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.

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.

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.

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.

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.

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 «codescript» 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.

The generation of meaningful information in molecular systems

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.

DNA as information

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.

Emergence of coding and its specificity as a physico-informatic problem

We explore the origin-of-life consequences of the view that biological systems are demarcated from inanimate matter by their possession of referential information, which is processed computationally to control choices of specific physico-chemical events. Cells are cybernetic: they use genetic information in processes of communication and control, subjecting physical events to a system of integrated governance. The genetic code is the most obvious example of how cells use information computationally, but the historical origin of the usefulness of molecular information is not well understood. Genetic coding made information useful because it imposed a modular metric on the evolutionary search and thereby offered a general solution to the problem of finding catalysts of any specificity. We use the term "quasispecies symmetry breaking" to describe the iterated process of self-organisation whereby the alphabets of distinguishable codons and amino acids increased, step by step.

Spontaneous mutual ordering of nucleic acids and proteins

It is proposed that the prebiotic ordering of nucleic acid and peptide sequences was a cooperative process in which nearly random populations of both kinds of polymers went through a codependent series of self-organisation events that simultaneously refined not only the accuracy of genetic replication and coding but also the functional specificity of protein catalysts, especially nascent aminoacyl-tRNA synthetase "urzymes".

Harnessing our very life

The Aristotelian ideas of nature (physis) and technology (techné) are taken as a starting point for understanding what it would mean for technology to be truly living. Heidegger's critique of the conflation of scientific and technological thinking in the current era is accepted as demonstrating that humanity does not have a deep enough appreciation of the nature of life to harness its essence safely. Could the vision of harnessing life be realized, which we strongly doubt, living technology would give selected humans transforming powers that could be expected to exacerbate, rather than solve, current global problems. The source of human purposefulness, and hence of both technology and ethics, is identified in nature's emergent capability to instantiate informational representations in material forms. Ethics that are properly grounded in an appreciation of intrinsic value, especially that of life, demand that proposals to give humanity the capabilities of living technology address the social, political, economic, and environmental problems inherent in its development and potential deployment. Before any development is embarked on, steps must be taken to avoid living technology, whatever the term eventually designates, becoming available for destructive or antisocial purposes such as those that might devastate humanity or irrevocably damage the natural world.

Frameshifted prion proteins as pathological agents: quantitative considerations

A quantitatively consistent explanation for the titres of infectivity found in a variety of prion-containing preparations is provided on the basis that the ætiological agents of transmissible spongiform encephalopathy comprise a very small population fraction of prion protein (PrP) variants, which contain frameshifted elements in their N-terminal octapeptide-repeat regions. A mechanism for the replication of frameshifted prions is described and calculations are performed to obtain estimates of the concentration of these PrP variants in normal and infected brain, as well as their enrichment in products of protein misfolding cyclic amplification. These calculations resolve the lack of proper quantitative correlation between measures of infectivity and the presence of conformationally-altered, protease-resistant variants of PrP. Experiments, which could confirm or eventually exclude the role of frameshifted variants in the ætiology of prion disease, are suggested.

Allowance for effects of thermodynamic nonideality in sedimentation equilibrium distributions reflecting protein dimerization

This reexamination of a high-speed sedimentation equilibrium distribution for α-chymotrypsin under slightly acidic conditions (pH 4.1, I(M) 0.05) has provided experimental support for the adequacy of nearest-neighbor considerations in the allowance for effects of thermodynamic nonideality in the characterization of protein self-association over a moderate concentration range (up to 8 mg/mL). A widely held but previously untested notion about allowance for thermodynamic nonideality effects is thereby verified experimentally. However, it has also been shown that a greater obstacle to better characterization of protein self-association is likely to be the lack of a reliable estimate of monomer net charge, a parameter that has a far more profound effect on the magnitude of the measured equilibrium constant than any deficiency in current procedures for incorporating the effects of thermodynamic nonideality into the analysis of sedimentation equilibrium distributions reflecting reversible protein self-association.

