Codon Content Research Articles

Systematic Comparison of Strategies to Achieve Soluble Expression of Plasmodium falciparum Recombinant Proteins in E. coli.

Constructs containing partial coding sequences of myosin A, myosin B, and glideosome-associated protein (50kDa) of Plasmodium falciparum were used to challenge several strategies designed in order to improve the production and solubility of recombinant proteins in Escherichia coli. Assays were carried out inducing expression in a late log phase culture, optimizing the inductor concentration, reducing the growth temperature for induced cultures, and supplementing additives in the lysis buffer. In addition, recombinant proteins were expressed as fusion proteins with three different tags (6His, GST, and MBP) in four different E. coli strains. We found that the only condition that consistently produced soluble proteins was the use of MBP as a fusion tag, which became a valuable tool for detecting the proteins used in this study and did not caused any interference in protein-protein interaction assays (Far Western Blot). Besides, we found that BL21-pG-KJE8 strain did not improve the solubility of any of the recombinant protein produced, while the BL21-CodonPlus(DE3)-RIL strain improved the expression of some of them independent of the rare codon content. Proteins with rare codons occurring at high frequencies (» 10%) were expressed efficiently in strains that do not supplement tRNAs for these triplets.

Tuning Relative Polypeptide Expression to Optimize Assembly, Yield and Downstream Processing of Bispecific Antibodies.

Bispecific antibodies (bsAbs) are often composed of several polypeptide chains that have to be expressed adequately to enable optimal assembly and yield of the bsAb. κλ bodies are a bispecific format with a native IgG structure, composed of two different light chains that pair with a common heavy chain. Introduction of non-optimal codons into the sequence of a particular polypeptide is an effective strategy for down modulating its expression. Here we applied this strategy but restricted the modification of the codon content to the constant domain of one light chain. This approach facilitates parallel optimization of several bsAbs by using the same modified constant domains. Partial sequence de-optimization reduced expression of the targeted polypeptide. Stable cell pools could be isolated displaying increased bispecific antibody titers as well as changes in the abundance of undesired by-products that require elimination during downstream processing. Thus, modulating the relative expression of polypeptides can have a significant impact on bsAb titer and product related impurities; which are important factors for large scale manufacturing for clinical supply.

Attenuated Codon Optimality Contributes to Neural-Specific mRNA Decay in Drosophila

SUMMARYTissue-specific mRNA stability is important for cell fate and physiology, but the mechanisms involved are not fully understood. We found that zygotic mRNA stability in Drosophila correlates with codon content: optimal codons are enriched in stable transcripts associated with metabolic functions like translation, while non-optimal codons are enriched in unstable transcripts, including those associated with neural development. Bioinformatic analyses and reporter assays revealed that similar codons stabilize or destabilize mRNAs in the nervous system and other tissues, but the link between codon content and stability is attenuated in the nervous system. We confirmed that optimal codons are decoded by abundant tRNAs while non-optimal codons are decoded by less abundant tRNAs in embryos and in the nervous system. We conclude that codon optimality is a general determinant of zygotic mRNA stability, and attenuation of codon optimality allows trans-acting factors to exert greater influence over mRNA decay in the nervous system.

Characterization of Chlamydial Rho and the Role of Rho-Mediated Transcriptional Polarity during Interferon Gamma-Mediated Tryptophan Limitation.

As an obligate intracellular, developmentally regulated bacterium, Chlamydia is sensitive to amino acid fluctuations within its host cell. When human epithelial cells are treated with the cytokine interferon gamma (IFN-γ), the tryptophan (Trp)-degrading enzyme, indoleamine-2,3-dioxygenase, is induced. Chlamydiae within such cells are starved for Trp and enter a state of so-called persistence. Chlamydia lacks the stringent response used by many eubacteria to respond to this stress. Unusually, chlamydial transcription is globally elevated during Trp starvation with transcripts for Trp codon-containing genes disproportionately increased. Yet, the presence of Trp codons destabilized 3' ends of transcripts in operons or large genes. We initially hypothesized that ribosome stalling on Trp codons rendered the 3' ends sensitive to RNase activity. The half-life of chlamydial transcripts containing different numbers of Trp codons was thus measured in untreated and IFN-γ-treated infected cells to determine whether Trp codons influenced the stability of transcripts. However, no effect of Trp codon content was detected. Therefore, we investigated whether Rho-dependent transcription termination could play a role in mediating transcript instability. Rho is expressed as a midcycle gene product, interacts with itself as predicted, and is present in all chlamydial species. Inhibition of Rho via the Rho-specific antibiotic, bicyclomycin, and overexpression of Rho are detrimental to chlamydiae. Finally, when we measured transcript abundance 3' to Trp codons in the presence of bicyclomycin, we observed that transcript abundance increased. These data are the first to demonstrate the importance of Rho in Chlamydia and the role of Rho-dependent transcription polarity during persistence.

