Evaluation of Statistical Complexity in Viral Genome Sequences

1994

A novel approach to measure sequences complexity and to objectively quantify two sequences similarity is presented. General genetic sequence complexity can be evaluated using sequence compression, for which we design speci c algorithms. A compression algorithm is an objective criterium to determine wether something is random or structured 5]. Every compression algorithm exploits some precise text regularities, codes them in an economic way, and then outputs a possibly shortened sequence. The fact that the resulting description is shorter than the original text, proves that the algorithm reveals a structure in choosing those regularities. This is the most interesting property of compression. Compression is a tool to exhibit the inner structure of a text. Consider the compressor which only deals with direct repeats. It rst looks for inside the input sequence which repeats can be coded, replaces the second occurrence of each repeat by a pointer to the rst and thus performs compression. But also can it compress the input sequence with respect to another sequence, and then measures, by the way of the compression rate, what proportion of the input sequence is signi cantly made of pieces of the reference one. This second use of DNA compression yields to an objective and clearly understandable measurement of sequences similarity (see 6]).

In the present work, we propose a new method to characterize the complexity of the genetic code in DNA strands by using a specific measure of the entropy. The target DNA sequences were the same as those reported by Peng et al. in 1992, analyzing not only the original sequence but also its coding segments and proteins. Also intron-containing sequences were modified to simulate intron-less sequences for comparison. The results reveal that there is not a significant difference for the entropy measure between intron-containing and intron-less sequences, which seems to be in correspondence with other results. In the case of proteins, they exhibit a well defined behavior as a function of the length of the peptide chain. Further work is pursued to analyze a larger database even for nucleotide and aminoacid sequences.

Physical Review Letters, 1999

Profiles of sequence compositional complexity provide a view of the spatial heterogeneity of symbolic sequences at different levels of detail. Sequence compositional complexity profiles are here decomposed into partial profiles using the branching property of the Shannon entropy. This decomposition shows the complexity contributed by each individual symbol or group of symbols. In particular, we apply this method to the mapping rules (symbol groupings) commonly used in DNA sequence analysis. We find that strong-weak bindings are remarkable homogeneously distributed as compared to purine pyrimidine, and that A and T are the most heterogeneous distributed bases.

2001

Kolmogorov Complexity (K (x)) is the optimal compression bound of a given string x. This incomputable yet fundamental property of information has vast implications and applications in the areas of network and system optimization, security, bioinformatics, and emergence (see [1],[2] for an introduction to Kolmogorov Complexity and [2],[3] and [7] for some applications). An ideal approach for compression of information with a known distribution is Huffman Coding, which approaches the entropy of the source distribution.

Computers & chemistry, 2000

A new statistical model for DNA considers a sequence to be a mixture of regions with little structure and regions that are approximate repeats of other subsequences, i.e. instances of repeats do not need to match each other exactly. Both forward- and reverse-complementary repeats are allowed. The model has a small number of parameters which are fitted to the data. In general there are many explanations for a given sequence and how to compute the total probability of the data given the model is shown. Computer algorithms are described for these tasks. The model can be used to compute the information content of a sequence, either in total or base by base. This amounts to looking at sequences from a data-compression point of view and it is argued that this is a good way to tackle intelligent sequence analysis in general.

Signal Processing …, 2007

Based on the normalized maximum likelihood model ]

2007 Data Compression Conference (DCC'07), 2007

This paper introduces a novel algorithm for biological sequence compression that makes use of both statistical properties and repetition within sequences. A panel of experts is maintained to estimate the probability distribution of the next symbol in the sequence to be encoded. Expert probabilities are combined to obtain the final distribution. The resulting information sequence provides insight for further study of the biological sequence. Each symbol is then encoded by arithmetic coding. Experiments show that our algorithm outperforms existing compressors on typical DNA and protein sequence datasets while maintaining a practical running time.

2006

We introduce a complexity measure for symbolic sequences. Starting from a segmentation procedure of the sequence, we define its complexity as the entropy of the distribution of lengths of the domains of relatively uniform composition in which the sequence is decomposed. We show that this quantity verifies the properties usually required for a ``good'' complexity measure. In particular it satisfies the one hump property, is super-additive and has the important property of being dependent of the level of detail in which the sequence is analyzed. Finally we apply it to the evaluation of the complexity profile of some genetic sequences.

A detailed entropy analysis by the recent novelty of 'lumping' is performed in some DNA sequences. On the basis of this, we first report here a negative answer to the question 'can the DNA sequences at the level of nucleotides be generated by a deterministic finite automaton of essentially a small number of states, in the statistical limit?'. What is observed in all cases is an almost linear scaling of the block entropies-up to the numerical precision-close to the one of a mixing ergodic system with a very high topological entropy. The basic result that we report here is that the all the examined biological sequences appear to be very little compressible (they lie near to the incompressible limit). The topological entropy of coding regions appears to be even higher than that of non-coding regions.

Journal of Theoretical Biology, 2008

We define the complexity of DNA sequences as the information content per nucleotide, calculated by means of some Lempel-Ziv data compression algorithm. It is possible to use the statistics of the complexity values of the functional regions of different complete genomes to distinguish among genomes of different domains of life (Archaea, Bacteria and Eukarya). We shall focus on the distribution function of the complexity of noncoding regions. We show that the three domains may be plotted in separate regions within the two-dimensional space where the axes are the skewness coefficient and the curtosis coefficient of the aforementioned distribution. Preliminary results on 15 genomes are introduced.