Autocatalytic Sets Research Articles

Serial transfer can aid the evolution of autocatalytic sets.

BackgroundThe concept of an autocatalytic set of molecules has been posited theoretically and demonstrated empirically with catalytic RNA molecules. For this concept to have significance in a realistic origins-of-life scenario, it will be important to demonstrate the evolvability of such sets. Here, we employ a Gillespie algorithm to improve and expand on previous simulations of an empirical system of self-assembling RNA fragments that has the ability to spontaneously form autocatalytic networks. We specifically examine the role of serial transfer as a plausible means to allow time-dependent changes in set composition, and compare the results to equilibrium, or “batch” scenarios.ResultsWe show that the simulation model produces results that are in close agreement with the original experimental observations in terms of generating varying autocatalytic (sub)sets over time. Furthermore, the model results indicate that in a “batch” scenario the equilibrium distribution is largely determined by competition for resources and stochastic fluctuations. However, with serial transfer the system is prevented from reaching such an equilibrium state, and the dynamics are mostly determined by differences in reaction rates. This is a consistent pattern that can be repeated, or made stronger or weaker by varying the reaction rates or the duration of the transfer steps. Increasing the number of molecules in the simulation actually strengthens the potential for selection.ConclusionsThese simulations provide a more realistic emulation of wet lab conditions using self-assembling catalytic RNAs that form interaction networks. In doing so, they highlight the potential evolutionary advantage to a prebiotic scenario that involves cyclic dehydration/rehydration events. We posit that such cyclicity is a plausible means to promote evolution in primordial autocatalytic sets, which could later lead to the establishment of individual-based biology.

Conditions for evolvability of autocatalytic sets: a formal example and analysis.

We provide a formal but visually clear example of how a set of minimal necessary conditions for evolvability of autocatalytic sets is satisfied in a simple model of chemical reaction systems. Furthermore, we show how these conditions can be captured and analyzed with RAF theory, and how the results can be generalized with a somewhat more elaborate example. Finally, we argue that our results clearly support the hypothesis that autocatalytic sets can be evolvable, and that this might even be an expected property of such sets.

Autocatalytic sets in a partitioned biochemical network.

BackgroundIn previous work, RAF theory has been developed as a tool for making theoretical progress on the origin of life question, providing insight into the structure and occurrence of self-sustaining and collectively autocatalytic sets within catalytic polymer networks. We present here an extension in which there are two “independent” polymer sets, where catalysis occurs within and between the sets, but there are no reactions combining polymers from both sets. Such an extension reflects the interaction between nucleic acids and peptides observed in modern cells and proposed forms of early life.ResultsWe present theoretical work and simulations which suggest that the occurrence of autocatalytic sets is robust to the partitioned structure of the network. We also show that autocatalytic sets remain likely even when the molecules in the system are not polymers, and a low level of inhibition is present. Finally, we present a kinetic extension which assigns a rate to each reaction in the system, and show that identifying autocatalytic sets within such a system is an NP-complete problem.ConclusionsRecent experimental work has challenged the necessity of an RNA world by suggesting that peptide-nucleic acid interactions occurred early in chemical evolution. The present work indicates that such a peptide-RNA world could support the spontaneous development of autocatalytic sets and is thus a feasible alternative worthy of investigation.

Robustness of Autocatalytic Set in a Model of Evolving Network

Complex networks can describe a variety of systems in biology and chemistry, especially the systems containing the autocatalytic set (ACS). However, the robustness of the ACS has not been explored in details. Now we investigate the evolution process to reveal the robustness of the ACS. By defining two variables on the dependency of every node, we find that the ratios of the fraction with maximum and minimum value are invariable. Moreover, the robustness of the ACS depends on the fraction with maximum value extremely.

Autocatalytic Sets and Biological Specificity

A universal feature of the biochemistry of any living system is that all the molecules and catalysts that are required for reactions of the system can be built up from an available food source by repeated application of reactions from within that system. RAF (reflexively autocatalytic and food-generated) theory provides a formal way to study such processes. Beginning with Kauffman's notion of "collectively autocatalytic sets," this theory has been further developed over the last decade with the discovery of efficient algorithms and new mathematical analysis. In this paper, we study how the behaviour of a simple binary polymer model can be extended to models where the pattern of catalysis more precisely reflects the ligation and cleavage reactions involved. We find that certain properties of these models are similar to, and can be accurately predicted from, the simple binary polymer model; however, other properties lead to slightly different estimates. We also establish a number of new results concerning the structure of RAFs in these systems.

