Periodicity of DNA in exons.

Abstract

The periodic pattern of DNA in exons is a known phenomenon. It was suggested that one of the initial causes of periodicity could be the universal (RNY)npattern (R = A or G, Y = C or U, N = any base) of ancient RNA. Two major questions were addressed in this paper. Firstly, the cause of DNA periodicity, which was investigated by comparisons between real and simulated coding sequences. Secondly, quantification of DNA periodicity was made using an evolutionary algorithm, which was not previously used for such purposes.
We have shown that simulated coding sequences, which were composed using codon usage frequencies only, demonstrate DNA periodicity very similar to the observed in real exons. It was also found that DNA periodicity disappears in the simulated sequences, when the frequencies of codons become equal. Frequencies of the nucleotides (and the dinucleotide AG) at each location along phase 0 exons were calculated for C. elegans, D. melanogaster and H. sapiens. Two models were used to fit these data, with the key objective of describing periodicity. Both of the models showed that the best-fit curves closely matched the actual data points. The first dynamic period determination model consistently generated a value, which was very close to the period equal to 3 nucleotides. The second fixed period model, as expected, kept the period exactly equal to 3 and did not detract from its goodness of fit.
Conclusion can be drawn that DNA periodicity in exons is determined by codon usage frequencies. It is essential to differentiate between DNA periodicity itself, and the length of the period equal to 3. Periodicity itself is a result of certain combinations of codons with different frequencies typical for a species. The length of period equal to 3, instead, is caused by the triplet nature of genetic code. The models and evolutionary algorithm used for characterising DNA periodicity are proven to be an effective tool for describing the periodicity pattern in a species, when a number of exons in the same phase are analysed.

