The GARD Prebiotic Reproduction Model Described in Order and Complexity.

Early steps in the origin of life were necessarily connected to the unlikely formation of self-reproducing structures from chaotic chemistry. Simulations of chemical kinetics based on the graded autocatalysis replication domain (GARD) model demonstrate the ability of a micellar system to become self-reproducing units away from equilibrium. Even though they may be very rare in the initial state of the system, the property of their endogenous mutually catalytic networks being dynamic attractors greatly enhanced reproduction propensity, revealing their potential for selection and Darwinian evolution processes. In parallel, order and complexity have been shown to be crucial parameters in successful evolution. Here, we probe these parameters in the dynamics of GARD-governed entities in an attempt to identify characteristic mechanisms of their development in non-covalent molecular assemblies. Using a virtual random walk perspective, a value for consecutive order is defined based on statistical thermodynamics. The complexity, on the other hand, is determined by the size of a minimal algorithm fully describing the statistical properties of the random walk. By referring to a previously published diagonal line in an order/complexity diagram that represents the progression of evolution, it is shown that the GARD model has the potential to advance in this direction. These results can serve as a solid foundation for identifying general criteria for future analyses of evolving systems.

Binding of Precursors to Replicator Assemblies Can Improve Replication Fidelity and Mediate Error Correction.

Copying information is vital for life's propagation. Current life forms maintain a low error rate in replication, using complex machinery to prevent and correct errors. However, primitive life had to deal with higher error rates, limiting its ability to evolve. Discovering mechanisms to reduce errors would alleviate this constraint. Here, we introduce a new mechanism that decreases error rates and corrects errors in synthetic self-replicating systems driven by self-assembly. Previous work showed that macrocycle replication occurs through the accumulation of precursor material on the sides of the fibrous replicator assemblies. Stochastic simulations now reveal that selective precursor binding to the fiber surface enhances replication fidelity and error correction. Centrifugation experiments show that replicator fibers can exhibit the necessary selectivity in precursor binding. Our results suggest that synthetic replicator systems are more evolvable than previously thought, encouraging further evolution-focused experiments.

Out-of-Equilibrium Self-Replication Allows Selection for Dynamic Kinetic Stability in a System of Competing Replicators.

Among the key characteristics of living systems are their ability to self-replicate and the fact that they exist in an open system away from equilibrium. Herein, we show how the outcome of the competition between two self-replicators, differing in size and building block composition, is different depending on whether the experiments are conducted in a closed vial or in an open and out-of-equilibrium replication-destruction regime. In the closed system, the slower replicator eventually prevails over the faster competitor. In a replication-destruction regime, implemented through a flow system, the outcome of the competition is reversed and the faster replicator dominates. The interpretation of the experimental observations is supported by a mass-action-kinetics model. These results represent one of the few experimental manifestations of selection among competing self-replicators based on dynamic kinetic stability and pave the way towards Darwinian evolution of abiotic systems.

Chemical Fueling Enables Molecular Complexification of Self-Replicators*.

Unravelling how the complexity of living systems can (have) emerge(d) from simple chemical reactions is one of the grand challenges in contemporary science. Evolving systems of self-replicating molecules may hold the key to this question. Here we show that, when a system of replicators is subjected to a regime where replication competes with replicator destruction, simple and fast replicators can give way to more complex and slower ones. The structurally more complex replicator was found to be functionally more proficient in the catalysis of a model reaction. These results show that chemical fueling can maintain systems of replicators out of equilibrium, populating more complex replicators that are otherwise not readily accessible. Such complexification represents an important requirement for achieving open-ended evolution as it should allow improved and ultimately also new functions to emerge.

All-Photochemical Rotation of Molecular Motors with a Phosphorus Stereoelement.