Allowance for the effect of protein charge in the characterization of nonideal solute self-association by sedimentation equilibrium

This theoretical investigation explores the use of statistical-mechanical approaches to characterize the reversible tetramerization of a protein monomer with the size and charge characteristics of serum albumin under conditions where consideration of nearest-neighbor interactions suffices to describe effects of thermodynamic non-ideality. Such analysis of simulated sedimentation equilibrium distributions points to the adequacy of both the scaled particle theory and potential-of-mean-force methods for determining the self-association constant. Although the latter method usually entails the assignment of a magnitude to monomer net charge, this requirement can be obviated to some extent by repeating the analysis for a range of monomer charges and identifying the most appropriate value as that associated with a minimum in the sum-of-squares-of-residuals (SSR) of the best-fit descriptions of the sedimentation equilibrium distribution. Reasonable estimates of the association constant are usually obtained from corresponding analyses of the same sedimentation equilibrium distributions with activity coefficients obtained by scaled particle theory, an approach which also involves the identification of parameters on the basis of a minimum in SSR. However, the value of monomer charge determined must be regarded as a curve-fitting parameter rather than a true measure of monomer charge. Similar qualifications are shown to prevail in the scaled particle theory approach, which also involves the identification of parameters (the effective monomer volume and the polymer/monomer volume ratio) on the basis of a minimum in SSR. We therefore recommend discontinuation of the practice whereby quite precise distinction between modes of self-association has been attempted on the grounds of the physical credibility of the magnitudes of these additional curve-fitting parameters.

Direct allowance for the effects of thermodynamic nonideality in the quantitative characterization of protein self-association by osmometry

A procedure is described for the direct analysis of osmotic pressure data for reversibly dimerizing proteins that makes allowance for effects of thermodynamic nonideality on the statistical-mechanical basis of the potential-of-mean-force between molecules. Detailed consideration is also given to calculation of the magnitudes of the required virial coefficients. After illustration of the approach with analysis of simulated osmotic pressure data, the method is used to obtain dimerization constants from published osmotic pressure data for soybean proteinase inhibitor, hemoglobin and alpha-chymotrypsin.

Excluded-volume effect of inert macromolecules on the melting of nucleic acids

It is shown on the basis of the excluded-volume effect that inert macromolecules may be expected to suppress the dissociation of double-helical nucleic acids into single helices and thus to raise the melting point of the double helix. The rise in melting temperature of the ribonucleic acid [poly(I).poly(C)] caused by dextran polymers and by poly(ethylene oxide) is described and compared with the theoretical prediction. Good agreement was found in respect of the extent of the rise in melting point and in respect of its dependence upon polymer length. An additional dependence upon the identify of the polymer was attributed to detailed effects of shape in solution.

A simpler analysis for the measurement of second virial coefficients by self-interaction chromatography

We describe a thermodynamic approach that supports the adoption of a simplified procedure for the determination of protein second virial coefficients (B(2)) by self-interaction chromatography. Its major advantage over the original method is a decrease in the number of parameters to which magnitudes must be assigned for the determination of B(2). Improved correlation of virial coefficients obtained by the chromatographic procedure with those obtained by light scattering is achieved by taking into account the twofold larger magnitudes of the former because of the experimental distinction between free and immobilized protein molecules in self-interaction chromatography.

Nonequivalence of second virial coefficients from sedimentation equilibrium and static light scattering studies of protein solutions

Experimental data for ovalbumin and lysozyme are presented to highlight the nonequivalence of second virial coefficients obtained for proteins by sedimentation equilibrium and light scattering. Theoretical considerations confirm that the quantity deduced from sedimentation equilibrium distributions is B(22), the osmotic second virial coefficient describing thermodynamic nonideality arising solely from protein self-interaction. On the other hand, the virial coefficient determined by light scattering is shown to reflect the combined contributions of protein-protein and protein-buffer interactions to thermodynamic nonideality of the protein solution. Misidentification of the light scattering parameter as B(22) accounts for published reports of negative osmotic second virial coefficients as indicators of conditions conducive to protein crystal growth. Finally, textbook assertions about the equivalence of second virial coefficients obtained by sedimentation equilibrium and light scattering reflect the restriction of consideration to single-solute systems. Although sedimentation equilibrium distributions for buffered protein solutions are, indeed, amenable to interpretation in such terms, the same situation does not apply to light scattering measurements because buffer constituents cannot be regarded as part of the solvent: instead they must be treated as non-scattering cosolutes.

