Models of Protocells Undergoing Asymmetrical Division

The conditions that allow for the sustained growth of a protocell population are investigated in the case of asymmetrical division. The results are compared to those of previous studies concerning models of symmetrical division, where synchronization (between duplication of the genetic material and fission of the lipid container) was found under a variety of different assumptions about the kinetic equations and about the place where molecular replication takes place. Such synchronization allows a sustained proliferation of the protocell population. In the asymmetrical case, there can be no true synchronization, since the time to duplication may depend upon the initial size, but we introduce a notion of homogeneous growth that actually allows for the sustained reproduction of a population of protocells. We first analyze Surface Reaction Models, defined in the text, and we show that in many cases they undergo homogeneous growth under the same kinetic laws that lead to synchronization in the symmetrical case. This is the case also for Internal Reaction Models (IRMs), which, however, require a deeper understanding of what homogeneous growth actually means, as discussed below.

The limits of metabolic heredity in protocells

The universal core of metabolism could have emerged from thermodynamically favoured prebiotic pathways at the origin of life. Starting with H 2 and CO 2 , the synthesis of amino acids and mixed fatty acids, which self-assemble into protocells, is favoured under warm anoxic conditions. Here, we address whether it is possible for protocells to evolve greater metabolic complexity, through positive feedbacks involving nucleotide catalysis. Using mathematical simulations to model metabolic heredity in protocells, based on branch points in protometabolic flux, we show that nucleotide catalysis can indeed promote protocell growth. This outcome only occurs when nucleotides directly catalyse CO 2 fixation. Strong nucleotide catalysis of other pathways (e.g. fatty acids and amino acids) generally unbalances metabolism and slows down protocell growth, and when there is competition between catalytic functions cell growth collapses. Autocatalysis of nucleotide synthesis can promote growth but only if nucleotides also catalyse CO 2 fixation; autocatalysis alone leads to the accumulation of nucleotides at the expense of CO 2 fixation and protocell growth rate. Our findings offer a new framework for the emergence of greater metabolic complexity, in which nucleotides catalyse broad-spectrum processes such as CO 2 fixation, hydrogenation and phosphorylation important to the emergence of genetic heredity at the origin of life.

When Is a Reaction Network a Metabolism? Criteria for Simple Metabolisms That Support Growth and Division of Protocells

With the aim of better understanding the nature of metabolism in the first cells and the relationship between the origin of life and the origin of metabolism, we propose three criteria that a chemical reaction system must satisfy in order to constitute a metabolism that would be capable of sustaining growth and division of a protocell. (1) Biomolecules produced by the reaction system must be maintained at high concentration inside the cell while they remain at low or zero concentration outside. (2) The total solute concentration inside the cell must be higher than outside, so there is a positive osmotic pressure that drives cell growth. (3) The metabolic rate (i.e., the rate of mass throughput) must be higher inside the cell than outside. We give examples of small-molecule reaction systems that satisfy these criteria, and others which do not, firstly considering fixed-volume compartments, and secondly, lipid vesicles that can grow and divide. If the criteria are satisfied, and if a supply of lipid is available outside the cell, then continued growth of membrane surface area occurs alongside the increase in volume of the cell. If the metabolism synthesizes more lipid inside the cell, then the membrane surface area can increase proportionately faster than the cell volume, in which case cell division is possible. The three criteria can be satisfied if the reaction system is bistable, because different concentrations can exist inside and out while the rate constants of all the reactions are the same. If the reaction system is monostable, the criteria can only be satisfied if there is a reason why the rate constants are different inside and out (for example, the decay rates of biomolecules are faster outside, or the formation rates of biomolecules are slower outside). If this difference between inside and outside does not exist, a monostable reaction system cannot sustain cell growth and division. We show that a reaction system for template-directed RNA polymerization can satisfy the requirements for a metabolism, even if the small-molecule reactions that make the single nucleotides do not.