Unidirectional molecular rotation based on alternating photochemical and thermal isomerizations of overcrowded alkenes is well established, but rotary cycles based purely on photochemical isomerizations are rare. Herein we report three new second-generation molecular motors featuring a phosphorus center in the lower half, which engenders a unique element of axial chirality. These motors exhibit unusual behavior, in that all four diastereomeric states can interconvert solely photochemically. Kinetic analysis and modeling reveal that the behavior of the new motors is consistent with all-photochemical unidirectional rotation. Furthermore, X-ray crystal structures of all four diastereomeric states of two of these new motors were obtained, which constitute the first achievements of crystallographic characterization of the full 360° rotational cycle of overcrowded-alkene-based molecular motors. Finally, the axial phosphorus stereoelement in the phosphine motor can be thermally inverted, and this epimerization enables a "shortcut" of the traditional rotational cycle of these compounds.

Caught in the Act: Mechanistic Insight into Supramolecular Polymerization-Driven Self-Replication from Real-Time Visualization.

Self-assembly features prominently in fields ranging from materials science to biophysical chemistry. Assembly pathways, often passing through transient intermediates, can control the outcome of assembly processes. Yet, the mechanisms of self-assembly remain largely obscure due to a lack of experimental tools for probing these pathways at the molecular level. Here, the self-assembly of self-replicators into fibers is visualized in real-time by high-speed atomic force microscopy (HS-AFM). Fiber growth requires the conversion of precursor molecules into six-membered macrocycles, which constitute the fibers. HS-AFM experiments, supported by molecular dynamics simulations, revealed that aggregates of precursor molecules accumulate at the sides of the fibers, which then diffuse to the fiber ends where growth takes place. This mechanism of precursor reservoir formation, followed by one-dimensional diffusion, which guides the precursor molecules to the sites of growth, reduces the entropic penalty associated with colocalizing precursors and growth sites and constitutes a new mechanism for supramolecular polymerization.

Automated device for continuous stirring while sampling in liquid chromatography systems.

Ultra-performance liquid chromatography is a common analysis tool, and stirring is common in many laboratory setups. Here we show a device which enables continuous stirring of samples whilst inside an ultra-performance liquid chromatography system. Utilizing standard magnetic stirring bars that fit standard vials, the device allows for the automation of experimental setups that require stirring. The device is designed such that it can replace the standard sample holder and fits in its place, while being battery operated. The use of three-dimensional (3D) printing and commercially available parts enables low-effort and low-cost device production, as well as easy modifications. Testing the device was performed by video analysis and by following the kinetics of a dynamic combinatorial library that is known to be exquisitely sensitive to agitation, as a result of involving a fiber growth-breakage mechanism. Design files and schematics are provided.

Systems protobiology: origin of life in lipid catalytic networks.

Life is that which replicates and evolves, but there is no consensus on how life emerged. We advocate a systems protobiology view, whereby the first replicators were assemblies of spontaneously accreting, heterogeneous and mostly non-canonical amphiphiles. This view is substantiated by rigorous chemical kinetics simulations of the graded autocatalysis replication domain (GARD) model, based on the notion that the replication or reproduction of compositional information predated that of sequence information. GARD reveals the emergence of privileged non-equilibrium assemblies (composomes), which portray catalysis-based homeostatic (concentration-preserving) growth. Such a process, along with occasional assembly fission, embodies cell-like reproduction. GARD pre-RNA evolution is evidenced in the selection of different composomes within a sparse fitness landscape, in response to environmental chemical changes. These observations refute claims that GARD assemblies (or other mutually catalytic networks in the metabolism first scenario) cannot evolve. Composomes represent both a genotype and a selectable phenotype, anteceding present-day biology in which the two are mostly separated. Detailed GARD analyses show attractor-like transitions from random assemblies to self-organized composomes, with negative entropy change, thus establishing composomes as dissipative systems-hallmarks of life. We show a preliminary new version of our model, metabolic GARD (M-GARD), in which lipid covalent modifications are orchestrated by non-enzymatic lipid catalysts, themselves compositionally reproduced. M-GARD fills the gap of the lack of true metabolism in basic GARD, and is rewardingly supported by a published experimental instance of a lipid-based mutually catalytic network. Anticipating near-future far-reaching progress of molecular dynamics, M-GARD is slated to quantitatively depict elaborate protocells, with orchestrated reproduction of both lipid bilayer and lumenal content. Finally, a GARD analysis in a whole-planet context offers the potential for estimating the probability of life's emergence. The invigorated GARD scrutiny presented in this review enhances the validity of autocatalytic sets as a bona fide early evolution scenario and provides essential infrastructure for a paradigm shift towards a systems protobiology view of life's origin.

