HetMM: A Michaelis-Menten model for non-homogeneous enzyme mixtures.

The Michaelis-Menten model requires its reaction velocities to come from a preparation of homogeneous enzymes, with identical or near-identical catalytic activities. However, this condition is not always met. We introduce a kinetic model that relaxes this requirement, by assuming there are an unknown number of enzyme species drawn from a probability distribution whose standard deviation is estimated. Through simulation studies, we demonstrate the method accurately discriminates between homogeneous and heterogeneous data, even with moderate levels of experimental error. We applied this model to three homogeneous and three heterogeneous biological systems, showing that the standard and heterogeneous models outperform respectively. Lastly, we show that heterogeneity is not readily distinguished from negatively cooperative binding under the Hill model. These two distinct attributes-inequality in catalytic ability and interference between binding sites-yield similar Michaelis-Menten curves that are not readily resolved without further experimentation. Our user-friendly software package allows homogeneity testing and parameter estimation.

Genomic database furnishes a spontaneous example of a functional Class II glycyl-tRNA synthetase urzyme.

The chief barrier to studies of how genetic coding emerged is the lack of experimental models for ancestral aminoacyl-tRNA synthetases (AARS). We hypothesized that conserved core catalytic sites could represent such ancestors. That hypothesis enabled engineering functional "urzymes" from TrpRS, LeuRS, and HisRS. We describe here a fourth urzyme, GlyCA, detected in an open reading frame from the genomic record of the arctic fox, Vulpes lagopus. GlyCA is homologous to a bacterial heterotetrameric Class II GlyRS-B. Alphafold2 predicted that the N-terminal 81 amino acids would adopt a 3D structure nearly identical to the HisRS urzyme (HisCA1). We expressed and purified that N-terminal segment. Enzymatic characterization revealed a robust single-turnover burst size and a catalytic rate for ATP consumption well in excess of that previously published for HisCA1. Time-dependent aminoacylation of tRNAGly proceeds at a rate consistent with that observed for amino acid activation. In fact, GlyCA is actually 35 times more active in glycine activation by ATP than the full-length GlyRS-B α-subunit dimer. ATP-dependent activation of the 20 canonical amino acids favors Class II amino acids that complement those favored by HisCA and LeuAC. These properties reinforce the notion that urzymes represent the requisite ancestral catalytic activities to implement a reduced genetic coding alphabet.

Enzymic recognition of amino acids drove the evolution of primordial genetic codes.

How genetic information gained its exquisite control over chemical processes needed to build living cells remains an enigma. Today, the aminoacyl-tRNA synthetases (AARS) execute the genetic codes in all living systems. But how did the AARS that emerged over three billion years ago as low-specificity, protozymic forms then spawn the full range of highly-specific enzymes that distinguish between 22 diverse amino acids? A phylogenetic reconstruction of extant AARS genes, enhanced by analysing modular acquisitions, reveals six AARS with distinct bacterial, archaeal, eukaryotic, or organellar clades, resulting in a total of 36 families of AARS catalytic domains. Small structural modules that differentiate one AARS family from another played pivotal roles in discriminating between amino acid side chains, thereby expanding the genetic code and refining its precision. The resulting model shows a tendency for less elaborate enzymes, with simpler catalytic domains, to activate amino acids that were not synthesised until later in the evolution of the code. The most probable evolutionary route for an emergent amino acid type to establish a place in the code was by recruiting older, less specific AARS, rather than adapting contemporary lineages. This process, retrofunctionalisation, differs from previously described mechanisms through which amino acids would enter the code.

Origins of Genetic Coding: Self-Guided Molecular Self-Organisation.

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.

Multidimensional Phylogenetic Metrics Identify Class I Aminoacyl-tRNA Synthetase Evolutionary Mosaicity and Inter-Modular Coupling.

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.

The Roots of Genetic Coding in Aminoacyl-tRNA Synthetase Duality.