Codon usage and codon pair patterns in non-grass monocot genomes.

Studies on codon usage in monocots have focused on grasses, and observed patterns of this taxon were generalized to all monocot species. Here, non-grass monocot species were analysed to investigate the differences between grass and non-grass monocots. First, studies of codon usage in monocots were reviewed. The current information was then extended regarding codon usage, as well as codon-pair context bias, using four completely sequenced non-grass monocot genomes (Musa acuminata, Musa balbisiana, Phoenix dactylifera and Spirodela polyrhiza) for which comparable transcriptome datasets are available. Measurements were taken regarding relative synonymous codon usage, effective number of codons, derived optimal codon and GC content and then the relationships investigated to infer the underlying evolutionary forces. The research identified optimal codons, rare codons and preferred codon-pair context in the non-grass monocot species studied. In contrast to the bimodal distribution of GC3 (GC content in third codon position) in grasses, non-grass monocots showed a unimodal distribution. Disproportionate use of G and C (and of A and T) in two- and four-codon amino acids detected in the analysis rules out the mutational bias hypothesis as an explanation of genomic variation in GC content. There was found to be a positive relationship between CAI (codon adaptation index; predicts the level of expression of a gene) and GC3. In addition, a strong correlation was observed between coding and genomic GC content and negative correlation of GC3 with gene length, indicating a strong impact of GC-biased gene conversion (gBGC) in shaping codon usage and nucleotide composition in non-grass monocots. Optimal codons in these non-grass monocots show a preference for G/C in the third codon position. These results support the concept that codon usage and nucleotide composition in non-grass monocots are mainly driven by gBGC.

The link between adjacent codon pairs and mRNA stability

BackgroundEvidence in diverse organisms suggests that codon optimality is a major determinant of mRNA translation and degradation. Codon optimality is thought to act by modulating the efficiency of ribosome elongation. In Saccharomyces cerevisiae, a recent study has identified 17 adjacent codon pairs that mediate strong inhibition of translation elongation. However, relationships between the inhibitory codon pairs and other aspects of gene expression are unknown.ResultsTo gain insights into how the inhibitory codon pairs may affect aspects of gene expression, we utilized existing datasets to conduct genome-scale analyses in S. cerevisiae. Our analysis revealed the following points. First, the inhibitory codon pairs are significantly associated with faster mRNA decay. The association is not solely due to the content of nucleotides, individual codons, or dipeptides encoded by the inhibitory codon pairs. Second, the inhibitory codon pairs cannot fully explain the previously known relationship of codon optimality with mRNA stability, suggesting that optimality of individual codons and properties of adjacent codon pairs both contribute to gene regulation. Finally, although the inhibitory codon pairs are associated with slower mRNA synthesis and protein instability, the associations can be attributed to usage bias in individual codons.ConclusionsThis study suggests an association of inhibitory codon pairs with mRNA stability and thus another layer of complexity in the codon-mediated gene regulation.

Efficient secretory expression of recombinant proteins in Escherichia coli with a novel actinomycete signal peptide

