Metabolic network dynamics in open chaotic flow

Flows of Substances in Networks and Network Channels: Selected Results and Applications

This review paper is devoted to a brief overview of results and models concerning flows in networks and channels of networks. First of all, we conduct a survey of the literature in several areas of research connected to these flows. Then, we mention certain basic mathematical models of flows in networks that are based on differential equations. We give special attention to several models for flows of substances in channels of networks. For stationary cases of these flows, we present probability distributions connected to the substance in the nodes of the channel for two basic models: the model of a channel with many arms modeled by differential equations and the model of a simple channel with flows of substances modeled by difference equations. The probability distributions obtained contain as specific cases any probability distribution of a discrete random variable that takes values of 0,1,…. We also mention applications of the considered models, such as applications for modeling migration flows. Special attention is given to the connection of the theory of stationary flows in channels of networks and the theory of the growth of random networks.

From self-replication to replicator systems en route to de novo life

The process by which chemistry can give rise to biology remains one of the biggest mysteries in contemporary science. The de novo synthesis and origin of life both require the functional integration of three key characteristics - replication, metabolism and compartmentalization - into a system that is maintained out of equilibrium and is capable of open-ended Darwinian evolution. This Review takes systems of self-replicating molecules as starting points and describes the steps necessary to integrate additional characteristics of life. We analyse how far experimental self-replicators have come in terms of Darwinian evolution. We also cover models of replicator communities that attempt to solve Eigen's paradox, whereby accurate replication needs complex machinery yet obtaining such complex self-replicators through evolution requires accurate replication. Successful models rely on a collective metabolism and a way of (transient) compartmentalization, suggesting that the invention and integration of these two characteristics is driven by evolution. Despite our growing knowledge, there remain numerous key challenges that may be addressed by a combined theoretical and experimental approach.

Dynamics and stability in prebiotic information integration: an RNA World model from first principles

The robust coevolution of catalytically active, metabolically cooperating prebiotic RNA replicators were investigated using an RNA World model of the origin of life based on physically and chemically plausible first principles. The Metabolically Coupled Replicator System assumes RNA replicators to supply metabolically essential catalytic activities indispensable to produce nucleotide monomers for their own template replication. Using external chemicals as the resource and the necessary ribozyme activities, Watson-Crick type replication produces complementary strands burdened by high-rate point mutations (insertions, deletions, substitutions). Metabolic ribozyme activities, replicabilities and decay rates are assigned to certain sequence and/or folding (thermodynamical) properties of single-stranded RNA molecules. Short and loosely folded sequences are given replication advantage, longer and tightly folded ones are better metabolic ribozymes and more resistant to hydrolytic decay. We show that the surface-bound MCRS evolves stable and metabolically functional communities of replicators of almost equal lengths, replicabilities and ribozyme activities. Being highly resistant to the invasion of parasitic (non-functional) replicators, it is also stable in the evolutionary sense. The template replication mechanism selects for catalytic “promiscuity”: the two (complementary) strands of the same evolved replicator will often carry more than a single catalytically active motif, thus maximizing functionality in a minimum of genetic information.

Ecology and Evolution in the RNA World Dynamics and Stability of Prebiotic Replicator Systems

As of today, the most credible scientific paradigm pertaining to the origin of life on Earth is undoubtedly the RNA World scenario. It is built on the assumption that catalytically active replicators (most probably RNA-like macromolecules) may have been responsible for booting up life almost four billion years ago. The many different incarnations of nucleotide sequence (string) replicator models proposed recently are all attempts to explain on this basis how the genetic information transfer and the functional diversity of prebiotic replicator systems may have emerged, persisted and evolved into the first living cell. We have postulated three necessary conditions for an RNA World model system to be a dynamically feasible representation of prebiotic chemical evolution: (1) it must maintain and transfer a sufficient diversity of information reliably and indefinitely, (2) it must be ecologically stable and (3) it must be evolutionarily stable. In this review, we discuss the best-known prebiotic scenarios and the corresponding models of string-replicator dynamics and assess them against these criteria. We suggest that the most popular of prebiotic replicator systems, the hypercycle, is probably the worst performer in almost all of these respects, whereas a few other model concepts (parabolic replicator, open chaotic flows, stochastic corrector, metabolically coupled replicator system) are promising candidates for development into coherent models that may become experimentally accessible in the future.

