Towards theoretical formalisms

This article deals with the relationship between vocabulary (total number of distinct oligomers or “words”) and text-length (total number of oligomers or “words”) for a coding DNA sequence (CDS). For natural human languages, Heaps established a mathematical formula known as Heaps’ law, which relates vocabulary to text-length. Our analysis shows that Heaps’ law fails to model this relationship for CDSs. Here we develop a mathematical model to establish the relationship between the number of type of words (vocabulary) and the number of words sampled (text-length) for CDSs, when non-overlapping nucleotide strings with the same length are treated as words. We use tangent-hyperbolic function, which captures the saturation property of vocabulary. Based on the parameters of the model, we formulate a mathematical equation, known as “equation of word organization”, whose parameters essentially indicate that nucleotide organization of coding sequences are different from one another. We also compare the word organization of CDSs with the random word distribution and conclude that a CDS is neither similar to a natural human language nor to a random one. Moreover, these sequences have their unique nucleotide organization and it is completely structured for specific biological functioning.     

Word organization in coding DNA: A mathematical model

This article deals with the relationship between vocabulary (total number of distinct oligomers or “words”) and text-length (total number of oligomers or “words”) for a coding DNA sequence (CDS). For natural human languages, Heaps established a mathematical formula known as Heaps' law, which relates vocabulary to text-length. Our analysis shows that Heaps' law fails to model this relationship for CDSs. Here we develop a mathematical model to establish the relationship between the number of type of words (vocabulary) and the number of words sampled (text-length) for CDSs, when non-overlapping nucleotide strings with the same length are treated as words. We use tangent-hyperbolic function, which captures the saturation property of vocabulary. Based on the parameters of the model, we formulate a mathematical equation, known as “equation of word organization”, whose parameters essentially indicate that nucleotide organization of coding sequences are different from one another. We also compare the word organization of CDSs with the random word distribution and conclude that a CDS is neither similar to a natural human language nor to a random one. Moreover, these sequences have their unique nucleotide organization and it is completely structured for specific biological functioning. IM and AS contributed equally to this work.     

Switching effect in prey--predator system

Statistical analysis of DNA base sequences generated from nearest neighbor frequencies by a Monte Carlo technique yields distributions of pyrimidine tracts in good agreement with experimental results. Better agreement with experiment is obtained with nearest-neighbor-frequency based calculations than with calculations based on base composition which assume random base arrangements. The nearest-neighbor-frequency method can also be applied to the analysis of high resolution thermal denaturation profiles, the sequence specific interaction of drugs and proteins, and the distribution of photoproducts produced in DNA by ultraviolet radiation.     

Relationship between DNA Polymorphism and Fixation Time

When there is no recombination among nucleotide sites in DNA sequences, DNA polymorphism and fixation of mutants at nucleotide sites are mutually related. Using the method of gene genealogy, the relationship between the DNA polymorphism and the fixation of mutant nucleotide was quantitatively investigated under the assumption that mutants are selectively neutral, that there is no recombination among nucleotide sites, and that the population is a random mating population with N diploid individuals. The results obtained indicate that the expected number of nucleotide differences between two DNA sequences randomly sampled from the population is 42% less when a mutant at a particular nucleotide site reaches fixation than at a random time, and that heterozygosity is also expected to be less when fixation takes place than at a random time, but the amount of reduction depends on the value of 4Nv in this case, where v is the mutation rate per DNA sequence per generation. The formula for obtaining the expected number of nucleotide differences between the two DNA sequences for a given fixation time is also derived, and indicates that, even when it takes a large number of generations for a mutant to reach fixation, this number is 33% less than at a random time. The computer simulation conducted suggests that the expected number of nucleotide differences between the two DNA sequences at the time when an advantageous mutant becomes fixed is essentially the same as that of neutral mutant if the fixation time is the same. The effect of recombination on the amount of DNA polymorphism was also investigated by using computer simulation.     

Nucleotide, dinucleotide and trinucleotide frequencies explain patterns observed in chaos game representations of DNA sequences.

The chaos game representation (CGR) is a scatter plot derived from a DNA sequence, with each point of the plot corresponding to one base of the sequence. If the DNA sequence were a random collection of bases, the CGR would be a uniformly filled square; conversely, any patterns visible in the CGR represent some pattern (information) in the DNA sequence. In this paper, patterns previously observed in a variety of DNA sequences are explained solely in terms of nucleotide, dinucleotide and trinucleotide frequencies.     

A computer method for finding common base paired helices in aligned sequences: application to the analysis of random sequences.