Exponential trajectories, cell size fluctuations, and the adder property in bacteria follow from simple chemical dynamics and division control

Experiments on steady-state bacterial cultures have uncovered several quantitative regularities at the system level. These include, first, the exponential growth of cell size with time and the balanced growth of intracellular chemicals between cell birth and division, which are puzzling given the nonlinear and decentralized chemical dynamics in the cell. We model a cell as a set of chemical populations undergoing nonlinear mass action kinetics in a container whose volume is a linear function of the chemical populations. This turns out to be a special class of dynamical systems that generically has attractors in which all populations grow exponentially with time at the same rate. This explains exponential balanced growth of bacterial cells without invoking any regulatory mechanisms and suggests that this could be a robust property of protocells as well. Second, we consider the hypothesis that cells commit themselves to division when a certain internal chemical population reaches a threshold of N molecules. We show that this hypothesis leads to a simple explanation of some of the variability observed across cells in a bacterial culture. In particular, it reproduces the adder property of cell size fluctuations observed recently in E. coli; the observed correlations among interdivision time, birth volume, and added volume in a generation; and the observed scale of the fluctuations (CV ≈ 10-30%) when N is between 10 and 100. Third, upon including a suitable regulatory mechanism that optimizes the growth rate of the cell, the model reproduces the observed bacterial growth laws including the dependence of the growth rate and ribosomal protein fraction on the medium. Thus, the models provide a framework for unifying diverse aspects of bacterial growth physiology under one roof. They also suggest new questions for experimental and theoretical enquiry.

The Construction of Biological 'Inter-Identity' as the Outcome of a Complex Process of Protocell Development in Prebiotic Evolution

The concept of identity is used both (i) to distinguish a system as a particular material entity that is conserved as such in a given environment (token-identity: i.e., identity as permanence or endurance over time), and (ii) to relate a system with other members of a set (type-identity: i.e., identity as an equivalence relationship). Biological systems are characterized, in a minimal and universal sense, by a highly complex and dynamic, far-from-equilibrium organization of very diverse molecular components and transformation processes (i.e., 'genetically instructed cellular metabolisms') that maintain themselves in constant interaction with their corresponding environments, including other systems of similar nature. More precisely, all living entities depend on a deeply convoluted organization of molecules and processes (a naturalized von Neumann constructor architecture) that subsumes, in the form of current individuals (autonomous cells), a history of ecological and evolutionary interactions (across cell populations). So one can defend, on those grounds, that living beings have an identity of their own from both approximations: (i) and (ii). These transversal and trans-generational dimensions of biological phenomena, which unfold together with the actual process of biogenesis, must be carefully considered in order to understand the intricacies and metabolic robustness of the first living cells, their underlying uniformity (i.e., their common biochemical core) and the eradication of previous -or alternative- forms of complex natural phenomena. Therefore, a comprehensive approach to the origins of life requires conjugating the actual properties of the developing complex individuals (fusing and dividing protocells, at various stages) with other, population-level features, linked to their collective-evolutionary behavior, under much wider and longer-term parameters. On these lines, we will argue that life, in its most basic sense, here on Earth or anywhere else, demands crossing a high complexity threshold and that the concept of 'inter-identity' can help us realize the different aspects involved in the process. The article concludes by pointing out some of the challenges ahead if we are to integrate the corresponding explanatory frameworks, physiological and evolutionary, in the hope that a more general theory of biology is on its way.

The Origin of a Trans-Generational Organization in the Phenomenon of Biogenesis

One of the central issues of the whole process of biogenesis is how to understand the progressive constitution of a large (in spatial and temporal terms) system that transcends the individual sphere of proto-metabolic organizations and includes collective networks, both synchronous (i.e., proto-ecosystem webs) and asynchronous (i.e., trans-generational protocell populations). This paper analyzes the appearance of a minimal form of reproduction in the process of biogenesis from an organizational perspective. This perspective highlights the problem of how a process transcending the actual organization of the reproducing entities (i.e., protocells) could have a causal power. It is proposed that this problem may be explained if we consider that reproduction generates a kind of feedback between the actual concatenation of the processes of each reproducing cycle and the type continuity that a reliable iteration of these cycles creates. Thus, reproduction generates a new form of self-maintaining system linking "organismal" and "evolutionary" domains, since the consequence of the iteration of self-reproducing cycles is the long-term continuity of a specific type of SM compartmentalized organization, and the functional role of a particular self-reproducing organization (token) lies in its capacity to trigger a diachronic succession of similar self-reproducing organizations, i.e., a lineage.