Autocatalytic Sets

The origin of life is one of the most important but also one of the most difficult problems in science. Autocatalytic sets are believed to have played an important role in the origin of life. An autocatalytic set is a collection of molecules and the chemical reactions between them, such that the set as a whole forms a functionally closed and self-sustaining system. In this article, I present an overview of recent work on the theory of autocatalytic sets and on how this theory can be used to study the probability of emergence, the overall structure, and the further evolution of such systems, both in simple mathematical models and in real chemical systems. I also describe some (still speculative) ideas of how this theory can potentially be applied to living systems in general and perhaps even to social systems such as the economy.

Recent developments in research on catalytic reaction networks

Over the last years, analyses performed on a stochastic model of catalytic reaction networks have provided some indications about the reasons why wet-lab experiments hardly ever comply with the phase transition typically predicted by theoretical models with regard to the emergence of collectively self-replicating sets of molecule (also defined as autocatalytic sets, ACSs), a phenomenon that is often observed in nature and that is supposed to have played a major role in the emergence of the primitive forms of life. The model at issue has allowed to reveal that the emerging ACSs are characterized by a general dynamical fragility, which might explain the difficulty to observe them in lab experiments. In this work, the main results of the various analyses are reviewed, with particular regard to the factors able to affect the generic properties of catalytic reactions network, for what concerns, not only the probability of ACSs to be observed, but also the overall activity of the system, in terms of production of new species, reactions and matter.

Autocatalytic Sets and the Origin of Life

Autocatalytic Sets and the Origin of Life

Simulating a Model of Metabolic Closure

The goal of synthetic biology is to create artificial organisms. To achieve this it is essential to understand what life is. Metabolism-replacement systems, or (M, R)-systems, constitute a theory of life developed by Robert Rosen, characterized in the statement that organisms are closed to efficient causation, which means that they must themselves produce all the catalysts they need. This theory overlaps in part with other current theories, including autopoiesis, the chemoton, and autocatalytic sets, all of them invoking some idea of closure. A simple model of an (M, R)-system has been implemented in the computer, and behaves in ways that may shed light on the requirements for a prebiotic self-organizing system. In addition to a trivial steady state in which nothing happens, it can establish a non-trivial steady state in which all intermediates have finite concentrations, with their rates of degradation balanced by their rates of synthesis. The system can be regenerated from the set of food components plus a single intermediate, and maintain itself in that state indefinitely, despite continuous degradation. At the very low compartment volumes that may have existed in prebiotic conditions, for example in cavities in minerals, or in micelles formed by simple amphiphiles, statistical fluctuations in the numbers of molecules need to be taken into account. With the stochastic approach there is no non-trivial steady state in strict mathematical terms, because the system will always collapse to the trivial state after sufficient time. However, the average time before collapse is so long for volumes greater than \(10^{-19}\;{\textsc{l}}\) (much smaller than the volume of the order of \(10^{-15}\;{\textsc{l}}\) for a typical bacterial cell) that for practical purposes the self-maintaining state of non-null concentrations becomes significant, recalling the situation of bistability that is observed in deterministic analysis. In turn, there exists a minimum size below which the self-organizing system cannot maintain itself on chemically relevant time scales. The value of the critical volume depends on the particular concentrations and rate constants assumed, but the principle could apply generally.

What Is Life, and Can We Create It?

n three recent scientific meetings about the origin of life, at the Princ- eton Center for Theoretical Science, at CERN (the European Organization for Nuclear Research), and at the Tokyo Institute of Technology, the RNA world- view, the collectively autocatalytic set worldview, and geological aspects of the origin of life, respectively, were explored. One wonderful hope is that workers with diverse views, long sepa- rated, are beginning to talk to one another. Carl Woese argued (with Nigel Gold- enfeld, http://mmbr.asm.org/content/73/ 1/14.full) that life and its evolution are a process, not a thing. I think Woese is deeply right. The RNA worldview The lipid world Whatever a protocell might be, any system of reproducing organic poly- mers would need to be confined in order to avoid dispersion by diffusion. An obvious candidate for this is bud- ding liposomes, demonstrated by Luigi Luisi. Liposomes alone are unlikely to be the sole basis of life. Life, as Tibor Ganti argued in 1971, seems to require a container, a reproducing molecule or molecules, and also a metabolism bringing food and energy. The autocatalytic worldview I am a guilty party here. In 1971, doubting that life needed so special a basis as DNA or RNA template replica- tion, I wondered about a single mol- ecule that catalyzes its own formation from precursors or, more generally, a set of such molecules that formed a reaction network of—say—peptides and reactions among the peptides, in which the peptides were candi- dates to catalyze the very same reac- tions in the reaction network. These might form a collectively autocatalytic set (CAS) in which no peptide (or RNA) catalyzed its own formation, but each catalyzed the formation of another peptide in the set. The CAS as a whole would catalyze its forma- tion from precursors. Experimentally, DNA, peptide, and RNA CASs have been achieved. Peptide CASs dem- onstrate that molecular reproduc- tion does not require polynucleotide nucleotide-by-nucleotide reproduc- tion, the cornerstone of the RNA worldview. Recently, a library of halved