We describe a new computer program that identifies conserved secondary structures in aligned nucleotide sequences of related single-stranded RNAs. The program employs a series of hash tables to identify and sort common base paired helices that are located in identical positions in more than one sequence. The program gives information on the total number of base paired helices that are conserved between related sequences and provides detailed information about common helices that have a minimum of one or more compensating base changes. The program is useful in the analysis of large biological sequences. We have used it to examine the number and type of complementary segments (potential base paired helices) that can be found in common among related random sequences similar in base composition to 16S rRNA from Escherichia coli. Two types of random sequences were analyzed. One set consisted of sequences that were independent but they had the same mononucleotide composition as the 16S rRNA. The second set contained sequences that were 80% similar to one another. Different results were obtained in the analysis of these two types of random sequences. When 5 sequences that were 80% similar to one another were analyzed, significant numbers of potential helices with two or more independent base changes were observed. When 5 independent sequences were analyzed, no potential helices were found in common. The results of the analyses with random sequences were compared with the number and type of helices found in the phylogenetic model of the secondary structure of 16S ribosomal RNA. Many more helices are conserved among the ribosomal sequences than are found in common among similar random sequences. In addition, conserved helices in the 16S rRNAs are, on the average, longer than the complementary segments that are found in comparable random sequences. The significance of these results and their application in the analysis of long non-ribosomal nucleotide sequences is discussed.     

Diversity in isochore structure among cold-blooded vertebrates based on GC content of coding and non-coding sequences

To review the general consideration about the different compositional structure of warm and cold-blooded vertebrates genomes, we used of the increasing number of genetic sequences, including coding (exons) and non-coding (introns) regions, that have been deposited on the databases throughout last years. The nucleotide distributions of the third codon positions (GC3) have been analyzed in 1510 coding sequences (CDS) of fish, 1414 CDS of amphibians and 320 CDS of reptiles. Also, the relationship between GC content of 74, 56 and 25 CDS of fish, amphibians and reptiles, respectively and that of their corresponding introns (GCI) have been considerated. In accordance with recent data, sequence analysis showed the presence of very GC3-rich CDS in these poikilotherm vertebrates. However, very high diversity in compositional patterns among different orders of fish, amphibians and reptiles was found. Significant positive correlations between GC3 and GCI was also confirmed for the genes analyzed. Nevertheless, introns resulted to be poorer in GC than their corresponding CDS, this difference being larger than in human genome. Because the limited number of available sequences including exons and introns we must be cautious about the results derived from them. However, the indicious of higher GC richness of coding sequences than of their corresponding introns could aid to understand the discrepancy of sequence analysis with the ultracentrifugation studies in cold-blooded vertebrates that did not predict the existence of GC-rich isochores.     

Palindromic Nucleotide Analysis in Human T Cell Receptor Rearrangements

Diversity of T cell receptor (TCR) genes is primarily generated by nucleotide insertions upon rearrangement from their germ line-encoded V, D and J segments. Nucleotide insertions at V-D and D-J junctions are random, but some small subsets of these insertions are exceptional, in that one to three base pairs inversely repeat the sequence of the germline DNA. These short complementary palindromic sequences are called P nucleotides. We apply the ImmunoSeq deep-sequencing assay to the third complementarity determining region (CDR3) of the β chain of T cell receptors, and use the resulting data to study P nucleotides in the repertoire of naïve and memory CD8⁺ and CD4⁺ T cells. We estimate P nucleotide distributions in a cross section of healthy adults and different T cell subtypes. We show that P nucleotide frequency in all T cell subtypes ranges from 1% to 2%, and that the distribution is highly biased with respect to the coding end of the gene segment. Classification of observed palindromic sequences into P nucleotides using a maximum conditional probability model shows that single base P nucleotides are very rare in VDJ recombination; P nucleotides are primarily two bases long. To explore the role of P nucleotides in thymic selection, we compare P nucleotides in productive and non-productive sequences of CD8⁺ naïve T cells. The naïve CD8⁺ T cell clones with P nucleotides are more highly expanded.     

Conformations of A,T-rich DNAs.

DNAs from the genomes of Clostridium perfringens and Cytophaga johnsonii display orthodox A-DNA and B-DNA structures despite their high (A+L) nucleotide content. Unique structures, such as those found for synthetic DNAs having specific special sequences, do therefore not necessarily occur for DNAs having more random base sequence even if these have unusual base compositions. Clostridium perfringens DNA exhibits unusual structural properties only prior to purification by gel filtration.     

Rate of divergence of cellular sequences homologous to segments of Moloney sarcoma virus.

