Circular Code Research Articles

Systematic exchanges between nucleotides: Genomic swinger repeats and swinger transcription in human mitochondria

Chargaff׳s second parity rule, quasi-equal single strand frequencies for complementary nucleotides, presumably results from insertion of repeats and inverted repeats during sequence genesis. Vertebrate mitogenomes escape this rule because repeats are counterselected: their hybridization produces loop bulges whose deletion is deleterious. Some DNA/RNA sequences match mitogenomes only after assuming one among 23 systematic nucleotide exchanges (swinger DNA/RNA: nine symmetric, e.g. A↔C; and 14 asymmetric, e.g. A→C→G→A). Swinger-transformed repeats do not hybridize, escaping selection against deletions due to bulge formation. Blast analyses of the human mitogenome detect swinger repeats for all 23 swinger types, more than in randomized sequences with identical length and nucleotide contents. Mean genomic swinger repeat lengths increase with observed human swinger RNA frequencies: swinger repeat and swinger RNA productions appear linked, perhaps by swinger RNA retrotranscription. Mean swinger repeat lengths are proportional to reading frame retrievability, post-swinger transformation, by the natural circular code. Genomic swinger repeats confirm at genomic level, independently of swinger RNA detection, occurrence of swinger polymerizations. They suggest that repeats, and swinger repeats in particular, contribute to genome genesis.

The maximal C3 self-complementary trinucleotide circular code X in genes of bacteria, eukaryotes, plasmids and viruses

In 1996, a set X of 20 trinucleotides is identified in genes of both prokaryotes and eukaryotes which has in average the highest occurrence in reading frame compared to the two shifted frames (Arquès and Michel, 1996). Furthermore, this set X has an interesting mathematical property as X is a maximal C3 self-complementary trinucleotide circular code (Arquès and Michel, 1996). In 2014, the number of trinucleotides in prokaryotic genes has been multiplied by a factor of 527. Furthermore, two new gene kingdoms of plasmids and viruses contain enough trinucleotide data to be analysed. The approach used in 1996 for identifying a preferential frame for a trinucleotide is quantified here with a new definition analysing the occurrence probability of a complementary/permutation (CP) trinucleotide set in a gene kingdom. Furthermore, in order to increase the statistical significance of results compared to those of 1996, the circular code X is studied on several gene taxonomic groups in a kingdom. Based on this new statistical approach, the circular code X is strengthened in genes of prokaryotes and eukaryotes, and now also identified in genes of plasmids. A subset of X with 18 or 16 trinucleotides is identified in genes of viruses. Furthermore, a simple probabilistic model based on the independent occurrence of trinucleotides in reading frame of genes explains the circular code frequencies and asymmetries observed in the shifted frames in all studied gene kingdoms. Finally, the developed approach allows to identify variant X codes in genes, i.e. trinucleotide codes which differ from X. In genes of bacteria, eukaryotes and plasmids, 14 among the 47 studied gene taxonomic groups (about 30%) have variant X codes. Seven variant X codes are identified with at least 16 trinucleotides of X. Two variant X codes XA in cyanobacteria and plasmids of cyanobacteria, and XD in birds are self-complementary, without permuted trinucleotides but non-circular. Five variant X codes XB in deinococcus, plasmids of chloroflexi and deinococcus, mammals and kinetoplasts, XC in elusimicrobia and apicomplexans, XE in fishes, XF in insects, and XG in basidiomycetes and plasmids of spirochaetes are C3 self-complementary circular. In genes of viruses, no variant X code is found.

An extended genetic scale of reading frame coding.

The reading frame coding (RFC) of codes (sets) of trinucleotides is a genetic concept which has been largely ignored during the last 50 years. An extended definition of the statistical parameter PrRFC (Michel, 2014) is proposed here for analysing the probability (efficiency) of reading frame coding of usage of any trinucleotide code. It is applied to the analysis of the RFC efficiency of usage of the C(3) self-complementary trinucleotide circular code X identified in prokaryotic and eukaryotic genes (Arquès and Michel, 1996). The usage of X is called usage XU. The highest RFC probabilities of usage XU are identified in bacterial plasmids and bacteria (about 49.0%). Then, by decreasing values, the RFC probabilities of usage XU are observed in archaea (47.5%), viruses (45.4%) and nuclear eukaryotes (42.8%). The lowest RFC probabilities of usage XU are found in mitochondria and chloroplasts (about 36.5%). Thus, genes contain information for reading frame coding. Such a genetic property which to our knowledge has never been identified, may bring new insights in the origin and evolution of the genetic code.