Thermodynamics of Duplication Thresholds in Synthetic Protocell Systems

Understanding the thermodynamics of the duplication process is a fundamental step towards a comprehensive physical theory of biological systems. However, the immense complexity of real cells obscures the fundamental tensions between energy gradients and entropic contributions that underlie duplication. The study of synthetic, feasible systems reproducing part of the key ingredients of living entities but overcoming major sources of biological complexity is of great relevance to deepen the comprehension of the fundamental thermodynamic processes underlying life and its prevalence. In this paper an abstract-yet realistic-synthetic system made of small synthetic protocell aggregates is studied in detail. A fundamental relation between free energy and entropic gradients is derived for a general, non-equilibrium scenario, setting the thermodynamic conditions for the occurrence and prevalence of duplication phenomena. This relation sets explicitly how the energy gradients invested in creating and maintaining structural-and eventually, functional-elements of the system must always compensate the entropic gradients, whose contributions come from changes in the translational, configurational, and macrostate entropies, as well as from dissipation due to irreversible transitions. Work/energy relations are also derived, defining lower bounds on the energy required for the duplication event to take place. A specific example including real ternary emulsions is provided in order to grasp the orders of magnitude involved in the problem. It is found that the minimal work invested over the system to trigger a duplication event is around ~ 10 - 13 J , which results, in the case of duplication of all the vesicles contained in a liter of emulsion, in an amount of energy around ~ 1 kJ . Without aiming to describe a truly biological process of duplication, this theoretical contribution seeks to explicitly define and identify the key actors that participate in it.

Population Dynamics of Autocatalytic Sets in a Compartmentalized Spatial World

Autocatalytic sets are self-sustaining and collectively catalytic chemical reaction networks which are believed to have played an important role in the origin of life. Simulation studies have shown that autocatalytic sets are, in principle, evolvable if multiple autocatalytic subsets can exist in different combinations within compartments, i.e., so-called protocells. However, these previous studies have so far not explicitly modeled the emergence and dynamics of autocatalytic sets in populations of compartments in a spatial environment. Here, we use a recently developed software tool to simulate exactly this scenario, as an important first step towards more realistic simulations and experiments on autocatalytic sets in protocells.

The origin and early evolution of life in chemical composition space

Life can be viewed as a localized chemical system that sits in the basin of attraction of a metastable dynamical attractor state that remains out of equilibrium with the environment. To explore the implications of this conception, I introduce an abstract coordinate system, chemical composition (CC Space), which summarizes the degree to which chemical systems are out of equilibrium with the bulk environment. A system's chemical disequilibrium (CD) is defined to be proportional to the Euclidean distance between the composition of a small region of physical space, a pixel, and the origin of CC space. Such a model implies that new living states arise through chance changes in local chemical concentration ("mutations") that cause chemical systems to move in CC space and enter the basin of attraction of a life state. The attractor of a life state comprises an autocatalytic set of chemicals whose essential ("keystone") species are produced at a higher rate than they are lost to the environment by diffusion, such that spatial growth of the life state is expected. This framework suggests that new life states are most likely to form at the interface between different physical phases, where the rate of diffusion of keystone species is tied to the low-diffusion regime, whereas food and waste products are subject to the more diffusive regime. Once life nucleates, for example on a mineral surface, it will tend to grow and generate variants as a result of additional mutations that find alternative life states. By jumping from life state to life state, systems can eventually occupy areas of CC space that are too far out of equilibrium with the environment to ever arise in a single mutational step. Furthermore, I propose that variation in the capacity of different surface associated life states to persist and compete may systematically favor states that have higher chemical disequilibrium. The model also suggests a simple and predictable path from surface-associated life to cell-like individuation. This dynamical systems theoretical framework provides an integrated view of the origin and early evolution of life and supports novel empirical approaches.

A Cell-Mimicking Structure Converting Analog Volume Changes to Digital Colorimetric Output with Molecular Selectivity

We herein report a three-component cell-mimicking structure with a peroxidase-like iron oxide nanozyme as the nucleus, a molecularly imprinted hydrogel shell as cytoplasm, and a lipid bilayer membrane. The structure was characterized by cryo and negative stain TEM and also by a calcein leakage test. By introducing charged monomers, the gel shell can swell or shrink in response to salt concentration. By lowering the salt concentration, the gradual "analog" gel volume change was reflected in a switch-like "digital" colorimetric output by the burst of membrane and oxidation of substrates such as 3,3',5,5'-tetramethylbenzidine (TMB). Controlled access was also achieved by using melittin to insert channels cross the membrane, and selective molecular transport was realized by the molecularly imprinted gel. The functions of each component are coupled, and this sophisticated tripartite structure provides a new platform for modular design of new materials. Our cell-mimicking structure is functional and it is complementary to the current protocell work that aims to understand the origin of life.