Predicting species emergence in simulated complex pre-biotic networks.

An intriguing question in evolution is what would happen if one could "replay" life's tape. Here, we explore the following hypothesis: when replaying the tape, the details ("decorations") of the outcomes would vary but certain "invariants" might emerge across different life-tapes sharing similar initial conditions. We use large-scale simulations of an in silico model of pre-biotic evolution called GARD (Graded Autocatalysis Replication Domain) to test this hypothesis. GARD models the temporal evolution of molecular assemblies, governed by a rates matrix (i.e. network) that biases different molecules' likelihood of joining or leaving a dynamically growing and splitting assembly. Previous studies have shown the emergence of so called compotypes, i.e., species capable of replication and selection response. Here, we apply networks' science to ascertain the degree to which invariants emerge across different life-tapes under GARD dynamics and whether one can predict these invariant from the chemistry specification alone (i.e. GARD's rates network representing initial conditions). We analysed the (complex) rates' network communities and asked whether communities are related (and how) to the emerging species under GARD's dynamic, and found that the communities correspond to the species emerging from the simulations. Importantly, we show how to use the set of communities detected to predict species emergence without performing any simulations. The analysis developed here may impact complex systems simulations in general.

Quasispecies in population of compositional assemblies.

BACKGROUND: The quasispecies model refers to information carriers that undergo self-replication with errors. A quasispecies is a steady-state population of biopolymer sequence variants generated by mutations from a master sequence. A quasispecies error threshold is a minimal replication accuracy below which the population structure breaks down. Theory and experimentation of this model often refer to biopolymers, e.g. RNA molecules or viral genomes, while its prebiotic context is often associated with an RNA world scenario. Here, we study the possibility that compositional entities which code for compositional information, intrinsically different from biopolymers coding for sequential information, could show quasispecies dynamics. RESULTS: We employed a chemistry-based model, graded autocatalysis replication domain (GARD), which simulates the network dynamics within compositional molecular assemblies. In GARD, a compotype represents a population of similar assemblies that constitute a quasi-stationary state in compositional space. A compotype's center-of-mass is found to be analogous to a master sequence for a sequential quasispecies. Using single-cycle GARD dynamics, we measured the quasispecies transition matrix (Q) for the probabilities of transition from one center-of-mass Euclidean distance to another. Similarly, the quasispecies' growth rate vector (A) was obtained. This allowed computing a steady state distribution of distances to the center of mass, as derived from the quasispecies equation. In parallel, a steady state distribution was obtained via the GARD equation kinetics. Rewardingly, a significant correlation was observed between the distributions obtained by these two methods. This was only seen for distances to the compotype center-of-mass, and not to randomly selected compositions. A similar correspondence was found when comparing the quasispecies time dependent dynamics towards steady state. Further, changing the error rate by modifying basal assembly joining rate of GARD kinetics was found to display an error catastrophe, similar to the standard quasispecies model. Additional augmentation of compositional mutations leads to the complete disappearance of the master-like composition. CONCLUSIONS: Our results show that compositional assemblies, as simulated by the GARD formalism, portray significant attributes of quasispecies dynamics. This expands the applicability of the quasispecies model beyond sequence-based entities, and potentially enhances validity of GARD as a model for prebiotic evolution.

Multispecies population dynamics of prebiotic compositional assemblies.

