Skip to main content
SpringerLink
Log in

Simulating a Model of Metabolic Closure

  • Thematic Issue Article: Synthesis (σύνθεσις)
  • Published:
Biological Theory Aims and scope Submit manuscript

Abstract

The goal of synthetic biology is to create artificial organisms. To achieve this it is essential to understand what life is. Metabolism-replacement systems, or (M, R)-systems, constitute a theory of life developed by Robert Rosen, characterized in the statement that organisms are closed to efficient causation, which means that they must themselves produce all the catalysts they need. This theory overlaps in part with other current theories, including autopoiesis, the chemoton, and autocatalytic sets, all of them invoking some idea of closure. A simple model of an (M, R)-system has been implemented in the computer, and behaves in ways that may shed light on the requirements for a prebiotic self-organizing system. In addition to a trivial steady state in which nothing happens, it can establish a non-trivial steady state in which all intermediates have finite concentrations, with their rates of degradation balanced by their rates of synthesis. The system can be regenerated from the set of food components plus a single intermediate, and maintain itself in that state indefinitely, despite continuous degradation. At the very low compartment volumes that may have existed in prebiotic conditions, for example in cavities in minerals, or in micelles formed by simple amphiphiles, statistical fluctuations in the numbers of molecules need to be taken into account. With the stochastic approach there is no non-trivial steady state in strict mathematical terms, because the system will always collapse to the trivial state after sufficient time. However, the average time before collapse is so long for volumes greater than \(10^{-19}\;{\textsc{l}}\) (much smaller than the volume of the order of \(10^{-15}\;{\textsc{l}}\) for a typical bacterial cell) that for practical purposes the self-maintaining state of non-null concentrations becomes significant, recalling the situation of bistability that is observed in deterministic analysis. In turn, there exists a minimum size below which the self-organizing system cannot maintain itself on chemically relevant time scales. The value of the critical volume depends on the particular concentrations and rate constants assumed, but the principle could apply generally.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. This sort of approximation was useful when computer time and storage were orders of magnitude more expensive than they are now. Today one would simply store the entire table, or calculate the appropriate value to any desired precision with the proper statistical theory.

  2. It is an everyday observation that the chemical output of any organism is different from the food taken in, and it should be obvious from thermodynamic considerations that that must be the case.

  3. The collapse would not be totally irreversible if we allow uncatalyzed production of minimal amounts of intermediates: in this case the system could regain the non-trivial steady state if all of the degradation rate constants were sufficiently low.

  4. For example, for k = 0.1 s−1, a starting concentration of STU of at least \(0.135\; \text{m}{\textsc{m}}\) would allow the whole system to construct itself.

  5. This is much smaller than the volume of more than \(10^{-15}\; {\textsc{l}}\; (1\; \upmu\text{m}^3\)) for a bacterium such as Escherichia coli.

  6. In their recent paper on osmotic structures resembling Leduc’s osmotic gardens, Barge et al. (2012) do not give estimates of the internal volumes of their structures. They have informed us (Barge, personal communication, 8 March 2012) that although these volumes are very difficult to estimate with any accuracy they are certainly orders of magnitude larger than the volumes we are considering here.

  7. It is easy to forget that supposedly improbable events occur very frequently. In a human population of 109 individuals the probability that one of them will experience an event of probability 10−9 at any particular moment is close to certainty.

  8. This is just one illustration of the point that all current theories of life lack some features that an ideal theory ought to have (Letelier et al. 2011). On the other hand the chemical nature of the catalysts—absolutely necessary for the specificity that any self-organizing set of reactions must have—is too vague in autopoiesis and the chemoton to be satisfactory.

References

  • Barge LM, Doloboff IJ, White LM, Stucky GD, Russell MJ, Kanik I (2012) Characterization of iron–phosphate–silicate chemical garden structures. Langmuir 28(8):3714–3721 doi:10.1021/la203727g

    Article  Google Scholar 

  • Brenner K, You L, Arnold FH (2008) Engineering microbial consortia: a new frontier in synthetic biology. Trends Biotechnol. 26(9):483–489 doi:10.1016/j.tibtech.2008.05.004

    Article  Google Scholar 

  • Briggs DE (1962) Simplification of assay of enzymes using non-linear reaction-progress graphs. Enzymologia 24(2):97–104

    Google Scholar 

  • Briones C, Stich M, Manrubia SC (2009) The dawn of the RNA World: toward functional complexity through ligation of random RNA oligomers. RNA Publ RNA Soc 15(5):743–749 doi:10.1261/rna.1488609

    Article  Google Scholar 

  • Cárdenas ML, Letelier JC, Gutierrez C, Cornish-Bowden A, Soto-Andrade J (2010) Closure to efficient causation, computability and artificial life. J Theor Biol 263(1):79–92 doi:10.1016/j.jtbi.2009.11.010