Characterization of weak protein dimerization by direct analysis of sedimentation equilibrium distributions: the INVEQ approach

Closer scrutiny has been accorded a recently reported procedure for characterizing weak protein dimerization by sedimentation equilibrium (INVEQ) in which the equilibrium distribution is analyzed as a dependence of radial distance on solute concentration rather than of solute concentration on radial distance. By demonstrating theoretically that the fundamental parameter derived from the analysis is simply the difference between the dimerization constant and the osmotic second virial coefficient for monomer-monomer interaction, this investigation refutes the original claim that independent estimates of these two parameters can be obtained by nonlinear curve fitting of the sedimentation equilibrium distribution. This criticism also applies to conventional analyses of sedimentation distributions by the commonly employed Beckman Origin and NONLIN software. Numerically simulated distributions are then analyzed to demonstrate limitations of the procedure and also to indicate a means of improving the reliability of the returned estimate of the dimerization constant. These features are illustrated by applying the original and revised analytical procedures to a sedimentation equilibrium distribution for alpha-chymotrypsin (pH 4.0, I 0.05 M).

Prion diseases and the frame-shifting hypothesis

A group of neurological diseases, which includes scrapie, bovine spongiform encephalopathy and Creutzfeldt-Jakob disease, is caused by prion agents which appear to be comprised solely of an abnormal variant of a cellular protein, PrP. Infectious agents which contain no genetic material pose a conundrum for molecular biologists. Theoretical analysis of the gene encoding PrP has suggested a possible mechanism of replication for this proteinaceous infectious agent. The putative mechanism involves frame-shifting during translation of the PrP gene. The normal and abnormal forms of PrP are predicted to have different amino acid sequences.

Molecular crowding effects of linear polymers in protein solutions

Measurement of protein-polymer second virial coefficients (BAP) by sedimentation equilibrium studies of carbonic anhydrase and cytochrome c in the presence of dextrans (T10-T80) has revealed an inverse dependence of BAP upon dextran molecular mass that conforms well with the behaviour predicted for the excluded-volume interaction between a spherical protein solute A and a random-flight representation of the polymeric cosolute P. That model of the protein-polymer interaction is also shown to provide a reasonable description of published gel chromatographic and equilibrium dialysis data on the effect of polymer molecular mass on BAP for human serum albumin in the presence of polyethylene glycols, a contrary finding from analysis of albumin solubility measurements being rejected on theoretical grounds. Inverse dependence upon polymer chainlength is also the predicted excluded-volume effect on the strength of several types of macromolecular equilibria-protein isomerization, protein dimerization, and 1:1 complex formation between dissimilar protein reactants. It is therefore concluded that published experimental observations of the reverse dependence, preferential reaction enhancement within DNA replication complexes by larger polyethylene glycols, must reflect the consequences of cosolute chemical interactions that outweigh those of thermodynamic nonideality arising from excluded-volume effects.

van der Waals phase transition in protein solutions

The van der Waals equation of state for imperfect gases is applied to solutions of macromolecules, especially to explain the fluid-fluid phase transition in protein solutions, a phenomenon of much interest in relation to protein crystallization. The van der Waals b parameter corresponds to the total excluded volume per pair of molecules and can be calculated from independently known molecular properties. It is comprised of terms resulting from hard-sphere and net charge-charge interactions. The experimentally determined second virial coefficient B2 can then be used to obtain the equilibrium constant for dimerization K2, a phenomenologically accessible measure of the van der Waals a parameter. Sedimentation equilibrium is recommended as the technique for measuring B2 most accurately. More general results are used to make a minor quantitative correction to the van der Waals prediction concerning the criterion for the fluid-fluid phase transition. Calculations of the effect of inert co-solutes on the phase transition may prove useful in choosing crystallization conditions.

Allowance for thermodynamic non-ideality in the characterization of protein self-association by frontal exclusion chromatography: hemoglobin revisited

This investigation re-examines theoretical aspects of the allowance for effects of thermodynamic non-ideality on the characterization of protein self-association by frontal exclusion chromatography, and thereby provides methods of analysis with greater thermodynamic rigor than those used previously. Their application is illustrated by reappraisal of published exclusion chromatography data for hemoglobin on the controlled-pore-glass matrix CPG-120. The equilibrium constant of 100/M that is obtained for dimerization of the alpha(2)beta(2) species by this means is also deduced from re-examination of published studies of concentrated hemoglobin solutions by osmotic pressure and sedimentation equilibrium methods.

Simulation of a Chemical Autonomous Agent

A chemical autonomous agent is defined as a reproducing molecular system that carries out a thermodynamic work cycle, reminiscent of the earliest prebiotic replicators that harnessed free energy. The efficiency with which free energy is utilized to promote replication is a measure of the selective fitness of such a system. Simulations of the operation of a typical autonomous agent over a wide range of possible parameter settings reveals a fitness landscape with a well-defined maximum and a variety of features that are amenable to interpretation in terms of evolutionary concepts.