In well-established heterologous hosts, such as Escherichia coli, recombinant proteins are usually intracellular and frequently found as inclusion bodies—especially proteins possessing high rare codon content. In this study, successful secretory expression of three hydrolases, in a constructed inducible or constitutive system, was achieved by fusion with a novel signal peptide (Kp-SP) from an actinomycete. The signal peptide efficiently enabled extracellular protein secretion and also contributed to the active expression of the intracellular recombinant proteins. The thermophilic α-amylase gene of Bacillus licheniformis was fused with Kp-SP. Both recombinants, carrying inducible and constitutive plasmids, showed remarkable increases in extracellular and intracellular amylolytic activity. Amylase activity was observed to be > 10-fold in recombinant cultures with the constitutive plasmid, pBSPPc, compared to that in recombinants lacking Kp-SP. Further, the signal peptide enabled efficient secretion of a thermophilic cellulase into the culture medium, as demonstrated by larger halo zones and increased enzymatic activities detected in both constructs from different plasmids. For heterologous proteins with a high proportion of rare codons, it is difficult to obtain high expression in E. coli owing to the codon bias. Here, the fusion of an archaeal homologue of the amylase encoding gene, FSA, with Kp-SP resulted in > 5-fold higher extracellular activity. The successful extracellular expression of the amylase indicated that the signal peptide also contributed significantly to its active expression and signified the potential value of this novel and versatile signal peptide in recombinant protein production.

G + C content differs in conserved and variable amino acid residues of flaviviruses and other evolutionary groups

Flaviviruses are small RNA viruses that exhibit genetic and ecological diversity and a wide range of G+C content (GC%). We discovered that, amongst flaviviruses, the GC% of nucleotides encoding conserved amino acid (AA) residues was consistently higher than that of nucleotides encoding variable AAs. This intriguing phenomenon was also identified for a wide range of other viruses, and some non-viral evolutionary groups. Here, we analyse the possible mechanisms underlying this imbalanced nucleotide content (in particular the role of the specific G content and the AA composition in flaviviral genomes) and discuss its evolutionary implications. Our findings suggest that one of the most simple characteristics of the genetic code (i.e., the G or G+C content of codons) is linked with the evolutionary behavior of the corresponding encoded AAs.

Incorporation of a tag helps to overcome expression variability in a recombinant host

Epigenetics have witnessed a renewed interest over the past decade and assays with recombinant histones has become an important tool for uncovering various aspects of histone biology. However, at times absence of recombinant histone accumulation in bacteria is encountered which is also commonly observed for many eukaryotic proteins in general. In this study, we have investigated the effect of multiple parameters on heterologous expression of proteins. We show that there is marked variability in the accumulation of H2A.2, H2B.1, H3.2 and H4 in the recombinant host, possibly owing to translational variability and degradation by the host proteases. We found that the variability could be overcome by incorporation of the commonly used purification tags, like GST or MBP, of appropriate size and position. Our results provide compelling evidence that transcript parameters like rare codon and GC content, mRNA secondary structure etc. together modulate translation kinetics and govern recombinant protein accumulation.

Tryptophan Codon-Dependent Transcription in Chlamydia pneumoniae during Gamma Interferon-Mediated Tryptophan Limitation

In evolving to an obligate intracellular niche, Chlamydia has streamlined its genome by eliminating superfluous genes as it relies on the host cell for a variety of nutritional needs like amino acids. However, Chlamydia can experience amino acid starvation when the human host cell in which the bacteria reside is exposed to interferon gamma (IFN-γ), which leads to a tryptophan (Trp)-limiting environment via induction of the enzyme indoleamine-2,3-dioxygenase (IDO). The stringent response is used to respond to amino acid starvation in most bacteria but is missing from Chlamydia Thus, how Chlamydia, a Trp auxotroph, responds to Trp starvation in the absence of a stringent response is an intriguing question. We previously observed that C. pneumoniae responds to this stress by globally increasing transcription while globally decreasing translation, an unusual response. Here, we sought to understand this and hypothesized that the Trp codon content of a given gene would determine its transcription level. We quantified transcripts from C. pneumoniae genes that were either rich or poor in Trp codons and found that Trp codon-rich transcripts were increased, whereas those that lacked Trp codons were unchanged or even decreased. There were exceptions, and these involved operons or large genes with multiple Trp codons: downstream transcripts were less abundant after Trp codon-rich sequences. These data suggest that ribosome stalling on Trp codons causes a negative polar effect on downstream sequences. Finally, reassessing previous C. pneumoniae microarray data based on codon content, we found that upregulated transcripts were enriched in Trp codons, thus supporting our hypothesis.