Codon-dependent translation underlies genetics and phylogenetic inferences, but its origins pose two challenges. Prevailing narratives cannot account for the fact that aminoacyl-tRNA synthetases (aaRSs), which translate the genetic code, must collectively enforce the rules used to assemble themselves. Nor can they explain how specific assignments arose from rudimentary differentiation between ancestral aaRSs and corresponding transfer RNAs (tRNAs). Experimental deconstruction of the two aaRS superfamilies created new experimental tools with which to analyze the emergence of the code. Amino acid and tRNA substrate recognition are linked to phase transfer free energies of amino acids and arise largely from aaRS class-specific differences in secondary structure. Sensitivity to protein folding rules endowed ancestral aaRS-tRNA pairs with the feedback necessary to rapidly compare alternative genetic codes and coding sequences. These and other experimental data suggest that the aaRS bidirectional genetic ancestry stabilized the differentiation and interdependence required to initiate and elaborate the genetic coding table.

Reciprocally-Coupled Gating: Strange Loops in Bioenergetics, Genetics, and Catalysis.

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.

Impedance Matching and the Choice Between Alternative Pathways for the Origin of Genetic Coding.

We recently observed that errors in gene replication and translation could be seen qualitatively to behave analogously to the impedances in acoustical and electronic energy transducing systems. We develop here quantitative relationships necessary to confirm that analogy and to place it into the context of the minimization of dissipative losses of both chemical free energy and information. The formal developments include expressions for the information transferred from a template to a new polymer, Iσ; an impedance parameter, Z; and an effective alphabet size, neff; all of which have non-linear dependences on the fidelity parameter, q, and the alphabet size, n. Surfaces of these functions over the {n,q} plane reveal key new insights into the origin of coding. Our conclusion is that the emergence and evolutionary refinement of information transfer in biology follow principles previously identified to govern physical energy flows, strengthening analogies (i) between chemical self-organization and biological natural selection, and (ii) between the course of evolutionary trajectories and the most probable pathways for time-dependent transitions in physics. Matching the informational impedance of translation to the four-letter alphabet of genes uncovers a pivotal role for the redundancy of triplet codons in preserving as much intrinsic genetic information as possible, especially in early stages when the coding alphabet size was small.

Author Correction: Octa-repeat domain of the mammalian prion protein mRNA forms stable A-helical hairpin structure rather than G-quadruplexes.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

The Ancient Operational Code is Embedded in the Amino Acid Substitution Matrix and aaRS Phylogenies.

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.

Reflexivity, coding and quantum biology.

Biological systems are fundamentally computational in that they process information in an apparently purposeful fashion rather than just transferring bits of it in a purely syntactical manner. Biological information, such has genetic information stored in DNA sequences, has semantic content. It carries meaning that is defined by the molecular context of its cellular environment. Information processing in biological systems displays an inherent reflexivity, a tendency for the computational information-processing to be "about" the behaviour of the molecules that participate in the computational process. This is most evident in the operation of the genetic code, where the specificity of the reactions catalysed by the aminoacyl-tRNA synthetase (aaRS) enzymes is required to be self-sustaining. A cell's suite of aaRS enzymes completes a reflexively autocatalytic set of molecular components capable of making themselves through the operation of the code. This set requires the existence of a body of reflexive information to be stored in an organism's genome. The genetic code is a reflexively self-organised mapping of the chemical properties of amino acid sidechains onto codon "tokens". It is a highly evolved symbolic system of chemical self-description. Although molecular biological coding is generally portrayed in terms of classical bit-transfer events, various biochemical events explicitly require quantum coherence for their occurrence. Whether the implicit transfer of quantum information, qbits, is indicative of wide-ranging quantum computation in living systems is currently the subject of extensive investigation and speculation in the field of Quantum Biology.

Experimental solutions to problems defining the origin of codon-directed protein synthesis.