On the hierarchy of trinucleotide n-circular codes and their corresponding amino acids

Circular codes are putative remnants of primeval comma-free codes and are potentially involved in detecting and maintaining the normal reading frame in protein coding sequences. In Michel and Pirillo (2013a) it was shown by computer algorithm that no maximal trinucleotide circular code can encode more than 18 different amino acids under the standard version of the genetic code. For comma-free codes the maximum is even less, namely 13 (Michel, 2014). The main purpose of this paper is to investigate these facts from a mathematical point of view and to show why the codes with the best-known error detecting properties are limited in the number of amino acids they can encode. We introduce five hierarchically ordered classes of trinucleotide codes including the well-known comma-free and circular codes and prove combinatorically that it is impossible to encode all amino acids using codes from four out of the five classes that have the strongest error detecting properties. However, it is possible to encode all 20 amino acids using codes from the largest class with the weakest properties. Additionally, we develop a handy criterion for circularity. As an application, it is shown that all codes from a special class of trinucleotide codes which includes the RNY-primeval code (Shepherd, 1986) are automatically circular. We also list which amino acids these codes encode.

Circular code motifs in the ribosome decoding center

A translation (framing) code based on the circular code was proposed in Michel (2012) with the identification of X circular code motifs (X motifs shortly) in the bacterial rRNA of Thermus thermophilus, in particular in the ribosome decoding center. Three classes of X motifs are now identified in the rRNAs of bacteria Escherichia coli and Thermus thermophilus, archaea Pyrococcus furiosus, nuclear eukaryotes Saccharomyces cerevisiae, Triticum aestivum and Homo sapiens, and chloroplast Spinacia oleracea. The universally conserved nucleotides A1492 and A1493 in all studied rRNAs (bacteria, archaea, nuclear eukaryotes, and chloroplasts) belong to X motifs (called mAA). The conserved nucleotide G530 in rRNAs of bacteria and archaea belongs to X motifs (called mG). Furthermore, the X motif mG is also found in rRNAs of nuclear eukaryotes and chloroplasts. Finally, a potentially important X motif, called m, is identified in all studied rRNAs. With the available crystallographic structures of the Protein Data Bank PDB, we also show that these X motifs mAA, mG, and m belong to the ribosome decoding center of all studied rRNAs with possible interaction with the mRNA X motifs and the tRNA X motifs. The three classes of X motifs identified here in rRNAs of several and different organisms strengthen the concept of translation code based on the circular code.

Circular codes, symmetries and transformations

Circular codes, putative remnants of primeval comma-free codes, have gained considerable attention in the last years. In fact they represent a second kind of genetic code potentially involved in detecting and maintaining the normal reading frame in protein coding sequences. The discovering of an universal code across species suggested many theoretical and experimental questions. However, there is a key aspect that relates circular codes to symmetries and transformations that remains to a large extent unexplored. In this article we aim at addressing the issue by studying the symmetries and transformations that connect different circular codes. The main result is that the class of 216 C3 maximal self-complementary codes can be partitioned into 27 equivalence classes defined by a particular set of transformations. We show that such transformations can be put in a group theoretic framework with an intuitive geometric interpretation. More general mathematical results about symmetry transformations which are valid for any kind of circular codes are also presented. Our results pave the way to the study of the biological consequences of the mathematical structure behind circular codes and contribute to shed light on the evolutionary steps that led to the observed symmetries of present codes.

Design of circular dot pattern code (CDPC) for maximum information capacity and robustness on geometric distortion/noise

One dimensional or linear bar code has been used for distribution purposes such as product information and distribution channel identification. Those linear bar codes can support only one direction...