On the Relation between Chemical Oscillations and Self-Replication

One proposed scenario for the emergence of biochemical oscillations is that they may have provided the basic mechanism behind cellular self-replication by growth and division. However, alternative scenarios not requiring any chemical oscillation have also been proposed. Each of the various protocell models proposed to support one or another scenario comes with its own set of specific assumptions, which makes it difficult to ascertain whether chemical oscillations are required or not for cellular self-replication. This article compares these two cases within a single whole-cell model framework. This model relies upon a membrane embedding a chemical reaction network (CRN) synthesizing all the cellular constituents, including the membrane, by feeding from an external nutrient. Assuming the osmolarity is kept constant, the system dynamics are governed by a set of nonlinear differential equations coupling the chemical concentrations and the surface-area-to-volume ratio. The resulting asymptotic trajectories are used to determine the cellular shape by minimizing the membrane bending energy (within an approximate predefined family of shapes). While the stationary case can be handled quite generally, the oscillatory one is investigated using a simple oscillating CRN example, which is used to identify features that are expected to hold for any network. It is found that cellular self-replication can be reached with or without chemical oscillations, and that a requirement common to both stationary and oscillatory cases is that a minimum spontaneous curvature of the membrane is required for the cell to divide once its area and volume are both doubled. The oscillatory case can result in a greater variety of cellular shape trajectories but raises additional constraints for cellular division and self-replication: (i) the ratio of doubling time to oscillation period should be an integer, and (ii) if the oscillation amplitude is sufficiently high, then the spontaneous curvature must be below a maximum value to avoid early division before the end of the cycle. Because of these additional stringent constraints, it is likely that early protocells did not rely upon chemical oscillations. Biochemical oscillations typical of modern evolved cells may have emerged later through evolution for other reasons (e.g., metabolic advantage) and must have required additional feedback mechanisms for such a self-replicating system to be robust against even slight environmental variations (e.g., temperature fluctuations).

Framing major prebiotic transitions as stages of protocell development: three challenges for origins-of-life research

Conceiving the process of biogenesis as the evolutionary development of highly dynamic and integrated protocell populations provides the most appropriate framework to address the difficult problem of how prebiotic chemistry bridged the gap to full-fledged living organisms on the early Earth. In this contribution we briefly discuss the implications of taking dynamic, functionally integrated protocell systems (rather than complex reaction networks in bulk solution, sets of artificially evolvable replicating molecules, or even these same replicating molecules encapsulated in passive compartments) as the proper units of prebiotic evolution. We highlight, in particular, how the organisational features of those chemically active and reactive protocells, at different stages of the process, would strongly influence their corresponding evolutionary capacities. As a result of our analysis, we suggest three experimental challenges aimed at constructing protocell systems made of a diversity of functionally coupled components and, thereby, at characterizing more precisely the type of prebiotic evolutionary dynamics that such protocells could engage in.

Permeability-driven selection in a semi-empirical protocell model: the roots of prebiotic systems evolution

The origin-of-life problem has been traditionally conceived as the chemical challenge to find the type of molecule and free-solution reaction dynamics that could have started Darwinian evolution. Different autocatalytic and ‘self-replicative’ molecular species have been extensively investigated, together with plausible synthetic pathways that might have led, abiotically, to such a minimalist scenario. However, in addition to molecular kinetics or molecular evolutionary dynamics, other physical and chemical constraints (like compartmentalization, differential diffusion, selective transport, osmotic forces, energetic couplings) could have been crucial for the cohesion, functional integration, and intrinsic stability/robustness of intermediate systems between chemistry and biology. These less acknowledged mechanisms of interaction and molecular control might have made the initial pathways to prebiotic systems evolution more intricate, but were surely essential for sustaining far-from-equilibrium chemical dynamics, given their functional relevance in all modern cells. Here we explore a protocellular scenario in which some of those additional constraints/mechanisms are addressed, demonstrating their ‘system-level’ implications. In particular, an experimental study on the permeability of prebiotic vesicle membranes composed of binary lipid mixtures allows us to construct a semi-empirical model where protocells are able to reproduce and undergo an evolutionary process based on their coupling with an internal chemistry that supports lipid synthesis.