A formal model of autocatalytic sets emerging in an RNA replicator system

The idea that autocatalytic sets played an important role in the origin of life is not new. However, the likelihood of autocatalytic sets emerging spontaneously has long been debated. Recently, progress has been made along two different lines. Experimental results have shown that autocatalytic sets can indeed emerge in real chemical systems, and theoretical work has shown that the existence of such self-sustaining sets is highly likely in formal models of chemical systems. Here, we take a first step towards merging these two lines of work by constructing and investigating a formal model of a real chemical system of RNA replicators exhibiting autocatalytic sets. We show that the formal model accurately reproduces recent experimental results on an RNA replicator system, in particular how the system goes through a sequence of larger and larger autocatalytic sets, and how a cooperative (autocatalytic) system can outcompete an equivalent selfish system. Moreover, the model provides additional insights that could not be obtained from experiments alone, and it suggests several experimentally testable hypotheses. Given these additional insights and predictions, the modeling framework provides a better and more detailed understanding of the nature of chemical systems in general and the emergence of autocatalytic sets in particular. This provides an important first step in combining experimental and theoretical work on autocatalytic sets in the context of the orgin of life.

Cycles and the qualitative evolution of chemical systems.

Cycles are abundant in most kinds of networks, especially in biological ones. Here, we investigate their role in the evolution of a chemical reaction system from one self-sustaining composition of molecular species to another and their influence on the stability of these compositions. While it is accepted that, from a topological standpoint, they enhance network robustness, the consequence of cycles to the dynamics are not well understood. In a former study, we developed a necessary criterion for the existence of a fixed point, which is purely based on topological properties of the network. The structures of interest we identified were a generalization of closed autocatalytic sets, called chemical organizations. Here, we show that the existence of these chemical organizations and therefore steady states is linked to the existence of cycles. Importantly, we provide a criterion for a qualitative transition, namely a transition from one self-sustaining set of molecular species to another via the introduction of a cycle. Because results purely based on topology do not yield sufficient conditions for dynamic properties, e.g. stability, other tools must be employed, such as analysis via ordinary differential equations. Hence, we study a special case, namely a particular type of reflexive autocatalytic network. Applications for this can be found in nature, and we give a detailed account of the mitotic spindle assembly and spindle position checkpoints. From our analysis, we conclude that the positive feedback provided by these networks' cycles ensures the existence of a stable positive fixed point. Additionally, we use a genome-scale network model of the Escherichia coli sugar metabolism to illustrate our findings. In summary, our results suggest that the qualitative evolution of chemical systems requires the addition and elimination of cycles.

The Structure of Autocatalytic Sets: Evolvability, Enablement, and Emergence

This paper presents new results from a detailed study of the structure of autocatalytic sets. We show how autocatalytic sets can be decomposed into smaller autocatalytic subsets, and how these subsets can be identified and classified. We then argue how this has important consequences for the evolvability, enablement, and emergence of autocatalytic sets. We end with some speculation on how all this might lead to a generalized theory of autocatalytic sets, which could possibly be applied to entire ecologies or even economies.

Autocatalytic sets extended: Dynamics, inhibition, and a generalization

Autocatalytic sets are often considered a necessary (but not sufficient) condition for the origin and early evolution of life. Although the idea of autocatalytic sets was already conceived of many years ago, only recently have they gained more interest, following advances in creating them experimentally in the laboratory. In our own work, we have studied autocatalytic sets extensively from a computational and theoretical point of view. We present results from an initial study of the dynamics of self-sustaining autocatalytic sets (RAFs). In particular, simulations of molecular flow on autocatalytic sets are performed, to illustrate the kinds of dynamics that can occur. Next, we present an extension of our (previously introduced) algorithm for finding autocatalytic sets in general reaction networks, which can also handle inhibition. We show that in this case detecting autocatalytic sets is fixed parameter tractable. Finally, we formulate a generalized version of the algorithm that can also be applied outside the context of chemistry and origin of life, which we illustrate with a toy example from economics. Having shown theoretically (in previous work) that autocatalytic sets are highly likely to exist, we conclude here that also in terms of dynamics such sets are viable and outcompete non-autocatalytic sets. Furthermore, our dynamical results confirm arguments made earlier about how autocatalytic subsets can enable their own growth or give rise to other such subsets coming into existence. Finally, our algorithmic extension and generalization show that more realistic scenarios (e.g., including inhibition) can also be dealt with within our framework, and that it can even be applied to areas outside of chemistry, such as economics.

