PACE REPORT

The emergence of cellular life is one of the major transitions in evolution. It involves the emergence of a well-defined boundary allowing metabolism and genetic information to be part of a well-defined compartment. Theoretical models and experimental data support the idea that simple protocells should be obtainable from a simple systems of coupled reactions dealing with the three previous components. The building of an artificial cell would be a fundamental breakthrough in our understanding of life, its origins and evolution, not to mention a wide array of potential medical and technological applications.

Understanding the origins of life requires the understanding of a few key events that define the so called major transitions in evolution. One of them is the emergence of cellular structures. Cellularization allowed the emergence of separated compartments (the protocells) able to evolve and maintain a well-defined integrity of all the components.  We have developed several modelling tools allowing to explore the behavior of in silico models of protocell and replicator dynamics. Using dynamical instabilities inspired in Turing reaction-diffusion models, we have developed a new class of models defining a RD mechanism coupled with a flexible membrane container. Using this approach, we have been able to show that self-replicating protocells including membrane and metabolism can be obtained under physically and chemically reasonable conditions. Membrane growth under non-uniform osmotic pressure could be the basis for devoloping  new active mechanisms, which control protocell division cycles. Here we present different metabolic scenarios whics.h are able to create non-uniform osmotic pressures and the simulation tools to study the membrane shape evolution in these contexts.

A first theoretical step when looking at replicator dynamics involves considering nonlinear interactions with no explicit or implicit definition of cell membranes. Models of this type deal with generic features exhibited by replicator dynamics, which have been widely explored over the last decades. We are exploring a new class of replicator dynamics models involving as particular cases hipercyclic organization (see Hypercycles: an introduction) . Both spatial degrees of freedom and host-parasite dynamics are being analysed. By using an explicit definition of genome complexity in terms of small strings of traits, it is possible to follow the evolutionary dynamics of simple models of replicators and to explore how the presence of parasites can either destroy the organization of cycles or instead trigger the emergence of complexity. Since several possible genomes can be simultaneously present, these models actually explore a network of interacting replicators. The models will be extended from the standard deterministic behavior to explicit stochastic implementation. We will extend our results to models where compartents are allowed to be formed, so that sets of replicators can be eventually isolated from each other and new types of interactions, now at the protocellular level, can emerge.

The most studied examples of the two types of reaction-diffusion systems are the Meinhardt system (Gierer &Meinhardt; 2000) and the diffusive Gray-Scott system (Pearson 1993), respectively. Interesting enough, the replication characteristic is a particularity of the diffusive Gray-Scott model alone, which makes it the ideal model for developmental research - see more details. In such cases, cell-like localized structures grow, deform and make replica of themselves until they occupy the entire space , a theoretical result that also was confirmed experimentally (Lee, McCormick, Swinney & Pearson, 1994). This model was also a target for investigations resulting from the considerable interest of the scientific community in the implications of stochasticity in the evolution of biological and chemical systems. In particular, Lesmes et al. (2003) have carried out the first study of the noise-controlled pattern formation in the Pearson model, with emphasis on the self-replicating patterns. They found that for a specific set of parameters' values, the noise drives the system from the non-multiplicative, stripe-like pattern to the spot-multiplication one . Our results suggest the existence of an interval of optimum noise-intensity values leading to a maximum number of spots, rather than a single optimum value, as suggested by Lesmes and co-workers. Other models from the literature consider hypercycle networks modeling RNA-like polymers catalysing the replication of each other in a cyclic way (Cronhjort & Bloomberg, 1997). They obtain the formation and division of clusters or "spots" and will be also explored.

Abstract models of inimal cells, consisting of a collectively autocatalytic network of reactions enclosed within a membrane, are a first step in modelling simple cellular replicators. An example of them is the so called Ganti's chemoton. The chemoton differs from the minimal autopoiesis model suggested by Varela and co-workers in explicitly including a genetic subsystem. It is also rather more detailed in its analysis of the required chemical dynamics, and aims at supporting self-reproduction by growth and fission even in the minimal version. The chemoton has been presented mainly in papers and books by his creator, Tibor Ganti. Most of this work has been done in terms of formalizing the connection between the different components and how they relate each other. A few attempts to explore the real dynamical behavior have also been conducted, providing evidence for a primitive form of replicating cellular dynamics which exhibits some interesting homeostatic capabilities. We will explore the a whole family of simple chemoton-like models of replicating protocells both involving deterministic and stochastic dynamics. These models will provide useful intuition for further exploration of models with explicit membrane dynamics. Since they contain three coupled components (metabolism, membrane and information molecules) they are actually describable in terms of networks of reactions. We will study their stability, time evolution and adaptation to different external conditions.

A previous step before a realistic model of realistic protocell dynamics involves considering toy models of replicating systems forming aggregates in space. One possible approach involves considering dynamics of membrane components and water as happening on a discrete, regular lattice where each site can be occupied by a single molecule or part of it. Interactions include a simplified energy function which takes into account physical interactions through an Ising-like Hamiltonian. Molecular movements in such lattice model are allowed provided that energy is (tipically) minimized. The rules include a Boltzmann probabilistic update that explicitly takes into account the noise. Beyond the modelling of micelle formation and the presence of phase transitions as non-covalent forces are changed, we will also explore evolutionary dynamics of lipid aggregates. By using a given pool of available lipid molecules and other precursors, it is possible to model the emergence of compositional genomes and to observe the selection of whole replicating networks of interacting molecules. The model will be completed by considering in- and out-flow of particles thus mimicking microfluidic environments.

Towards the modeling of more realistic protocells, consideration of more accurate physical interactions is required. Our main goal is to provide a platform that includes the basic implementation of a physically reasonable picture of micelle formation coupled with evolving dynamics. We will consider a set of minimal reaction networks coupled to membrane instability that will help understand the role of molecular fluctuations in the evolution of protocells. Using different types of molecular sets we should be able to characterize, at this level, the impact of external and internal noise on protocell evolution and relevant types of evolution towards stable, robust replicating entities. The emergence of parasites, symbiotic relations and other forms of cell-cell interaction will be also explored.