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Phenotypic Diversity and Chaos in a Minimal Cell Model ARTICLE IN PRESS Journal of Theoretical Biology 240 (2006) 434–442 www.elsevier.com/locate/yjtbi Phenotypic diversity and chaos in a minimal cell model Andreea Munteanua,Ã, Ricard V. Sole´a,b aICREA-Complex Systems Lab, Universitat Pompeu Fabra (GRIB), Dr. Aiguader 80, 08003 Barcelona, Spain bSanta Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA Received 4 April 2005; received in revised form 10 October 2005; accepted 12 October 2005 Available online 5 December 2005 Abstract Ga´nti’s chemoton model (Ga´nti, 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. r 2005 Elsevier Ltd. All rights reserved. Keywords: Protocell; Origins of life; Chemoton; Cellular networks; Chaos 1. Introduction pursued in the experiments. For the latter, no intentional implications concerning the birth of primordial cells are Cells are the basic building blocks of all life on our sought and its proper functioning is based on present planet. They are the minimal systems able to self-replicate biogenic and/or abiogenic chemistry. in a regular manner and evolve through changes in genetic What are the minimal building blocks of a self- information. Understanding how cellular life emerged is replicating protocell? This is a fundamental question of one of the most challenging problems in life sciences. The both theoretical and practical relevance. At its fundamental early origin of cellular life certainly could not have level, it becomes linked with early conjectures about what is consisted of a complex membrane with a long genome required in order to have self-replication. Pioneering work and intricate metabolic pathways. Instead, it is believed to by von Neumann revealed that a machine able to replicate have been the result of coupled, simple chemical reactions itself needed a few basic subsystems which can be easily that allowed evolution to act on replicating nanostructures. identified with the key components found in real cells in Theoretically, this hypothesis is the basis of the most our current biosphere (von Neumann, 1966; Sipper and relevant modelling approaches available in the literature Reggia, 2001; Freitas and Merkle, 2004). In this context, (see Segre´and Lancet, 2004, for a review). Experimentally, reproduction is a system-property of the total ensemble of the moment of the synthesis of an artificial nanocell based components (Emmeche, 1994). Cells are living systems with on this theory seems to be closer than ever (Bartel and a kinematic structure close to von Neumann’s view. More Unrau, 1999; Szostak et al., 2001; Luisi, 2002; Pohorille precisely, all cells consist of three basic components of and Deamer, 2002; Rasmussen et al., 2004). However, cellular networks: metabolism, information and membrane there is a conceptual difference between an origin-of-life (Ga´nti, 1975; Alberts et al., 2002). These components allow protocell and an artificial protocell whose synthesis is building of new constituents and eventually self-replica- tion. Modern cells use template polymerization to replicate ÃCorresponding author. Tel.: +34 935422834; fax: +34 932213237. their genetic information, which is stored in the same linear E-mail address: [email protected] (A. Munteanu). chemical code (the DNA), thus being a sequence-based 0022-5193/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtbi.2005.10.013 ARTICLE IN PRESS A. Munteanu, R.V. Sole´ / Journal of Theoretical Biology 240 (2006) 434–442 435 information system, with the base-pairing mechanism allowing for unlimited heredity (Szathma´ry and Maynard Smith, 1997). In order to sustain life, cells have to be in a none- qulibrium state, taking free energy from the environment and using raw materials to drive the chemical reactions inside the cell body. In the same spirit, simple minimal protocells should be able to sustain a reliable replication cycle, properly coupling the components in a way that they support each other’s proper functioning, with the driving forces being chemical energy or light. Clearly, once a threshold of chemical complexity is reached, nonlinear phenomena are likely to develop. In this context, it is relevant to ask what types of dynamical patterns are expected to occur when a given set of components is used to build a protocell: are stable replication cycles a generic feature of a coupled set of cellular components? Can nonlinearities jeopardize the presence of a stable cell cycle and potential heredity? Is the complexity of templates a key ingredient in sustaining reliable replication? In this paper, we want to address these questions by means of a numerical study of a minimal cell model in the framework of artificial protocell design. Thus, our inves- Fig. 1. The chemoton: the metabolic unit, the template (information) tigation is directed neither toward extracting explicit subunit and the membrane subsystem. The dots in the template subsystem indicate the iterative development of the template replication from pV V 1 implications related to the origins-of-life studies nor n to pV nV nÀ1. Adapted from Ga´nti (2002). toward modeling present-day cell functioning. However, it is natural that related implications be the by-products of such an investigation. consumption in the copying process, depending on the Our simulations concern a version of the minimal cell number and the length of the template molecules. As the model introduced by Ga´nti (1975) and referred to as the templates are doubled, the number of monomers should chemoton model. A few distinct implementations of the also double in order to ensure the functioning of the chemoton’s chemical reactions network exist in the automata, a condition fulfilled by the autocatalytic nature literature (Be´ke´s, 1975; Csendes, 1984; Fernando and Di of the metabolic subunit. Paolo, 2004) and in the same spirit of these studies, ours is The third subunit is a model of a two-dimensional not aimed at characterizing the chemoton model itself, but membrane enclosing the metabolic and the template a chemoton-like one. We report here on very complex polymerization subsystems. Once the concentration of dynamical patterns, thus suggesting a wealth of potential monomers passes the required threshold value, the dynamical behaviors exhibited by protocells. We also template replication starts and its by-products react with comment on the differences between the studies existent the actual membrane precursors producing real membrane in the literature. molecules which are spontaneously incorporated in the membrane. Thus the membrane’s surface increases and 2. Chemoton model implicitly the chemoton’s volume (for a recent review on replicating vesicles, see Hanczyc and Szostak, 2004). The chemoton model consists of three stoichiometrically The correct functioning of the chemoton lies in the coupled autocatalytic subsystems: the metabolic chemical precise stoichiometric coupling of the three subunits, more network, the template polymerization and the membrane precisely the coordination between the accumulation of subsystem enclosing them all (Fig. 1). The self-reproducing molecules and the surface increase in order to achieve an metabolic network transforms the external nutrients into equilibrium of the osmotic pressure relative to the the chemoton’s internal material necessary for template environment. If the concentration of molecules increases replication and membrane growth (see Ga´nti, 2002, 2003). rapidly, the microsphere bursts when the osmotic pressure The second subunit consists in the self-replication cycle of a reaches a critical value. On the other hand, if the increase homopolymer whose by-product is a specific precursor of the cytosolic and membrane molecules (and thus molecule necessary for membrane growth. The template microsphere surface) is parallel and exponential, the liquid replication has a program-controlling role consisting in the becomes diluted and the sphere decompresses. Ga´nti (2002) fact that the monomers would start to polymerize only argues that the latter instability is solved by the division when they have reached a certain threshold concentration. into two identical spheres in osmotic equilibrium with their The control implies the regulation of the monomers’ environment. At this precise moment, it is implicitly ARTICLE IN PRESS 436 A. Munteanu, R.V. Sole´ / Journal of Theoretical Biology 240 (2006) 434–442 assumed that, due to the concentration decay, an osmotic treatment of the template replication is coupled with a vacuum develops and the membrane sphere is elongated, continuous deterministic treatment of the metabolism and with a neck forming in the middle leading to the membrane subunits. However, no complete stochastic subsequent division. simulation of the chemoton model has been performed so As defined in chemoton theory, the model is based on far. A stochastic implementation
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