How genetic coding differentiated biology from chemistry is a long-standing challenge in Biology, for which there have been few experimental approaches, despite a wide-ranging speculative literature. We summarize five coordinated areas-experimental characterization of functional approximations to the minimal peptides (protozymes and urzymes) necessary to activate amino acids and acylate tRNA; showing that specificities of these experimental models match those expected from the synthetase Class division; population of disjoint regions of amino acid sequence space via bidirectional coding ancestry of the two synthetase Classes; showing that the phase transfer equilibria of amino acid side chains that form a two-dimensional basis set for protein folding are embedded in patterns of bases in the tRNA acceptor stem and anticodon; and identification of molecular signatures of ancestral synthetases and tRNAs necessary to define the earliest cognate synthetase:tRNA pairs-that now compose an extensive experimentally testable paradigm for progress toward understanding the coordinated emergence of the codon table and viable mRNA coding sequences. We briefly discuss recent progress toward identifying the remaining outstanding questions-the nature of the earliest amino acid alphabets and the origin of binding discrimination via distinct amino acid sequence-independent protein secondary structures-and how these, too, might be addressed experimentally.

Class I and II aminoacyl-tRNA synthetase tRNA groove discrimination created the first synthetase-tRNA cognate pairs and was therefore essential to the origin of genetic coding.

The genetic code likely arose when a bidirectional gene replicating as a quasi-species began to produce ancestral aminoacyl-tRNA synthetases (aaRS) capable of distinguishing between two distinct sets of amino acids. The synthetase class division therefore necessarily implies a mechanism by which the two ancestral synthetases could also discriminate between two different kinds of tRNA substrates. We used regression methods to uncover the possible patterns of base sequences capable of such discrimination and find that they appear to be related to thermodynamic differences in the relative stabilities of a hairpin necessary for recognition of tRNA substrates by Class I aaRS. The thermodynamic differences appear to be exploited by secondary structural differences between models for the ancestral aaRS called synthetase Urzymes and reinforced by packing of aromatic amino acid side chains against the nonpolar face of the ribose of A76 if and only if the tRNA CCA sequence forms a hairpin. The patterns of bases 1, 2, and 73 and stabilization of the hairpin by structural complementarity with Class I, but not Class II, aaRS Urzymes appear to be necessary and sufficient to have enabled the generation of the first two aaRS-tRNA cognate pairs, and the launch of a rudimentary binary genetic coding related recognizably to contemporary cognate pairs. As a consequence, it seems likely that nonrandom aminoacylation of tRNAs preceded the advent of the tRNA anticodon stem-loop. Consistent with this suggestion, coding rules in the acceptor-stem bases also reveal a palimpsest of the codon-anticodon interaction, as previously proposed. © 2019 IUBMB Life, 2019 © 2019 IUBMB Life, 71(8):1088-1098, 2019.

Quantitative interpretation of isopiestic measurements on aqueous solutions: Urea revisited.

This investigation amends the analysis of isopiestic measurements of solvent thermodynamic activity by taking into account the fact that the solvent activity, traditionally expressed in mole-fraction terms, is a molal parameter because of the constraints (constant temperature and pressure) under which the measurements are made. Application of the revised procedure to published isopiestic measurements on aqueous urea solutions at 25 °C yields a dimerization constant of 0.066 molal-1, which is two-fold larger than an earlier published estimate based on an incorrect definition of the solute activity coefficient. Despite amendments to the quantitative detail, the present study confirms the existence of a large negative entropic contribution that largely counters its enthalpic counterpart arising from the hydrogen bonding responsible for dimer formation. This evidence of enthalpy-entropy compensation is entirely consistent with quantum-mechanical predictions of the adverse effect of water on urea dimerization. Changes in water structure thus contribute significantly to the energetics of urea dimerization in aqueous solution.

Octa-repeat domain of the mammalian prion protein mRNA forms stable A-helical hairpin structure rather than G-quadruplexes.

