Detecting autocatalytic, self-sustaining sets in chemical reaction systems

The ability of systems of molecular reactions to be simultaneously autocatalylic and sustained by some ambient 'food source' of simple molecules may have been an essential step in the origin of life. In this paper we first describe a polynomial-time algorithm that determines whether any given set of molecules, reactions and catalysations contains a subsystem that is both autocatalytic and able to be sustained from a given subset of the molecules. We also describe some combinatorial properties of this algorithm, and show how it can be used to find irreducible auto-catalysing and sustaining subsystems. In the second part of the paper we use the algorithm to investigate random catalytic networks-in particular, a model described by Kauffman. Using simulations and some analytic techniques we investigate the rate of catalysis that is required for the emergence of autocatalytic and sustaining subsystems.     

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.     

A Michaelis-Menten-style model for the autocatalytic enzyme prostaglandin H synthase

Prostaglandin H synthase (PGHS) is an autocatalytic enzyme which plays a key role in the arachidonic acid metabolic pathway. PGHS mediates the formation of prostaglandin H₂, the precursor for a number of prostaglandins which are important in a wide variety of biological processes, including inflammation, blood clotting, renal function, and tumorigenesis. Here we present a Michaelis-Menten-style model for PGHS. A stability analysis determines when the reaction becomes self-sustaining, and can help explain the regulation of PGHS activity in vivo. We also consider a quasi-steady-state approximation (QSSA) for the model, and present conditions under which the QSSA is expected to be a good approximation. Applying the QSSA for this model can be useful in computationally intensive modeling endeavors involving PGHS.     

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.     

Competition between Primary Nucleation and Autocatalysis in Amyloid Fibril Self-Assembly

Kinetic measurements of the self-assembly of proteins into amyloid fibrils are often used to make inferences about molecular mechanisms. In particular, the lag time—the quiescent period before aggregates are detected—is often found to scale with the protein concentration as a power law, whose exponent has been used to infer the presence or absence of autocatalytic growth processes such as fibril fragmentation. Here we show that experimental data for lag time versus protein concentration can show signs of kinks: clear changes in scaling exponent, indicating changes in the dominant molecular mechanism determining the lag time. Classical models for the kinetics of fibril assembly suggest that at least two mechanisms are at play during the lag time: primary nucleation and autocatalytic growth. Using computer simulations and theoretical calculations, we investigate whether the competition between these two processes can account for the kinks which we observe in our and others’ experimental data. We derive theoretical conditions for the crossover between nucleation-dominated and growth-dominated regimes, and analyze their dependence on system volume and autocatalysis mechanism. Comparing these predictions to the data, we find that the experimentally observed kinks cannot be explained by a simple crossover between nucleation-dominated and autocatalytic growth regimes. Our results show that existing kinetic models fail to explain detailed features of lag time versus concentration curves, suggesting that new mechanistic understanding is needed. More broadly, our work demonstrates that care is needed in interpreting lag-time scaling exponents from protein assembly data.     

A Quasistationary Analysis of a Stochastic Chemical Reaction: Keizer’s Paradox

For a system of biochemical reactions, it is known from the work of T.G. Kurtz [J. Appl. Prob. 8, 344 (1971)] that the chemical master equation model based on a stochastic formulation approaches the deterministic model based on the Law of Mass Action in the infinite system-size limit in finite time. The two models, however, often show distinctly different steady-state behavior. To further investigate this “paradox,” a comparative study of the deterministic and stochastic models of a simple autocatalytic biochemical reaction, taken from a text by the late J. Keizer, is carried out. We compute the expected time to extinction, the true stochastic steady state, and a quasistationary probability distribution in the stochastic model. We show that the stochastic model predicts the deterministic behavior on a reasonable time scale, which can be consistently obtained from both models. The transition time to the extinction, however, grows exponentially with the system size. Mathematically, we identify that exchanging the limits of infinite system size and infinite time is problematic. The appropriate system size that can be considered sufficiently large, an important parameter in numerical computation, is also discussed.     