Present life portrays a two-tier phenomenology: molecules compose supramolecular structures, such as cells or organisms, which in turn portray population behaviors, including selection, evolution and ecological dynamics. Prebiotic models have often focused on evolution in populations of self-replicating molecules, without explicitly invoking the intermediate molecular-to-supramolecular transition. Here, we explore a prebiotic model that allows one to relate parameters of chemical interaction networks within molecular assemblies to emergent population dynamics. We use the graded autocatalysis replication domain (GARD) model, which simulates the network dynamics within amphiphile-containing molecular assemblies, and exhibits quasi-stationary compositional states termed compotype species. These grow by catalyzed accretion, divide and propagate their compositional information to progeny in a replication-like manner. The model allows us to ask how molecular network parameters influence assembly evolution and population dynamics parameters. In 1000 computer simulations, each embodying different parameter set of the global chemical interaction network parameters, we observed a wide range of behaviors. These were analyzed by a multi species logistic model often used for analyzing population ecology (r-K or Lotka-Volterra competition model). We found that compotypes with a larger intrinsic molecular repertoire show a higher intrinsic growth (r) and lower carrying capacity (K), as well as lower replication fidelity. This supports a prebiotic scenario initiated by fast-replicating assemblies with a high molecular diversity, evolving into more faithful replicators with narrower molecular repertoires.

Is there an optimal level of open-endedness in prebiotic evolution?

In this paper we explore the question of whether there is an optimal set up for a putative prebiotic system leading to open-ended evolution (OEE) of the events unfolding within this system. We do so by proposing two key innovations. First, we introduce a new index that measures OEE as a function of the likelihood of events unfolding within a universe given its initial conditions. Next, we apply this index to a variant of the graded autocatalysis replication domain (GARD) model, Segre et al. (P Natl Acad Sci USA 97(8):4112-4117, 2000; Markovitch and Lancet Artif Life 18(3), 2012), and use it to study--under a unified and concise prebiotic evolutionary framework--both a variety of initial conditions of the universe and the OEE of species that evolve from them.

Excess mutual catalysis is required for effective evolvability.

It is widely accepted that autocatalysis constitutes a crucial facet of effective replication and evolution (e.g., in Eigen's hypercycle model). Other models for early evolution (e.g., by Dyson, Gánti, Varela, and Kauffman) invoke catalytic networks, where cross-catalysis is more apparent. A key question is how the balance between auto- (self-) and cross- (mutual) catalysis shapes the behavior of model evolving systems. This is investigated using the graded autocatalysis replication domain (GARD) model, previously shown to capture essential features of reproduction, mutation, and evolution in compositional molecular assemblies. We have performed numerical simulations of an ensemble of GARD networks, each with a different set of lognormally distributed catalytic values. We asked what is the influence of the catalytic content of such networks on beneficial evolution. Importantly, a clear trend was observed, wherein only networks with high mutual catalysis propensity (p(mc)) allowed for an augmented diversity of composomes, quasi-stationary compositions that exhibit high replication fidelity. We have reexamined a recent analysis that showed meager selection in a single GARD instance and for a few nonstationary target compositions. In contrast, when we focused here on compotypes (clusters of composomes) as targets for selection in populations of compositional assemblies, appreciable selection response was observed for a large portion of the networks simulated. Further, stronger selection response was seen for high p(mc) values. Our simulations thus demonstrate that GARD can help analyze important facets of evolving systems, and indicate that excess mutual catalysis over self-catalysis is likely to be important for the emergence of molecular systems capable of evolutionlike behavior.

Replication of simulated prebiotic amphiphile vesicles controlled by experimental lipid physicochemical properties.

We present a new embodiment of the graded autocatalysis replication domain (GARD) for the growth, replication and evolution of lipid vesicles based on a semi-empirical foundation using experimentally measured kinetic values of selected extant lipid species. Extensive simulations using this formalism elucidated the details of the dependence of the replication and properties of the vesicles on the physicochemical properties and concentrations of the lipids, both in the environment and in the vesicle. As expected, the overall concentration and number of amphiphilic components strongly affect average replication time. Furthermore, variations in acyl chain length and unsaturation of vesicles also influence replication rate, as do the relative concentrations of individual lipid types. Understanding of the dependence of replication rates on physicochemical parameters opens a new direction in the study of prebiotic vesicles and lays the groundwork for future studies involving the competition between lipid vesicles for available amphiphilic monomers.

Spontaneous chiral symmetry breaking in early molecular networks.