Modulated Expression of Specific tRNAs Drives Gene Expression and Cancer Progression

Transfer RNAs (tRNAs) are primarily viewed as static contributors to gene expression. By developing a high-throughput tRNA profiling method, we find that specific tRNAs are upregulated in human breast cancer cells as they gain metastatic activity. Through loss-of-function, gain-of-function, and clinical-association studies, we implicate tRNAGluUUC and tRNAArgCCG as promoters of breast cancer metastasis. Upregulation of these tRNAs enhances stability and ribosome occupancy of transcripts enriched for their cognate codons. Specifically, tRNAGluUUC promotes metastatic progression by directly enhancing EXOSC2 expression and enhancing GRIPAP1-constituting an "inducible" pathway driven by a tRNA. The cellular proteomic shift toward a pro-metastatic state mirrors global tRNA shifts, allowing for cell-state and cell-type transgene expression optimization through codon content quantification. TRNA modulation represents a mechanism by which cells achieve altered expression of specific transcripts and proteins. TRNAs are thus dynamic regulators of gene expression and the tRNA codon landscape can causally and specifically impact disease progression.

Expression of a Chimeric Allergen with High Rare Codons Content in Codon Bias-Adjusted Escherichia coli: Escherichia coli BL21 (DE3)-Codon Plus RIL as an Efficient Host.

The expression of heterologous proteins in Escherichia coli (E. coli) is importantly affected by codon bias. Hence, the aim of the current study was to determine which codon bias-adjusted E. coli strain is sufficient for expression of a chimeric allergen coded by high rare codon content. To investigate the expression level, a chimeric protein of Chenopodium album (C. album) was used as an appropriate model. An expression construct was assembled and was transformed to four strains of codon bias-adjusted E. coli including origami, BL21 (DE3), BL21 (DE3)-codon plus RIL, and Rosetta. The level of expression and solubility of the chimeric allergen was analyzed by SDS-PAGE. In addition, the allergenicity of chimeric allergen was determined using immunoblotting. Our results showed that the chimeric allergen was expressed at high level in E. coli BL21 (DE3)-codon plus RIL and Rosetta. In detail, this recombinant allergen was isolated from soluble fraction in the codon bias-adjusted strains of E. coli BL21 (DE3)-codon plus RIL and Rosetta. Moreover, some lower molecular weight proteins were observed in Rosetta, which could be related to inappropriate expression or broken compartments of the chimeric allergen. The immunoblotting assay confirmed that the IgE-specific immune reactivity of our chimeric allergen expressed in BL21 (DE3)-codon plus RIL was significantly higher than the other strains. Our results showed that the expression of the chimeric allergen with high rare codons content in a codon bias-adjusted strain E. coli BL21 (DE3)-codon plus RIL improves the quality and solubility of the heterologous protein production.

Codon influence on protein expression in E. coli correlates with mRNA levels.

Degeneracy in the genetic code, which enables a single protein to be encoded by a multitude of synonymous gene sequences, has an important role in regulating protein expression, but substantial uncertainty exists concerning the details of this phenomenon. Here we analyse the sequence features influencing protein expression levels in 6,348 experiments using bacteriophage T7 polymerase to synthesize messenger RNA in Escherichia coli. Logistic regression yields a new codon-influence metric that correlates only weakly with genomic codon-usage frequency, but strongly with global physiological protein concentrations and also mRNA concentrations and lifetimes in vivo. Overall, the codon content influences protein expression more strongly than mRNA-folding parameters, although the latter dominate in the initial ~16 codons. Genes redesigned based on our analyses are transcribed with unaltered efficiency but translated with higher efficiency in vitro. The less efficiently translated native sequences show greatly reduced mRNA levels in vivo. Our results suggest that codon content modulates a kinetic competition between protein elongation and mRNA degradation that is a central feature of the physiology and also possibly the regulation of translation in E. coli.

Cross-species conservation of complementary amino acid-ribonucleobase interactions and their potential for ribosome-free encoding.

The role of amino acid-RNA nucleobase interactions in the evolution of RNA translation and protein-mRNA autoregulation remains an open area of research. We describe the inference of pairwise amino acid-RNA nucleobase interaction preferences using structural data from known RNA-protein complexes. We observed significant matching between an amino acid’s nucleobase affinity and corresponding codon content in both the standard genetic code and mitochondrial variants. Furthermore, we showed that knowledge of nucleobase preferences allows statistically significant prediction of protein primary sequence from mRNA using purely physiochemical information. Interestingly, ribosomal primary sequences were more accurately predicted than non-ribosomal sequences, suggesting a potential role for direct amino acid-nucleobase interactions in the genesis of amino acid-based ribosomal components. Finally, we observed matching between amino acid-nucleobase affinities and corresponding mRNA sequences in 35 evolutionarily diverse proteomes. We believe these results have important implications for the study of the evolutionary origins of the genetic code and protein-mRNA cross-regulation.

