Two different template replicators coexisting in the same protocell: stochastic simulation of an extended chemoton model

The simulation of complex biochemical systems, consisting of intertwined subsystems, is a challenging task in computational biology. The complex biochemical organization of the cell is effectively modeled by the minimal cell model called chemoton, proposed by Gánti. Since the chemoton is a system consisting of a large but fixed number of interacting molecular species, it can effectively be implemented in a process algebra-based language such as the BlenX programming language. The stochastic model behaves comparably to previous continuous deterministic models of the chemoton. Additionally to the well-known chemoton, we also implemented an extended version with two competing template cycles. The new insight from our study is that the coupling of reactions in the chemoton ensures that these templates coexist providing an alternative solution to Eigen's paradox. Our technical innovation involves the introduction of a two-state switch to control cell growth and division, thus providing an example for hybrid methods in BlenX. Further developments to the BlenX language are suggested in the Appendix.     

Generic Darwinian selection in catalytic protocell assemblies

To satisfy the minimal requirements for life, an information carrying molecular structure must be able to convert resources into building blocks and also be able to adapt to or modify its environment to enhance its own proliferation. Furthermore, new copies of itself must have variable fitness such that evolution is possible. In practical terms, a minimal protocell should be characterized by a strong coupling between its metabolism and genetic subsystem, which is made possible by the container. There is still no general agreement on how such a complex system might have been naturally selected for in a prebiotic environment. However, the historical details are not important for our investigations as they are related to assembling and evolution of protocells in the laboratory. Here, we study three different minimal protocell models of increasing complexity, all of them incorporating the coupling between a 'genetic template', a container and, eventually, a toy metabolism. We show that for any local growth law associated with template self-replication, the overall temporal evolution of all protocell's components follows an exponential growth (efficient or uninhibited autocatalysis). Thus, such a system attains exponential growth through coordinated catalytic growth of its component subsystems, independent of the replication efficiency of the involved subsystems. As exponential growth implies the survival of the fittest in a competitive environment, these results suggest that protocell assemblies could be efficient vehicles in terms of evolving through Darwinian selection.     

An overlooked riddle of life's origins: energy-dependent nucleic acid unzipping

The imposing progress in understanding contemporary life forms on Earth and in manipulating them has not been matched by a comparable progress in understanding the origins of life. This paper argues that a crucial problem of unzipping of the double helix molecule of nucleic acid during its replication has been underrated, if not plainly overlooked, in the theories of life's origin and evolution. A model is presented of how evolution may have solved the problem in its early phase. Similar to several previous models, the model envisages the existence of a protocell, in which osmotic disbalance is being created by accumulation of synthetic products resulting in expansion and division of the protocell. Novel in the model is the presence in the protocell of a double-stranded nucleic acid, with each of its two strands being affixed by its 3'-terminus to the opposite sides of the membrane of a protocell. In the course of the protocell expansion, osmotic force is utilized to pull the two strands longitudinally in opposite directions, unzipping the helix and partitioning the strands between the two daughter protocells. The model is also being used as a background for arguments of why life need operate in cycles. Many formal models of life's origin and evolution have not taken into account the fact that logical possibility does not equal thermodynamic feasibility. A system of self-replication has to consist of both replicators and replicants.     