A genetic scale of reading frame coding

The reading frame coding (RFC) of codes (sets) of trinucleotides is a genetic concept which has been largely ignored during the last 50 years. A first objective is the definition of a new and simple statistical parameter PrRFC for analysing the probability (efficiency) of reading frame coding (RFC) of any trinucleotide code. A second objective is to reveal different classes and subclasses of trinucleotide codes involved in reading frame coding: the circular codes of 20 trinucleotides and the bijective genetic codes of 20 trinucleotides coding the 20 amino acids. This approach allows us to propose a genetic scale of reading frame coding which ranges from 1/3 with the random codes (RFC probability identical in the three frames) to 1 with the comma-free circular codes (RFC probability maximal in the reading frame and null in the two shifted frames). This genetic scale shows, in particular, the reading frame coding probabilities of the 12,964,440 circular codes (PrRFC=83.2% in average), the 216 C3 self-complementary circular codes (PrRFC=84.1% in average) including the code X identified in eukaryotic and prokaryotic genes (PrRFC=81.3%) and the 339,738,624 bijective genetic codes (PrRFC=61.5% in average) including the 52 codes without permuted trinucleotides (PrRFC=66.0% in average). Otherwise, the reading frame coding probabilities of each trinucleotide code coding an amino acid with the universal genetic code are also determined. The four amino acids Gly, Lys, Phe and Pro are coded by codes (not circular) with RFC probabilities equal to 2/3, 1/2, 1/2 and 2/3, respectively. The amino acid Leu is coded by a circular code (not comma-free) with a RFC probability equal to 18/19. The 15 other amino acids are coded by comma-free circular codes, i.e. with RFC probabilities equal to 1. The identification of coding properties in some classes of trinucleotide codes studied here may bring new insights in the origin and evolution of the genetic code.

Bijective transformation circular codes and nucleotide exchanging RNA transcription

The C(3) self-complementary circular code X identified in genes of prokaryotes and eukaryotes is a set of 20 trinucleotides enabling reading frame retrieval and maintenance, i.e. a framing code (Arquès and Michel, 1996; Michel, 2012, 2013). Some mitochondrial RNAs correspond to DNA sequences when RNA transcription systematically exchanges between nucleotides (Seligmann, 2013a,b). We study here the 23 bijective transformation codes ΠX of X which may code nucleotide exchanging RNA transcription as suggested by this mitochondrial observation. The 23 bijective transformation codes ΠX are C(3) trinucleotide circular codes, seven of them are also self-complementary. Furthermore, several correlations are observed between the Reading Frame Retrieval (RFR) probability of bijective transformation codes ΠX and the different biological properties of ΠX related to their numbers of RNAs in GenBank's EST database, their polymerization rate, their number of amino acids and the chirality of amino acids they code. Results suggest that the circular code X with the functions of reading frame retrieval and maintenance in regular RNA transcription, may also have, through its bijective transformation codes ΠX, the same functions in nucleotide exchanging RNA transcription. Associations with properties such as amino acid chirality suggest that the RFR of X and its bijective transformations molded the origins of the genetic code's machinery.

Triplex DNA:RNA, 3′-to-5′ Inverted RNA and Protein Coding in Mitochondrial Genomes

Triple-stranded DNA:RNA helices of unknown function in vertebrate mitochondria associate with replication and transcription. Antiparallel Hoogsteen pairings form triplexes at physiological conditions. Intermolecular antiparallel triplexes require inverted 3'-to-5' RNA polymerization, which was never observed. Three rare, long natural 3'-to-5' inverted GenBank RNAs from mice mitochondria suggest occasional inverted transcription, putatively coding for proteins. BLAST aligns 18 GenBank-stored proteins with hypothetical proteins translated from the 3'-to-5' inverted Mus musculus mitochondrial genome. Three are DNA-binding, five are membrane proteins. 25% of main frame codons contribute to their 3'-to-5' overlap coding. Properties of these codons match those of overlap coding protein genes, as compared to codons not expected involved in inverted coding: a) nucleotide contents at synonymous codon positions in mitochondrial genomes fit replicational deamination gradients (A->G and C->T), but digress from gradients when functioning as nonsynonymous positions in putative 3'-to-5' overlapping genes; b) bias against 'circular code' codons (codon groups creating unambiguity between frames), and favouring homogenous codons (AAA, CCC, GGG, TTT) characterize overlapping genes, including putative 3'-to-5' overlapping genes, as compared to nonoverlapping coding sequences from the same main frame gene. This signature correlates with digression from deamination gradients. Deamination and circular code tests confirm independently alignment-based predictions of overlapping 3'-to-5' protein coding genes. Results indicate varying expression for different 3'-to-5' overlapping genes. Inverted 3'-to-5' RNA is produced, perhaps by an unknown RNA polymerase (invertase) putatively coded by 3'-to-5' inverted RNA.