A method for modeling life based on physical attributes

An incremental method for modeling the essential system of life, in which physical attributes of life are brought together to improve the model of life, is explained. We present a tiny example that uses only four attributes, i.e. locality, metabolism, entropy reduction, and chemotaxis. These four attributes are translated into physical formulae and evaluated in a two dimensional simulation of an autocatalytic reaction. Autocatalysts injected into a vessel begin to flow toward the source of their substrate similarly to chemotaxis. At the front line of this flow, a subsystem associated with the four properties is detected. This kind of subsystem could be increasingly life-like if more critical attributes are used for detection. A database of the attributes is being made.     

Spontaneous Mirror Symmetry Breaking in the Aldol Reaction and its Potential Relevance in Prebiotic Chemistry

The origin of the single chirality of most biomolecules is still a great puzzle. Carbohydrates could form in the formose reaction, which is proposed to be autocatalytic and contains aldol reaction steps. Based on our earlier observation of organoautocatalysis and spontaneous enantioenrichment in absence of deliberate chiral influences in the aldol reaction of acetone and p-nitrobenzaldehyde we suggest that a similar effect might be present also in the aldol reactions involved in gluconeogenesis. Herein we show that reactant precipitation observed in our earlier reported experiments does not affect the asymmetric autocatalysis in the aldol reaction we studied. We explain the phenomenon of spontaneous mirror symmetry breaking in such organocatalytic homogenous systems qualitatively by non-linear reaction network kinetics and classical transition state theory.     

The origin of autonomous agents by natural selection

We propose conditions in which an autonomous agent could arise, and increase in complexity. It is assumed that on the primitive Earth there arose a recycling flow-reactor containing spontaneously formed oil droplets or lipid aggregates. These droplets grew at a basal rate by simple incorporation of lipid phase material, and divided by external agitation. This type of system was able to implement a natural selection algorithm once heredity was added. Macroevolution became possible by selection for rarely occurring chemical reactions that produced holistic autocatalytic molecular replicators (contained within the aggregate) capable of doubling at least as fast as the lipid aggregate, and which were also capable of benefiting the growth of its lipid aggregate container. No nucleotides or monomers capable of modular heredity were required at the outset. To explicitly state this hypothesis, a computer model was developed that employed an artificial chemistry, exhibiting conservation of mass and energy, incorporated within each individual of a population of lipid aggregates. This model evolved increasingly complex self-sustaining processes of constitution, a result that is also expected in real chemistry.     

A “strategic” model of material cycling in a closed ecosystem

The aim of this paper is to reconcile the observed vulnerability of self-sustaining (materially closed) experimental ecosystems with demonstrations of virtually unconditional stability in mathematical models incorporating material recycling. We prove deterministic local stability in a generalized version of a model previously investigated by two of us (Nisbet and Gurney), but show that, except with rather narrowly specified parameter values, the system is likely to be extremely sensitive to external perturbations.     

Chiral symmetry breaking: Experimental results and computer analysis of a liquid-phase autoxidation

The autoxidation of tetralin is treated as a model reaction system to define the applicability of stereospecific autocatalysis. This concept, predicting a spontaneous amplification of enantiomeric excess generated by an autocatalytic chemical reaction, is used in several theoretical models as an explanation for the origin of natural optical activity. The reaction system investigated obeys the basic criteria of these models: a chiral intermediate (tetralin hydroperoxide) is produced from an achiral substrate (tetralin) via an autocatalytic pathway where the feedback mechanism is expected to generate a state of broken chiral symmetry. In order to test the amplification capacity of this reaction a computer analysis of the kinetic scheme is performed. This simulation is derived from the known kinetic scheme of autoxidation and is validated by fitting the experimentally observed data of hydroperoxide evolution. Calculations show that this model allows powerful amplification of enantiomeric excess and a transient amplification of the optical rotation. It is also demonstrated that the model system exhibits pronounced sensitivity toward any loss of absolute configuration of the involved chiral species. Since an amplification effect results exclusively at a high degree of stereoselectivity, it is concluded that stereospecific autocatalysis is possible in systems which show template reactions, crystallization, or colloidal effects. © 1993 Wiley-Liss, Inc.     

