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Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees yield insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies at different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and real world networks. We put forward a multi-scale picture of graph structure wherein we study the effect of global and local structures on changes in distance measures. We make recommendations on the applicability of different distance measures to the analysis of empirical graph data based on this multi-scale view. Finally, we introduce the Python library NetComp that implements the graph distances used in this work.

The origin of genetic coding is characterised as an event of cosmic significance in which quantum mechanical causation was transcended by constructive computation. Computational causation entered the physico-chemical processes of the pre-biotic world by the incidental satisfaction of a condition of reflexivity between polymer sequence information and system elements able to facilitate their own production through translation of that information. This event, which has previously been modelled in the dynamics of Gene–Replication–Translation systems, is properly described as a process of self-guided self-organisation. The spontaneous emergence of a primordial genetic code between two-letter alphabets of nucleotide triplets and amino acids is easily possible, starting with random peptide synthesis that is RNA-sequence-dependent. The evident self-organising mechanism is the simultaneous quasi-species bifurcation of the populations of information-carrying genes and enzymes with aminoacyl-tRNA synthetase-like activities. This mechanism allowed the code to evolve very rapidly to the ~20 amino acid limit apparent for the reflexive differentiation of amino acid properties using protein catalysts. The self-organisation of semantics in this domain of physical chemistry conferred on emergent molecular biology exquisite computational control over the nanoscopic events needed for its self-construction.

Genetic coding is generally thought to have required ribozymes whose functions were taken over by polypeptide aminoacyl-tRNA synthetases (aaRS). Two discoveries about aaRS and their interactions with tRNA substrates now furnish a unifying rationale for the opposite conclusion: that the key processes of the Central Dogma of molecular biology emerged simultaneously and naturally from simple origins in a peptide•RNA partnership, eliminating the epistemological utility of a prior RNA world. First, the two aaRS classes likely arose from opposite strands of the same ancestral gene, implying a simple genetic alphabet. The resulting inversion symmetries in aaRS structural biology would have stabilized the initial and subsequent differentiation of coding specificities, rapidly promoting diversity in the proteome. Second, amino acid physical chemistry maps onto tRNA identity elements, establishing reflexive, nanoenvironmental sensing in protein aaRS. Bootstrapping of increasingly detailed coding is thus intrinsic to polypeptide aaRS, but impossible in an RNA world. These notions underline the following concepts that contradict gradual replacement of ribozymal aaRS by polypeptide aaRS: 1) aaRS enzymes must be interdependent; 2) reflexivity intrinsic to polypeptide aaRS production dynamics promotes bootstrapping; 3) takeover of RNA-catalyzed aminoacylation by enzymes will necessarily degrade specificity; and 4) the Central Dogma’s emergence is most probable when replication and translation error rates remain comparable. These characteristics are necessary and sufficient for the essentially de novo emergence of a coupled gene–replicase–translatase system of genetic coding that would have continuously preserved the functional meaning of genetically encoded protein genes whose phylogenetic relationships match those observed today.

The physico-chemical processes occurring inside cells are under the computational control of genetic (DNA) and epigenetic (internal structural) programming. The origin and evolution of genetic information (nucleic acid sequences) is reasonably well understood, but scant attention has been paid to the origin and evolution of the molecular biological interpreters that give phenotypic meaning to the sequence information that is quite faithfully replicated during cellular reproduction. The near universality and age of the mapping from nucleotide triplets to amino acids embedded in the functionality of the protein synthetic machinery speaks to the early development of a system of coding which is still extant in every living organism. We take the origin of genetic coding as a paradigm of the emergence of computation in natural systems, focusing on the requirement that the molecular components of an interpreter be synthesized autocatalytically. Within this context, it is seen that interpreters of increasing complexity are generated by series of transitions through stepped dynamic instabilities (non-equilibrium phase transitions). The early phylogeny of the amino acyl-tRNA synthetase enzymes is discussed in such terms, leading to the conclusion that the observed optimality of the genetic code is a natural outcome of the processes of self-organization that produced it.

Abstract All known living systems make proteins from the same 20 canonically coded amino acids, but this was not always the case. Early genetic coding systems likely operated with a restricted pool of amino acid types and limited means to distinguish between them. Despite this, amino acid substitution models like LG and WAG all assume a constant coding alphabet over time. That makes them especially inappropriate for the aminoacyl-tRNA synthetases (aaRS)—the enzymes that govern translation. To address this limitation, we created a class of substitution models that account for evolutionary changes in the coding alphabet size by defining the transition from 19 states in a past epoch to 20 now. We use a Bayesian phylogenetic framework to improve phylogeny estimation and testing of this two-alphabet hypothesis. The hypothesis was strongly rejected by datasets composed exclusively of “young” eukaryotic proteins. It was generally supported by “old” (aaRS and non-aaRS) proteins whose origins date from before the last universal common ancestor. Standard methods overestimate the divergence ages of proteins that originated under reduced coding alphabets in both simulated and aaRS alignments. The new model provides a timeline slightly more consistent with the Earth’s history. Our findings suggest that aaRS functional bifurcation events can explain much of the genetic code’s evolution, but there remain other unknown forces at play too. This work provides a robust, seamless framework for reconstructing phylogenies from ancient protein datasets and offers further insights into the dawn of molecular biology.

