Molecular Codes Through Complex Formation in a Model of the Human Inner Kinetochore

We apply molecular code theory to a rule-based model of the human inner kinetochore and study how complex formation in general can give rise to molecular codes. We analyze 105 reaction networks generated from the rule-based inner kinetochore model in two variants: with and without dissociation of complexes. Interestingly, we found codes only when some but not all complexes are allowed to dissociate. We show that this is due to the fact that in the kinetochore model proteins can only bind at kinetochores by attaching to already attached proteins and cannot form complexes in free solution. Using a generalized linear mixed model we study which centromere protein (CENP) can take which role in a molecular code (sign, meaning, context). By this, associations between CENPs (CenpA, CenpQ, CenpU and CenpI) and code roles are found. We observed that CenpA is a major risk factor (increases probability for code role) while CenpQ is a major protection factor (decreases probability for code role). Finally we show, using an abstract model of copolymer formation, that molecular codes can also be realized solely by the formation of stable complexes, which do not dissociate. For example, with particular dimers as context a molecular code mapping from two different monomers to two particular trimers can be realized just by non-selective complex formation. We conclude that the formation of protein complexes can be utilized by the cell to implement molecular codes. Living cells thus facilitate a subsystem allowing for an enormous flexibility in the realization of mappings, which can be used for specific regulatory processes, e.g. via the context of a mapping.     

Theory of degenerate coding and informational parameters of protein coding genes

The theory of degenerate coding is presented in a way enabling further application to molecular biology. There are two kinds of redundancy of a degenerate code. The first is due to the excess in codon length and the second to the code degeneracy. If the code is asymmetrically degenerate, the second kind of redundancy can be profitable for control of error rate. This control can be performed just by selective synonymous codon usage. Utilisation of the genetic code is partially influenced by this theoretical possibility. In particular the degree of error protectivity is well correlated with deviation from equiprobability in synonymous codon usage. The biological significance of this fact is discussed.     

Evolution of a genetic code simulated with the computer

A simple selforganizing model system of molecules is considered and it is demonstrated by a computer simulation, that a genetic code of 16 elements (aminoacids) can gradually be formed by such a system in the course of many generations. By a number of rare chance events, each suppressing other events of equal a priori probability, a single code results out of an immense number of possible codes of the same a priori probability. The result is discussed in relation to the uniqueness of the genetic code in living systems. The computer simulation emphasizes a particular step in a model pathway discussed elsewhere consisting of many assumed physicochemical steps leading to a genetic apparatus.     

Stability of the genetic code and optimal parameters of amino acids

The standard genetic code is known to be much more efficient in minimizing adverse effects of misreading errors and one-point mutations in comparison with a random code having the same structure, i.e. the same number of codons coding for each particular amino acid. We study the inverse problem, how the code structure affects the optimal physico-chemical parameters of amino acids ensuring the highest stability of the genetic code. It is shown that the choice of two or more amino acids with given properties determines unambiguously all the others. In this sense the code structure determines strictly the optimal parameters of amino acids or the corresponding scales may be derived directly from the genetic code. In the code with the structure of the standard genetic code the resulting values for hydrophobicity obtained in the scheme “leave one out” and in the scheme with fixed maximum and minimum parameters correlate significantly with the natural scale. The comparison of the optimal and natural parameters allows assessing relative impact of physico-chemical and error-minimization factors during evolution of the genetic code. As the resulting optimal scale depends on the choice of amino acids with given parameters, the technique can also be applied to testing various scenarios of the code evolution with increasing number of codified amino acids. Our results indicate the co-evolution of the genetic code and physico-chemical properties of recruited amino acids.     

Hypothetical stages in the mutational evolution of the present-day genetic code from its RNY,comma-free ancestor

The primitive comma-free genetic code may have had 16 triplets of the form RNY, where R = purine, N = purine or pyrimidine, and Y = pyrimidine, specifying eight (present-day) amino acids. Calculations reveal that in this primitive code all transition changes (A?G, C?U) are either silent or missense i.e. result in the same or another one of these particular eight amino acids. There are no single transitions to non-RNY codons. Single transversions in the primitive codons can, individually, generate new (present-day) codons for four or eight amino acids. Present-day glutamine, tryptophan and stop (UGA, UAA, UAG) codons cannot be so derived., by single transversions, from any of the eight primitive codons. The modern initiation codons, AUG and GUG, can however be generated by both C → G and U → G single transversions in primitive codons. Overall, a total of 32 modern sense codons, not represented in the primitive RNY code, can be derived from this code by single transversions. Many modern codons, including all those not generated by single transversions in the primitive code, can also be produced by either of the two types of frameshift possible in runs of U- or C-rich primitive codons. Present-day stop codons are generated by +1 (-2) type frameshifts in U-rich primitive runs; AUG and GUG initiation codons are produced by the other type, +2 (-1), frameshifts in U-rich runs.     