Some conceptual issues in the transition from chemistry to biology

The transition from chemistry to biology is an extremely complex issue because of the huge phenomenological differences between the two domains and because this transition has many different aspects and dimensions. In this paper, I will try to analyze how chemical systems have developed a cohesive, self-maintaining and functionally differentiated system that recruits its organization to stay far from equilibrium. This organization cannot exist but in an individualized form, and yet, it unfolds both a diachronic-historical and a synchronic collective dimension. I will argue that, far from being a problem, these different dimensions of the phenomenon of life, appear as a consequence of the nature of this individualized organization.

Synthetic transitions: towards a new synthesis

The evolution of life in our biosphere has been marked by several major innovations. Such major complexity shifts include the origin of cells, genetic codes or multicellularity to the emergence of non-genetic information, language or even consciousness. Understanding the nature and conditions for their rise and success is a major challenge for evolutionary biology. Along with data analysis, phylogenetic studies and dedicated experimental work, theoretical and computational studies are an essential part of this exploration. With the rise of synthetic biology, evolutionary robotics, artificial life and advanced simulations, novel perspectives to these problems have led to a rather interesting scenario, where not only the major transitions can be studied or even reproduced, but even new ones might be potentially identified. In both cases, transitions can be understood in terms of phase transitions, as defined in physics. Such mapping (if correct) would help in defining a general framework to establish a theory of major transitions, both natural and artificial. Here, we review some advances made at the crossroads between statistical physics, artificial life, synthetic biology and evolutionary robotics.This article is part of the themed issue 'The major synthetic evolutionary transitions'.

Necessary and sufficient conditions for protocell growth

We consider a generic protocell model consisting of any conservative chemical reaction network embedded within a membrane. The membrane results from the self-assembly of a membrane precursor and is semi-permeable to some nutrients. Nutrients are metabolized into all other species including the membrane precursor, and the membrane grows in area and the protocell in volume. Faithful replication through cell growth and division requires a doubling of both cell volume and surface area every division time (thus leading to a periodic surface area-to-volume ratio) and also requires periodic concentrations of the cell constituents. Building upon these basic considerations, we prove necessary and sufficient conditions pertaining to the chemical reaction network for such a regime to be met. A simple necessary condition is that every moiety must be fed. A stronger necessary condition implies that every siphon must be either fed, or connected to species outside the siphon through a pass reaction capable of transferring net positive mass into the siphon. And in the case of nutrient uptake through passive diffusion and of constant surface area-to-volume ratio, a sufficient condition for the existence of a fixed point is that every siphon be fed. These necessary and sufficient conditions hold for any chemical reaction kinetics, membrane parameters or nutrient flux diffusion constants.

Filamentation as primitive growth mode?

Osmotic pressure influences cellular shape. In a growing cell, chemical reactions and dilution induce changes in osmolarity, which in turn influence the cellular shape. Using a protocell model relying upon random conservative chemical reaction networks with arbitrary stoichiometry, we find that when the membrane is so flexible that its shape adjusts itself quasi-instantaneously to balance the osmotic pressure, the protocell either grows filamentous or fails to grow. This behavior is consistent with a mathematical proof. This suggests that filamentation may be a primitive growth mode resulting from the simple physical property of balanced osmotic pressure. We also find that growth is favored if some chemical species are only present inside the protocell, but not in the outside growth medium. Such an insulation requires specific chemical schemes. Modern evolved cells such as E. coli meet these requirements through active transport mechanisms such as the phosphotransferase system.

Experiments on and Numerical Modeling of the Capture and Concentration of Transcription-Translation Machinery inside Vesicles

Synthetic or semi-synthetic minimal cells are those cell-like artificial compartments that are based on the encapsulation of molecules inside lipid vesicles (liposomes). Synthetic cells are currently used as primitive cell models and are very promising tools for future biotechnology. Despite the recent experimental advancements and sophistication reached in this field, the complete elucidation of many fundamental physical aspects still poses experimental and theoretical challenges. The interplay between solute capture and vesicle formation is one of the most intriguing ones. In a series of studies, we have reported that when vesicles spontaneously form in a dilute solution of proteins, ribosomes, or ribo-peptidic complexes, then, contrary to statistical predictions, it is possible to find a small fraction of liposomes (<1%) that contain a very large number of solutes, so that their local (intravesicular) concentrations largely exceed the expected value. More recently, we have demonstrated that this effect (spontaneous crowding) operates also on multimolecular mixtures, and can drive the synthesis of proteins inside vesicles, whereas the same reaction does not proceed at a measurable rate in the external bulk phase. Here we firstly introduce and discuss these already published observations. Then, we present a computational investigation of the encapsulation of transcription-translation (TX-TL) machinery inside vesicles, based on a minimal protein synthesis model and on different solute partition functions. Results show that experimental data are compatible with an entrapment model that follows a power law rather than a Gaussian distribution. The results are discussed from the viewpoint of origin of life, highlighting open questions and possible future research directions.