The Origins of Cellular Life

Understanding the origin of cellular life on Earth requires the discovery of plausible pathways for the transition from complex prebiotic chemistry to simple biology, defined as the emergence of chemical assemblies capable of Darwinian evolution. We have proposed that a simple primitive cell, or protocell, would consist of two key components: a protocell membrane that defines a spatially localized compartment, and an informational polymer that allows for the replication and inheritance of functional information. Recent studies of vesicles composed of fatty-acid membranes have shed considerable light on pathways for protocell growth and division, as well as means by which protocells could take up nutrients from their environment. Additional work with genetic polymers has provided insight into the potential for chemical genome replication and compatibility with membrane encapsulation. The integration of a dynamic fatty-acid compartment with robust, generalized genetic polymer replication would yield a laboratory model of a protocell with the potential for classical Darwinian biological evolution, and may help to evaluate potential pathways for the emergence of life on the early Earth. Here we discuss efforts to devise such an integrated protocell model.The emergence of the first cells on the early Earth was the culmination of a long history of prior chemical and geophysical processes. Although recognizing the many gaps in our knowledge of prebiotic chemistry and the early planetary setting in which life emerged, we will assume for the purpose of this review that the requisite chemical building blocks were available, in appropriate environmental settings. This assumption allows us to focus on the various spontaneous and catalyzed assembly processes that could have led to the formation of primitive membranes and early genetic polymers, their coassembly into membrane-encapsulated nucleic acids, and the chemical and physical processes that allowed for their replication. We will discuss recent progress toward the construction of laboratory models of a protocell (Fig. 1), evaluate the remaining steps that must be achieved before a complete protocell model can be constructed, and consider the prospects for the observation of spontaneous Darwinian evolution in laboratory protocells. Although such laboratory studies may not reflect the specific pathways that led to the origin of life on Earth, they are proving to be invaluable in uncovering surprising and unanticipated physical processes that help us to reconstruct plausible pathways and scenarios for the origin of life.Open in a separate windowFigure 1.A simple protocell model based on a replicating vesicle for compartmentalization, and a replicating genome to encode heritable information. A complex environment provides lipids, nucleotides capable of equilibrating across the membrane bilayer, and sources of energy (left), which leads to subsequent replication of the genetic material and growth of the protocell (middle), and finally protocellular division through physical and chemical processes (right). (Reproduced from Mansy et al. 2008 and reprinted with permission from Nature Publishing ©2008.)The term protocell has been used loosely to refer to primitive cells or to the first cells. Here we will use the term protocell to refer specifically to cell-like structures that are spatially delimited by a growing membrane boundary, and that contain replicating genetic information. A protocell differs from a true cell in that the evolution of genomically encoded advantageous functions has not yet occurred. With a genetic material such as RNA (or perhaps one of many other heteropolymers that could provide both heredity and function) and an appropriate environment, the continued replication of a population of protocells will lead inevitably to the spontaneous emergence of new coded functions by the classical mechanism of evolution through variation and natural selection. Once such genomically encoded and therefore heritable functions have evolved, we would consider the system to be a complete, living biological cell, albeit one much simpler than any modern cell (Szostak et al. 2001).     

The "protocell": a mathematical model of self-maintenance

The concepts of self-generation, autonomous boundary and self-maintenance are explained briefly. The "protocell" is presented as a model of self-maintenance which is based on simple physical mechanisms of diffusion and reaction. The time evolution of the surface of the protocell is taken into account explicitly in the form of a Stefan condition giving rise to a non-linear feedback of the surface motion to the reaction and diffusion processes inside the protocell. The spatio-temporal dynamics are investigated, particularly in the neighbourhood of the stationary states, showing a self-maintaining behaviour under a certain range of nutritional conditions. Under another set of conditions we find an instability leading to a division process so that the population of protocells becomes self-maintaining instead of the single individual. The presented formulation of the protocell model is crucially improved compared with a previous version which required boundary conditions at infinity. The previous version was not strictly self-maintaining since dynamics outside the cell were essential for its behaviour.     

From geochemistry and biochemistry to prebiotic evolution...we necessarily enter into Gánti's fluid automata

The present study is just an overview of the opening of the geochemical stage for the appearance of life. But that opening would not have been sufficient for the intellectual discovery of the origin of life! The excellent works and many commendable efforts that advance this explanation have not shown the fundamental elements that participate in the theoretical frame of biological evolution. The latter imply the existence of evolutionary transitions and the production of new levels of organization. In this brief analysis we do not intend to introduce the audience to the philosophy of biology. But we do expect to provide a modest overview, in which the geochemical chemolithoautotrophic opening of the stage should be seen, at most, as the initial metabolism that enabled organic compounds to follow the road where a chemical fluid machinery was thus able to undertake the more "sublime" course of organic biological evolution. We think that Tibor Gánti's chemoton is the most significant contribution to theoretical biology, and the only course now available to comprehend the unit of evolution problem without the structuralist and functionalist conflict prevalent in theoretical biology. In our opinion Gánti's chemoton theory travels to the "locus" where evolutionary theory dares to extend itself to entities at many levels of structural organization, beyond the gene or the group above. Therefore, in this and subsequent papers on the prebiotic conditions for the eventual appearance of the genetic code, we explore the formation and the presence of metal sulfide minerals, from the assembly of metal sulfide clusters through the precipitation of nanocrystals and the further reactions resulting in bulk metal sulfide phases. We endeavor to characterize pristine reactions and the modern surfaces, utilizing traditional surface science techniques and computational methods. Moreover, mechanistic details of the overall oxidation of metal sulfide minerals are set forth. We hope that this paper will lead our audience to accept that in a chemically oscillating system the chemoton is a model fluid state automaton capable of growth and self-reproduction. This is not simply a matter of transmitting a pattern, as in inorganic crystals; such self-reproduction must be more complex than crystal growth. Indeed that is what Gánti's theoretical and abstract model offers to us all: we finally have a philosophy of evolutionary units in theoretical biology.     