Misfolding and aggregation of prion protein (PrP) causes neurodegenerative diseases like Creutzfeldt-Jakob disease (CJD) and scrapie. Besides the consensus that spontaneous conversion of normal cellular PrPC into misfolded and aggregating PrPSc is the central event in prion disease, an alternative hypothesis suggests the generation of pathological PrPSc by rare translational frameshifting events in the octa-repeat domain of the PrP mRNA. Ribosomal frameshifting most commonly relies on a slippery site and an adjacent stable RNA structure to stall translating ribosome. Hence, it is crucial to unravel the secondary structure of the octa-repeat domain of PrP mRNA. Each of the five octa-repeats contains a motif (GGCGGUGGUGGCUGGG) which alone in vitro forms a G-quadruplex. Since the propensity of mRNA to form secondary structure depends on the sequence context, we set to determine the structure of the complete octa-repeat region. We assessed the structure of full-length octa-repeat domain of PrP mRNA using dynamic light scattering (DLS), small angle X-ray scattering (SAXS), circular dichroism (CD) spectroscopy and selective 2'-hydroxyl acylation analysis by primer extension (SHAPE). Our data show that the PrP octa-repeat mRNA forms stable A-helical hairpins with no evidence of G-quadruplex structure even in the presence of G-quadruplex stabilizing agents.

Hierarchical groove discrimination by Class I and II aminoacyl-tRNA synthetases reveals a palimpsest of the operational RNA code in the tRNA acceptor-stem bases.

Class I and II aaRS recognition of opposite grooves was likely among the earliest determinants fixed in the tRNA acceptor stem bases. A new regression model identifies those determinants in bacterial tRNAs. Integral coefficients relate digital dependent to independent variables with perfect agreement between observed and calculated grooves for all twenty isoaccepting tRNAs. Recognition is mediated by the Discriminator base 73, the first base pair, and base 2 of the acceptor stem. Subsets of these coefficients also identically compute grooves recognized by smaller numbers of aaRS. Thus, the model is hierarchical, suggesting that new rules were added to pre-existing ones as new amino acids joined the coding alphabet. A thermodynamic rationale for the simplest model implies that Class-dependent aaRS secondary structures exploited differential tendencies of the acceptor stem to form the hairpin observed in Class I aaRS•tRNA complexes, enabling the earliest groove discrimination. Curiously, groove recognition also depends explicitly on the identity of base 2 in a manner consistent with the middle bases of the codon table, confirming a hidden ancestry of codon-anticodon pairing in the acceptor stem. That, and the lack of correlation with anticodon bases support prior productive coding interaction of tRNA minihelices with proto-mRNA.

Interdependence, Reflexivity, Fidelity, Impedance Matching, and the Evolution of Genetic Coding.

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.

Insuperable problems of the genetic code initially emerging in an RNA world.

Differential equations for error-prone information transfer (template replication, transcription or translation) are developed in order to consider, within the theory of autocatalysis, the advent of coded protein synthesis. Variations of these equations furnish a basis for comparing the plausibility of contrasting scenarios for the emergence of specific tRNA aminoacylation, ultimately by enzymes, and the relationship of this process with the origin of the universal system of molecular biological information processing embodied in the Central Dogma. The hypothetical RNA World does not furnish an adequate basis for explaining how this system came into being, but principles of self-organisation that transcend Darwinian natural selection furnish an unexpectedly robust basis for a rapid, concerted transition to genetic coding from a peptide·RNA world.

Life’s most distinguishing feature: meaningful information processing.

The origin of life out of molecular disorder represents an extraordinary transition in the local fabric of the cosmos. The result can only be described by language that is imbued with echoes of purpose and agency. The «codescript¼ information stored in genes cannot be adequately understood in terms of Shannon’s syntactical measure. Biology requires a molecular-level explanation of the origin and maintenance of meaning, not just the emergence of functionally integrated nano-machinery. The highly ordered, autonomously maintained structure and functional organisation inside cells would be impossible without the precision afforded by information stored in read-only memory. Genetic information provides patterned boundary conditions that constrain the outcome of a biological system’s mechanically determined stochastic dynamics so that it is maintained in a continual state of self-construction. The evolution of genetic coding is the key to understanding how biological systems have reflexively embedded a representation of their own chemistry in DNA molecules. From the point of view of chemistry the genetic code is rule based, providing a map of very deep aspects of the physical phenomena an organism must control in order to exist. The map from genetic information onto functional molecular machinery that interprets genetic information reflects information onto its meaning and vice versa. It is the means whereby mechanical causation is commandeered and controlled by self-constructing semantic structures that unfold their own existence upon a material substrate.