Upstream AUGs and upstream ORFs can regulate the downstream ORF in Plasmodium falciparum.

BackgroundUpstream open reading frames (uORFs) and upstream AUGs (uAUGs) can regulate the translation of downstream ORFs. The AT rich genome of Plasmodium falciparum, due to the higher AT content of start and stop codons, has the potential to give rise to a large number of uORFs and uAUGs that may affect expression of their flanking ORFs.MethodsA bioinformatics approach was used to detect uATGs associated with different genes in the parasite. To study the effect of some of these uAUGs on the expression of the downstream ORF, promoters and 5′ leaders containing uAUGs and uORFs were cloned upstream of a luciferase reporter gene. Luciferase assays were carried out in transient transfection experiments to assess the effects of uAUGs and mutations on reporter expression.ResultsThe average number of uATGs and uORFs seen in P. falciparum coding sequences (CDS) is expectedly high compared to other less biased genomes. Certain genes, including the var gene family contain the maximum number of uATGs and uORFs in the parasite. They possess ~5 times more uORFs and ~4.5 times more uAUGs within 100 bases upstream of the start codons than other CDS of the parasite. A 60 bp upstream region containing three ORFs and five ATGs from var gene PF3D7_0400100 and a gene of unknown function (PF3D7_0517100) when cloned upstream of the luciferase start codon, driven by the hsp86 promoter, resulted in loss of luciferase activity. This was restored when all the ATGs present in the −60 bp were mutated to TTGs. Point mutations in the ATGs showed that even one AUG was sufficient to repress the luciferase gene.ConclusionsOverall, this work indicates that the P. falciparum genome has a large number of uATGs and uORFs that can repress the expression of flanking ORFs. The role of AUGs in translation initiation suggests that this repression is mediated by preventing the translation initiation complex from reaching the main AUG of the downstream ORF. How the P. falciparum ribosome is able to bypass these uAUGs and uORFs for highly expressed genes remains a question for future research.Electronic supplementary materialThe online version of this article (doi:10.1186/s12936-015-1040-5) contains supplementary material, which is available to authorized users.

The evolutionary dynamics of tRNA-gene copy number and codon-use in E. coli.

BackgroundThe introduction of foreign DNA by Lateral Gene Transfer (LGT) can quickly and drastically alter genome composition. Problems can arise if the genes introduced by LGT use codons that are not suited to the host’s translational machinery. Here we investigate compensatory adaptation of E. coli in response to the introduction of large volumes of codons that are rarely used by the host genome.ResultsWe analyze genome sequences from the E. coli/Shigella complex, and find that certain tRNA genes are present in multiple copies in two pathogenic Shigella and O157:H7 subgroups of E. coli. Furthermore, we show that the codons that correspond to these multi-copy number tRNA genes are enriched in the high copy number Selfish Genetic Elements (SGE’s) in Shigella and laterally introduced genes in O157:H7. We analyze the duplicate copies and find evidence for the selective retention of tRNA genes introduced by LGT in response to the changed codon content of the genome.ConclusionThese data support a model where the relatively rapid influx of LGT genes and SGE’s introduces a large number of genes maladapted to the host’s translational machinery. Under these conditions, it becomes advantageous for the host to retain tRNA genes that are required for the incorporation of amino acids at these codons. Subsequently, the increased number of copies of these specific tRNA genes adjusts the cellular tRNA pool to the demands set by global shifts in codon usage.Electronic supplementary materialThe online version of this article (doi:10.1186/s12862-015-0441-y) contains supplementary material, which is available to authorized users.

Codon Optimality Is a Major Determinant of mRNA Stability

mRNA degradation represents a critical regulated step in gene expression. Although the major pathways in turnover have been identified, accounting for disparate half-lives has been elusive. We show that codon optimality is one feature that contributes greatly to mRNA stability. Genome-wide RNA decay analysis revealed that stable mRNAs are enriched in codons designated optimal, whereas unstable mRNAs contain predominately non-optimal codons. Substitution of optimal codons with synonymous, non-optimal codons results in dramatic mRNA destabilization, whereas the converse substitution significantly increases stability. Further, we demonstrate that codon optimality impacts ribosome translocation, connecting the processes of translation elongation and decay through codon optimality. Finally, we show that optimal codon content accounts for the similar stabilities observed in mRNAs encoding proteins with coordinated physiological function. This work demonstrates that codon optimization exists as a mechanism to finely tune levels of mRNAs and, ultimately, proteins.

