Universal Sequence Replication, Reversible Polymerization and Early Functional Biopolymers: A Model for the Initiation of Prebiotic Sequence Evolution

“polymers [2–5].”

“polymers [2–5].”

“During the dehydrated phase, each lattice site x on the two-dimensional lattice is diffusively isolated and treated individually with the standard Gillespie algorithm [62].”

“Specifically, our model suggests that the optimal conditions for the earliest stage of abiotic chemical evolution, prior to the onset of functional evolution, would not have been those that promote stringent maintenance of sequence information per se, which is considered optimum for most autonomous replicator models […”

“As an added measure of the spatial diversity of the polymer population we utilize a generalization of the of the Jaccard similarity index used in population ecology [7, 8].”

“polymers had already emerged [6–10].”

“a processive polymer replicase [54]), or for the diverse members of a set of enzymes to emerge de novo at the same point in space and time [68].”

“coincided with the selection of the first functional sequences [11,12].”

“. On the contrary, the optimum conditions for early informational polymer evolution would have allowed the spontaneous appearance of completely new sequences, and for the existence of new sequences to be just long enough for functional sequences to gain a local selective advantage during subsequent cycles of replicati…”

“It also remains challenging to determine the environmental context from which the first informational polymers emerged, as illustrated by the wide variety of proposed sites for the origin of life, including (but not limited to): tidal shores [19,20], deserts [21], hydrothermal vents [22], mineral surfaces [23–25], the…”

“Specifically, our model suggests that the optimal conditions for the earliest stage of abiotic chemical evolution, prior to the onset of functional evolution, would not have been those that promote stringent maintenance of sequence information per se, which is considered optimum for most autonomous replicator models […”

“It also remains challenging to determine the environmental context from which the first informational polymers emerged, as illustrated by the wide variety of proposed sites for the origin of life, including (but not limited to): tidal shores [19,20], deserts [21], hydrothermal vents [22], mineral surfaces [23–25], the…”

“The simulations were implemented via a spatially-explicit hybrid kinetic Monte Carlo algorithm [59,60].”

“Many origin of life researchers consider polymer compartmentalization, such as nucleic acid encapsulation in lipid vesicles [71], to be a prerequisite for evolution.”

“polymers [2–5].”

“The same general characteristics have been proposed by Woese for the earliest biological systems, but for reasons based on bioinformatics analyses of extant organisms [72,73].”

“Incomplete mixing, limited diffusion, and surface attachment have been shown to promote template-directed synthesis [51,52] and to limit the deleterious effects of ‘‘parasites’’ (non-functional polymers) on selection of functional sequences [31,35,53].”

“It also remains challenging to determine the environmental context from which the first informational polymers emerged, as illustrated by the wide variety of proposed sites for the origin of life, including (but not limited to): tidal shores [19,20], deserts [21], hydrothermal vents [22], mineral surfaces [23–25], the…”

“It also remains challenging to determine the environmental context from which the first informational polymers emerged, as illustrated by the wide variety of proposed sites for the origin of life, including (but not limited to): tidal shores [19,20], deserts [21], hydrothermal vents [22], mineral surfaces [23–25], the…”

“It also remains challenging to determine the environmental context from which the first informational polymers emerged, as illustrated by the wide variety of proposed sites for the origin of life, including (but not limited to): tidal shores [19,20], deserts [21], hydrothermal vents [22], mineral surfaces [23–25], the…”

“It also remains challenging to determine the environmental context from which the first informational polymers emerged, as illustrated by the wide variety of proposed sites for the origin of life, including (but not limited to): tidal shores [19,20], deserts [21], hydrothermal vents [22], mineral surfaces [23–25], the…”

“Incomplete mixing, limited diffusion, and surface attachment have been shown to promote template-directed synthesis [51,52] and to limit the deleterious effects of ‘‘parasites’’ (non-functional polymers) on selection of functional sequences [31,35,53].”

“enzymatic replication and sequence evolution of prebiotic informational polymers, including: informational polymers with reversible backbone linkages [38–43], environmental cycling [21,44–49], limited molecular diffusion [31,35,36], monomer recycling [16,48–50], and template-directed synthesis without sequence restric…”

“A critical stage in the origin of life was the emergence of the first functional informational polymers [56].”

“It also remains challenging to determine the environmental context from which the first informational polymers emerged, as illustrated by the wide variety of proposed sites for the origin of life, including (but not limited to): tidal shores [19,20], deserts [21], hydrothermal vents [22], mineral surfaces [23–25], the…”

“Although using shorter length sequences would have enhanced numerical efficiency, we used oligomers of length 20, as nucleic acids of this length are sufficiently long to adopt folded structures and, arguably, large enough to exhibit initial levels of catalytic activity [61].”

“Exploring this early stage in chemical evolution is particularly difficult, being so obscured by the ensuing evolutionary history that even the identity of the first replicating material remains a subject of debate, with hypotheses ranging from RNA or some variety of proto-RNA [11,13–16], to peptides [17], and even in…”

“Spontaneous polymer assembly occurs with (second-order) reaction propensity as = ksAB , (1) and USR via template-directed assembly occurs with (third-order) reaction propensity ari = krAB Ni .”

