A content-centric organization of the genetic code

The codon table for the canonical genetic code can be rearranged in such a way that the code is divided into four quarters and two halves according to the variability of their GC and purine contents, respectively. For prokaryotic genomes, when the genomic GC content increases, their amino acid contents tend to be restricted to the GC-rich quarter and the purine-content insensitive half, where all codons are fourfold degenerate and relatively mutation-tolerant. Conversely, when the genomic GC content decreases, most of the codons retract to the AUrich quarter and the purine-content sensitive half; most of the codons not only remain encoding physicochemically diversified amino acids but also vary when transversion （between purine and pyrimidine） happens. Amino acids with sixfolddegenerate codons are distributed into all four quarters and across the two halves; their fourfold-degenerate codons are all partitioned into the purine-insensitive half in favorite of robustness against mutations. The features manifested in the rearranged codon table explain most of the intrinsic relationship between protein coding sequences （the informational content） and amino acid compositions （the functional content）. The renovated codon table is useful in predicting abundant amino acids and positioning the amino acids with related or distinct physicochemical properties.     

A self-referential model for the formation of the genetic code

A model for the formation of the genetic code is presented where protein synthesis is directed initially by tRNA dimers. Proteins that are resistant to degradation and efficient RNA-binders protect the RNAs. Replication becomes elongational producing poly-tRNAs from which the mRNAs and ribosomes are derived. Attributions are successively fixed to tRNAs paired through the perfect palindromic anticodons, with the same bases at the extremities (5′ANA: UNU 3′; GNG: CNC; principal dinucleotides, pDiN). The 5′ degeneracy is then developed. The first pairs to be encoded correspond to the hydropathy correlation outliers (Gly-CC: Pro-GG and Ser-GA: Ser-CU) and to the sector of homogeneous pDiN, composed by two pyrimidines or two purines. These amino acids are preferred in the N-ends of proteins, stabilizers of proteins against catabolism and strong RNA-binders. The next pairs complete the sector of homogeneous pDiN (Asp, Glu-UC: Leu-AG and Asn, Lys-UU: Phe-AA). This set of nine amino acids forms the protein cores with the predominant aperiodic conformation. Next enter the pairs with mixed pDiN (one purine and one pyrimidine), the RY attributions composing the protein N-ends and the YR attributions the C-ends. The last pair contains the main punctuation signs (Ile, Met, iMet-AU: Tyr, Stop-UA). The model indicates that genetic information emerged during the process of formation of the coding/decoding system and that genes were defined by the proteins. Stable proteins constructed the nucleoprotein system by binding to the RNAs that produced them. In this circular rationale, genes are memories in a metabolic system for production of proteins that stabilize it. The simplicity and the highly deterministic character of the process suggest that the Last Universal Common Ancestor populations could be composed, in early stages, of lineages bearing similar genetic codes.     

Some mathematical refinements concerning error minimization in the genetic code

The genetic code is known to have a high level of error robustness and has been shown to be very error robust compared to randomly selected codes, but to be significantly less error robust than a certain code found by a heuristic algorithm. We formulate this optimization problem as a Quadratic Assignment Problem and use this to formally verify that the code found by the heuristic algorithm is the global optimum. We also argue that it is strongly misleading to compare the genetic code only with codes sampled from the fixed block model, because the real code space is orders of magnitude larger. We thus enlarge the space from which random codes can be sampled from approximately 2.433 × 10(18) codes to approximately 5.908 × 10(45) codes. We do this by leaving the fixed block model, and using the wobble rules to formulate the characteristics acceptable for a genetic code. By relaxing more constraints, three larger spaces are also constructed. Using a modified error function, the genetic code is found to be more error robust compared to a background of randomly generated codes with increasing space size. We point out that these results do not necessarily imply that the code was optimized during evolution for error minimization, but that other mechanisms could be the reason for this error robustness.     

Word organization in coding DNA: A mathematical model

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

A statistical test of hypotheses on the organization and origin of the genetic code

Summary Theories of the origin of the genetic code assign different weights to amino acid properties such as polarity and precursor-product relationship. Previous statistical work on the origin of the genetic code has produced controversial results. We analyze relationships between various amino acid and tRNA properties by one and the same statistical method. It is shown that polarities as well as precursor-product relationships are both likely to have been important in shaping the genetic code, together with codon swapping that left protein sequences intact.     

Some aspects of the organization and evolution of the genetic code

In this paper, I define a measure of the relative position of each amino acid in the genetic code by means of a 21-dimensional vector describing its potential for mutation, in a single step, to each of the other amino acids, or to a chain termination codon. This measure allows us to make a systematic investigation of the type and number of the physicochemical properties of the amino acids that were involved in evolution. The polar character and size of amino acids are identified in this analysis as properties that played a leading role in the evolutionary history of the genetic code. The application of cluster analysis and discriminant analysis reveals the characteristics of the structural organization of the genetic code. Finally, I suggest the existence of a relationship between the molecular weight of the amino acids and the number of synonymous codons.     