    Article  Google Scholar 

  • Chemero A, Turvey MT (2006) Complexity and closure to efficient cause. In: Ruiz-Mirazo K, Barandiaran R (eds) ALIFE X: workshop on artificial autonomy. MIT Press, Cambridge, MA, pp 13–18

    Google Scholar 

  • Chen IA, Walde P (2010) From self-assembled vesicles to protocells. Cold Spring Harbor Perspect. Biol. 2(7) doi:10.1101/cshperspect.a002170

  • Chiarabelli C, Stano P, Anella F, Carrara P, Luisi P (2012) Approaches to chemical synthetic biology. FEBS Lett 586(15):2138–2145 doi:10.1016/j.febslet.2012.01.014

    Article  Google Scholar 

  • Cornish-Bowden A, Cárdenas ML, Letelier JC, Soto-Andrade J (2007) Beyond reductionism: metabolic circularity as a guiding vision for a real biology of systems. Proteomics 7(6):839–845 doi:10.1002/pmic.200600431

    Article  Google Scholar 

  • de la Mettrie JJO (1748) L’Homme machine. Elie Luzac, Leyden

    Google Scholar 

  • Eigen M, Schuster P (1977) The hypercycle—a principle of natural self-organization. A. Emergence of the hypercycle. Naturwissenschaften 64(11):541–565 doi:10.1007/BF00450633

    Article  Google Scholar 

  • Gánti T (2003) The principles of life. Oxford University Press, Oxford

    Book  Google Scholar 

  • Gibson DG, Glass JI, Lartigue C, Noskov VN, Chuang RY, Algire MA, Benders GA, Montague MG, Ma L, Moodie MM, Merryman C, Vashee S, Krishnakumar R, Assad-Garcia N, Andrews-Pfannkoch C, Denisova EA, Young L, Qi ZQ, Segall-Shapiro TH, Calvey CH, Parmar PP, Hutchison III, CA, Smith HO, Venter JC (2010) Creation of a bacterial cell controlled by a chemically synthesized genome. Science 329(5987): 52–56

    Article  Google Scholar 

  • Gillespie DT (1976) A general method for numerically simulating stochastic time evolution of coupled chemical-reactions. J Comput Phys 22(4):403–434 doi:10.1016/0021-9991(76)90041-3

    Article  Google Scholar 

  • Gillespie DT (1977) Exact stochastic simulation of coupled chemical-reactions. J Phys Chem 81(25):2340–2361 doi:10.1021/j100540a008

    Article  Google Scholar 

  • Hanczyc MM, Fujikawa SM, Szostak JW (2003) Experimental models of primitive cellular compartments: encapsulation, growth, and division. Science 302(5645):618–622 doi:10.1126/science.1089904

    Article  Google Scholar 

  • Hoops S, Sahle S, Gauges R, Lee C, Pahle J, Simus N, Singhal M, Xu L, Mendes P, Kummer U (2006) COPASI—a Complex pathway simulator. Bioinformatics 22(24):3067–3074 doi:10.1093/bioinformatics/btl485

    Article  Google Scholar 

  • Hordijk W, Fontanari JF (2003) Catalytic reaction sets, decay, and the preservation of information. In: Hexmoor H (ed) International conference on integration of knowledge intensive multi-agent systems: KIMAS’03: Modeling, exploration, and engineering. IEEE, New York, pp 133–138 doi:10.1109/KIMAS.2003.1245035

  • Kauffman SA (1986) Autocatalytic sets of proteins. J Theor Biol 119(1):1–24 doi:10.1016/S0022-5193(86)80047-9

    Article  Google Scholar 

  • Leduc S (1912) La Biologie Synthétique. Poinat, Paris

    Google Scholar 

  • Letelier JC, Cárdenas ML, Cornish-Bowden A (2011) From L’Homme machine to metabolic closure: steps towards understanding life. J Theor Biol 286:100–113 doi:10.1016/j.jtbi.2011.06.033

    Article  Google Scholar 

  • Letelier JC, Kuboyama T, Yasuda TH, Cárdenas ML, Cornish-Bowden A (2005) A self-referential equation, f(f) = f, obtained using the theory of (M, R) systems: overview and applications. In: Anai H, Horimoto K (eds) Algebraic biology. Universal Academy Press, Tokyo, pp 115–126

    Google Scholar 

  • Letelier JC, Soto-Andrade J, Guíñez Abarzua F., Cornish-Bowden A., Cárdenas ML (2006) Organizational invariance and metabolic closure: analysis in terms of (M, R) systems. J Theor Biol 238(4):949–961 doi:10.1016/j.jtbi.2005.07.007