Evolution before genes

BackgroundOur current understanding of evolution is so tightly linked to template-dependent replication of DNA and RNA molecules that the old idea from Oparin of a self-reproducing 'garbage bag' ('coacervate') of chemicals that predated fully-fledged cell-like entities seems to be farfetched to most scientists today. However, this is exactly the kind of scheme we propose for how Darwinian evolution could have occurred prior to template replication.ResultsWe cannot confirm previous claims that autocatalytic sets of organic polymer molecules could undergo evolution in any interesting sense by themselves. While we and others have previously imagined inhibition would result in selectability, we found that it produced multiple attractors in an autocatalytic set that cannot be selected for. Instead, we discovered that if general conditions are satisfied, the accumulation of adaptations in chemical reaction networks can occur. These conditions are the existence of rare reactions producing viable cores (analogous to a genotype), that sustains a molecular periphery (analogous to a phenotype).ConclusionsWe conclude that only when a chemical reaction network consists of many such viable cores, can it be evolvable. When many cores are enclosed in a compartment there is competition between cores within the same compartment, and when there are many compartments, there is between-compartment competition due to the phenotypic effects of cores and their periphery at the compartment level. Acquisition of cores by rare chemical events, and loss of cores at division, allows macromutation, limited heredity and selectability, thus explaining how a poor man's natural selection could have operated prior to genetic templates. This is the only demonstration to date of a mechanism by which pre-template accumulation of adaptation could occur.ReviewersThis article was reviewed by William Martin and Eugene Koonin.

The Origin of Large Molecules in Primordial Autocatalytic Reaction Networks

Large molecules such as proteins and nucleic acids are crucial for life, yet their primordial origin remains a major puzzle. The production of large molecules, as we know it today, requires good catalysts, and the only good catalysts we know that can accomplish this task consist of large molecules. Thus the origin of large molecules is a chicken and egg problem in chemistry. Here we present a mechanism, based on autocatalytic sets (ACSs), that is a possible solution to this problem. We discuss a mathematical model describing the population dynamics of molecules in a stylized but prebiotically plausible chemistry. Large molecules can be produced in this chemistry by the coalescing of smaller ones, with the smallest molecules, the ‘food set’, being buffered. Some of the reactions can be catalyzed by molecules within the chemistry with varying catalytic strengths. Normally the concentrations of large molecules in such a scenario are very small, diminishing exponentially with their size. ACSs, if present in the catalytic network, can focus the resources of the system into a sparse set of molecules. ACSs can produce a bistability in the population dynamics and, in particular, steady states wherein the ACS molecules dominate the population. However to reach these steady states from initial conditions that contain only the food set typically requires very large catalytic strengths, growing exponentially with the size of the catalyst molecule. We present a solution to this problem by studying ‘nested ACSs’, a structure in which a small ACS is connected to a larger one and reinforces it. We show that when the network contains a cascade of nested ACSs with the catalytic strengths of molecules increasing gradually with their size (e.g., as a power law), a sparse subset of molecules including some very large molecules can come to dominate the system.

Predicting template-based catalysis rates in a simple catalytic reaction model

We show that in a particular model of catalytic reaction systems, known as the binary polymer model, there is a mathematical concordance between two versions of the model: (1) random catalysis and (2) template-based catalysis. In particular, we derive an analytical calculation that allows us to accurately predict the (observed) required level of catalysis in one version of the model from that in the other version, for a given probability of having self-sustaining autocatalytic sets exist in instances of both model versions. This provides a tractable connection between two models that have been investigated in theoretical origin-of-life studies.

Approaches to the origin of life on Earth.