A search for symmetries in the genetic code

A search for symmetrics based on the classification theorem of Cartan for the compact simple Lie algebras is performed to verify to what extent the genetic code is a manifestation of some underlying symmetry. An exact continuous symmetry group can not be found to reproduce the present, universal code. However a unique approximate symmetry group is compatible with codon assignment for the fundamental amino acids and the termination codon. In order to obtain the actual genetic code, the symmetry must be slightly broken.     

Origin of the genetic code: A physical-chemical model of primitive codon assignments

Selective compartmentalization of amino acids and nucleotides according to their polarities is proposed as a physical-chemical model for the origin of the genetic code. Assumptions made in this hypothesis are: (1) an oil-slick covered the surface of the primitive ocean, constituents of which formed association colloids or micelles at the water-oil-air interfaces; (2) depending on the polarity of the media, these aggregates possessed hydrophilic and hydrophobic interiors where selective uptake of amino acids and nucleic acid constituents could take place; and 93) condensation and polymerization in the micellar phase were enhanced. According to the chromatographically observed polarities, for example, lysine and uridylate fall into the hydrophilic compartment, and phenylalanine and adenylate are enriched in the hydrophobic environment. These components could eventually be condensed to form a charged adaptor loop with an anticodon which is complementary to the presently valid codon. Only two groups of amino acids, hydrophilic and hydrophobic, were recognized by the primitive translation mechanism. Implications of this hypothesis for the further development of the genetic code is discussed. The catalytic power of micelles have been substantiated by successful synthesis of nucleotides under relatively mild conditions using thiophosphates as high energy phosphates.     

A mathematical model for prediction of plasmid copy number and genetic stability in Escherichia coli

The design of bioreactors for genetically modified bacterial cultures would benefit from predictive models. Of particular importance is the interaction of the external environment, cell physiology, and control of plasmid copy number. We have recently developed a model based on the molecular mechanisms for control of replication of Co1E1 type plasmids. The inclusion of the plasmid model into a single-cell E. coli model allows the explicit prediction of the interaction of cell physiology and plasmid-encoded functions. The model predictions of the copy number of plasmids with the Co1E1 origin of replication carrying a variety of regulatory mutations is very close to that observed experimentally.All of the model parameters for plasmid replication control can be obtained independently and no adjustable parameters are needed for the plasmid model. In this article we discuss the model's use in predicting the effect of operating conditions on production of a protein from a plasmid encoded gene and the stability of the recombinant cells in a continuous culture.     

A harmonic structure of the genetic code

In this paper is presented a new, very harmonic structure of the genetic code (GC) within a system of "4 x 5" (and/or of "5 x 4") of amino acids (AAs) in two variants. In first variant, the five rows within the system start with one polar charged amino acid (AA) each, making first column, consisting from five polar charged AAs (D, R, K, H, E). Five polar non-charged AAs (N, P, Y, W, Q) follow, then five non-polar AAs as last column (A, L, F, V, I) and, finally, five polar or non-polar AAs, in a combination, as first to last column (A as non-polar; S, T as polar, and G, P as ambivalent AAs). A second variant is subsequent to this one-"4 x 5" system with five nitrogen AAs (K, R, P, H, W), five oxygen (D, E, Y, S, T), five solely carbon (A, L, F, V, I) and five "combined" AAs (G with hydrogen as side chain; C and M with carbon and sulfur; N and Q with carbon, oxygen and nitrogen). A strict balance of atom and nucleon number as well as molecule mass follows the classification in both system variants.     

A biophysical basis for the emergence of the genetic code in protocells

The origin of the genetic code is an abiding mystery in biology. Hints of a ‘code within the codons’ suggest biophysical interactions, but these patterns have resisted interpretation. Here, we present a new framework, grounded in the autotrophic growth of protocells from CO₂ and H₂. Recent work suggests that the universal core of metabolism recapitulates a thermodynamically favoured protometabolism right up to nucleotide synthesis. Considering the genetic code in relation to an extended protometabolism allows us to predict most codon assignments. We show that the first letter of the codon corresponds to the distance from CO₂ fixation, with amino acids encoded by the purines (G followed by A) being closest to CO₂ fixation. These associations suggest a purine-rich early metabolism with a restricted pool of amino acids. The second position of the anticodon corresponds to the hydrophobicity of the amino acid encoded. We combine multiple measures of hydrophobicity to show that this correlation holds strongly for early amino acids but is weaker for later species. Finally, we demonstrate that redundancy at the third position is not randomly distributed around the code: non-redundant amino acids can be assigned based on size, specifically length. We attribute this to additional stereochemical interactions at the anticodon. These rules imply an iterative expansion of the genetic code over time with codon assignments depending on both distance from CO₂ and biophysical interactions between nucleotide sequences and amino acids. In this way the earliest RNA polymers could produce non-random peptide sequences with selectable functions in autotrophic protocells.     

