Symmetry in DNA domains of Yeast chromosomes

INTRODUCTION

Stanley et al. [1, 2] have discovered long-range, power law correlations in sequences of nucleotides in DNA molecules. Occurrence of the correlations has been next approved several times, but the nature of their generation and causes are still obscure [1] -- [7]. The group of Stanley [1, 2] has claimed, that the correlations could be found only in noncoding sequences whereas coding sequences disturb their occurrence. Recently we have found some DNA features which seem to explain previous findings in long-range correlations. In particular, we have analyzed the Yeast chromosomes and found that:

• the distribution of coding sequences is highly correlated [8], there are long-range power-law correlations in their apparance,
• in general, the sense strands of coding sequences are richer in purines than in pyrimidines [8, 9, 10],
• these both features generate long-range correlations in purines and pyrimidines distribution [9].

The finding that sense strand of coding sequences tends to be richer in purines means that there is an asymmetry between sense and antisense strands of the coding sequences. This asymmetry has very important methodological implications: the statistical analysis of DNA molecule has to be done in separate strands of DNA molecule, absolutely with differentiating for sequences: noncoding, coding in the analysed strand (sense) and coding in the complementary strand (antisense). This means that one should take into consideration not only if the sequence is coding but also how it is read what could be very important, since there are strong correlations in the distribution of nucleotides in specific codon positions. Statistical analysis of DNA molecule organization without considering its logical structure has no sense.

RESULTS

It has been found by Feldman et al. [11] that in Yeast chromosome II (Ych2) genes are distributed in regions relatively rich in GC. Nevertheless, recently Carels, Barakat and Bernardi [12] reported that the distribution of coding sequences in human and maize genomes in respect to GC contents of the region are different and that this is not because of gene base composition but because of the composition of noncoding sequences. We have analysed five Yeast chromosomes (1, 2, 3, 6, 11) and we have found that the ORFs longer than 150 triplets (supposed to be coding) have higher GC content and that noncoding sequences have lower GC content than average composition chromosome. But the other striking feature of the Yeast chromosomes is that the ratio of purines to pyrimidines in coding sequences is significantly higher in the sense strand than in antisense strand of gene (especially, high ratio [A]/[T]). Since the whole chromosome are rather well balanced (differences between purines number and pyrimidines number in one strand are below 1%) the asymmetry of coding seqences has to be compensated along the DNA molecule.

Base composition of DNA strand should be reflected in its triplet composition (we use the name triplet for all triplets independently of their position in coding sequence).

We have found almost identical triplet composition for all five analysed chromosomes and for all six phases for each chromosome. What is more important, all these triplet compositions are significantly different from expected abundance counted from the base composition of the DNA strands (Fig. 1).

We have observed the tendency to keep the same deviation from expected value for any triplet and its complementary sequence (we called it antitriplet). That is why we have divided all triplets into two groups - one group consists of triplets rich in purines and the second one - complementary triplets rich in pyrimidines. Each triplet of the first group corresponds to one triplet of the second group. In the Fig. 2 we have shown the abundance of triplets in phase 1 of the Ych2 strand W (stands for Watson). Two plots represent triplets rich in purines and its complementary sequences whereas the third and the fourth plots represent values counted from the base composition of the strand. The observed striking symmetry means that the chromosome is a specific dispersed palindrome - there exist a sequence and somewhere in the same strand another sequence complementary to the first one (!). Since such a symmetry can be found for the stochastic sequence one could find it as trivial observation. However, in the chromosome, the purine/pyrimidine distribution is significantly deviated from statistically expected.

The significant differences in base composition of coding sequences in comparison to noncoding sequences should be reflected in this specific triplet/antitriplet symmetry. We have analysed these differences using chi square values where: is the number of specific triplet rich in purines and is the difference between the number of i-th triplet and a triplet complementary to it. We have counted the chi square values for the whole phases of chromosomes, sequences in Open Reading Frames (ORFs) longer than 150 triplets (presumed coding sequences) and for sequences which are outside ORFs longer than 70 triplets (almost absolutely sure noncoding sequences). Since the whole DNA phases are symmetrical, the asymmetry of coding sequences has to be compensated somewhere along the strand. The compensation of coding sequence in one strand could be done by a coding sequence lying in the opposite strand. This could be possible if:

• the triplet composition of coding sequences is random, or
• there are general rules for triplet composition of all coding sequences and there is a balanced coding function of phases and strands in chromosome, or
• there is no general rule for triplet composition of coding sequences but the distribution of these sequences is not random - it obeys the rule of preservation the symmetry of DNA phase and strand, or
• the organisation of chromosome respects the rule of symmetry by both: nonrandom coding sequence distribution and by compensation the disturbances in the symmetry introduced by coding sequences with intervening noncoding sequences.