Emergence of protocellular growth laws

Template-directed replication is known to obey a parabolic growth law due to product inhibition (Sievers & Von Kiedrowski 1994 Nature 369, 221; Lee et al. 1996 Nature 382, 525; Varga & Szathmáry 1997 Bull. Math. Biol. 59, 1145). We investigate a template-directed replication with a coupled template catalysed lipid aggregate production as a model of a minimal protocell and show analytically that the autocatalytic template-container feedback ensures balanced exponential replication kinetics; both the genes and the container grow exponentially with the same exponent. The parabolic gene replication does not limit the protocellular growth, and a detailed stoichiometric control of the individual protocell components is not necessary to ensure a balanced gene-container growth as conjectured by various authors (Gánti 2004 Chemoton theory). Our analysis also suggests that the exponential growth of most modern biological systems emerges from the inherent spatial quality of the container replication process as we show analytically how the internal gene and metabolic kinetics determine the cell population's generation time and not the growth law (Burdett & Kirkwood 1983 J. Theor. Biol. 103, 11-20; Novak et al. 1998 Biophys. Chem. 72, 185-200; Tyson et al. 2003 Curr. Opin. Cell Biol. 15, 221-231). Previous extensive replication reaction kinetic studies have mainly focused on template replication and have not included a coupling to metabolic container dynamics (Stadler et al. 2000 Bull. Math. Biol. 62, 1061-1086; Stadler & Stadler 2003 Adv. Comp. Syst. 6, 47). The reported results extend these investigations. Finally, the coordinated exponential gene-container growth law stemming from catalysis is an encouraging circumstance for the many experimental groups currently engaged in assembling self-replicating minimal artificial cells (Szostak 2001 et al. Nature 409, 387-390; Pohorille & Deamer 2002 Trends Biotech. 20 123-128; Rasmussen et al. 2004 Science 303, 963-965; Szathma ry 2005 Nature 433, 469-470; Luisi et al. 2006 Naturwissenschaften 93, 1-13).     

Steps Towards the Formation of A Protocell: The Possible Role of Short Peptides

The paper deals with molecular self-organization leading to formation of a protocell. Plausible steps towards a protocell include: polymerization of peptides and oligonucleotides on mineral surfaces; coevolution of peptides and oligonucleotides with formation of collectively autocatalytic sets; self-organization of short peptides into vesicles; entrapment of the peptide/oligonucleotide systems in mixed peptide and simple amphiphile membranes; and formation of functioning protocells with metabolism and cell division. The established propensity of short peptides to self-ordering and to formation of vesicles makes this sequence plausible. We further suggest that evolution of a protocell produced cellular ancestors of viruses as well as ancestors of cellular organisms.     

Quantum processes in evolution of regulation of living systems (mathematical modeling)

We have developed an imitation model of the appearance of regulation of physiological functions of protocell at initial stages of evolution of living system. It is based on suggestion of the appearance of signal function in spontaneously formed products of partial hydrolysis of the protocell polypeptides, based on which there appear the regulatory molecules—quanta of regulation. For construction of the model, the mathematical apparatus of final automats and of genetic algorithm is used. The model has demonstrated the positive role of involvement of regulatory peptides in the system of regulation of protocell functions to provide its viability under the changing envelopment conditions.     