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BioMed Central
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BMC Molecular Biology
Open Access
Research article
Periodicity of DNA in exons
Stephen T Eskesen1, Frank N Eskesen2, Brian Kinghorn1 and
Anatoly Ruvinsky*1
Address: 1Institute of Genetics and Bioinformatics, University of New England, Armidale, NSW, Australia and 2Thomas J. Watson Research Center,
Yorktown Heights, NY, USA
Email: Stephen T Eskesen - seskesen@hvc.rr.com; Frank N Eskesen - eskesen@us.ibm.com; Brian Kinghorn - bkinghor@une.edu.au;
Anatoly Ruvinsky* - aruvinsk@une.edu.au
* Corresponding author
Codon usageDNA periodicitysimulated sequencesevolutionary algorithm
Abstract
Background: The periodic pattern of DNA in exons is a known phenomenon. It was suggested
that one of the initial causes of periodicity could be the universal (RNY)npattern (R = A or G, Y
= C or U, N = any base) of ancient RNA. Two major questions were addressed in this paper.
Firstly, the cause of DNA periodicity, which was investigated by comparisons between real and
simulated coding sequences. Secondly, quantification of DNA periodicity was made using an
evolutionary algorithm, which was not previously used for such purposes.
Results: We have shown that simulated coding sequences, which were composed using codon
usage frequencies only, demonstrate DNA periodicity very similar to the observed in real exons.
It was also found that DNA periodicity disappears in the simulated sequences, when the
frequencies of codons become equal.
Frequencies of the nucleotides (and the dinucleotide AG) at each location along phase 0 exons
were calculated for C. elegans, D. melanogaster and H. sapiens. Two models were used to fit these
data, with the key objective of describing periodicity. Both of the models showed that the best-fit
curves closely matched the actual data points. The first dynamic period determination model
consistently generated a value, which was very close to the period equal to 3 nucleotides. The
second fixed period model, as expected, kept the period exactly equal to 3 and did not detract
from its goodness of fit.
Conclusions: Conclusion can be drawn that DNA periodicity in exons is determined by codon
usage frequencies. It is essential to differentiate between DNA periodicity itself, and the length of
the period equal to 3. Periodicity itself is a result of certain combinations of codons with different
frequencies typical for a species. The length of period equal to 3, instead, is caused by the triplet
nature of genetic code. The models and evolutionary algorithm used for characterising DNA
periodicity are proven to be an effective tool for describing the periodicity pattern in a species,
when a number of exons in the same phase are analysed.
Published: 18 August 2004
BMC Molecular Biology 2004, 5:12 doi:10.1186/1471-2199-5-12
Received: 05 November 2003
Accepted: 18 August 2004
This article is available from: http://www.biomedcentral.com/1471-2199/5/12
© 2004 Eskesen et al; licensee BioMed Central Ltd.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0),
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Background
Periodicity of DNA in exons, with the period being equal
to 3 nucleotides, has been well known for some time [1-
6]. This periodicity reflects correlations between nucle-
otide positions along coding sequences [7], which is
caused by the asymmetry in base composition at the three
coding positions [8]. This periodicity has also been sug-
gested as a reading-frame monitoring device during trans-
lation, due to interrupted periodic patterns matching with
frame shifts downstream where the periodic pattern
returns [9].
The triplet code has undergone evolution itself, from the
earliest form of the triplet code to what exists today. The
universal DNA periodicity observed in exons suggests a
(RNY)npattern (R = A or G, Y = C or U, N = any base),
which probably was inherited from the earliest mRNA
sequences [10,11].
In this study comparisons between real and simulated
coding sequences were used in attempt to better under-
stand the cause of the DNA periodicity. The only data used
by the simulation program were codon usage frequencies
from real species. Thus the simulated coding sequences
had frequencies of codons very similar to real species. The
major difference, however, was a random position of
codons in simulated sequences.
The periodicity of exons, as well as other coding statistics
can be an additional tool for exon prediction programs
[7]. The distance between two types of nucleotides is
counted, and a period is determined by the distance
between the similar frequencies. For example, if there is a
nucleotide A at one point in a sequence, and other A's are
more common when there are 2, 5, 8 and so on nucle-
otides between them, a period of three can be determined
[7]. Additional methods of finding periodicity include
Fourier analysis [12], the length shuffle Fourier transform
algorithm [13], autocorrelation functions [14] and dis-
tance analysis [15]. We applied two models of an evolu-
tionary algorithm [16,17] to quantify DNA periodicity.
Thus the second objective of this study was investigation
of a new method for quantification of DNA periodicity.
Results
Periodicity of DNA in exons
As mentioned in the Background, periodic 3-nucleotide
pattern has been known for eukaryotic exons for some
time. We studied a question whether DNA periodicity
similar to that observed in exons can be simulated in com-
puter experiments utilising codon usage frequencies
(CUF) of real species as the only source of information.
The computer program GENERATE, which was used in
these experiments, composed artificial coding sequences
using CUF of several species as the only source of informa-
tion. Thus despite random choice the frequencies of
codons in simulated sequences were very similar to the
real CUF.
As an example of these experiments, Figure 1A shows dis-
tribution of Adenine nucleotides in real Drosophila mela-
nogaster exons (phase 0) and in simulated (Figure 1B)
coding sequences (phase 0) created by GENERATE using
D. melanogaster CUF. To avoid any significant influences
of splicing signals, D. melanogaster exons aligned at the 5'
end start from the 10th nucleotide (4th codon). In the sim-
ulated coding sequences periodicity is also highly pro-
nounced and the periodicity patterns observed in D.
melanogaster exons and simulated sequences are nearly
identical (Figure 1A &1B). Other studied species C. elegans
and H. sapiens despite significant differences in AT and GC
content also show high similarity in the periodicity pat-
tern between exons and simulated sequences (data are not
shown). Periodicity of other nucleotides was also
observed and it shown high similarity in both DNA of real
exons and simulated sequences (data are not shown). The
obvious conclusion following from this study is that CUF,
which was the only source of information for the simu-
lated coding sequences, is the crucial factor determining
periodicity.
DNA periodicity in simulated coding sequences was dra-
matically reduced in the experiments where the frequen-
cies of all non-stop codons were made equal (Figure 1C).
This observation strongly supports the conclusion that
codon usage frequencies determine DNA periodicity in
exons. A very light periodicity of Adenine and Thymine
(data are not shown) was caused by the fact that 3 stop
codons and the corresponding combinations of nucle-
otides were present in the simulated coding sequences in
different and much lesser frequencies than other codons.
Cytosine, which is not a component of any stop-codon,
does not show periodic pattern at all because frequencies
of Cytosine containing codons were equal to frequencies
of all other non stop codons. Finally, when frequencies of
all codons, including stop codons, were made equal, no
periodicity was observed in the simulated sequences (Fig-
ure 1D).
Thus the computer simulations lead to a firm conclusion
that 3 nucleotide periodicity observed in DNA of exons is
determined by codon usage frequencies. The triplet nature
of genetic code is rather responsible for the length of the
period but not periodicity itself, as some people might
think.
Quantification of DNA periodicity using an evolutionary
algorithm
Data sets on frequency of the nucleotides and all 16 dinu-
cleotides at each location were constructed for Caenorhab-