Evolution in Systems of Ligation-Based Replicators

The population dynamics of macromolecules that reproduce by means of template-directed ligation of two fragments are shown to be represented by a replicator equation with a special non-linear response function. This result is obtained through detailed consideration of the mechanism of ligation autocatalysis. In contrast to treatments which involve simplification to a parabolic growth law and the expectation of global coexistence of all species, we find that strong selection can take place in such systems, even when there is slow uncatalysed synthesis of replicators. Also, systems of this type are subject to invasion by new species that have a selective advantage. An expression is derived for the survival threshold in terms of species parameters and it is shown that this threshold depends on the total concentration of all species in the system. For a plausible distribution of species parameters, the number of surviving species coexisting above the threshold increases monotonically with increasing concentration. Illustrative numerical simulations are presented.

Studies of solute self-association by sedimentation equilibrium: allowance for effects of thermodynamic non-ideality beyond the consequences of nearest-neighbor interactions

A sedimentation equilibrium study of alpha-chymotrypsin self-association in acetate-chloride buffer, pH 4.1 I 0.05, has been used to illustrate determination of a dimerization constant under conditions where thermodynamic non-ideality is manifested beyond the consequences of nearest-neighbor interactions. Because the expressions for the experimentally determinable interaction parameters comprise a mixture of equilibrium constant and excluded volume terms, the assignment of reasonable magnitudes to the relevant virial coefficients describing non-associative cluster formation is essential for the evaluation of a reliable estimate of the dimerization constant. Determination of these excluded volume parameters by numerical integration over the potential-of-mean-force is shown to be preferable to their calculation by approximate analytical solutions of the integral for this relatively small enzyme monomer with high net charge (+10) under conditions of low ionic strength (0.05 M).

Autocatalysis, information and coding

Autocatalytic self-construction in macromolecular systems requires the existence of a reflexive relationship between structural components and the functional operations they perform to synthesise themselves. The possibility of reflexivity depends on formal, semiotic features of the catalytic structure-function relationship, that is, the embedding of catalytic functions in the space of polymeric structures. Reflexivity is a semiotic property of some genetic sequences. Such sequences may serve as the basis for the evolution of coding as a result of autocatalytic self-organisation in a population of assignment catalysts. Autocatalytic selection is a mechanism whereby matter becomes differentiated in primitive biochemical systems. In the case of coding self-organisation, it corresponds to the creation of symbolic information. Prions are present-day entities whose replication through autocatalysis reflects aspects of biological semiotics less obvious than genetic coding.

Analysis of sedimentation equilibrium distributions reflecting nonideal macromolecular associations

A rigorous statistical-mechanical approach is adopted to derive general quantitative expressions that allow for the effects of thermodynamic nonideality in equilibrium measurements reflecting interaction between dissimilar macromolecular reactants. An analytical procedure based on these expressions is then formulated for obtaining global estimates of equilibrium constants and the corresponding reference thermodynamic activities of the free reactants in each of several sedimentation equilibrium experiments. The method is demonstrated by application to results from an ultracentrifugal study of an electrostatic interaction between ovalbumin and cytochrome c (Winzor, D. J., M. P. Jacobsen, and P. R. Wills. 1998. Biochemistry. 37:2226-2233). It is demonstrated that reliable estimates of relevant thermodynamic parameters are extracted from the data through statistical analysis by means of a simple nonlinear fitting procedure.

Interpretation of thermodynamic non-ideality in sedimentation equilibrium experiments on proteins

This investigation re-examines theoretical aspects of the allowance for effects of thermodynamic non-ideality on the sedimentation equilibrium distribution for a single macromolecular solute, and thereby resolves the question of the constraints that pertain to the definition of the activity coefficient term in the basic sedimentation equilibrium expression. Sedimentation equilibrium results for ovalbumin are then presented to illustrate a simple procedure for evaluating the net charge (valence) of a protein from the magnitude of the second virial coefficient in situations where the effective radius of the protein can be assigned. Finally, published sedimentation equilibrium results on lysozyme are reanalysed to demonstrate the feasibility of employing the dependence of the second virial coefficient upon ionic strength to evaluate both the valence and the effective radius of the non-interacting solute.