Rapid RNA Exchange in Aqueous Two-Phase System and Coacervate Droplets

Compartmentalization in a prebiotic setting is an important aspect of early cell formation and is crucial for the development of an artificial protocell system that effectively couples genotype and phenotype. Aqueous two-phase systems (ATPSs) and complex coacervates are phase separation phenomena that lead to the selective partitioning of biomolecules and have recently been proposed as membrane-free protocell models. We show in this study through fluorescence recovery after photobleaching (FRAP) microscopy that despite the ability of such systems to effectively concentrate RNA, there is a high rate of RNA exchange between phases in dextran/polyethylene glycol ATPS and ATP/poly-L-lysine coacervate droplets. In contrast to fatty acid vesicles, these systems would not allow effective segregation and consequent evolution of RNA, thus rendering these systems ineffective as model protocells.     

A Fission-Fusion Origin for Life

To develop a comprehensive cells-first approach to the origin of life, we propose that protocells form spontaneously and that the fission and fusion of these protocells drives the dynamics of their evolution. The fitness criterion for this evolution is taken to be the the stability (conservation) of domains in the protocellular membrane as determined by non-covalent molecular associations between the amphiphiles of the membrane and a subset of the macromolecules in the protocell. In the presence of a source of free energy the macromolecular content of the protocell (co-)evolves as the result of (domain-dependent) membrane-catalysed polymerisation of the prebiotic constituents delivered to the protocell by fusion. The metabolism of the cell therefore (co-)evolves on a rugged fitness landscape. We indicate how domain evolution with the same fitness criterion can potentially give rise to coding. Membrane domains may therefore provide the link between protocells and the RNA/DNA-world.     

The Gárdos channel: a review of the Ca2+-activated K+ channel in human erythrocytes

Ca²⁺-dependent K⁺ efflux from human erythrocytes was first described in the 1950s. Subsequent studies revealed that a K⁺-specific membrane protein (the Gárdos channel) was responsible for this phenomenon (the Gárdos effect). In recent years several types of Ca-activated K⁺ channel have been identified and studied in a wide range of cells, with the erythrocyte Gárdos channel serving as both a model for a broader physiological perspective, and an intriguing component of erythrocyte function.The existence of this channel has raised a number of questions. For example, what is its role in the establishment and maintenance of ionic distribution across the red cell membrane? What role might it play in erythrocyte development? To what extent is it active in circulating erythrocytes? What are the cell-physiological implications of its dysfunction?This review summarises current knowledge of this membrane protein with respect to its function and structure, its physiological roles (some putative) and its contribution to various disease states, and it provides an introduction to adaptable NMR methods, which is our own area of technical expertise, for such ion transport analysis.     

Quantum processes in evolution of regulation of living system (mathematical modelling)

We have developed an imitation model of the appearance of regulation of physiological functions of protocell at the initial stages of evolution of living system. It is based on suggestion of the appearance of signal function in spontaneously formed products of partial hydrolysis of the protocell polypeptides, based on which there appear the regulatory molecules--quanta of regulation. For construction of the model, the mathematical apparatus of final automats and of genetic algorithm is used. The model has demonstrated the positive role of involvement of regulatory peptides in the system of regulation of protocell functions to provide its viability under the changing envelopment conditions.     

The evolutionary significance of phase-separated microsystems

The source, preparation, and properties of phase-separated systems such as lipid layers, coacervate droplets, sulphobes, and proteinoid microspheres are reviewed. These microsystems are of interest as partial models for the cell and as partial or total models for the protocell. Conceptual benefits from study of such models are: clues to experiments on origins, insights into principles of action and, in some instances, presumable models of the origin of the protocell. The benefits to evolution of organized chemical units are many, and can in part be analyzed. Ease of formation suggests that such units would have arisen early in primordial organic evolution. Integration of these various concepts and the results of consequent experiments have contributed to the developing theory of the origins of primordial and of contemporary life.Invited paper. Presented at the International Seminar Origin of Life, 2–7 August 1974, Moscow, U.S.S.R.     

