Optimization of the standard genetic code in terms of two mutation types: Point mutations and frameshifts

The calculus of codes - From entropy, complexity, and information to life

Exploring the core components that define living systems and their operational mechanisms within emerging biological entities is a complex endeavor. In the realm of biological systems literature, the terms matter, energy, information, complexity, and entropy are frequently referenced. However, possessing these concepts alone does not guarantee a comprehensive understanding or the ability to reconstruct the intricate nature of life. This study aims to illuminate the trajectory of these organic attributes, presenting a theoretical framework that delves into the integrated role of these concepts in biology. We assert that Code Biology serves as a pivotal steppingstone for unraveling the mechanisms underlying life. Biological codes (BCs) emerge not only from the interplay of matter and energy but also from Information. Contrary to deriving information from the former elements, we propose that information holds its place as a fundamental physical aspect. Consequently, we propose a continuum perspective called Calculus of Fundamentals involving three fundamentals: Matter, Energy, and Information, to depict the dynamics of BCs. To achieve this, we emphasize the necessity of studying Entropy and Complexity as integral organic descriptors. This perspective also facilitates the introduction of a mathematical theoretical framework that aids in comprehending continuous changes, the driving dynamics of biological fundamentals. We posit that Energy, Matter, and Information constitute the essential building blocks of living systems, and their interactions are governed by Entropy and Complexity analyses, redefined as biological descriptors. This interdisciplinary perspective of Code Biology sheds light on the intricate interplay between the controversial phenomenon of life and advances the idea of constructing a theory rooted in information as an organic fundamental.

Alternative Reading Frames are an Underappreciated Source of Protein Sequence Novelty

Protein-coding DNA sequences can be translated into completely different amino acid sequences if the nucleotide triplets used are shifted by a non-triplet amount on the same DNA strand or by translating codons from the opposite strand. Such "alternative reading frames" of protein-coding genes are a major contributor to the evolution of novel protein products. Recent studies demonstrating this include examples across the three domains of cellular life and in viruses. These sequences increase the number of trials potentially available for the evolutionary invention of new genes and also have unusual properties which may facilitate gene origin. There is evidence that the structure of the standard genetic code contributes to the features and gene-likeness of some alternative frame sequences. These findings have important implications across diverse areas of molecular biology, including for genome annotation, structural biology, and evolutionary genomics.

Self-similarity and the maximum entropy principle in the genetic code

This paper addresses the relationship between information and structure of the genetic code. The code has two puzzling anomalies: First, when viewed as 64 sub-cubes of a [Formula: see text] cube, the codons for serine (S) are not contiguous, and there are amino acid codons with zero redundancy, which goes counter to the objective of error correction. To make sense of this, the paper shows that the genetic code must be viewed not only on stereochemical, co-evolution, and error-correction considerations, but also on two additional factors of significance to natural systems, that of an information-theoretic dimensionality of the code data, and the principle of maximum entropy. One implication of non-integer dimensionality associated with data dimensions is self-similarity to different scales, and it is shown that the genetic code does satisfy this property, and it is further shown that the maximum entropy principle operates through the scrambling of the elements in the sense of maximum algorithmic information complexity, generated by an appropriate exponentiation mapping. It is shown that the new considerations and the use of maximum entropy transformation create new constraints that are likely the reasons for the non-uniform codon groups and codons with no redundancy.

The Influence of the Selection at the Amino Acid Level on Synonymous Codon Usage from the Viewpoint of Alternative Genetic Codes

Synonymous codon usage can be influenced by mutations and/or selection, e.g., for speed of protein translation and correct folding. However, this codon bias can also be affected by a general selection at the amino acid level due to differences in the acceptance of the loss and generation of these codons. To assess the importance of this effect, we constructed a mutation-selection model model, in which we generated almost 90,000 stationary nucleotide distributions produced by mutational processes and applied a selection based on differences in physicochemical properties of amino acids. Under these conditions, we calculated the usage of fourfold degenerated (4FD) codons and compared it with the usage characteristic of the pure mutations. We considered both the standard genetic code (SGC) and alternative genetic codes (AGCs). The analyses showed that a majority of AGCs produced a greater 4FD codon bias than the SGC. The mutations producing more thymine or adenine than guanine and cytosine increased the differences in usage. On the other hand, the mutational pressures generating a lot of cytosine or guanine with a low content of adenine and thymine decreased this bias because the nucleotide content of most 4FD codons stayed in the compositional equilibrium with these pressures. The comparison of the theoretical results with those for real protein coding sequences showed that the influence of selection at the amino acid level on the synonymous codon usage cannot be neglected. The analyses indicate that the effect of amino acid selection cannot be disregarded and that it can interfere with other selection factors influencing codon usage, especially in AT-rich genomes, in which AGCs are usually used.

