Prebiotic network evolution: six key parameters

Nghe, Philippe; Hordijk, Wim; Kauffman, Stuart; Walker, Sara Imari; Schmidt, Francis J.; Kemble, Harry; Yeates, Jessica A. M.; Lehman, Niles

doi:10.1039/c5mb00593k

Cited by 107 publications

(101 citation statements)

References 85 publications

(140 reference statements)

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“…In both cases, the λ K is real and λ K Re[λ α ] for α<K , and we find this to be a robust feature under variation of kinetic rates. This is consistent with the Perron-Frobenius theorem, which guarantees a maximal real eigenvalue for a matrix representing a strongly connected graph (30). In our example, the 83 clusters from the largest cycle form the largest strongly connected component and lead to the maximal real eigenvalue.…”

Section: Resultssupporting

confidence: 69%

Spontaneous emergence of catalytic cycles with colloidal spheres

Zeravcic

Brenner

2017

Proc. Natl. Acad. Sci. U.S.A.

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Colloidal particles endowed with specific time-dependent interactions are a promising route for realizing artificial materials that have the properties of living ones. Previous work has demonstrated how this system can give rise to self-replication. Here, we introduce the process of colloidal catalysis, in which clusters of particles catalyze the creation of other clusters through templating reactions. Surprisingly, we find that simple templating rules generically lead to the production of huge numbers of clusters. The templating reactions among this sea of clusters give rise to an exponentially growing catalytic cycle, a specific realization of Dyson's notion of an exponentially growing metabolism. We demonstrate this behavior with a fixed set of interactions between particles chosen to allow a catalysis of a specific sixparticle cluster from a specific seven-particle cluster, yet giving rise to the catalytic production of a sea of clusters of sizes between 2 and 11 particles. The fact that an exponentially growing cycle emerges naturally from such a simple scheme demonstrates that the emergence of exponentially growing metabolisms could be simpler than previously imagined.catalytic cycles | DNA-coated colloids | metabolism | templating T he origin of life is usually associated with self-replication, the ability of an entity to create copies of itself (1). Thus inspired, there have been many efforts in recent years aimed at creating artificial systems with self-replicative capacity. These are typically inspired by the linear chain mechanism of DNA. However, living systems are more than individual entities that can replicate themselves. Dyson (2) and Oparin (3) argued that a more critical aspect of living systems is the creation of a metabolism, a complex cascade of chemical reactions that together are able to accomplish more than any single chemical reaction can do on its own. Using a simple mathematical model, the so-called "garbage bag model," Dyson presented a scenario through which such a complex metabolism could arise spontaneously. His idea is that a random set of catalysts will catalyze arbitrary chemical reactions in a nonsynergistic fashion. However, if each catalyst is more likely to function when there are others that are synergistic with it, then there is a critical amount of cooperativity above which metabolic cycles spontaneously emerge. This idea has been explored through abstract simulations (4). In a similar spirit, Kauffman and coworkers have shown that if the probability of one species catalyzing the formation of another is above a threshold, then catalytic cycles naturally emerge (5-7).Whether this scenario can naturally occur in practice remains obscure. The fundamental question is to determine how likely it is for a soup of interacting catalysts to self-organize into an exponentially growing catalytic cycle. How special do the interactions between the different components need to be for spontaneous exponentially growing catalytic cycles to emerge? In this work, we present an explicit demon...

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Section: Resultssupporting

confidence: 69%

Spontaneous emergence of catalytic cycles with colloidal spheres

Zeravcic

Brenner

2017

Proc. Natl. Acad. Sci. U.S.A.

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“…To explain the trends in period and amplitude of the oscillations, and the nature of the bifurcations at low and high limiting values of SV, we constructed a simple kinetic model [1][2][3][4] to rate constants, and k 0 to space velocity. Linear stability analysis 13 carried out with this model shows that increasing k 0 from low to high values causes two transitions: first, the system transitions from one having a stable focus (damped oscillations) to one having a stable orbit (sustained oscillations); this transition marks an Andronov-Hopf bifurcation.…”

mentioning

confidence: 99%

Autocatalytic, bistable, oscillatory networks of biologically relevant organic reactions