The RNA genome of the Moloney isolate of murine sarcoma virus (M-MSV) consists of two parts--a sarcoma-specific region with no homology to known leukemia viral RNAs, and a shared region present also in Moloney murine leukemia virus RNA. Complementary DNA was isolated which was specific for each part of the M-MSV genome. The DNA of a number of mammalian species was examined for the presence of nucleotide sequences homologous with the two M-MSV regions. Both sets of viral sequences had homologous nucleotide sequences present in normal mouse cellular DNA. MSV-specific sequences found in mouse cellular DNA closely matched those nucleotide sequences found in M-MSV as seen by comparisons of thermal denaturation profiles. In all normal mouse cells tested, the cellular set of M-MSV-specific nucleotide sequences was present in DNA as one to a few copies per cell. The rate of base substitution of M-MSV nucleotide sequences was compared with the rate of evolution of both unique sequences and the hemoglobin gene of various species. Conservation of MSV-specific nucleotide sequences among species was similar to that of mouse globin gene(s) and greater than that of average unique cellular sequences. In contrast, cellular nucleotide sequences that are homologous to the M-MSV-murine leukemia virus "common" nucleotide region were present in multiple copies in mouse cells and were less well matched, as seen by reduced melting profiles of the hybrids. The cellular common nucleotide sequences diverged very rapidly during evolution, with a base substitution rate similar to that reported for some primate and avian endogenous virogenes. The observation that two sets of covalently linked viral sequences evolved at very different rates suggests that the origin of M-MSV may be different from endogenous helper viruses and that cellular sequences homologous to MSV-specific nucleotide sequences may be important to survival.     

Significance of nucleotide sequence alignments: a method for random sequence permutation that preserves dinucleotide and codon usage

The similarity of two nucleotide sequences is often expressed in terms of evolutionary distance, a measure of the amount of change needed to transform one sequence into the other. Given two sequences with a small distance between them, can their similarity be explained by their base composition alone? The nucleotide order of these sequences contributes to their similarity if the distance is much smaller than their average permutation distance, which is obtained by calculating the distances for many random permutations of these sequences. To determine whether their similarity can be explained by their dinucleotide and codon usage, random sequences must be chosen from the set of permuted sequences that preserve dinucleotide and codon usage. The problem of choosing random dinucleotide and codon-preserving permutations can be expressed in the language of graph theory as the problem of generating random Eulerian walks on a directed multigraph. An efficient algorithm for generating such walks is described. This algorithm can be used to choose random sequence permutations that preserve (1) dinucleotide usage, (2) dinucleotide and trinucleotide usage, or (3) dinucleotide and codon usage. For example, the similarity of two 60-nucleotide DNA segments from the human beta-1 interferon gene (nucleotides 196-255 and 499-558) is not just the result of their nonrandom dinucleotide and codon usage.      

Mutants generated by the insertion of random oligonucleotides into the active site of the beta-lactamase gene

We have remodeled the gene coding for beta-lactamase by replacing DNA at the active site with random nucleotide sequences. The oligonucleotide replacement (Phe66XXXSer70XXLys73) preserves the codon for the active serine-70 but also contains 15 base pairs of chemically synthesized random sequences that code for 2.5 x 10(6) amino acid substitutions. From a population of Escherichia coli infected with plasmids containing these random inserts, we have selected seven new active-site mutants that render E. coli resistant to carbenicillin and a series of related analogues. Each of the new mutants contains multiple nucleotide substitutions that code for different amino acids surrounding serine-70. Each of the mutants exhibits a temperature-sensitive beta-lactamase activity. This technique offers the possibility of constructing alternative active sites in enzymes on the basis of biological selection for functional variants.     

A dimer satellite sequence in bonnet monkey DNA consists of distinct monomer subunits

A family of 342 nucleotide fragments was isolated from total bonnet monkey DNA by the restriction endonuclease HaeIII and its base sequence was determined. This family was found to consist of a dimer of two related but distinct nucleotide sequences. Both sequences are closely related to previously reported sequences from African green monkey and human DNA. The two bonnet monkey sequences are unequally divergent from the African green monkey sequence, and have fewer bases in common with each other than they do with African green monkey. Restriction of the dimer with other endonucleases confirms the inequality of the two monomers.     

