Phenotypic diversity and chaos in a minimal cell model

Gánti's chemoton model (Gánti, T., 2002. On the early evolution of biological periodicity. Cell. Biol. Int. 26, 729) is considered as an iconic example of a minimal protocell including three key subsystems: membrane, metabolism and information. The three subsystems are connected through stoichiometrical coupling which ensures the existence of a replication cycle for the chemoton. Our detailed exploration of a version of this model indicates that it displays a wide range of complex dynamics, from regularity to chaos. Here, we report the presence of a very rich set of dynamical patterns potentially displayed by a protocell as described by this implementation of a chemoton-like model. The implications for early cellular evolution and synthesis of artificial cells are discussed.     

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).     

Protocell self-reproduction in a spatially extended metabolism-vesicle system

Cellular life requires the presence of a set of biochemical mechanisms in order to maintain a predictable process of growth and division. Several attempts have been made towards the building of minimal protocells from a top-down approach, i.e. by using available biomolecules. This type of synthetic approach has so far been only partially successful, and appropriate models of the synthetic protocell cycle might be needed to guide future experiments. In this paper, we present a simple biochemically and physically feasible model of cell replication involving a discrete semi-permeable vesicle with an internal minimal metabolism involving two reactive centers. It is shown that such a system can effectively undergo a whole cell replication cycle. The model can be used as a basic framework to model whole protocell dynamics including more complex sets of reactions. The possible implementation of our design in future synthetic protocells is outlined.     

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.     

Evolution and self-assembly of protocells

Cells define the minimal building blocks of life. How cellular life emerged and evolved implies to cross the boundary between living and nonliving matter. Here we explore this problem by presenting several relevant components of the whole picture involving chemistry, physics and natural selection. Available evidence suggests that the basic logic of life can be understood and eventually translated into synthetic forms of cellular life. A simple, physically sound model of information-free protocell replication suggests that the basic logic of how to couple metabolism and container can be more relevant than the specific set of parameters used, thus indicating that the emergence of cells might have been easier than we would expect.     

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).     

Molar growth yield of Nitrobacter winogradskyi during exponential growth

A numerical analysis of experimental growth curves obtained for Nitrobacter by observing changes in cell numbers, substrate concentration and rate of heat evolution has allowed the calculation of the growth rate constants during the phase of balanced growth. The molar growth yield was smaller during that phase than during the phase preceding it. On the other hand, the rate of heat evolution was larger during exponential growth by a factor of about 1.5 than during the stages up to and including this phase. The two observations being in agreement since, if less efficient synthesis occurs during exponential growth, more free energy must be dissipated as heat.     

Functional blueprints: an approach to modularity in grown systems

The engineering of grown systems poses fundamentally different system integration challenges than ordinary engineering of static designs. On the one hand, a grown system must be capable of surviving not only in its final form, but at every intermediate stage, despite the fact that its subsystems may grow unevenly or be subject to different scaling laws. On the other hand, the ability to grow offers much greater potential for adaptation, either to changes in the environment or to internal stresses developed as the system grows. I observe that the ability of subsystems to tolerate stress can be used to transform incremental adaptation into the dynamic discovery of viable growth trajectories for the system as a whole. Using this observation, I propose an engineering approach based on functional blueprints, under which a system is specified in terms of desired performance and means of incrementally correcting deficiencies. I explore how manifold geometric programming can support such an approach by simplifying the construction of distortion-tolerant programs, then demonstrate the functional blueprints approach by applying it to integrate simplified models of tissue growth and vascularization, and further show how the composed system may itself be modulated for use as a component in a more complex design.     

An environmental perspective on metabolism

In principle the knowledge of an organism's metabolic network allows to infer its biosynthetic capabilities. Handorf et al. [2005. Expanding metabolic networks: scopes of compounds, robustness, and evolution. J. Mol. Evol. 61, 498-512] developed a method of network expansion generating the set of all possible metabolites that can be produced from a set of compounds, given the structure of a metabolic network. Here we investigate the inverse problem: which chemical compounds or sets of compounds must be provided as external resources in order to sustain the growth or maintenance of an organism, given the structure of its metabolic network? Although this problem is highly combinatorial, we show that it is possible to calculate locally minimal nutrient sets that can be interpreted in terms of resource types. Using these types we predict broad nutritional requirements for 447 organisms, providing clues for possible environments from the knowledge of their metabolic networks.     

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.     

The influence of different potassium and sodium ion concentrations on the rate of abiogenic peptide synthesis

The physicochemical conditions of the aqueous environment at the dawn of biological evolution were of key importance for abiogenic peptide synthesis. Recently, we have shown theoretical and experimental evidence for the unique role of potassium ions in the exponential acceleration of undirected peptide synthesis from L-glutamic acid. These data have confirmed our previous hypothesis that the first protocell emerged in a potassium rather than sodium-rich aqueous solution (seawater). The present work provides experimental data for an interpretation of concentration dependence and of optimal effective concentration of potassium and sodium ions in L-glutamic acid peptide formation.     