The first possibility could explain the finding of Stanley's group [1, 2] that there are no long range correlations in coding sequences, but if this possibility is true, the abundance of triplets in coding sequences should correspond to the stochastic abundance of triplets counted from the base composition, which is not the case.

The assumption that one of the other possibilities is true should implicate that the compensation is a rule imposed in shorter distances than the whole chromosome. We have checked this hypothesis counting the chi square values for symmetry triplet/antitriplet for different parts of Ych2 and plotting the triplets/antitriplets distribution. To cut properly the chromosome we performed the random walk for coding capacity of Ych2 (shown in Fig. 3). The walker has moved along the chromosome and it is going up if it is in the triplet coding in the strand W and down if it is in the triplet coding in the strand C (stands for Crick). Otherwise it has been moving horizontally.

We have divided the Ych2 into parts marked in the picture and next we have analysed the parts for symmetry triplet/antitriplet. The standardized values for abundance of triplets and their antitriplets have been plotted in the Fig. 4. (each pair of the lines in the Fig. 4 representing different parts marked in Fig. 3. differs from the preceding one by the added constant values 0.05 to get clear presentation of the Figure). Notice, that there are two lines (!) - for each X value two data are plotted - one for triplet rich in purines and the second for triplet complementary to the first one, rich in pyrimidines. The plot (B) represents the triplet and antitriplet composition of five Yeast chromosomes (1,2,3,6, and 11), (A) - the whole W strand of Ych2. The plot (d) represents the triplet and antitriplet composition of the sequence of 2903 triplets what is less than 0,4% of the sequences represented in plot (B). The plots (a) - (d) represent hierarchically ordered DNA domains. The self-similarity od DNA is evident on large range of scales - the DNA has appeared as a fractal. For each domain the chi square value for triplet/antitriplet symmetry was up to two orders smaller than for differences between the found codon abundance and its expected (stochastic) values.

In Fig. 5, the plots represent the symmetry triplet/antitriplet in coding sequences (in ORFs longer than 150 codons). The lowest pair of lines represents the codon composition of all ORFs longer than 150 codons in strand W of Ych2. It is easy to notice, that the symmetry of codon/anticodon is broken in the coding sequences. The second pair of lines represents the sum of coding sequences of both strands, but read in the strand W and in the direction of strand W. That means that in fact, the coding sequences of strand C are represented by their complementary sequences. Chi square value for triplet/antitriplet for both strands together is more than two orders lower than for separate strands. Next two pairs show, that the expected values of triplet abundance for nucleotide composition of whole chromosome or for coding sequences are different from realy found in coding sequences. That means that coding sequences of one strand compensate the coding sequences of the another strand restituting the symmetry triplet/antitriplet. Futhermore, this compensation is not connected with stochastic process - the reached symmetry does not represent the expected (stochastic) triplet abundance. The compensation can be even shown in very short sequences. The three top plots represent the symmetry in short sequence (domain d - the last 2903 codons of Ych2). The first represents coding sequence of strand W, the second - coding sequence of strand C and the third one - the whole sequence of strand W of the fragment.

DISCUSSION

To understand the organization of Yeast chromosome we have compiled three findings:

• the longe-range power-like correlations in distribution of coding sequences (proving that distribution of coding sequences along the chromosome is not random),
• asymmetry of coding sequences and
• local symmetry in DNA molecules.

The nonrandom distribution of coding sequences has been proved by statistical analysis of several Yeast chromosomes and by simulation of artificial chromosome with superimposed rules resulting from this analysis, in which we have succeeded in generating the distribution of ORF legth resembling the natural chromosome [8, 9]. The asymmetry of coding sequence is trivial, since we have found the simple asymmetry in nucleotide composition of sense and antisense strand [10]. One can argue that the symmetry triplet/antitriplet is just a result of stochastic rules, since the stochastic DNA with the nucleotide composition of Ych2 is symmetrical. This would be true, nevertheless, the stochastic DNA has a stochastic triplet composition while Ych2 has triplet composition significantly deviated from the stochastic one but still has preserved symmetry. We would like to stress, that symmetry triplet/antitriplet is arbitrarely assumed by us, but in fact the symmetry could probably be found in the sequences of different length.