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ditis elegans, Drosophila melanogaster and Homo sapiens
phase 0 exons. The frequencies of Adenine and dinucle-
otide pair AG are shown in this paper as an example. Two
models were used to fit to these data, with the key objec-
tive of describing periodicity in the data.
Inspection of Figures 2 to 5 shows that periodicity is quite
apparent, and that the frequencies between peak and
trough frequencies are generally consistent, but some-
times trending in value. Two models were used to accom-
modate this shifting pattern. The first model is:
- where
and b1 to b5 are parameters to be estimated from data.
Because of irregularities in frequencies close to the 5' end
of exons, nucleotide position 20 was take as position i = 1.
- where the value of Offset depends on nucleotide posi-
is predicted frequency at nucleotide position i,
The component b1 + b2i fits an overall linear trend in fre-
quencies, independently from finer-scale periodicity. For
some data sets it could be useful to include a quadratic
term for i.
Parameter b3 gives the amplitude of periodic waves. As 2π
radians describes a full cycle, periodicity is given by
parameter b5. However, if b5 differs from exactly 3, this
generates a shift in phase that is linear with nucleotide
position. This shift combines with static phase shift
parameter b4 to fit the relative frequencies in adjacent
groups of three locations. This is not an ideal model, in
that parameter b5 does not cleanly describe periodicity,
but it proves to work well in practice.
The second model is:
tion I as follows:
A. Adenine periodicity in Drosophila melanogaster exons (Nexons = 32,760)
Figure 1
A. Adenine periodicity in Drosophila melanogaster exons (Nexons = 32,760); B. Adenine periodicity in simulated coding
sequences (Ngenes = 13,065) created by GENERATE using D. melanogaster CUF; C. Adenine periodicity in simulated coding
sequences (Ngenes = 13,065) created by GENERATE using equal frequencies of all non-stop codons and D. melanogaster fre-
quencies of stop codons and D. Adenine periodicity in simulated coding sequences (Ngenes = 13,065) created by GENERATE
using equal frequencies of all codons including frequencies of stop codons. The length of coding sequences was determined by
the program.
A.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
147 1013 16 19 22 25 28 31 34 37 40 43 46 49
B.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
14710 13 16 19 22 25 28 31 34 37 40 43 46 49
C.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
13579 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
D.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
147 10 131619 22 25 28 3134374043 4649
ˆ
....
Ybb i
2
b Sin
3
b
b
i
i=++
+
()






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1
1
4
5
2π
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ˆ
....
Yb b i
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b Sin
3
i
i=++
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
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2
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π Offset

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Curves of best-fit for Adenine in phase 0 exons compared to actual frequencies
Figure 2
Curves of best-fit for Adenine in phase 0 exons compared to actual frequencies. Pink points represent frequencies of nucle-
otide A in phase 0 C. elegans, D. melanogaster and H. sapiens exons aligned at the 5' end. Blue points represent the best-fit curve
for the data points in an ideal situation, from position 20–100. The scales of the graphs were altered to provide better contrast
between the data points.
Curve of best-fit in phase 0 C. elegans exons - Adenine
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
16
1116 2126313641465156616671 7681869196
Nucleotide position
Frequency
Curve of best-fit in D. melanogaster phase 0 exons - Adenine
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
159
1317 21 2529 333741 454953 57 61656973 77 8185 899397
Nucleotide position
Frequency
Curve of best-fit in H. sapiens phase 0 exons - Adenine
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
159
13172125 29 3337 414549 53 5761 6569 7377 8185 899397
Nucleotide position
Frequency

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Curves of best-fit for dinucleotide AG in phase 0 exons compared to actual frequencies
Figure 3
Curves of best-fit for dinucleotide AG in phase 0 exons compared to actual frequencies. Pink points represent frequencies of
AG in phase 0 C. elegans D. melanogaster and H. sapiens exons aligned at the 5' end. Blue points represent the best-fit curve for
the data points in an ideal situation, from position 20–100. The scales of the graphs were altered to provide better contrast
between the data points.
Curve of best-fit in phase 0 C. elegans phase 0 exons - dinucleotide AG
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
159
13172125293337 41454953 57616569 73778185 8993 97
Nucleotide position
Frequency
Curve of best-fit in D. melanogaster phase 0 exons - dinucleotide AG
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
159
1317 2125 293337 414549 535761 656973 7781 858993 97
Nucleotide position
Frequency
Curve of best-fit in H. sapiens phase 0 exons - dinucleotide AG
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
159
13 1721252933 3741 45 4953576165697377 8185 89 9397
Nucleotide position
Frequency