Relationship of Genomic G+C Content between Phages/Plasmids and Their Hosts

Aims: We compared genomic G+C content between bacteriophages/plasmids and their host genomes of 46 species to reveal their relation. To examine the large deviation in the G+C content between bacteriophages and their host genomes, the ancestral bacteriophage which infected early was estimated using homologous genes of bacteriophages based on G+C content at the third codon positions. Place and Duration of Study: Department of Clinical Laboratory Science, Graduate Course of Medical Science and Technology, School of Health Sciences, Kanazawa University, Japan. Methodology: The bacteria employed in this study consist of 6 species from Archaea and 40 species from Eubacteria. Orthologs were identified by the two-directional best hit approach of homology search. A phylogenetic tree was obtained by multiple sequence alignment of homologous genes. The ancestral bacteriophage which infected early was estimated based on G+C content at the third codon positions. We assumed that the two bacteriophages have evolved from a common ancestor, and their identical codons were thought to represent their ancestor type. Results: The relationship of G+C content between bacteriophages/plasmids and host genomes was almost linear. Three bacteriophages were largely deviated from the linear relation. A phylogenetic Original Research Article Nakashima et al.; BBJ, 9(1): 1-9, 2015; Article no.BBJ.20046 2 tree obtained using the orthologs of Mycobacterium smegmatis indicated which bacteriophage branched early. Assuming that the G+C content of identical codons represents their common ancestor, the ancestor was estimated that it had similar G+C content with its host.

Codon usage patterns in Chinese bayberry (Myrica rubra) based on RNA-Seq data.

BackgroundCodon usage analysis has been a classical topic for decades and has significances for studies of evolution, mRNA translation, and new gene discovery, etc. While the codon usage varies among different members of the plant kingdom, indicating the necessity for species-specific study, this work has mostly been limited to model organisms. Recently, the development of deep sequencing, especial RNA-Seq, has made it possible to carry out studies in non-model species.ResultRNA-Seq data of Chinese bayberry was analyzed to investigate the bias of codon usage and codon pairs. High frequency codons (AGG, GCU, AAG and GAU), as well as low frequency ones (NCG and NUA codons) were identified, and 397 high frequency codon pairs were observed. Meanwhile, 26 preferred and 141 avoided neighboring codon pairs were also identified, which showed more significant bias than the same pairs with one or more intervening codons. Codon patterns were also analyzed at the plant kingdom, organism and gene levels. Changes during plant evolution were evident using RSCU (relative synonymous codon usage), which was even more significant than GC3s (GC content of 3rd synonymous codons). Nine GO categories were differentially and independently influenced by CAI (codon adaptation index) or GC3s, especially in 'Molecular function’ category. Within a gene, the average CAI increased from 0.720 to 0.785 in the first 50 codons, and then more slowly thereafter. Furthermore, the preferred as well as avoided codons at the position just following the start codon AUG were identified and discussed in relation to the key positions in Kozak sequences.ConclusionA comprehensive codon usage Table and number of high-frequency codon pairs were established. Bias in codon usage as well as in neighboring codon pairs was observed, and the significance of this in avoiding DNA mutation, increasing protein production and regulating protein synthesis rate was proposed. Codon usage patterns at three levels were revealed and the significance in plant evolution analysis, gene function classification, and protein translation start site predication were discussed. This work promotes the study of codon biology, and provides some reference for analysis and comprehensive application of RNA-Seq data from other non-model species.

Selfcomplementary, selfreverse cyclic nucleotide sequences codonically invariant under frame shifting

A cyclic nucleotide sequence is selfcomplementary if some circular permutation transfers it to a complementary sequence and (independently) is selfreverse if the cyclic order of nucleotides in both directions is the same. Moreover, it is codonically invariant under frame shifting if any shift of its frame does not alter the content and cyclic order of codons. We discuss sequences which may simultaneously have these three properties and exhibit color symmetry. Our considerations are also adapted for respective linear sequences.