Metabolically Coupled Replicator Systems: Overview of an RNA-world model concept of prebiotic evolution on mineral surfaces

Metabolically Coupled Replicator Systems (MCRS) are a family of models implementing a simple, physico-chemically and ecologically feasible scenario for the first steps of chemical evolution towards life. Evolution in an abiotically produced RNA-population sets in as soon as any one of the RNA molecules become autocatalytic by engaging in template directed self-replication from activated monomers, and starts increasing exponentially. Competition for the finite external supply of monomers ignites selection favouring RNA molecules with catalytic activity helping self-replication by any possible means. One way of providing such autocatalytic help is to become a replicase ribozyme. An additional way is through increasing monomer supply by contributing to monomer synthesis from external resources, i.e., by evolving metabolic enzyme activity. Retroevolution may build up an increasingly autotrophic, cooperating community of metabolic ribozymes running an increasingly complicated and ever more efficient metabolism. Maintaining such a cooperating community of metabolic replicators raises two serious ecological problems: one is keeping the system coexistent in spite of the different replicabilities of the cooperating replicators; the other is constraining parasitism, i.e., keeping "cheaters" in check. Surface-bound MCRS provide an automatic solution to both problems: coexistence and parasite resistance are the consequences of assuming the local nature of metabolic interactions. In this review we present an overview of results published in previous articles, showing that these effects are, indeed, robust in different MCRS implementations, by considering different environmental setups and realistic chemical details in a few different models. We argue that the MCRS model framework naturally offers a suitable starting point for the future modelling of membrane evolution and extending the theory to cover the emergence of the first protocell in a self-consistent manner. The coevolution of metabolic, genetic and membrane functions is hypothesized to follow the progressive sequestration scenario, the conceptual blueprint for the earliest steps of protocell evolution.

Template directed replication supports the maintenance of the metabolically coupled replicator system

The RNA World scenario of prebiotic chemical evolution is among the most plausible conceptual framework available today for modelling the origin of life. RNA offers genetic and catalytic (metabolic) functionality embodied in a single chemical entity, and a metabolically cooperating community of RNA molecules would constitute a viable infrabiological subsystem with a potential to evolve into proto-cellular life. Our Metabolically Coupled Replicator System (MCRS) model is a spatially explicit computer simulation implementation of the RNA-World scenario, in which replicable ribozymes cooperate in supplying each other with monomers for their own replication. MCRS has been repeatedly demonstrated to be viable and evolvable, with different versions of the model improved in depth (chemical detail of metabolism) or in extension (additional functions of RNA molecules). One of the dynamically relevant extensions of the MCRS approach to prebiotic RNA evolution is the explicit inclusion of template replication into its assumptions, which we have studied in the present version. We found that this modification has not changed the behaviour of the system in the qualitative sense, just the range of the parameter space which is optimal for the coexistence of metabolically cooperating replicators has shifted in terms of metabolite mobility. The system also remains resistant and tolerant to parasitic replicators.

Active centrum hypothesis: the origin of chiral homogeneity and the RNA-world

I propose a hypothesis on the origin of chiral homogeneity of bio-molecules based on chiral catalysis. The first chiral active centre may have formed on the surface of complexes comprising metal ions, amino acids, other coenzymes and oligomers (short RNAs). The complexes must have been dominated by short RNAs capable of self-reproduction with ligation. Most of the first complexes may have catalysed the production of nucleotides. A basic assumption is that such complexes can be assembled from their components almost freely, in a huge variety of combinations. This assumption implies that "a few" components can constitute "a huge" number of active centre types. Moreover, an experiment is proposed to test the performance of such complexes in vitro. If the complexes were built up freely from their elements, then Darwinian evolution would operate on the assembly mechanism of complexes. For the production of complexes, first their parts had to appear by forming a proper three-dimensional structure. Three possible re-building mechanisms of the proper geometric structure of complexes are proposed. First, the integration of RNA parts of complexes was assisted presumably by a pre-intron. Second, the binding of RNA parts of a complex may give rise to a "polluted" RNA world. Third, the pairing of short RNA parts and their geometric conformation may have been supported by a pre-genetic code. Finally, an evolutionary step-by-step scenario of the origin of homochirality and a "polluted" RNA world is also introduced based on the proposed combinatorial complex chemistry. Homochirality is evolved by Darwinian selection whenever the efficiency of the reflexive autocatalysis of a dynamical combinatorial library increases with the homochirality of the active centres of reactions cascades and the homochirality of the elements of the dynamical combinatorial library. Moreover, the potential importance of phospholipid membrane is also discussed.