Transition and Transversion on the Common Trinucleotide Circular Code

In 1996, a trinucleotide circular code which is maximum, self-complementary, and , called , was identified statistically on a large gene population of eukaryotes and prokaryotes (Arquès and Michel (1996)). Transition and transversions I and II are classical molecular evolution processes. A comprehensive computer analysis of these three evolution processes in the code shows some new results; in particular (i) transversion I on the 2nd position of any subset of trinucleotides of generates trinucleotide circular codes which are always and (ii) transversion II on the three positions of any subset of trinucleotides of yields no trinucleotide circular codes. These new results extend our theory of circular code in genes to its evolution under transition and transversion.

Circular code motifs in transfer RNAs

In 1996, a trinucleotide circular code X is identified in genes of prokaryotes and eukaryotes (Arquès and Michel, 1996). In 2012, X motifs are identified in the transfer RNA (tRNA) Phe and 16S ribosomal RNA (Michel, 2012). A statistical analysis of X motifs in all available tRNAs of prokaryotes and eukaryotes in the genomic tRNA database (September 2012, http://lowelab.ucsc.edu/GtRNAdb/, Lowe and Eddy, 1997) is carried out here. For this purpose, a search algorithm of X motifs in a DNA sequence is developed. Two definitions allow to determine the occurrence probabilities of X motifs and the circular codes X, X1=P(X) and X2=P2(X) (P being a circular permutation map applied on X) in a population of tRNAs. This approach identifies X motifs in the 5′ and/or 3′ regions of 16 isoaccepting tRNAs (except for the tRNAs Arg, His, Ser and Trp). The statistical analyses are performed on different and large tRNA populations according to the taxonomy (prokaryotes and eukaryotes), tRNA length and tRNA score. Finally, a circular code property observed in genes of prokaryotes and eukaryotes is identified in the 3′ regions of 19 isoaccepting tRNAs of prokaryotes and eukaryotes (except for the tRNA Leu). The identification of X motifs and a gene circular code property in tRNAs strengthens the concept proposed in Michel (2012) of a possible translation (framing) code based on a circular code.

Dinucleotide Circular Codes

We begin here a combinatorial study of dinucleotide circular codes. A word written on a circle is called circular. A set of dinucleotides is a circular code if all circular words constructed with this set have a unique decomposition. Propositions based on a letter necklace allow to determine the 24 maximum dinucleotide circular codes (of 6 elements). A partition property is also identified with eight self-complementary maximum dinucleotide circular codes and two classes of eight maximum dinucleotide circular codes in bijective correspondence by the complementarity map.

Polymerization of non-complementary RNA: Systematic symmetric nucleotide exchanges mainly involving uracil produce mitochondrial RNA transcripts coding for cryptic overlapping genes

Usual DNA→RNA transcription exchanges T→U. Assuming different systematic symmetric nucleotide exchanges during translation, some GenBank RNAs match exactly human mitochondrial sequences (exchange rules listed in decreasing transcript frequencies): C↔U, A↔U, A↔U+C↔G (two nucleotide pairs exchanged), G↔U, A↔G, C↔G, none for A↔C, A↔G+C↔U, and A↔C+G↔U. Most unusual transcripts involve exchanging uracil. Independent measures of rates of rare replicational enzymatic DNA nucleotide misinsertions predict frequencies of RNA transcripts systematically exchanging the corresponding misinserted nucleotides. Exchange transcripts self-hybridize less than other gene regions, self-hybridization increases with length, suggesting endoribonuclease-limited elongation. Blast detects stop codon depleted putative protein coding overlapping genes within exchange-transcribed mitochondrial genes. These align with existing GenBank proteins (mainly metazoan origins, prokaryotic and viral origins underrepresented). These GenBank proteins frequently interact with RNA/DNA, are membrane transporters, or are typical of mitochondrial metabolism. Nucleotide exchange transcript frequencies increase with overlapping gene densities and stop densities, indicating finely tuned counterbalancing regulation of expression of systematic symmetric nucleotide exchange-encrypted proteins. Such expression necessitates combined activities of suppressor tRNAs matching stops, and nucleotide exchange transcription. Two independent properties confirm predicted exchanged overlap coding genes: discrepancy of third codon nucleotide contents from replicational deamination gradients, and codon usage according to circular code predictions. Predictions from both properties converge, especially for frequent nucleotide exchange types. Nucleotide exchanging transcription apparently increases coding densities of protein coding genes without lengthening genomes, revealing unsuspected functional DNA coding potential.