Frameshift and wild-type proteins are often highly similar because the genetic code and genomes were optimized for frameshift tolerance

Frameshift mutations have been considered of significant importance for the molecular evolution of proteins and their coding genes, while frameshift protein sequences encoded in the alternative reading frames of coding genes have been considered to be meaningless. However, functional frameshifts have been found widely existing. It was puzzling how a frameshift protein kept its structure and functionality while substantial changes occurred in its primary amino-acid sequence. This study shows that the similarities among frameshifts and wild types are higher than random similarities and are determined at different levels. Frameshift substitutions are more conservative than random substitutions in the standard genetic code (SGC). The frameshift substitutions score of SGC ranks in the top 2.0-3.5% of alternative genetic codes, showing that SGC is nearly optimal for frameshift tolerance. In many genes and certain genomes, frameshift-resistant codons and codon pairs appear more frequently than expected, suggesting that frameshift tolerance is achieved through not only the optimality of the genetic code but, more importantly, the further optimization of a specific gene or genome through the usages of codons/codon pairs, which sheds light on the role of frameshift mutations in molecular and genomic evolution.

Model of Genetic Code Structure Evolution under Various Types of Codon Reading

The standard genetic code (SGC) is a set of rules according to which 64 codons are assigned to 20 canonical amino acids and stop coding signal. As a consequence, the SGC is redundant because there is a greater number of codons than the number of encoded labels. This redundancy implies the existence of codons that encode the same genetic information. The size and organization of such synonymous codon blocks are important characteristics of the SGC structure whose evolution is still unclear. Therefore, we studied possible evolutionary mechanisms of the codon block structure. We conducted computer simulations assuming that coding systems at early stages of the SGC evolution were sets of ambiguous codon assignments with high entropy. We included three types of reading systems characterized by different inaccuracy and pattern of codon recognition. In contrast to the previous study, we allowed for evolution of the reading systems and their competition. The simulations performed under minimization of translational errors and reduction of coding ambiguity produced the coding system resistant to these errors. The reading system similar to that present in the SGC dominated the others very quickly. The survived system was also characterized by low entropy and possessed properties similar to that in the SGC. Our simulation show that the unambiguous SGC could emerged from a code with a lower level of ambiguity and the number of tRNAs increased during the evolution.

Average and Standard Deviation of the Error Function for Random Genetic Codes with Standard Stop Codons

The origin of the genetic code has been attributed in part to an accidental assignment of codons to amino acids. Although several lines of evidence indicate the subsequent expansion and improvement of the genetic code, the hypothesis of Francis Crick concerning a frozen accident occurring at the early stage of genetic code evolution is still widely accepted. Considering Crick's hypothesis, mathematical descriptions of hypothetical scenarios involving a huge number of possible coexisting random genetic codes could be very important to explain the origin and evolution of a selected genetic code. This work aims to contribute in this regard, that is, it provides a theoretical framework in which statistical parameters of error functions are calculated. Given a genetic code and an amino acid property, the functional code robustness is estimated by means of a known error function. In this work, using analytical calculations, general expressions for the average and standard deviation of the error function distributions of completely random codes with standard stop codons were obtained. As a possible biological application of these results, any set of amino acids and any pure or mixed amino acid properties can be used in the calculations, such that, in case of having to select a set of amino acids to create a genetic code, possible advantages of natural selection of the genetic codes could be discussed.

Little Evidence the Standard Genetic Code Is Optimized for Resource Conservation

Selection for resource conservation can shape the coding sequences of organisms living in nutrient-limited environments. Recently, it was proposed that selection for resource conservation, specifically for nitrogen and carbon content, has also shaped the structure of the standard genetic code, such that the missense mutations the code allows tend to cause small increases in the number of nitrogen and carbon atoms in amino acids. Moreover, it was proposed that this optimization is not confounded by known optimizations of the standard genetic code, such as for polar requirement or hydropathy. We challenge these claims. We show the proposed optimization for nitrogen conservation is highly sensitive to choice of null model and the proposed optimization for carbon conservation is confounded by the known conservative nature of the standard genetic code with respect to the molecular volume of amino acids. There is therefore little evidence the standard genetic code is optimized for resource conservation. We discuss our findings in the context of null models of the standard genetic code.

On the Origin of Frameshift-Robustness of the Standard Genetic Code

The standard genetic code (SGC) has been extensively analyzed for the biological ramifications of its nonrandom structure. For instance, mismatch errors due to point mutation or mistranslation have an overall smaller effect on the amino acid polar requirement under the SGC than under random genetic codes (RGCs). A similar observation was recently made for frameshift errors, prompting the assertion that the SGC has been shaped by natural selection for frameshift-robustness-conservation of certain amino acid properties upon a frameshift mutation or translational frameshift. However, frameshift-robustness confers no benefit because frameshifts usually create premature stop codons that cause nonsense-mediated mRNA decay or production of nonfunctional truncated proteins. We here propose that the frameshift-robustness of the SGC is a byproduct of its mismatch-robustness. Of 564 amino acid properties considered, the SGC exhibits mismatch-robustness in 93-133 properties and frameshift-robustness in 55 properties, respectively, and that the latter is largely a subset of the former. For each of the 564 real and 564 randomly constructed fake properties of amino acids, there is a positive correlation between mismatch-robustness and frameshift-robustness across one million RGCs; this correlation arises because most amino acid changes resulting from a frameshift are also achievable by a mismatch error. Importantly, the SGC does not show significantly higher frameshift-robustness in any of the 55 properties than RGCs of comparable mismatch-robustness. These findings support that the frameshift-robustness of the SGC need not originate through direct selection and can instead be a site effect of its mismatch-robustness.