New Insights into the Growth and Transformation of Vesicles: A Free-Flow Electrophoresis Study

The spontaneous formation of lipid vesicles, in particular fatty acid vesicles, is considered an important physical process at the roots of cellular life. It has been demonstrated previously that the addition of fatty acid micelles to preformed vesicles induces vesicle self-reproduction by a growth-division mechanism. Despite multiple experimental efforts, it remains unresolved how vesicles rearrange upon the addition of fresh membrane-forming compounds, and whether solutes that are initially encapsulated inside the mother vesicles are evenly redistributed among the daughter ones. Here we investigate the growth-division of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC) vesicles, which, following the addition of oleate micelles, form mixed oleate/POPC vesicles. Our approach is based on free-flow electrophoresis (FFE) and cryogenic transmission electronmicroscopy (cryo-TEM). Two new features emerge from this study. FFE analysis unexpectedly reveals that the uptake of oleate micelles by POPC vesicles follows two different pathways depending on the micelles/vesicles ratio. At low oleate molar fractions (<0.35), plain incorporation of oleate into pre-existing POPC vesicles is our dominant observation. In contrast, oleate-rich and oleate-poor daughter vesicles are generated from parent POPC vesicles when the oleate molar fraction exceeds 0.35. Cryo-TEM reveals that when ferritin-filled vesicles grow and divide, some vesicles contain ferritin at increased concentrations, others are empty. Intriguingly, in some cases, ferritin appears to be highly concentrated inside the vesicles. These observations imply a specific redistribution (partitioning) of encapsulated solutes among nascent vesicles during the growth-division steps. We have interpreted our observations by assuming that freshly added oleate molecules are taken-up preferentially (cooperatively) by oleate-rich membrane regions that form spontaneously in POPC/oleate vesicles when a certain threshold (oleate molar fraction ca. 0.35) is surpassed. The proposed cooperative mechanism could be based on differential microscopic constants for oleate/oleic acid dynamics in oleate-rich and oleate-poor membrane regions, which eventually generate populations of oleate-rich and oleate-poor vesicles.

Emergent properties arising from the assembly of amphiphiles. Artificial vesicle membranes as reaction promoters and regulators

This article deals with artificial vesicles and their membranes as reaction promoters and regulators. Among the various molecular assemblies which can form in an aqueous medium from amphiphilic molecules, vesicle systems are unique. Vesicles compartmentalize the aqueous solution in which they exist, independent on whether the vesicles are biological vesicles (existing in living systems) or whether they are artificial vesicles (formed in vitro from natural or synthetic amphiphiles). After the formation of artificial vesicles, their aqueous interior (the endovesicular volume) may become - or may be made - chemically different from the external medium (the exovesicular solution), depending on how the vesicles are prepared. The existence of differences between endo- and exovesicular composition is one of the features on the basis of which biological vesicles contribute to the complex functioning of living organisms. Furthermore, artificial vesicles can be formed from mixtures of amphiphiles in such a way that the vesicle membranes become molecularly, compositionally and organizationally highly complex, similarly to the lipidic matrix of biological membranes. All the various properties of artificial vesicles as membranous compartment systems emerge from molecular assembly as these properties are not present in the individual molecules the system is composed of. One particular emergent property of vesicle membranes is their possible functioning as promoters and regulators of chemical reactions caused by the localization of reaction components, and possibly catalysts, within or on the surface of the membranes. This specific feature is reviewed and highlighted with a few selected examples which range from the promotion of decarboxylation reactions, the selective binding of DNA or RNA to suitable vesicle membranes, and the reactivation of fragmented enzymes to the regulation of the enzymatic synthesis of polymers. Such type of emergent properties of vesicle membranes may have been important for the prebiological evolution of protocells, the hypothetical compartment systems preceding the first cells in those chemical and physico-chemical processes that led to the origin of life.