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.     

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.     

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.     

Mineral interface in extreme habitats: a niche for primitive molecular evolution for the appearance of different forms of life on earth

Innumerable primitive membrane and protocell models in latter stages of chemical evolution are based on the properties of minerals' interfaces with primitive seawater. The ordering mechanism induced by mineral interfaces has been the basis of several prebiotic models of molecular complexification and compartmentalization towards the appearance and evolution of different forms of life. Since mineral-aqueous media interfaces have been considered as initial stages of prebiotic models dealing with the formation of energy-transducing systems, the interface formed by pyrite in the presence of artificial primitive seawater was chosen to show the functional richness of this special niche. Interfaces--especially sulphide interfaces--were proposed as suitable niches for a two-carbon extant metabolism, synthesis and polymerization of nucleotides--to form ancient RNA strands--and assembly of amino acids synthesized in its vicinity. Accumulation of precursors at sulphide interfaces could have avoided their dilution into the Hadean seas and provided a suitable geochemical environment for a variety of molecular interactions. In this essay, we present a short review of the proposed roles of mineral interfaces in chemical evolution towards the appearance of primitive membranes, which might have been relevant for the advent of cellular life before its divergent evolution and differentiation. This survey covers several previous studies on the early cycles of energy conservation and of the formation of molecules carrying genetic information.     

Minimal model of self-replicating nanocells: a physically embodied information-free scenario

The building of minimal self-reproducing systems with a physical embodiment (generically called protocells) is a great challenge, with implications for both theory and applied sciences. Although the classical view of a living protocell assumes that it includes information-carrying molecules as an essential ingredient, a dividing cell-like structure can be built from a metabolism-container coupled system only. An example of such a system, modelled with dissipative particle dynamics, is presented here. This article demonstrates how a simple coupling between a precursor molecule and surfactant molecules forming micelles can experience a growth-division cycle in a predictable manner, and analyses the influence of crucial parameters on this replication cycle. Implications of these results for origins of cellular life and living technology are outlined.     

The origin of replicators and reproducers

Replicators are fundamental to the origin of life and evolvability. Their survival depends on the accuracy of replication and the efficiency of growth relative to spontaneous decay. Infrabiological systems are built of two coupled autocatalytic systems, in contrast to minimal living systems that must comprise at least a metabolic subsystem, a hereditary subsystem and a boundary, serving respective functions. Some scenarios prefer to unite all these functions into one primordial system, as illustrated in the lipid world scenario, which is considered as a didactic example in detail. Experimentally produced chemical replicators grow parabolically owing to product inhibition. A selection consequence is survival of everybody. The chromatographized replicator model predicts that such replicators spreading on surfaces can be selected for higher replication rate because double strands are washed away slower than single strands from the surface. Analysis of real ribozymes suggests that the error threshold of replication is less severe by about one order of magnitude than thought previously. Surface-bound dynamics is predicted to play a crucial role also for exponential replicators: unlinked genes belonging to the same genome do not displace each other by competition, and efficient and accurate replicases can spread. The most efficient form of such useful population structure is encapsulation by reproducing vesicles. The stochastic corrector model shows how such a bag of genes can survive, and what the role of chromosome formation and intragenic recombination could be. Prebiotic and early evolution cannot be understood without the models of dynamics.     

SALARECON connects the Atlantic salmon genome to growth and feed efficiency

Atlantic salmon (Salmo salar) is the most valuable farmed fish globally and there is much interest in optimizing its genetics and rearing conditions for growth and feed efficiency. Marine feed ingredients must be replaced to meet global demand, with challenges for fish health and sustainability. Metabolic models can address this by connecting genomes to metabolism, which converts nutrients in the feed to energy and biomass, but such models are currently not available for major aquaculture species such as salmon. We present SALARECON, a model focusing on energy, amino acid, and nucleotide metabolism that links the Atlantic salmon genome to metabolic fluxes and growth. It performs well in standardized tests and captures expected metabolic (in)capabilities. We show that it can explain observed hypoxic growth in terms of metabolic fluxes and apply it to aquaculture by simulating growth with commercial feed ingredients. Predicted limiting amino acids and feed efficiencies agree with data, and the model suggests that marine feed efficiency can be achieved by supplementing a few amino acids to plant- and insect-based feeds. SALARECON is a high-quality model that makes it possible to simulate Atlantic salmon metabolism and growth. It can be used to explain Atlantic salmon physiology and address key challenges in aquaculture such as development of sustainable feeds.     

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.