This article reviews contributions to this theme issue covering the topic 'DNA as information' in relation to the structure of DNA, the measure of its information content, the role and meaning of information in biology and the origin of genetic coding as a transition from uninformed to meaningful computational processes in physical systems.

Kelp forests provide key habitat on the Pacific Coast of Canada; however, the long-term changes in their distribution and abundance remain poorly understood. With advances in satellite technology, floating kelp forests can now be monitored across large-scale areas. We present a methodological framework using an object-based image analysis approach that enables the combination of imagery from multiple satellites at different spatial resolutions and temporal coverage, to map kelp forests with floating canopy through time. The framework comprises four steps: (1) compilation and quality assessment; (2) preprocessing; (3) an object-oriented classification; and (4) an accuracy assessment. Additionally, the impact of spatial resolution on the detectability of floating kelp forests is described. Overall, this workflow was successful in producing accurate maps of floating kelp forests, with global accuracy scores of between 88% and 94%. When comparing the impact of resolution on detectability, lower resolutions were less reliable at detecting small kelp forests in high slope areas. Based on the analysis, we suggest removing high slope areas (11.4%) from time series analyses using high- to medium-resolution satellite imagery and that error, in this case up to 7%, be considered when comparing imagery at different resolutions in low–mid slope areas through time.

The role of aminoacyl-tRNA synthetases (aaRS) in the emergence and evolution of genetic coding poses challenging questions concerning their provenance. We seek evidence about their ancestry from curated structure-based multiple sequence alignments of a structurally invariant “scaffold” shared by all 10 canonical Class I aaRS. Three uncorrelated phylogenetic metrics—mutation frequency, its uniformity, and row-by-row cladistic congruence—imply that the Class I scaffold is a mosaic assembled from successive genetic sources. Metrics for different modules vary in accordance with their presumed functionality. Sequences derived from the ATP– and amino acid– binding sites exhibit specific two-way coupling to those derived from Connecting Peptide 1, a third module whose metrics suggest later acquisition. The data help validate: (i) experimental fragmentations of the canonical Class I structure into three partitions that retain catalytic activities in proportion to their length; and (ii) evidence that the ancestral Class I aaRS gene also encoded a Class II ancestor in frame on the opposite strand. A 46-residue Class I “protozyme” roots the Class I tree prior to the adaptive radiation of the Rossmann dinucleotide binding fold that refined substrate discrimination. Such rooting implies near simultaneous emergence of genetic coding and the origin of the proteome, resolving a conundrum posed by previous inferences that Class I aaRS evolved after the genetic code had been implemented in an RNA world. Further, pinpointing discontinuous enhancements of aaRS fidelity establishes a timeline for the growth of coding from a binary amino acid alphabet.

Bioenergetics, genetic coding, and catalysis are all difficult to imagine emerging without pre-existing historical context. That context is often posed as a “Chicken and Egg” problem; its resolution is concisely described by de Grasse Tyson: “The egg was laid by a bird that was not a chicken”. The concision and generality of that answer furnish no details—only an appropriate framework from which to examine detailed paradigms that might illuminate paradoxes underlying these three life-defining biomolecular processes. We examine experimental aspects here of five examples that all conform to the same paradigm. In each example, a paradox is resolved by coupling “if, and only if” conditions for reciprocal transitions between levels, such that the consequent of the first test is the antecedent for the second. Each condition thus restricts fluxes through, or “gates” the other. Reciprocally-coupled gating, in which two gated processes constrain one another, is self-referential, hence maps onto the formal structure of “strange loops”. That mapping uncovers two different kinds of forces that may help unite the axioms underlying three phenomena that distinguish biology from chemistry. As a physical analog for Gödel’s logic, biomolecular strange-loops provide a natural metaphor around which to organize a large body of experimental data, linking biology to information, free energy, and the second law of thermodynamics.

The underlying structure of the canonical amino acid substitution matrix (aaSM) is examined by considering stepwise improvements in the differential recognition of amino acids according to their chemical properties during the branching history of the two aminoacyl-tRNA synthetase (aaRS) superfamilies. The evolutionary expansion of the genetic code is described by a simple parameterization of the aaSM, in which (i) the number of distinguishable amino acid types, (ii) the matrix dimension and (iii) the number of parameters, each increases by one for each bifurcation in an aaRS phylogeny. Parameterized matrices corresponding to trees in which the size of an amino acid sidechain is the only discernible property behind its categorization as a substrate, exclusively for a Class I or II aaRS, provide a significantly better fit to empirically determined aaSM than trees with random bifurcation patterns. A second split between polar and nonpolar amino acids in each Class effects a vastly greater further improvement. The earliest Class-separated epochs in the phylogenies of the aaRS reflect these enzymes’ capability to distinguish tRNAs through the recognition of acceptor stem identity elements via the minor (Class I) and major (Class II) helical grooves, which is how the ancient operational code functioned. The advent of tRNA recognition using the anticodon loop supports the evolution of the optimal map of amino acid chemistry found in the later genetic code, an essentially digital categorization, in which polarity is the major functional property, compensating for the unrefined, haphazard differentiation of amino acids achieved by the operational code.