Minimal conditions for protocell stationary growth

We show that self-replication of a chemical system encapsulated within a membrane growing from within is possible without any explicit feature such as autocatalysis or metabolic closure, and without the need for their emergence through complexity. We use a protocell model relying upon random conservative chemical reaction networks with arbitrary stoichiometry, and we investigate the protocell's capability for self-replication, for various numbers of reactions in the network. We elucidate the underlying mechanisms in terms of simple minimal conditions pertaining only to the topology of the embedded chemical reaction network. A necessary condition is that each moiety must be fed, and a sufficient condition is that each siphon is fed. Although these minimal conditions are purely topological, by further endowing conservative chemical reaction networks with thermodynamically consistent kinetics, we show that the growth rate tends to increase on increasing the Gibbs energy per unit molecular weight of the nutrient and on decreasing that of the membrane precursor.

Emergent chemical behavior in variable-volume protocells

Artificial protocellular compartments and lipid vesicles have been used as model systems to understand the origins and requirements for early cells, as well as to design encapsulated reactors for biotechnology. One prominent feature of vesicles is the semi-permeable nature of their membranes, able to support passive diffusion of individual solute species into/out of the compartment, in addition to an osmotic water flow in the opposite direction to the net solute concentration gradient. Crucially, this water flow affects the internal aqueous volume of the vesicle in response to osmotic imbalances, in particular those created by ongoing reactions within the system. In this theoretical study, we pay attention to this often overlooked aspect and show, via the use of a simple semi-spatial vesicle reactor model, that a changing solvent volume introduces interesting non-linearities into an encapsulated chemistry. Focusing on bistability, we demonstrate how a changing volume compartment can degenerate existing bistable reactions, but also promote emergent bistability from very simple reactions, which are not bistable in bulk conditions. One particularly remarkable effect is that two or more chemically-independent reactions, with mutually exclusive reaction kinetics, are able to couple their dynamics through the variation of solvent volume inside the vesicle. Our results suggest that other chemical innovations should be expected when more realistic and active properties of protocellular compartments are taken into account.

Growth and division in a dynamic protocell model

In this paper a new model of growing and dividing protocells is described, whose main features are (i) a lipid container that grows according to the composition of the molecular milieu (ii) a set of “genetic memory molecules” (GMMs) that undergo catalytic reactions in the internal aqueous phase and (iii) a set of stochastic kinetic equations for the GMMs. The mass exchange between the external environment and the internal phase is described by simulating a semipermeable membrane and a flow driven by the differences in chemical potentials, thereby avoiding to resort to sometimes misleading simplifications, e.g., that of a flow reactor. Under simple assumptions, it is shown that synchronization takes place between the rate of replication of the GMMs and that of the container, provided that the set of reactions hosts a so-called RAF (Reflexive Autocatalytic, Food-generated) set whose influence on synchronization is hereafter discussed. It is also shown that a slight modification of the basic model that takes into account a rate-limiting term, makes possible the growth of novelties, allowing in such a way suitable evolution: so the model represents an effective basis for understanding the main abstract properties of populations of protocells.

Modelling lipid competition dynamics in heterogeneous protocell populations

Recent experimental work in the field of synthetic protocell biology has shown that prebiotic vesicles are able to 'steal' lipids from each other. This phenomenon is driven purely by asymmetries in the physical state or composition of the vesicle membranes, and, when lipid resource is limited, translates directly into competition amongst the vesicles. Such a scenario is interesting from an origins of life perspective because a rudimentary form of cell-level selection emerges. To sharpen intuition about possible mechanisms underlying this behaviour, experimental work must be complemented with theoretical modelling. The aim of this paper is to provide a coarse-grain mathematical model of protocell lipid competition. Our model is capable of reproducing, often quantitatively, results from core experimental papers that reported distinct types vesicle competition. Additionally, we make some predictions untested in the lab, and develop a general numerical method for quickly solving the equilibrium point of a model vesicle population.

Protocell design through modular compartmentalization

De novo synthetic biological design has the potential to significantly impact upon applications such as energy generation and nanofabrication. Current designs for constructing organisms from component parts are typically limited in scope, as they utilize a cut-and-paste ideology to create simple stepwise engineered protein-signalling pathways. We propose the addition of a new design element that segregates components into lipid-bound 'proto-organelles', which are interfaced with response elements and housed within a synthetic protocell. This design is inspired by living cells, which utilize multiple types of signalling molecules to facilitate communication between isolated compartments. This paper presents our design and validation of the components required for a simple multi-compartment protocell machine, for coupling a light transducer to a gene expression system. This represents a general design concept for the compartmentalization of different types of artificial cellular machinery and the utilization of non-protein signal molecules for signal transduction.