I discuss briefly the history of the origin of life field, focusing on the “Miller” era of prebiotic synthesis, through the “Orgel” era seeking enzyme free template replication of single stranded RNA or similar polynucleotides, to the RNA world era with one of its foci on a ribozyme with the capacity to act as a polymerase able to copy itself. I give the history of the independent invention in 1971 by T. Ganti, M. Eigen and myself of three alternative theories of the origin of molecular replication: the Chemotron, the Hypercycle, and Collectively Autocatalytic Sets, CAS, respectively. To date, only collectively autocatalytic DNA, RNA, and peptide sets have achieved molecular reproduction of polymers. Theoretical work and experimental work on CAS both support their plausibility as models of openly evolvable protocells, if housed in dividing compartments such as dividing liposomes. My own further hypothesis beyond that of CAS in themselves, of their formation as a phase transition in complex chemical reaction systems of substrates, reactions and products, where the molecules in the system are candidates to catalyze the very same reactions, now firmly established as theorems, awaits experimental proof using combinatorial chemistry to make libraries of stochastic DNA, RNA and/or polypeptides, or other classes of molecules to test the hypothesis that molecular polymer reproduction has emerged as a true phase transition in complex chemical reaction systems. I remark that my colleague Marc Ballivet of the University of Geneva and I, may have issued the first publications discussing what became combinatorial chemistry, in published issued patents in 1987, 1989 and later, in this field.

Comparison of the Roles of Nucleotide Synthesis, Polymerization, and Recombination in the Origin of Autocatalytic Sets of RNAs

Ribozymes that act as polymerases and nucleotide synthases are known experimentally, even though no fully self-replicating system has yet been found. If the RNA World hypothesis is true, ribozymes must have arisen initially from within a random abiotic polymerization system. To investigate the origin of the RNA world, we studied a mathematical model of a chemical reaction system describing RNA polymerization. It is supposed that, in absence of ribozymes, polymerization occurs at a small spontaneous rate, and that in the presence of polymerase ribozymes, polymerization occurs at a faster rate that is proportional to the ribozyme concentration. Chains must be longer than a minimum threshold length in order to have the possibility of acting as ribozymes. The reaction system has two stable states that we term dead and living. The dead state is controlled by the small spontaneous rate and has negligible concentration of ribozymes. The living state has high concentration of ribozymes, and the reaction rates are determined by the ribozymes; thus, the system is autocatalytic. Concentration fluctuations in a finite volume can cause a transition to occur from the dead to the living state, that is, an origin of life occurs within this model. We also consider ribozymes that catalyze nucleotide synthesis. We show that living and dead states arise in the presence of synthase ribozymes in the same way as for polymerases. It has been proposed that recombination reactions are a way of generating long RNA chains in the early stages of life. We show that if the possibility of random reversible recombination reactions is added to our model, this does not lead to an increase in long polymer concentration. Thus, if recombination is fully reversible, there is no autocatalytic state controlled by recombination. Nevertheless, recombination can play an important role in ribozyme synthesis if there is an additional process that keeps the recombination reactions out of equilibrium. We modeled a case studied experimentally in which building block strands of moderate length associate due to RNA secondary structure formation. A recombination reaction then occurs between these strands to form a longer sequence that catalyzes its own formation via the recombination reaction. This system has an autocatalytic state, and it is possible for it to arise within our random polymerization system. If complexes formed by associations of shorter strands can act as catalysts without the requirement that the strands be covalently linked, this would alleviate the need for synthesis of very long strands; hence, it makes the emergence of an autocatalytic system from an abiotic random polymerization system much more likely.

A stochastic model of the emergence of autocatalytic cycles

Autocatalytic cycles are rather common in biological systems and they might have played a major role in the transition from non-living to living systems. Several theoretical models have been proposed to address the experimentalists during the investigation of this issue and most of them describe a phase transition depending upon the level of heterogeneity of the chemical soup. Nevertheless, it is well known that reproducing the emergence of autocatalytic sets in wet laboratories is a hard task. Understanding the rationale at the basis of such a mismatch between theoretical predictions and experimental observations is therefore of fundamental importance. We here introduce a novel stochastic model of catalytic reaction networks, in order to investigate the emergence of autocatalytic cycles, sensibly considering the importance of noise, of small-number effects and the possible growth of the number of different elements in the system. Furthermore, the introduction of a temporal threshold that defines how long a specific reaction is kept in the reaction graph allows to univocally define cycles also within an asynchronous framework. The foremost analyses have been focused on the study of the variation of the composition of the incoming flux. It was possible to show that the activity of the system is enhanced, with particular regard to the emergence of autocatalytic sets, if a larger number of different elements is present in the incoming flux, while the specific length of the species seems to entail minor effects on the overall dynamics.