“However, limited diffusion (or incomplete mixing) has been shown to provide a possible alternative to encapsulation [9,32,36], at least in the earliest stages of prebiotic evolution.”

“explicit Gillespie algorithm [64]) reproduces our hybrid results.”

“The simulations were implemented via a spatially-explicit hybrid kinetic Monte Carlo algorithm [59,60].”

“polymers [2–5].”

“), but the population is temporally varying with respect to the distribution of polymers among existing sequences and due to the appearance of new sequences – a state of dynamic kinetic stability (DKS)”

“with a reversible linkage) [38,39,41,43], or binding of template strands to a surface (e.”

“However, limited diffusion (or incomplete mixing) has been shown to provide a possible alternative to encapsulation [9,32,36], at least in the earliest stages of prebiotic evolution.”

“enzymatic replication and sequence evolution of prebiotic informational polymers, including: informational polymers with reversible backbone linkages [38–43], environmental cycling [21,44–49], limited molecular diffusion [31,35,36], monomer recycling [16,48–50], and template-directed synthesis without sequence restric…”

“enzymatic replication and sequence evolution of prebiotic informational polymers, including: informational polymers with reversible backbone linkages [38–43], environmental cycling [21,44–49], limited molecular diffusion [31,35,36], monomer recycling [16,48–50], and template-directed synthesis without sequence restric…”

“enzymatic replication and sequence evolution of prebiotic informational polymers, including: informational polymers with reversible backbone linkages [38–43], environmental cycling [21,44–49], limited molecular diffusion [31,35,36], monomer recycling [16,48–50], and template-directed synthesis without sequence restric…”

“It also remains challenging to determine the environmental context from which the first informational polymers emerged, as illustrated by the wide variety of proposed sites for the origin of life, including (but not limited to): tidal shores [19,20], deserts [21], hydrothermal vents [22], mineral surfaces [23–25], the…”

“It also remains challenging to determine the environmental context from which the first informational polymers emerged, as illustrated by the wide variety of proposed sites for the origin of life, including (but not limited to): tidal shores [19,20], deserts [21], hydrothermal vents [22], mineral surfaces [23–25], the…”

“Spontaneous polymer assembly occurs with (second-order) reaction propensity as = ksAB , (1) and USR via template-directed assembly occurs with (third-order) reaction propensity ari = krAB Ni .”

“Spontaneous polymer assembly occurs with (second-order) reaction propensity as = ksAB , (1) and USR via template-directed assembly occurs with (third-order) reaction propensity ari = krAB Ni .”

“enzymatic replication and sequence evolution of prebiotic informational polymers, including: informational polymers with reversible backbone linkages [38–43], environmental cycling [21,44–49], limited molecular diffusion [31,35,36], monomer recycling [16,48–50], and template-directed synthesis without sequence restric…”

“enzymatic replication and sequence evolution of prebiotic informational polymers, including: informational polymers with reversible backbone linkages [38–43], environmental cycling [21,44–49], limited molecular diffusion [31,35,36], monomer recycling [16,48–50], and template-directed synthesis without sequence restric…”

“coincided with the selection of the first functional sequences [11,12].”

“a processive polymer replicase [54]), or for the diverse members of a set of enzymes to emerge de novo at the same point in space and time [68].”

“with a reversible linkage) [38,39,41,43], or binding of template strands to a surface (e.”

“enzymatic replication and sequence evolution of prebiotic informational polymers, including: informational polymers with reversible backbone linkages [38–43], environmental cycling [21,44–49], limited molecular diffusion [31,35,36], monomer recycling [16,48–50], and template-directed synthesis without sequence restric…”

“Additionally, the emergence of a synthetase captures some properties of metabolic replicator models [34,37], demonstrating a possible pathway between the prefunctional stage of replicating nonfunctional sequences and the subsequent stage of functional sequence optimization.”

“polymers had already emerged [6–10].”

“It also remains challenging to determine the environmental context from which the first informational polymers emerged, as illustrated by the wide variety of proposed sites for the origin of life, including (but not limited to): tidal shores [19,20], deserts [21], hydrothermal vents [22], mineral surfaces [23–25], the…”

“It also remains challenging to determine the environmental context from which the first informational polymers emerged, as illustrated by the wide variety of proposed sites for the origin of life, including (but not limited to): tidal shores [19,20], deserts [21], hydrothermal vents [22], mineral surfaces [23–25], the…”

“Additionally, the emergence of a synthetase captures some properties of metabolic replicator models [34,37], demonstrating a possible pathway between the prefunctional stage of replicating nonfunctional sequences and the subsequent stage of functional sequence optimization.”

“enzymatic replication and sequence evolution of prebiotic informational polymers, including: informational polymers with reversible backbone linkages [38–43], environmental cycling [21,44–49], limited molecular diffusion [31,35,36], monomer recycling [16,48–50], and template-directed synthesis without sequence restric…”

“As an added measure of the spatial diversity of the polymer population we utilize a generalization of the of the Jaccard similarity index used in population ecology [75, 76].”