A mathematical model for the survivorship curve

A mathematical function describing the various kinds of survivorship curve is formulated with the useful parameter, environmental capacity. Three types of the survivorship curve illlustrated byDeevey can be obtained from changing the value of this function. When a cohort is large and the competition occurs in the scramble type, this function shows the third type ofDeevy 's and this to the first type in the case of low density and the contest type of competition. But the second type would rather be obtained by the action of density independent agencies.     

A mathematical model for the immunosenescence.

We propose a model for the dynamics of the immune system by considering the subpopulations of virgin and memory T lymphocytes on a time scale corresponding to the human life span. In the deterministic balance equation we introduce a fluctuating term in order to take into account the chronic antigenic stress. Starting from the hypothesis that the depletion of virgin cells with cytotoxic properties (CD8+) is a mortality marker, the model provides survival curves quite similar to the demographic curves.     

A change in the genetic code inMycoplasma capricolum

Summary Mycoplasma capricolum was previously found to use UGA instead of UGG as its codon for tryptophan and to contain 75%A+ T in its DNA. The codon change could have been due to mutational pressure to replace C+G by A+T, resulting in the replacement of UGA stop codons by UAA, change of the anticodon in tryptophan tRNA from CCA to UCA, and replacement of UGG tryptophan codons by UGA. None of these changes should have been deleterious.     

Molecular basis for the genetic code

Summary It was found by using the CPK molecular model that holes on the complexes of four nucleotides (C4N) on the tRNAs, namely complexes of the anticodon bases with the discriminator base at 4th position of 3 end, had lock and key relations to the corresponding protein amino acids. Various general features of the universal and mitochondrial genetic codes were easily explained in terms of the C4N model. The recognition mechanism of the tRNA by the aminoacyl-tRNA-synthetase is closely correlated with the formation of the C4N on the Rossmann fold on the synthetase. The meaning of the hypermodification of the tRNA base next to the third anticodon base and other phenomena were also discussed.     

A chemical toolkit for proteins--an expanded genetic code

Recently, a method to encode unnatural amino acids with diverse physicochemical and biological properties genetically in bacteria, yeast and mammalian cells was developed. Over 30 unnatural amino acids have been co-translationally incorporated into proteins with high fidelity and efficiency using a unique codon and corresponding transfer-RNA:aminoacyl-tRNA-synthetase pair. This provides a powerful tool for exploring protein structure and function in vitro and in vivo, and for generating proteins with new or enhanced properties.     

A discrete mathematical model applied to genetic regulation and metabolic networks

This paper describes the use of a discrete mathematical model to represent the basic mechanisms of regulation of the bacteria E. coli in batch fermentation. The specific phenomena studied were the changes in metabolism and genetic regulation when the bacteria use three different carbon substrates (glucose, glycerol, and acetate). The model correctly predicts the behavior of E. coli vis-à-vis substrate mixtures. In a mixture of glucose, glycerol, and acetate, it prefers glucose, then glycerol, and finally acetate. The model included 67 nodes; 28 were genes, 20 enzymes, and 19 regulators/biochemical compounds. The model represents both the genetic regulation and metabolic networks in an inrtegrated form, which is how they function biologically. This is one of the first attempts to include both of these networks in one model. Previously, discrete mathematical models were used only to describe genetic regulation networks. The study of the network dynamics generated 8 (2(3)) fixed points, one for each nutrient configuration (substrate mixture) in the medium. The fixed points of the discrete model reflect the phenotypes described. Gene expression and the patterns of the metabolic fluxes generated are described accurately. The activation of the gene regulation network depends basically on the presence of glucose and glycerol. The model predicts the behavior when mixed carbon sources are utilized as well as when there is no carbon source present. Fictitious jokers (Joker1, Joker2, and Repressor SdhC) had to be created to control 12 genes whose regulation mechanism is unknown, since glycerol and glucose do not act directly on the genes. The approach presented in this paper is particularly useful to investigate potential unknown gene regulation mechanisms; such a novel approach can also be used to describe other gene regulation situations such as the comparison between non-recombinant and recombinant yeast strain, producing recombinant proteins, presently under investigation in our group.     

Origin of the genetic code and specificity of tRNA aminoacylation. A testable model

Conclusion The specificity of tRNA aminoacylation as well as the origin of the genetic code are far from being understood at the molecular and evolutionnary level. The tRNA-tRNA interaction model could provide a missing link for resolving both problems. The model suggests a direct chemical interaction between the nucleotides in the anticodon, and the amino acid (adenylate) to be transferred to the 3-terminal adenosine, within the catalytic center (23). The experimental data reviewed here indicate that in many, but not all, systems the anticodon does play a major role during the aminoacylation and that the simultaneous binding of two tRNA molecules for aminoacylation (of only one of them) does not contradict enzymatic and crystallographic data (24).