Omer Markovitch

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 Eigens 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 (pmc) 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 pmc 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.

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.

Spontaneous chiral symmetry breaking in early molecular networks

BackgroundAn 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.ResultsWe 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.ConclusionIt 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.ReviewersThis article was reviewed by Boris Rubinstein (nominated by Arcady Mushegian), Arcady Mushegian, Meir Lahav (nominated by Yitzhak Pilpel) and Sergei Maslov.

Quasispecies in population of compositional assemblies

BackgroundThe 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.ResultsWe 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 compotypes 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.ConclusionsOur 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.

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.

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.

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.

Prebiotic Evolution of Molecular Assemblies: From Molecules to Ecology

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 supramolecules, without explicitly invoking the intermediate molecular-to-supramolecular stage. We explore a prebiotic model that allows one to relate parameters of chemical interaction networks within molecular assemblies to emergent ecological and evolutionary properties in populations of such assemblies. We use the graded autocatalysis replication domain (GARD) model, which simulates the network dynamics of amphipile-containing molecular assemblies, and exhibits quasistationary compositional states termed compotypes. 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 ecology, analyzable by a multi species logistic (r-K) model for population ecology (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. A main difference from classical ecology is that in GARD species inter convert into each other rather than consume each other or compete on resources, thus representing ‘fast forward’ of speciation.

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 lifes 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 lifes origin.