Package models and the information crisis of prebiotic evolution

The coexistence between different types of templates has been the choice solution to the information crisis of prebiotic evolution, triggered by the finding that a single RNA-like template cannot carry enough information to code for any useful replicase. In principle, confining d distinct templates of length L in a package or protocell, whose survival depends on the coexistence of the templates it holds in, could resolve this crisis provided that d is made sufficiently large. Here we review the prototypical package model of Niesert et al. [1981. Origin of life between Scylla and Charybdis. J. Mol. Evol. 17, 348-353] which guarantees the greatest possible region of viability of the protocell population, and show that this model, and hence the entire package approach, does not resolve the information crisis. In particular, we show that the total information stored in a viable protocell (Ld) tends to a constant value that depends only on the spontaneous error rate per nucleotide of the template replication mechanism. As a result, an increase of d must be followed by a decrease of L, so that the net information gain is null.     

Early Stages of the Evolution of Life: a Cybernetic Approach

Early stages of the evolution of life are considered in terms of control theory. A model is proposed for the transport of substances in a protocell possessing the property of robustness with regard to changes in the environmental concentration of a substance.     

Sufficient conditions for emergent synchronization in protocell models

In this paper, we study general protocell models aiming to understand the synchronization phenomenon of genetic material and container productions, a necessary condition to ensure sustainable growth in protocells and eventually leading to Darwinian evolution when applied to a population of protocells.Synchronization has been proved to be an emergent property in many relevant protocell models in the class of the so-called surface reaction models, assuming both linear- and non-linear dynamics for the involved chemical reactions. We here extend this analysis by introducing and studying a new class of models where the relevant chemical reactions are assumed to occur inside the protocell, in contrast with the former model where the reaction site was the external surface.While in our previous studies, the replicators were assumed to compete for resources, without any direct interaction among them, we here improve both models by allowing linear interaction between replicators: catalysis and/or inhibition. Extending some techniques previously introduced, we are able to give a quite general analytical answer about the synchronization phenomenon in this more general context. We also report on results of numerical simulations to support the theory, where applicable, and allow the investigation of cases which are not amenable to analytical calculations.     

Hylomorphism and the Metabolic Closure Conception of Life

This paper examines three exemplary theories of living organization with respect to their common feature of defining life in terms of metabolic closure: autopoiesis, (M, R) systems, and chemoton theory. Metabolic closure is broadly understood to denote the property of organized chemical systems that each component necessary for the maintenance of the system is produced from within the system itself, except for an input of energy. It is argued that two of the theories considered—autopoiesis and (M, R) systems—participate in a hylomorphist pattern of thinking which separates the “form” of the living system from its “matter.” The analysis and critique of hylomorphism found in the work of the philosopher Gilbert Simondon is then applied to these two theories, and on the basis of this critique it is argued that the chemoton model offers a superior theory of minimal life which overcomes many of the problems associated with the other two. Throughout, the relationship between hylomorphism and the understanding of living things as machines is explored. The paper concludes by considering how hylomorphism as a background ontology for theories of life fundamentally influences the way life is defined.     

Primordial transport of sugars and amino acids via Schiff bases

Experimental support is given for a model concerning the origin of a primordial transport system. The model is based on the facilitated diffusion of amino acids stimulated by aliphatic aldehyde carriers and sugars stimulated by aliphatic amine carriers. The lipid-soluble diffusing species is the Schiff base. The possible role of this simple transport system in the origin of an early protocell is discussed.     

Origin of sex

The competitive advantage of sex consists in being able to use redundancy to recover lost genetic information while minimizing the cost of redundancy. We show that the major selective forces acting early in evolution lead to RNA protocells in which each protocell contains one genome, since this maximizes the growth rate. However, damages to the RNA which block replication and failure of segregation make it advantageous to fuse periodically with another protocell to restore reproductive ability. This early, simple form of genetic recovery is similar to that occurring in extant segmented single stranded RNA viruses. As duplex DNA became the predominant form of the genetic material, the mechanism of genetic recovery evolved into the more complex process of recombinational repair, found today in a range of species. We thus conclude that sexual reproduction arose early in the evolution of life and has had a continuous evolutionary history. We cite reasons to reject arguments for gaps in the evolutionary sequence of sexual reproduction based on the presumed absence of sex in the cyanobacteria. Concerning the maintenance of the sexual cycle among current organisms, we take care to distinguish between the recombinational and outbreeding aspects of the sexual cycle. We argue that recombination, whether it be in outbreeding organisms, self-fertilizing organisms or automictic parthenogens, is maintained by the advantages of recombinational repair. We also discuss the role of DNA repair in maintaining the outbreeding aspects of the sexual cycle.