BACKGROUND: An important facet of early biological evolution is the selection of chiral enantiomers for molecules such as amino acids and sugars. The origin of this symmetry breaking is a long-standing question in molecular evolution. Previous models addressing this question include particular kinetic properties such as autocatalysis or negative cross catalysis. RESULTS: We propose here a more general kinetic formalism for early enantioselection, based on our previously described Graded Autocatalysis Replication Domain (GARD) model for prebiotic evolution in molecular assemblies. This model is adapted here to the case of chiral molecules by applying symmetry constraints to mutual molecular recognition within the assembly. The ensuing dynamics shows spontaneous chiral symmetry breaking, with transitions towards stationary compositional states (composomes) enriched with one of the two enantiomers for some of the constituent molecule types. Furthermore, one or the other of the two antipodal compositional states of the assembly also shows time-dependent selection. CONCLUSION: It follows that chiral selection may be an emergent consequence of early catalytic molecular networks rather than a prerequisite for the initiation of primeval life processes. Elaborations of this model could help explain the prevalent chiral homogeneity in present-day living cells.

Reversible geminate recombination of hydrogen-bonded water molecule pair.

The (history independent) autocorrelation function for a hydrogen-bonded water molecule pair, calculated from classical molecular dynamics trajectories of liquid water, exhibits a t(-3/2) asymptotic tail. Its whole time dependence agrees quantitatively with the solution for reversible diffusion-influenced geminate recombination derived by Agmon and Weiss [J. Chem. Phys. 91, 6937 (1989)]. Agreement with diffusion theory is independent of the precise definition of the bound state. Given the water self-diffusion constant, this theory enables us to determine the dissociation and bimolecular recombination rate parameters for a water dimer. (The theory is indispensable for obtaining the bimolecular rate coefficient.) Interestingly, the activation energies obtained from the temperature dependence of these rate coefficients are similar, rather than differing by the hydrogen-bond (HB) strength. This suggests that recombination requires displacing another water molecule, which meanwhile occupied the binding site. Because these activation energies are about twice the HB strength, cleavage of two HBs may be required to allow pair separation. The autocorrelation function without the HB angular restriction yields a recombination rate coefficient that is larger than that for rebinding to all four tetrahedral water sites (with angular restrictions), suggesting the additional participation of interstitial sites. Following dissociation, the probability of the pair to be unbound but within the reaction sphere rises more slowly than expected, possibly because binding to the interstitial sites delays pair separation. An extended diffusion model, which includes an additional binding site, can account for this behavior.

Special pair dance and partner selection: elementary steps in proton transport in liquid water.

Conditional and time-dependent radial distribution functions reveal the details of the water structure surrounding the hydronium during the proton mobility process. Using this methodology for classical multistate empirical valence bond (MS-EVB) and ab initio molecular dynamics trajectories, as well as quantal MS-EVB trajectories, we supply statistical proof that proton hops in liquid water occur by a transition from the H3O+[3H2O] Eigen-complex, via the H5O2+ Zundel-complex, to a H3O+[3H2O] centered on a neighboring water molecule. In the "resting period" before a transition, there is a distorted hydronium with one of its water ligands at a shorter distance and another at a longer distance than average. The identity of this "special partner" interchanges rapidly within the three first-shell water ligands. This is coupled to cleavage of an acceptor-type hydrogen bond. Just before the transition, a partner is selected by an additional translation of the H3O+ moiety in its direction, possibly enabled by loosening of donor-type hydrogen bonds on the opposite side. We monitor the transition in real time, showing how the average structure is converted to a distorted H5O2+ cation constituting the transitional complex for proton hopping between water molecules.

Structure and energetics of the hydronium hydration shells.

Proton solvation and proton mobility are both subjects of great interest in chemistry and biology. Here we have studied the hydration shells of H3O+ at temperatures ranging from 260 to 340 K using the multistate empirical valence-bond methodology (MS-EVB2). We have calculated the radial distribution functions for the protonium and its solvation shells. Furthermore, we have determined the Gibbs energy and the enthalpy for hydrogen bonds donated or accepted by the first two solvation shells, in comparison to bulk water. We find systematic bond-energy differences that appear to agree with a recent IR study on proton hydration. Implications of our results to various proton mobility mechanisms are discussed.