Noise immunity of the genetic code

Error detection and correction properties are fundamental for informative codes. Hamming's distance allows us to study this noise resistance. We present codes characterized by the resistance optimization to nonsense mutational effects. The calculation of the cumulated Hamming's distance allowing to determine the number of optimal codes and their structure can be detailed. The principle of these laws of optimization of resistance consists of choosing constituent codons connected by mutational neighbouring in such a way that random application of mutations on such a code minimize the occurrence of nonsense n-uplets or terminators. New coding symmetries are then described and screened using Galois's polynomials properties and Baudot's code. Such a study can be applied to any length of the codons. Here we present the principles of this optimization for the most simple doublet codes. Another constraint is discussed: the distribution of optimal subcodes for synonymity and the frequencies of utilization of the different codons.We compare these results to those of the present genetic code, and we observe that all coded amino acids (except the particular case of SER) are using optimal sub-codes of synonymity.This work suggests that the appearance of the genetic code was provoked by mutations while optimizing on several levels its resistance to their effects. Thus genetic coding would have been the best automata that could be produced in prebiotic conditions.     

The hidden code in genomics: a tool for gene discovery.

Among new insights coming from the completion of sequencing of the human genome, reported in Nature and Science, are clues of how evolution has increased the complexity of species, and in particular how the genetic code has enabled this process. It is clear that life has not only evolved by increasing the number of genes, but also by ingeniously evolving an efficient code for expressing diversity in the building blocks (i.e. the amino acids). The rules of nucleic acid base pairing and the classification of amino acids according to hydrophobicity/hydrophilicity relationships define a binary DNA code, which determines the general biophysical characteristics of proteins. Sense and antisense strands can encode protein segments having inverted and complementary hydropathy. The underlying binary code controls association and dissociation of proteins and presumably represents a primordial code that might have emerged in the early stages of self-organizing biochemical cycles. It is the purpose of this communication to provide a perspective of the code in the context of a binary language from its primordial origin to its present day format and to propose to use this code as a genomic mining tool.     

Supervisory control theory applied to swarm robotics

Currently, the control software of swarm robotics systems is created by ad hoc development. This makes it hard to deploy these systems in real-world scenarios. In particular, it is difficult to maintain, analyse, or verify the systems. Formal methods can contribute to overcome these problems. However, they usually do not guarantee that the implementation matches the specification, because the system’s control code is typically generated manually. Also, there is cultural resistance to apply formal methods; they may be perceived as an additional step that does not add value to the final product. To address these problems, we propose supervisory control theory for the domain of swarm robotics. The advantages of supervisory control theory, and its associated tools, are a reduction in the amount of ad hoc development, the automatic generation of control code from modelled specifications, proofs of properties over generated control code, and the reusability of formally designed controllers between different robotic platforms. These advantages are demonstrated in four case studies using the e-puck and Kilobot robot platforms. Experiments with up to 600 physical robots are reported, which show that supervisory control theory can be used to formally develop state-of-the-art solutions to a range of problems in swarm robotics.     

Snapshots of protein folding problem: implications of folding and misfolding studies

Deciphering the code that determines the three-dimensional structure of proteins and the ability to predict the final folded form of a protein is still elusive to molecular biophysists. In the case of several proteins a similar tertiary structure is not accompanied by any significant sequence similarity. The question now remains whether a code beyond the genetic code that describes the arrangement of the amino acid within a three dimensional protein structure. The available data undoubtedly demonstrates that the redundancy of this code must be tremendous. Several techniques such as nuclear magnetic resonance spectroscopy and laser detection techniques, coupled with fast initiation of the folding reaction, can now probe the folding events in milliseconds or even faster and provide highly relevant information. The thermodynamic analysis of the folding process and of kinetic intermediates opens whole new avenue of understanding. Breaking the protein folding code would enable scientists to look at a gene whose function is unknown and predict the three-dimensional structure of the protein it encodes. This would give them a very good idea of what the gene does. In this review we hope to bring together the information available about protein folding with particular emphasis on folding intermediate(s). Additionally, the practical consequences of the solution of the protein folding problem in medicine and biotechnology are also discussed.     

Theory of epigenetic coding

The logic of genetic control of development may be based on a binary epigenetic code. This paper revises the author's previous scheme dealing with the numerology of annelid metamerism in these terms. Certain features of the code had been deduced to be combinatorial, others not. This paradoxical contrast is resolved here by the interpretation that these features relate to different operations of the code; the combinatiorial to coding identity of units, the non-combinatorial to coding production of units. Consideration of a second paradox in the theory of epigenetic coding leads to a new solution which further provides a basis for epimorphic regeneration, and may in particular throw light on the "regeneration-duplication" phenomenon. A possible test of the model is also put forward.     

