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.     

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.     

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.     

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.     

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 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 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 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.     

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.     

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).     

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.     

A mathematical model for the vulnerable phase in myocardium

We present a model of excitable media with the feature that it has a vulnerable phase during which a premature current stimulus will result in the formation of a reentrant self-sustained wave of excitation. The model exploits anisotropic coupling of identical cells, and is therefore useful as a model for the myocardium. We discuss why there is a vulnerable phase and how to determine it quantitatively in models of excitable media, and we demonstrate numerically that permanently rotating waves are formed when a stimulus is applied during this vulnerable phase. Finally, it is shown that the direction of fastest propagation in myocardium is not necessarily the direction of highest safety factor, contrary to commonly accepted opinion. As a result, a reentrant wave is formed after a stimulus is blocked in the axial direction and successfully propagates away from the stimulus site in the lateral direction.     

A mathematical model for photoreceptor interactions

The interactions between rods and cones in the retina have been the focus of innumerable experimental and theoretical biological studies in previous decades yet the understanding of these interactions is still incomplete primarily due to the lack of a unified concept of cone photoreceptor organization and its role in retinal diseases. The low abundance of cones in many of the non-primate mammalian models that have been studied make conclusions about the human retina difficult. A more complete knowledge of the human retina is crucial for counteracting the events that lead to certain degenerative diseases, in particular those associated with photoreceptor cell death (e.g., retinitis pigmentosa). In an attempt to gain important insight into the role and interactions of the rods and the cones we develop and analyze a set of mathematical equations that model a system of photoreceptors and incorporate a direct rod-cone interaction. Our results show that the system can exhibit stable oscillations, which correspond to the rhythmic renewal and shedding of the photoreceptors. In addition, our results show the mathematical necessity of this rod-cone direct interaction for survival of both and gives insight into this mechanism.     

A mathematical model for dorsal closure

During embryogenesis, drosophila embryos undergo epithelial folding and unfolding, which leads to a hole in the dorsal epidermis, transiently covered by an extraembryonic tissue called the amnioserosa. Dorsal closure (DC) consists of the migration of lateral epidermis towards the midline, covering the amnioserosa. It has been extensively studied since numerous physical mechanisms and signaling pathways present in DC are conserved in other morphogenetic events and wound healing in many other species (including vertebrates).We present here a simple mathematical model for DC that involves a reduced number of parameters directly linked to the intensity of the forces in the presence and which is applicable to a wide range of geometries of the leading edge (LE). This model is a natural generalization of the very interesting model proposed in Hutson et al. (2003). Being based on an ordinary differential equation (ODE) approach, the previous model had the advantage of being even simpler, but this restricted significantly the variety of geometries that could be considered and thus the number of modified dorsal closures that could be studied.A partial differential equation (PDE) approach, as the one developed here, allows considering much more general situations that show up in genetically or physically perturbed embryos and whose study will be essential for a proper understanding of the different components of the DC process. Even for native embryos, our model has the advantage of being applicable since an early stages of DC when there is no antero-posterior symmetry (approximately verified only in the late phases of DC).We validate our model in a native setting and also test it further in embryos where the zipping force is perturbed through the expression of spastin (a microtubule severing protein). We obtain variations of the force coefficients that are consistent with what was previously described for this setting.     

A mathematical model for calcium homeostasis

In vivo control of calcium is analysed under the assumption that hormonal influences via plasma levels of parathormone and calcitonin are of prime (but not absolutely dominating) importance. A brief review concerning the physiological significance of body calcium and the mode of action of these two hormones is presented as an introduction to the basic philosophy of the study. A theoretical quasi-linear lumped-parameter model is developed to describe variations in ionic calcium, parathormone and calcitonin plasma concentrations to specific input stimuli. Formal evaluation of the system response requires the determination of ten constants, together with quantitation of ingested calcium entry into the plasma compartment which isindependent of hormonal influences. Values for various parameters are deduced from published data and experimental procedures are outlined to facilitate determination of the remaining unknowns. It is suggested that the proposed model should prove useful for investigations concerning general hormonal actions on calcium homeostatic mechanisms in both normal and diseased states, with particular reference to calcitonin.