Semenov

Kraft

Ainla

et al. 2016

Nature

293

274

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(ii) a trigger that controls autocatalytic growth; and (iii) inhibitory processes that remove activating thiol species produced during the autocatalytic cycle. In contrast to previous studies demonstrating oscillations and bistability using highly evolved biomolecules (i.e., enzymes 15 and DNA 16,17 ) or inorganic molecules of questionable biochemical relevance (e.g. those used in Belousov-Zhabotinsky-type reactions), 18,19 the organic molecules used in our network are relevant to current metabolism and similar to those that might have existed on early Earth. By using small organic molecules to build a network of organic reactions with autocatalytic, bistable, and oscillatory behavior, we identified principles that clarify how dynamic networks relevant to life might possibly have developed. In the future, modifications of this network will clarify the influence of molecular structure on the dynamics of reaction networks, and may enable the design of biomimetic networks, and of synthetic self-regulating and evolving chemical systems.3 Figure 1 summarizes the network of organic reactions that we used to assemble our model system. All of these reactions are nearly quantitative, and the structure of their reactants can be varied by synthesis to control rates of reactions. Thiols and thioesters, which are central to these reactions, are important in many biological processes (e.g., the formation of disulfide bonds in proteins, transformations involving coenzyme-A, the reduction of oxidized molecules by glutathione, 20 the synthesis of polyketides, 21 and the nonribosomal synthesis of peptides 21 ), and thus, might represent reactions that enabled life to emerge on early Earth. 22 To control the dynamics of these processes, we constructed a modular chemical reaction network (CRN) shown schematically in control-theoretic terms 23 in Fig. 1a. A "trigger" produces an initial chemical signal, and an "auto-amplifier" amplifies this signal, which may or may not be suppressed by inhibition. To keep the reactions out of equilibrium-and thus, to enable the self-organization of reactions by communication through concentrations of reactants and products -we used a continuous-stirred tank reactor (CSTR) to mix reactants and products, while allowing a flux of species into and out of the network over time. A biological cell has some conceptual analogies to a micron-scale, diffusively mixed, tank reactor. The dynamic behavior of this system -especially bistability and oscillationsreflects the balances of triggering, auto-amplification, and inhibition.We first constructed a chemical network capable of auto-amplification using thiols and thioesters (Fig. 1b). The starting components of the network are cystamine (CSSC, 3) and L-alanine ethyl thioester (AlaSEt, 2). Trace amounts of cysteamine (CSH, 1) are generated as follows: AlaSEt slowly hydrolyzes, generating alanine (8) and ethanethiol (ESH, 4); EtSH then reacts with CSSC via thiolate-disulfide interchange, 24 yielding disulfide 6 and CSH. With CSH present, self-amplification oc...

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“…Auspiciously, the mechanisms of network evolution are beginning to be unraveled (20)(21)(22)(23). For example, Aguirre et al (23) have recently provided a framework for studying how networks can actually compete with one another.…”

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confidence: 99%

Dynamics of prebiotic RNA reproduction illuminated by chemical game theory

Yeates

Hilbe

Zwick

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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Many origins-of-life scenarios depict a situation in which there are common and potentially scarce resources needed by molecules that compete for survival and reproduction. The dynamics of RNA assembly in a complex mixture of sequences is a frequencydependent process and mimics such scenarios. By synthesizing Azoarcus ribozyme genotypes that differ in their single-nucleotide interactions with other genotypes, we can create molecules that interact among each other to reproduce. Pairwise interplays between RNAs involve both cooperation and selfishness, quantifiable in a 2 × 2 payoff matrix. We show that a simple model of differential equations based on chemical kinetics accurately predicts the outcomes of these molecular competitions using simple rate inputs into these matrices. In some cases, we find that mixtures of different RNAs reproduce much better than each RNA type alone, reflecting a molecular form of reciprocal cooperation. We also demonstrate that three RNA genotypes can stably coexist in a rock-paper-scissors analog. Our experiments suggest a new type of evolutionary game dynamics, called prelife game dynamics or chemical game dynamics. These operate without templatedirected replication, illustrating how small networks of RNAs could have developed and evolved in an RNA world.RNA | prebiotic chemistry | origins of life | game theory | ribozyme A plausible description of a sequence of events that could have led to the origins of life on the Earth from a purely chemical milieu has long been desirable, yet remains elusive. The RNA world hypothesis has helped sharpen our focus on what could have taken place 4 Gya, in that RNA serves as a powerful model for a self-sustaining chemical system capable of evolutionary change (1-6). Although this hypothesis has engendered much debate, both in its general applicability and in the details of its implementation (7-9), there are some clear emerging trends. Among the recent advances in prebiotic RNA studies is the concept of an evolving "network" of RNAs being required to kick-start life, rather than a single selfish entity. This idea dates back to the formative studies of Eigen and Schuster in the 1970s (10, 11). However, it can be sharply seen in the 20+-y effort aimed at developing a generalized RNA replicase ribozyme in the laboratory: new successes have taken advantage of a fragmentation of the best such artificial ribozyme and invoke a network of reactions to provide for its assembly (12). Our own laboratories have focused on a variety of "prelife" (13, 14) and cooperative network (15, 16) approaches to understand how evolving RNA systems could have arisen from abiotic sources of nucleotides and short oligomers. Many others have also stressed the need for distributed functionality at the onset of life, both chemically (17) and in space and time (18,19).To advance a network approach to the "single biomolecule problem" in the RNA world, what is needed now is an understanding of how prebiotic networks could have evolved. Auspiciously, the mechanisms of network evol...

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Prebiotic network evolution: six key parameters

Cited by 107 publications

References 85 publications

Spontaneous emergence of catalytic cycles with colloidal spheres

Spontaneous emergence of catalytic cycles with colloidal spheres

Autocatalytic, bistable, oscillatory networks of biologically relevant organic reactions

Dynamics of prebiotic RNA reproduction illuminated by chemical game theory

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