Some theoretical aspects of reprogramming the standard genetic code

Reprogramming of the standard genetic code to include non-canonical amino acids (ncAAs) opens new prospects for medicine, industry, and biotechnology. There are several methods of code engineering, which allow us for storing new genetic information in DNA sequences and producing proteins with new properties. Here, we provided a theoretical background for the optimal genetic code expansion, which may find application in the experimental design of the genetic code. We assumed that the expanded genetic code includes both canonical and non-canonical information stored in 64 classical codons. What is more, the new coding system is robust to point mutations and minimizes the possibility of reversion from the new to old information. In order to find such codes, we applied graph theory to analyze the properties of optimal codon sets. We presented the formal procedure in finding the optimal codes with various number of vacant codons that could be assigned to new amino acids. Finally, we discussed the optimal number of the newly incorporated ncAAs and also the optimal size of codon groups that can be assigned to ncAAs.

Structure and function of naturally evolved de novo proteins

Comparative evolutionary genomics has revealed that novel protein coding genes can emerge randomly from non-coding DNA. While most of the myriad of transcripts which continuously emerge vanish rapidly, some attain regulatory regions, become translated and survive. More surprisingly, sequence properties of de novo proteins are almost indistinguishable from randomly obtained sequences, yet de novo proteins may gain functions and integrate into eukaryotic cellular networks quite easily. We here discuss current knowledge on de novo proteins, their structures, functions and evolution. Since the existence of de novo proteins seems at odds with decade-long attempts to construct proteins with novel structures and functions from scratch, we suggest that a better understanding of de novo protein evolution may fuel new strategies for protein design.

Negative CG dinucleotide bias: An explanation based on feedback loops between Arginine codon assignments and theoretical minimal RNA rings

Theoretical minimal RNA rings are candidate primordial genes evolved for non-redundant coding of the genetic code's 22 coding signals (one codon per biogenic amino acid, a start and a stop codon) over the shortest possible length: 29520 22-nucleotide-long RNA rings solve this min-max constraint. Numerous RNA ring properties are reminiscent of natural genes. Here we present analyses showing that all RNA rings lack dinucleotide CG (a mutable, chemically instable dinucleotide coding for Arginine), bearing a resemblance to known CG-depleted genomes. CG in "incomplete" RNA rings (not coding for all coding signals, with only 3-12 nucleotides) gradually decreases towards CG absence in complete, 22-nucleotide-long RNA rings. Presumably, feedback loops during RNA ring growth during evolution (when amino acid assignment fixed the genetic code) assigned Arg to codons lacking CG (AGR) to avoid CG. Hence, as a chemical property of base pairs, CG mutability restructured the genetic code, thereby establishing itself as genetically encoded biological information.

Why Is AUG the Start Codon?: Theoretical Minimal RNA Rings: Maximizing Coded Information Biases 1st Codon for the Universal Initiation Codon AUG

The rational design of theoretical minimal RNA rings predetermines AUG as the universal start codon. This design maximizes coded amino acid diversity over minimal sequence length, defining in silico theoretical minimal RNA rings, candidate ancestral genes. RNA rings code for 21 amino acids and a stop codon after three consecutive translation rounds, and form a degradation-delaying stem-loop hairpin. Twenty-five RNA rings match these constraints, ten start with the universal initiation codon AUG. No first codon bias exists among remaining RNA rings. RNA ring design predetermines AUG as initiation codon. This is the only explanation yet for AUG as start codon. RNA ring design determines additional RNA ring gene- and tRNA-like properties described previously, because it presumably mimics constraints on life's primordial RNAs.

Frameshifting preserves key physicochemical properties of proteins

Frameshifts in protein coding sequences are widely perceived as resulting in either nonfunctional or even deleterious protein products. Indeed, frameshifts typically lead to markedly altered protein sequences and premature stop codons. By analyzing complete proteomes from all three domains of life, we demonstrate that, in contrast, several key physicochemical properties of protein sequences exhibit significant robustness against +1 and -1 frameshifts. In particular, we show that hydrophobicity profiles of many protein sequences remain largely invariant upon frameshifting. For example, over 2,900 human proteins exhibit a Pearson's correlation coefficient R between the hydrophobicity profiles of the original and the +1-frameshifted variants greater than 0.7, despite an average sequence identity between the two of only 6.5% in this group. We observe a similar effect for protein sequence profiles of affinity for certain nucleobases as well as protein sequence profiles of intrinsic disorder. Finally, analysis of significance and optimality demonstrates that frameshift stability is embedded in the structure of the universal genetic code and may have contributed to shaping it. Our results suggest that frameshifting may be a powerful evolutionary mechanism for creating new proteins with vastly different sequences, yet similar physicochemical properties to the proteins from which they originate.