Neighboring-nucleotide effects on the mutation patterns of the rice genome

DNA composition dynamics across genomes of diverse taxonomy is a major subject of genome analyses. DNA composition changes are characteristics of both replication and repair machineries. We investigated 3,611,007 single nucleotide polymorphisms （SNPs） generated by comparing two sequenced rice genomes from distant inbred lines （subspecies）, including those from 242,811 introns and 45,462 protein-coding sequences （CDSs）. Neighboring-nucleotide effects （NNEs） of these SNPs are diverse, depending on structural content-based classifications （genomewide, intronic, and CDS） and sequence context-based categories （A/C, A/G, A/T, C/G, C/T, and G/T substitutions） of the analyzed SNPs. Strong and evident NNEs and nucleotide proportion biases surrounding the analyzed SNPs were observed in 1-3 bp sequences on both sides of an SNP. Strong biases were observed around neighboring nucleotides of protein-coding SNPs, which exhibit a periodicity of three in nucleotide content, constrained by a combined effect of codon-related rules and DNA repair mechanisms. Unlike a previous finding in the human genome, we found negative correlation between GC contents of chromosomes and the magnitude of corresponding bias of nucleotide C at -1 site and G at ＋1 site. These results will further our understanding of the mutation mechanism in rice as well as its evolutionary implications.     

RANDNA: a random DNA sequence generator

Monte Carlo simulations are useful to verify the significance of data. Genomic regularities, such as the nucleotide correlations or the not uniform distribution of the motifs throughout genomic or mature mRNA sequences, exist and their significance can be checked by means of the Monte Carlo test. The test needs good quality random sequences in order to work, moreover they should have the same nucleotide distribution as the sequences in which the regularities have been found. Random DNA sequences are also useful to estimate the background score of an alignment, that is a threshold below which the resulting score is merely due to chance. We have developed RANDNA, a free software which allows to produce random DNA or RNA sequences setting both their length and the percentage of nucleotide composition. Sequences having the same nucleotide distribution of exonic, intronic or intergenic sequences can be generated. Its graphic interface makes it possible to easily set the parameters that characterize the sequences being produced and saved in a text format file. The pseudo-random number generator function of Borland Delphi 6 is used, since it guarantees a good randomness, a long cycle length and a high speed. We have checked the quality of sequences generated by the software, by means of well-known tests, both by themselves and versus genuine random sequences. We show the good quality of the generated sequences. The software, complete with examples and documentation, is freely available to users from: http://www.introni.it/en/software.     

中国明对虾基因组小卫星重复序列分析

通过对中国明对虾基因组随机DNA片断的测序 ,我们获得了总长度约 6 4 10 0 0个碱基的基因组DNA序列 ,从中共找到 172 0个重复序列。其中 ,小卫星序列的数目为 398个 ,占重复序列总数目的 2 3 14 %。这些小卫星序列的重复单位长度为 7- 16 5个碱基 ,集中分布于 7- 2 1个碱基范围内 ,其中以重复单位长度为 12个碱基的重复序列数目最多 ,为 5 8个 ,占小卫星重复序列总数目的 14 5 7%。不同拷贝数目所对应的重复序列的数目情况为 :拷贝数目为 2的重复单位所组成的重复序列数目最多 ,为 137个 ;其次是拷贝数目为 3的重复序列 ,为12 2个 ,且随着拷贝数目的增加 ,由其所组成的重复序列的数目呈递减的趋势。其中一部分序列见GeneBank数据库 ,登录号为AY6 990 72 -AY6 990 76。 398个重复序列分别由 398种重复单位所组成 ,因而小卫星重复序列的类型很多 ,我们初步分成三类 :两种碱基组成类别、三种碱基组成类别和四种碱基组成类别 ,并进一步根据各个重复序列中所含有的碱基种类的数量从大到小排列这些碱基而分成若干小类。从这些分类中可以看出 ,中国明对虾基因组中的小卫星整体上是富含A T的重复序列 ,并具有一定的“等级制度” ,揭示了其与微卫星重复序列之间的关系 ,即一部分小卫星重复序列可能起源于微卫星     

Scoring functions for computational algorithms applicable to the design of spiked oligonucleotides.

Protein engineering by inserting stretches of random DNA sequences into target genes in combination with adequate screening or selection methods is a versatile technique to elucidate and improve protein functions. Established compounds for generating semi-random DNA sequences are spiked oligonucleotides which are synthesised by interspersing wild type (wt) nucleotides of the target sequence with certain amounts of other nucleotides. Directed spiking strategies reduce the complexity of a library to a manageable format compared with completely random libraries. Computational algorithms render feasible the calculation of appropriate nucleotide mixtures to encode specified amino acid subpopulations. The crucial element in the ranking of spiked codons generated during an iterative algorithm is the scoring function. In this report three scoring functions are analysed: the sum-of-square-differences function s, a modified cubic function c, and a scoring function m derived from maximum likelihood considerations. The impact of these scoring functions on calculated amino acid distributions is demonstrated by an example of mutagenising a domain surrounding the active site serine of subtilisin-like proteases. At default weight settings of one for each amino acid, the new scoring function m is superior to functions s and c in finding matches to a given amino acid population.