There is another premise suggesting that symmetry is not the result of stochastic compensation. This premise could be concluded from the data collected by Karlin and Burge [13]. The abundance of dublets in many genomes has specific features: there exist almost the same numbers of dublets and their complementary sequences and the dublet abundance does not correspond to the nucleotide composition of genome (what we have shown for triplets). Sequences the most deviated from the expected ones are the palindromes themselves (ApT, TpA, GpC, CpG). These dublets do not obey any rule of symmetry because they are symmetrical themselves and they do not need to be localy compensated. It has happened that these dublets play very important and specific functions in expression of genetic information.

All these features of DNA molecules have important biological implications. DNA molecule is not a facultative sequence of nucleotides just realizing the demand of information transfer. If we imagine a DNA molecule in a cell which does not need to transfer any information - the molecule would not be a random one (has Stanley's group [1, 5] found it for noncoding sequences?). We suggest that such a molecule would be a symmetrical one. The information can be superimposed on this primary sequence but this is connected with the destabilization of the molecule. The destabilization, if in long sequence, has to be localy compensated and it seems that the compensation could be done by preserving the dispersed palindromic symmetry of the sequence. The compensation can be obtain by specific distribution of these "information transferring sequences" along the strand, e.g. alternative coding by both strands.

The assumption that the information transfer has a secondary role in the organization DNA sequence has other implications. Since not every possible sequence of nucleotides could be realized, only some of theoretically possible sequences could be available by organisms and exploited by them. This could be considered as a restriction imposed on organisms but it maybe also considered as a mechanism which enables the evolution. It explains the famous Haldane Dylemma [14, 15]. In 1937 Haldane showed that organisms have to pay for maintaining active genes with elimination of harmful mutations. Taking together the mutation rate and the size of genome, the cost of this elimination seems to be unbearable and would exterminate the species.

Thus far, the only known mechanism of elimination of such mutations has been the Darwinian selection operating on the phenotypic level. The rules forcing the specific organization of DNA molecules into self-similar and symmetric domains lead to the stabilization of DNA, but simultaneously the number of possible molecular states is restricted. That means, that forbidden states on the molecular level are not and do not have to be checked by Darwinian, phenotypic selection and eliminated by genetic death.

REFERENCES

1. C. K. Peng, S.V. Buldyrev, A.L. Goldberger, S. Havlin, F. Sciortino, M. Simons and H.E. Stanley, Nature 356, 168-170 (1992)
2. H.E. Stanley, S.V. Buldyrev, A.L. Goldberger, J.M. Hausdorff, S. Havlin, J. Mietus, C. K. Peng , F. Sciortino and M. Simons, Physica A 191 1-12 (1992)
3. R.F. Voss, Phys. Rev. Lett. 68, 3805-3808 (1992)
4. R.F. Voss, Phys. Rev. Lett. 71, 1777 (1993)
5. C. K. Peng, S.V. Buldyrev, A.L. Goldberger, S. Havlin, R.N. Mantegna, M. Simons, and H.E. Stanley, Physica A 221180-193 (1995)
6. Mark Ya. Azbel, Phys. Rev. Lett. 75, 168-171 (1995)
7. A. Arneodo, E. Bacry, P.V. Graves and J.F. Muzy, Phys. Rev. Lett. 74 3293-3296 (1995)
8. S. Cebrat and M.R. Dudek (1995) preprint IFT UWr August 893/95, submitted to Phys. Rev. Letts. on August 24, 1995
9. M.R. Dudek and S. Cebrat, preprint IFT UWr October 897/95, submitted to Phys. Rev. Letts. on October 4, 1995
10. S. Cebrat, M.R. Dudek and A. Rogowska, submitted to Yeast
11. H. Feldmann + 96 coauthors, EMBL J. 13, 5795-5809 (1994)
12. N. Carels, A. Barakat and G. Bernardi, Proc. Natl. Acad. Sci. USA 92, 11057 - 11060 (1995)
13. S. Karlin and C. Burge, Trends Genet., 11, 283 - 290, (1995)
14. M. Kimura, The Neutral Theory of Molecular Evolution, Cambridge University Press (1983)
15. J.B.S. Haldane, Natural selection in Darwin's biological work, ed. P.R. Bell, pp 101-149, Cambridge University Press (1959)

Document created and maintained by Jerzy Kakol. Last revised: 17.07.1996