Systematic asymmetric nucleotide exchanges produce human mitochondrial RNAs cryptically encoding for overlapping protein coding genes

GenBank’s EST database includes RNAs matching exactly human mitochondrial sequences assuming systematic asymmetric nucleotide exchange-transcription along exchange rules: A→G→C→U/T→A (12 ESTs), A→U/T→C→G→A (4 ESTs), C→G→U/T→C (3 ESTs), and A→C→G→U/T→A (1 EST), no RNAs correspond to other potential asymmetric exchange rules. Hypothetical polypeptides translated from nucleotide-exchanged human mitochondrial protein coding genes align with numerous GenBank proteins, predicted secondary structures resemble their putative GenBank homologue’s. Two independent methods designed to detect overlapping genes (one based on nucleotide contents analyses in relation to replicative deamination gradients at third codon positions, and circular code analyses of codon contents based on frame redundancy), confirm nucleotide-exchange-encrypted overlapping genes. Methods converge on which genes are most probably active, and which not, and this for the various exchange rules. Mean EST lengths produced by different nucleotide exchanges are proportional to (a) extents that various bioinformatics analyses confirm the protein coding status of putative overlapping genes; (b) known kinetic chemistry parameters of the corresponding nucleotide substitutions by the human mitochondrial DNA polymerase gamma (nucleotide DNA misinsertion rates); (c) stop codon densities in predicted overlapping genes (stop codon readthrough and exchanging polymerization regulate gene expression by counterbalancing each other). Numerous rarely expressed proteins seem encoded within regular mitochondrial genes through asymmetric nucleotide exchange, avoiding lengthening genomes. Intersecting evidence between several independent approaches confirms the working hypothesis status of gene encryption by systematic nucleotide exchanges.

SOME PROPERTIES OF TRINUCLEOTIDES AND TETRANUCLEOTIDES

In 1994, with a statistical study of trinucleotide occurences per frame, D. Arquès and C. Michel identified the fol lowing set of 20 trin- ucleotides in the gene population of both eucaryotes E U K and procaryotes P RO: {AAC , AAT , AC C , ATC,ATT,CAG,CTC,CTG,GAA,GAC,GAG,GAT, GCC,GGC,GGT,GTA,GTC,GTT,TAC,TTC}.Thisset of words of length three on the genetic alphabet A4 = {A, C, G, T } has remarkable properties: it is a self-complementary set, it is a circular code, it is maximal and it has the C3- property. This and other identifications of trinucleotide circular codes in different genomes in the last twenty years raised interest in the concept of trinucleotide circular code for genetics. In 2003 we found an efficient algorithm for testing the circularity of a trinucleotide code and in 2005 we found the list of al l 528 maximal self-complementary circular codes. In 2008 we presented a hierarchy of the self-complementary circular codes and in 2012 we presented a hierarchy of al l circular codes. These circular codes could permit the identification, either in paral lel with or substituting existing methods used by biologist, of as yet unknown coding regions of DNA. A hierarchy of tetranucleotide circular codes is one of our aims in the future. In this paper we begin the study of the unbordered tetranucleotides and of the “forbidden configurations” for tetranucleotides and we give a first result.

A permuted set of a trinucleotide circular code coding the 20 amino acids in variant nuclear codes

We identify here a combinatorial property between circular code and genetic code. A circular code of 20 trinucleotides which allows to retrieve the reading frame has a permuted set of 20 trinucleotides which is a code, but not circular, coding the 20 amino acids in variant nuclear codes. This result is a contribution to the research field analysing the mathematical properties of genetic codes.

Putative mitochondrial polypeptides coded by expanded quadruplet codons, decoded by antisense tRNAs with unusual anticodons

Weak triplet codon–anticodon interactions render ribosome-free translation unlikely. Some modern tRNAs read quadruplet codons (tetracodons), suggesting vestigial ribosome-free translation. Here, mitochondrial genomes are explored for tetracoded overlapping protein coding (tetra)genes. Occasional single tetracodons within regular mitochondrial genes coevolve positively/negatively with antisense tRNAs with predicted reduced/expanded anticodons (depending on taxon), suggesting complex tetra-decoding mechanisms. Transcripts of antisense tRNAs with unusual anticodons are more abundant than of homologues with regular anticodons. Assuming overlapping tetracoding with silent 4th tetracodon position, BLAST aligns 10 putative tetragenes spanning 17% of regular human mitochondrial protein coding tricodons with 14 GenBank proteins. Various tests including predicted peptide secondary structures, 3rd codon position (of the regular main frame of the protein coding gene) conservation against replicational deamination mutation gradients, and circular code usage (overlapping genes avoid using circular code codons) confirm tetracoding in these overlapping tetragenes with silent 4th position, but not for BLAST-predicted tetragenes assuming silent 2nd or 3rd positions. This converges with tetradecoding mechanisms that are more compatible with silent 4th, than at other, tetracodon positions. Tetracoding increases with (a) GC-contents, perhaps conserved or switched on in high temperature conditions; (b) usage of theoretically predicted ‘tessera’ tetracodons; (c) 12s rRNA stability; and d) antisense tRNA numbers with predicted expanded anticodons. Most detected tetragenes are not evolutionarily conserved, apparently reflect specific, transient adaptations. Tetracoding increases with mammal longevity.

