Species, and Environmental Conditions

This work was funded by the project “MATISSE: A machine learning-based forecasting system for shellfish safety” (DSAIPA/DS/0026/2019). The work was also supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) with references CEECINST/00102/2018, CEECIND/01399/2017, UIDB/04326/2020, UIDP/04326/2020 and LA/P/0101/2020 (CCMAR), UIDB/04516/2020 (NOVA LINCS), UIDB/00297/2020 (NovaMath), and UIDB/50021/2020 (INESC-ID). This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 951970 (OLISSIPO project).Diarrhetic Shellfish Poisoning (DSP) is an acute intoxication caused by the consumption of contaminated shellfish, which is common in many regions of the world. To safeguard human health, most countries implement programs focused on the surveillance of toxic phytoplankton abundance and shellfish toxicity levels, an effort that can be complemented by a deeper understanding of the underlying phenomena. In this work, we identify patterns of seasonality in shellfish toxicity across the Portuguese coast and analyse time-lagged correlations between this toxicity and various potential risk factors. We extend the understanding of these relations through the introduction of temporal lags, allowing the analysis of time series at different points in time and the study of the predictive power of the tested variables. This study confirms previous findings about toxicity seasonality patterns on the Portuguese coast and provides further quantitative data about the relations between shellfish toxicity and geographical location, shellfish species, toxic phytoplankton abundances, and environmental conditions. Furthermore, multiple pairs of areas and shellfish species are identified as having correlations high enough to allow for a predictive analysis. These results represent the first step towards understanding the dynamics of DSP toxicity in Portuguese shellfish producing areas, such as temporal and spatial variability, and towards the development of a shellfish safety forecasting system.publishersversionpublishe