Autocatalytic networks with translation

We consider the kinetics of an autocatalytic reaction network in which replication and catalytic actions are separated by a translation step. We find that the behaviour of such a system is closely related to second-order replicator equations, which describe the kinetics of autocatalytic reaction networks in which the replicators act also as catalysts. In fact, the qualitative dynamics seems to be described almost entirely be the second-order reaction rates of the replication step. For two species we recover the qualitative dynamics of the replicator equations. Larger networks show some deviations, however. A hypercyclic system consisting of three interacting species can converge toward a stable limit cycle in contrast to the replicator equation case. A singular perturbation analysis shows that the replication-translation system reduces to a second-order replicator equation if translation is fast. The influence of mutations on replication-translation networks is also very similar to the behavior of selection-mutation equations.     

Towards the trophic structure of the Bouvet Island marine ecosystem

Although Bouvet Island is of considerable importance for Southern Ocean species conservation, information on the marine community species inventory and trophic functioning is scarce. Our combined study of stable isotopes and feeding relationships shows that (1) the marine system conforms to the trophic pattern described for other Antarctic systems within the Antarctic circumpolar current (ACC); (2) both the benthic and the pelagic subsystem are almost exclusively linked via suspended particulate organic matter (SPOM); and (3) there is no evidence of a subsystem driven by macroalgae. Bouvet Island can therefore be characterized as a benthic “oasis” within a self-sustaining open ocean pelagic system.     

Evolution of Autocatalytic Sets in Computational Models of Chemical Reaction Networks

Several computational models of chemical reaction networks have been presented in the literature in the past, showing the appearance and (potential) evolution of autocatalytic sets. However, the notion of autocatalytic sets has been defined differently in different modeling contexts, each one having some shortcoming or limitation. Here, we review four such models and definitions, and then formally describe and analyze them in the context of a mathematical framework for studying autocatalytic sets known as RAF theory. The main results are that: (1) RAF theory can capture the various previous definitions of autocatalytic sets and is therefore more complete and general, (2) the formal framework can be used to efficiently detect and analyze autocatalytic sets in all of these different computational models, (3) autocatalytic (RAF) sets are indeed likely to appear and evolve in such models, and (4) this could have important implications for a possible metabolism-first scenario for the origin of life.     

Parallel application-level behavioral attributes for performance and energy management of high-performance computing systems

Run time variability of parallel applications continues to present significant challenges to their performance and energy efficiency in high-performance computing (HPC) systems. When run times are extended and unpredictable, application developers perceive this as a degradation of system (or subsystem) performance. Extended run times directly contribute to proportionally higher energy consumption, potentially negating efforts by applications, or the HPC system, to optimize energy consumption using low-level control techniques, such as dynamic voltage and frequency scaling (DVFS). Therefore, successful systemic management of application run time performance can result in less wasted energy, or even energy savings. We have been studying run time variability in terms of communication time, from the perspective of the application, focusing on the interconnection network. More recently, our focus has shifted to developing a more complete understanding of the effects of HPC subsystem interactions on parallel applications. In this context, the set of executing applications on the HPC system is treated as a subsystem, along with more traditional subsystems like the communication subsystem, storage subsystem, etc. To gain insight into the run time variability problem, our earlier work developed a framework to emulate parallel applications (PACE) that stresses the communication subsystem. Evaluation of run time sensitivity to network performance of real applications is performed with a tool called PARSE, which uses PACE. In this paper, we propose a model defining application-level behavioral attributes, that collectively describes how applications behave in terms of their run time performance, as functions of their process distribution on the system (spacial locality), and subsystem interactions (communication subsystem degradation). These subsystem interactions are produced when multiple applications execute concurrently on the same HPC system. We also revisit our evaluation framework and tools to demonstrate the flexibility of our application characterization techniques, and the ease with which attributes can be quantified. The validity of the model is demonstrated using our tools with several parallel benchmarks and application fragments. Results suggest that it is possible to articulate application-level behavioral attributes as a tuple of numeric values that describe course-grained performance behavior.     