Overlapping genes coded in the 3′-to-5′-direction in mitochondrial genes and 3′-to-5′ polymerization of non-complementary RNA by an ‘invertase’

Suppressor tRNAs induce expression of additional (off-frame) genes coded by stopless genetic codes without lengthening genomes, decreasing DNA replication costs. RNA 3′-to-5′ polymerization by tRNAHis guanylyltransferase suggests further cryptic code: hypothetical ‘invertases’ polymerizing in the 3′-to-5′ direction, advancing in the 5′-to-3′ direction would produce non-complementary RNA templated by regular genes, with different coding properties. Assuming ‘invertase’ activity, BLAST analyses detect GenBank-stored RNA ESTs and proteins (some potentially coding for the hypothesized invertase) for human mitochondrial genes. These peptides’ predicted secondary structures resemble their GenBank homologues’. 3′-to-5′ EST lengths increase with their self-hybridization potential: Single-stranded RNA degradation perhaps limits 3′-to-5′ elongation. Independent methods confirm predicted 3′-to-5′ overlapping genes: (a) Presumed 3′-to-5′ overlapping genes avoid codons belonging to circular codes; (b) Spontaneous replicational deamination (mutation) gradients occur at 3rd codon positions, unless these are involved in overlap coding, because mutations are counter selected in overlapping genes. Tests a and b converge on predicted 3′-to-5′ gene expression levels. Highly expressed ones include also fewer stops, and mitochondrial genomes (in Primates and Drosophila) adapt to avoid dependence of 3′-to-5′ coding upon antitermination tRNA activity. Secondary structure, circular code, gradient and coevolution analyses yield each clear positive results independently confirming each other. These positive results (including physical evidence for 3′-to-5′ ESTs) indicate that 3′-to-5′ coding and invertase activity is an a priori improbable working hypothesis that cannot be dismissed. Note that RNAs produced by invertases potentially produce triple-stranded DNA:RNA helices by antiparallel Hoogsteen pairings at physiological pH, as previously observed for mitochondrial genomes.

Design of circular dot pattern code (CDPC) for maximum information capacity and robustness on geometric distortion/noise

One dimensional or linear bar code has been used for distribution purposes such as product information and distribution channel identification. Those linear bar codes can support only one directional code layout and also support limited code error detection capability. Two dimensional bar codes (e.g., QR code) extending one dimensional bar codes were developed in database and index based types. Database type barcodes embed full information bits and show weak recognition rate with geometric distortion. Index-based embed only the index information and requires additional network servers to interpret the index information, which leads to limited information storage capacity. Instead of using visible bar codes, we propose CDPC (circular dot pattern code), which is a dot based codes which is more invisible than bar codes. We design CDPC to be more robust to geometric distortion and noise than previous coding schemes using circular template matching. To maximize the information capacity and robustness, we use a circular dot patterns which is more robust to affine transformation. Code can be easily extended according to the number of data circles. If the number of data circle is n, then we can embed $$ \left( {5\sum {_{{k = 2}}^{{n + 1}}{\text{k}}} } \right) - {\text{n}} $$ data bits. In our experimentation, we set the number of circle to three, and resulting information capacity can be 42 bits per one code. To extract information from a CDPC codes, we perform (1) image capture, (2) identification of dots, (3) graph based topological analysis of dot patterns, (4) template matching between topological graphs using position symbols, and (5) information bit extraction with error correction capability. To evaluate information capacity under various geometric distortions, we experiment our CDPC with StirMark Benchmark's affine transformation (simulation of geometric and noise attacks) and with real cell phone image captures. Our experimental results also show that our CDPC scheme achieves more robust recognition performance than those proposed in previous research works including QR code.