Competitive exclusion and limiting similarity: A unified theory

Robustness of coexistence against changes of parameters is investigated in a model-independent manner by analyzing the feedback loop of population regulation. We define coexistence as a fixed point of the community dynamics with no population having zero size. It is demonstrated that the parameter range allowing coexistence shrinks and disappears when the Jacobian of the dynamics decreases to zero. A general notion of regulating factors/variables is introduced. For each population, its impact and sensitivity niches are defined as the differential impact on, and the differential sensitivity towards, the regulating variables, respectively. Either the similarity of the impact niches or the similarity of the sensitivity niches results in a small Jacobian and in a reduced likelihood of coexistence. For the case of a resource continuum, this result reduces to the usual "limited niche overlap" picture for both kinds of niche. As an extension of these ideas to the coexistence of infinitely many species, we demonstrate that Roughgarden's example for coexistence of a continuum of populations is structurally unstable.

Fractal scaling of microbial colonies affects growth

The growth dynamics of filamentary microbial colonies is investigated. Fractality of the fungal or actinomycetes colonies is shown both theoretically and in numerical experiments to play an important role. The growth observed in real colonies is described by the assumption of time-dependent fractality related to the different ages of various parts of the colony. The theoretical results are compared to a simulation based on branching random walks.

Reactions in flows with nonhyperbolic dynamics

We study the reaction dynamics of active particles that are advected passively by 2D incompressible open flows, whose motion is nonhyperbolic. This nonhyperbolicity is associated with the presence of persistent vortices near the wake, wherein fluid is trapped. We show that the fractal equilibrium distribution of the reactants is described by an effective dimension d(eff) , which is a finite resolution approximation to the fractal dimension. Furthermore, d(eff) depends on the resolution epsilon and on the reaction rate 1/tau . As tau is increased, the equilibrium distribution goes through a series of transitions where the effective dimension increases abruptly. These transitions are determined by the complex structure of Cantori surrounding the Kolmogorov-Arnold-Moser (KAM) islands.

Chemical and biological activity in three-dimensional flows

We study the dynamics of active particles advected by three-dimensional (3D) open incompressible flows, both analytically and numerically. We find that 3D reactive flows have fundamentally different dynamical features from those in 2D systems. In particular, we show that the reaction's productivity per reaction step can be enhanced, with respect to the 2D case, while the productivity per unit time in some 3D flows goes to zero in the limit of high mixing rates, in contrast to the 2D behavior, in which the productivity goes to a finite constant. These theoretical predictions are validated by numerical simulations on a generic map model.

Universality in active chaos

Many examples of chemical and biological processes take place in large-scale environmental flows. Such flows generate filamental patterns which are often fractal due to the presence of chaos in the underlying advection dynamics. In such processes, hydrodynamical stirring strongly couples into the reactivity of the advected species and might thus make the traditional treatment of the problem through partial differential equations difficult. Here we present a simple approach for the activity in inhomogeneously stirred flows. We show that the fractal patterns serving as skeletons and catalysts lead to a rate equation with a universal form that is independent of the flow, of the particle properties, and of the details of the active process. One aspect of the universality of our approach is that it also applies to reactions among particles of finite size (so-called inertial particles).

Spatial models of prebiotic evolution: soup before pizza?

The problem of information integration and resistance to the invasion of parasitic mutants in prebiotic replicator systems is a notorious issue of research on the origin of life. Almost all theoretical studies published so far have demonstrated that some kind of spatial structure is indispensable for the persistence and/or the parasite resistance of any feasible replicator system. Based on a detailed critical survey of spatial models on prebiotic information integration, we suggest a possible scenario for replicator system evolution leading to the emergence of the first protocells capable of independent life. We show that even the spatial versions of the hypercycle model are vulnerable to selfish parasites in heterogeneous habitats. Contrary, the metabolic system remains persistent and coexistent with its parasites both on heterogeneous surfaces and in chaotically mixing flowing media. Persistent metabolic parasites can be converted to metabolic cooperators, or they can gradually obtain replicase activity. Our simulations show that, once replicase activity emerged, a gradual and simultaneous evolutionary improvement of replicase functionality (speed and fidelity) and template efficiency is possible only on a surface that constrains the mobility of macromolecule replicators. Based on the results of the models reviewed, we suggest that open chaotic flows ('soup') and surface dynamics ('pizza') both played key roles in the sequence of evolutionary events ultimately concluding in the appearance of the first living cell on Earth.

Competing populations in flows with chaotic mixing

We investigate the effects of spatial heterogeneity on the coexistence of competing species in the case when the heterogeneity is dynamically generated by environmental flows with chaotic mixing properties. We show that one effect of chaotic advection on the passively advected species (such as phytoplankton, or self-replicating macro-molecules) is the possibility of coexistence of more species than that limited by the number of niches they occupy. We derive a novel set of dynamical equations for competing populations.