Towards a General Definition of Life

A new definition of life is proposed and discussed in the present article. It is formulated by modifying and extending NASA’s working definition of life, which postulates that life is a “self-sustaining chemical system capable of Darwinian evolution”. The new definition includes a thermodynamical aspect of life as a far from equilibrium system and considers the flow of information from the environment to the living system. In our derivation of the definition of life we have assumed the hypothesis, that during the emergence of life evolution had to first involve autocatalytic systems that only subsequently acquired the capacity of genetic heredity. The new proposed definition of life is independent of the mode of evolution, regardless of whether Lamarckian or Darwinian evolution operated at the origins of life and throughout evolutionary history. The new definition of life presented herein is formulated in a minimal manner and it is general enough that it does not distinguish between individual (metabolic) network and the collective (ecological) one. The newly proposed definition of life may be of interest for astrobiology, research into the origins of life or for efforts to produce synthetic or artificial life, and it furthermore may also have implications in the cognitive and computer sciences.

     

Autocatalytic cooperativity and self-regulation of ATPase pumps in membrane active transport

We investigate the effect of autocatalysis on the conformational changes of membrane pumps during active transport driven by ATP. The translocation process is described by means of an alternating access model. The usual kinetic scheme is extended by introducing autocatalytic steps and allowing for dynamic formation of enzyme complexes. The usual features of cooperative models are recovered, i.e., sigmoid shapes of flux versus concentration curves. We show also that two autocatalytic steps lead to a mechanism of inhibition by the substrate as experimentally observed for some ATPase pumps. In addition, when the formation of enzyme complexes is allowed, the model exhibits a multiple stationary states regime, which can be related to a self-regulation mechanism of the active transport in biological systems. Correspondence to: G. Weissmüller     

Patterns of patchy spread in multi-species reaction–diffusion models

Spread of populations in space often takes place via formation, interaction and propagation of separated patches of high species density, without formation of continuous fronts. This type of spread is called a ‘patchy spread’. In earlier models, this phenomenon was considered to be a result of a pronounced environmental or/and demographic stochasticity. Recently, it was found that a patchy spread can arise in a fully deterministic predator–prey system and in models of infectious diseases; in each case the process takes place in a homogeneous environment. It is well recognized that the observed patterns of patchy spread in nature are a result of interplay between stochastic and deterministic factors. However, the models considering deterministic mechanism of patchy spread are developed and studied much less compared to those based on stochastic mechanisms. A further progress in the understanding of the role of deterministic factors in the patchy spread would be extremely helpful. Here we apply multi-species reaction–diffusion models of two spatial dimensions in a homogeneous environment. We demonstrate that patterns of patchy spread are rather common for the considered approach, in particular, they arise both in mutualism and competition models influenced by predation. We show that this phenomenon can occur in a system without a strong Allee effect, contrary to what was assumed to be crucial in earlier models. We show, as well, a pattern of patchy spread having significantly different speeds in different spatial directions. We analyze basic features of spatiotemporal dynamics of patchy spread common for the reaction–diffusion approach. We discuss in which ecosystems we would observe patterns of deterministic patchy spread due to the considered mechanism.     

The autocatalytic step is an integral part of the hydrogenase cycle

We earlier proved the involvement of an autocatalytic step in the oxidation of H₂ by HynSL hydrogenase from Thiocapsa roseopersicina, and demonstrated that two enzyme forms interact in this step. Using a modified thin-layer reaction chamber which permits quantitative analysis of the concentration of the reaction product (reduced benzyl viologen) in the reaction volume during the oxidation of H₂, we now show that the steady-state concentration of the product displays a strong enzyme concentration dependence. This experimental fact can be explained only if the previously detected autocatalytic step occurs inside the catalytic enzyme-cycle and not in the enzyme activation process. Consequently, both interacting enzyme forms should participate in the catalytic cycle of the enzyme. As far as we are aware, this is the first experimental observation of such a phenomenon resulting in an apparent inhibition of the enzyme. It is additionally concluded that the interaction of the two enzyme forms should result in a conformational change in the enzyme–substrate form. This scheme is very similar to that of prion reactions. Since merely a few molecules are involved at some point of the reaction, this process is entirely stochastic in nature. We have therefore developed a stochastic calculation method, calculations with which lent support to the conclusion drawn from the experiment.