RNA minihelices and the decoding of genetic information

The rules of the genetic code are determined by the specific aminoacylation of transfer RNAs by aminoacyl transfer RNA synthetase. A straightforward analysis shows that a system of synthetase-tRNA interactions that relies on anticodons for specificity could, in principle, enable most synthetases to distinguish their cognate tRNA isoacceptors from all others. Although the anticodons of some tRNAs are recognition sites for the cognate aminoacyl tRNA synthetases, for other synthetases the anticodon is dispensable for specific aminoacylation. In particular, alanine and histidine tRNA synthetases aminoacylate small RNA minihelices that reconstruct the part of their cognate tRNAs that is proximate to the amino acid attachment site. Helices with as few as six base pairs can be efficiently aminoacylated. The specificity of aminoacylation is determined by a few nucleotides and can be converted from one amino acid to another by the change of only a few nucleotides. These findings suggest that, for a subgroup of the synthetases, there is a distinct code in the acceptor helix of transfer RNAs that determines aminoacylation specificity.     

Neural Coding: The enigma of the brain

Information may be coded in neuronal firing patterns in other ways than the instantaneous action-potential frequency; but proving that the brain uses a particular alternative code will not be easy.     

Rigorous and extended application of information theory to the afferent visual system of the cat. I. Basic concepts

Information theory is applied to data from microelectrode recordings of the cat's afferent visual system in a manner more general than hitherto usual. It is shown that it is not necessary to know the particular neuronal code for information calculations by taking the signal itself as the symbols. Uncontrollable errors thus can be avoided. It is further shown that by this approach the dynamical behaviour of the system is fully considered for information transfer. Quantities are defined to exhibit the time course of transmitted information.     

Codon reassignment in Candida species: An evolutionary conundrum

A number of Candida species translate the standard leucine CUG codon as serine rather than as leucine. Such codon reassignment in nuclear-encoded mRNAs is unusual and raises a number of important questions about the origin of the genetic code and its continuing evolution. In particular we must establish how a codon can come to be reassigned without extinction of the species and what, if any, selective pressure drives such potentially catastrophic changes. Recent studies on the structure and identity of the novel CUG-decoding tRNA^Ser from several different Candida species have begun to shed light on possible evolutionary mechanisms which could have facilitated such changes to the genetic code. These findings are reviewed here and a possible molecular mechanism proposed for how the standard leucine CUG codon could have become reassigned as a serine codon.     

The Genetic Code: What Is It Good For? An Analysis of the Effects of Selection Pressures on Genetic Codes

How did the ``universal' genetic code arise? Several hypotheses have been put forward, and the code has been analyzed extensively by authors looking for clues to selection pressures that might have acted during its evolution. But this approach has been ineffective. Although an impressive number of properties has been attributed to the universal code, it has been impossible to determine whether selection on any of these properties was important in the code's evolution or whether the observed properties arose as a consequence of selection on some other characteristic. Therefore we turned the question around and asked, what would a genetic code look like if it had evolved in response to various different selection pressures? To address this question, we constructed a genetic algorithm. We found first that selecting on a particular measure yields codes that are similar to each other. Second, we found that the universal code is far from minimized with respect to the effects of mutations (or translation errors) on the amino acid compositions of proteins. Finally, we found that the codes that most closely resembled real codes were those generated by selecting on aspects of the code's structure, not those generated by selecting to minimize the effects of amino acid substitutions on proteins. This suggests that the universal genetic code has been selected for a particular structure—a structure that confers an important flexibility on the evolution of genes and proteins—and that the particular assignments of amino acids to codons are secondary. Received: 29 December 1998 / Accepted: 8 July 1999     

The scene of a frozen accident

It has been suggested that in vitro selection experiments can provide information not only on what might have occurred during the evolution of the RNA world, but can in fact yield insights into particular features of the RNA world. In particular, it has been suggested that the sequences of anti-amino acid aptamers can provide clues to the origin of the genetic code, and that there is a statistically significant association between motifs found in aptamers and codons. We argue that the suggested connections between modern motifs and ancient sequences are logically tenuous, and show that there is no statistically meaningful association between motifs found in aptamers and codons.     

Frameshift signals in genes associated with the circular code

Three sets of 20 trinucleotides are preferentially associated with the reading frames and their 2 shifted frames of both eukaryotic and prokaryotic genes. These 3 sets are circular codes. They allow retrieval of any frame in genes (containing these circular code words), locally anywhere in the 3 frames and in particular without start codons in the reading frame, and automatically with the reading of a few nucleotides. The circular code in the reading frame, noted X, which can deduce the 2 other circular codes in the shifted frames by permutation, is the information used for analysing frameshift genes, i. e. genes with a change of reading frame during translation. This work studies the circular code signal around their frameshift sites. Two scoring methods are developed, a function P based on this code X and a function Q based both on this code X and the 4 trinucleotides with identical nucleotides. They detect a significant correlation between the code X and the -1 frameshift signals in both eukaryotic and prokaryotic genes, and the +1 frameshift signals in eukaryotic genes.