“As the system evolved, there is no reason not to expect that continued system dynamics would eventually permit more complicated catalytic functionalities to be selected and optimized, perhaps even culminating in the eventual appearance of polymerases [69] and ligases [70].”

“As the system evolved, there is no reason not to expect that continued system dynamics would eventually permit more complicated catalytic functionalities to be selected and optimized, perhaps even culminating in the eventual appearance of polymerases [69] and ligases [70].”

“with a reversible linkage) [38,39,41,43], or binding of template strands to a surface (e.”

“strand dissociation [63], however, it is not always explicitly”

“enzymatic replication and sequence evolution of prebiotic informational polymers, including: informational polymers with reversible backbone linkages [38–43], environmental cycling [21,44–49], limited molecular diffusion [31,35,36], monomer recycling [16,48–50], and template-directed synthesis without sequence restric…”

“see [6,8,31,35,37,54,55]).”

“Walker et al. (2012) used computer models to show how sequences of functional polymers can become established in a pre-existing pool of nonfunctional sequences and monomers.”

“[24] used computer models to show how sequences of functional polymers can become established in a preexisting pool of non-functional sequences and monomers subject to hydration-dehydration cycles.”

“One such parameter is the rate of hydration–dehydration cycling, where wet–dry cycles have recently become a prominent mechanism in origins of life research for driving the abiotic synthesis of far-fromequilibrium biopolymers (Hud and Anet, 2000; Walker et al., 2012; Mamajanov et al., 2013).”

“There are a number of models in recent years that begin to blur the boundary between ‘genetics’ and ‘metabolism’, for example in metabolic­replicator models as in [55, 107, 108].”

“For discussion of the relevance of the surface environment and its attendant processes to prebiotic chemistry, see, for example, Mulkidjanian et al. (2012), Walker et al. (2012), Forsythe et al. (2015), Mutschler et al. (2015), Rapf and Vaida (2016), Deamer and Damer (2017), He et al. (2017).”

“In another such model (20), chains undergo sequence-independent template-directed replication.”

“The importance of diffusion in models for the origin of life and replication has been noted before by several authors [27–29] and in our previous papers [10,11].”

“This model for early evolution is advantageous in that it allows nascent life to take advantage of the mess of prebiotic chemistry, rather than viewing the nonspecific products of prebiotic synthesis solely as a hindrance to evolutionary progress [53].”

“Other models [44-46] that deal with prebiotic replicators and consider the transition to a replicating state are closer to our work.”

“Environmentally driven recycling was proposed in a theoretical study as a robust mechanism for discovery of novel functionality from a finite pool of random sequence informational polymers (Walker et al., 2012).”

“For the final example, all sequences of length L ‡ 7 replicate with equal efficiency [as would occur if replication were environmentally driven (Walker et al., 2012)].”

“[101], one could study under which conditions local clusters of sequences with specific patterns can emerge and coexist.”

“recently presented a scenario and simulation to address these three questions, based on mass-action kinetics and Fickian diffusion [148].”

“Furthermore, these polymer clusters recycled the monomers they used to form polymers between the system’s interior and exterior and showed growth in particular diffusion settings (Walker et al., 2012).”

“There are a number of models in recent years that begin to blur the boundary between ‘genetics’ and ‘metabolism’, for example in metabolic­replicator models as in [55, 107, 108].”

“The quantity of monomers and minimal energy requirements vary greatly between organisms and within species, leading to the survival of fitness cells (Alberts et al. 2002; Walker et al. 2012; Powell 2019).”

“In models of prebiotic chemical evolution, spatial structure is frequently invoked to facilitate the accumulation of complexity [1, 2, 3, 4, 5, 6].”

“The wet-dry cycles model was initially proposed to simulate the effects of natural conditions, such as natural rainfall or tidal pools, on prebiotic polymerization (Walker et al. 2012; Higgs 2016).”

“Environmentally driven recycling has been proposed in a theoretical study as a robust mechanism for discovery of novel functionality from a finite pool of random sequence informational polymers (Walker et al., 2012).”

“2) There is one fairly recent work about complexity science that would fit well to the introduction in that this played a key role, namely Complex systems in the spotlight: Next steps after the 2021 Nobel Prize in Physics, J. Phys.”

“The coupling to the environment is defined via a fixed inlet flow rate of building materials into the system, different from many closed-mass models [5,8] in prebiotic chemistry.”

“nddestruction—under conditions of wet-dry cycling in heterogeneous environments. Simulation of this range of processes calls for stochastic modeling at a moderately high level of physical abstraction [WGH12]. A range of computational techniques, developed under the rubric of “agent-based modeling and simulation” (ABMS…”

“…systems have been investigated, but many of the existing models either assume the presence of an autocatalytic network, are deliberately vague about the identities of the molecules and mechanisms involved, or both (Kindermann 2005; Walker et al. 2012; Wynveen et al. 2014; Peng et al. 2020).”

“sets of surviving 2- mers. Note that, unlike the ligation rates λ ij, monomer concentrations c i (or equivalently their influxes φ i) could vary significantly from one spatial location to another (See [29] for a study of spatial inhomogeneity in the prebiotic context). This allows for an effective exploration of various…”