    Article  Google Scholar 

  • Luisi PL (2006) The emergence of life. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Martin W, Russell MJ (2003) On the origins of cells: a hypothesis for the evolutionary transitions from abiotic geochemistry to chemoautotrophic prokaryotes, and from prokaryotes to nucleated cells. Phil Trans R Soc B 358(1429):59–83 doi:10.1098/rstb.2002.1183

    Article  Google Scholar 

  • Maturana H, Varela F (1980) Autopoiesis and cognition: the realisation of the living. D. Reidel Publishing Company, Dordrecht

    Book  Google Scholar 

  • Mill JS (1846) A system of logic. Harper & Brothers, New York, pp 211

    Google Scholar 

  • Miller JC, Tan S, Qiao G, Barlow KA, Wang J, Xia DF, Meng X, Paschon DE, Leung E, Hinkley SJ, Dulay GP, Hua KL, Ankoudinova I, Cost GJ, Urnov FD, Zhang HS, Holmes MC, Zhang L, Gregory PD, Rebar EJ (2011) A TALE nuclease architecture for efficient genome editing. Nat Biotechnol 29(2):143–148 doi:10.1038/nbt.1755

    Article  Google Scholar 

  • Morán F, Moreno A, Minch E, Montero F (1996) Further steps towards a realistic description of the essence of life. In: Langton CG, Shimohara K (eds) Artificial life V. MIT Press, Cambridge, MA, pp 255–263

    Google Scholar 

  • Piedrafita G, Montero F, Morán F, Cárdenas ML, Cornish-Bowden A (2010) A simple self-maintaining metabolic system: robustness, autocatalysis, bistability. PLoS Comput Biol 6(8):e1000,872 doi:10.1371/journal.pcbi.1000872

    Article  Google Scholar 

  • Piedrafita G, Cornish-Bowden A, Morán F, Montero F (2012a) Size matters: influence of stochasticity on the self-maintenance of a simple model of metabolic closure. J Theor Biol 300:143–151

    Article  Google Scholar 

  • Piedrafita G, Ruiz-Mirazo K, Monnard PA, Cornish-Bowden A, Montero F (2012b) Viability conditions for a compartmentalized protometabolic system: a semi-empirical approach. PLoS ONE 7:e39,480

    Article  Google Scholar 

  • Rosen R (1971) Some realizations of (M, R)-systems and their interpretation. Bull Math Biophys 33(3):303–319 doi:10.1007/BF02476776

    Article  Google Scholar 

  • Rosen R (1973) On the dynamical realization of (M, R)-systems. Bull Math Biol 35(1-2):1–9

    Article  Google Scholar 

  • Rosen R (1991) Life itself. Columbia University Press, New York

    Google Scholar 

  • Ruiz-Mirazo K, Piedrafita G, Ciriaco F, Mavelli F (2011) Stochastic simulations of mixed-lipid compartments: from self-assembling vesicles to self-producing protocells. Adv Exp Med Biol 696:689–696

    Article  Google Scholar 

  • Sánchez-Izquierdo F, Blanco P, Busqué F, Alibés R, de March P, Figueredo Galimany M, Font J, Parella T (2007) Total synthesis of the putative structure of stemonidine: the definitive proof of misassignment. Org Lett 9(9):1769–1772 doi:10.1021/ol070486p

    Article  Google Scholar 

  • Schrödinger E (1944) What is life? Cambridge University Press, Cambridge, UK

    Google Scholar 

  • Smith MT, Cornish-Bowden A, Briggs DE (1979) Determination of barley α-amylase activity. J Inst Brew 85(4):157–159

    Article  Google Scholar 

  • Szathmáry E (2007) Coevolution of metabolic networks and membranes: the scenario of progressive sequestration. Philos Trans R Soc 362(1486):1781–1787 doi:10.1098/rstb.2007.2070

    Article  Google Scholar 

  • Szostak JW, Bartel DP, Luisi PL (2001) Synthesizing life. Nature 409(6818):387–390

    Article  Google Scholar 

  • Walde P (2006) Surfactant assemblies and their various possible roles for the origin(s) of life. Orig Life Evol Biosphere 36(2):109–150 doi:10.1007/s11084-005-9004-3

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by grant BFU2009-12895-C02-02 (Ministerio de Ciencia e Innovación, Spain). GP acknowledges support from PhD scholarship FPU (Formación del Profesorado Universitario, Ministry of Education, Spain). AC-B and MLC were supported by the Centre National de la Recherche Scientifique.

Author information

Authors and Affiliations

  1. Unité de Bioénergétique et Ingénierie des Protéines, Centre National de la Recherche Scientifique, Aix-Marseille Université, Marseille, France

    Athel Cornish-Bowden & María Luz Cárdenas

  2. Facultad de Ciencias Químicas, Universidad Complutense de Madrid, Madrid, Spain

    Gabriel Piedrafita, Federico Morán & Francisco Montero

Authors
  1. Athel Cornish-Bowden
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gabriel Piedrafita
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Federico Morán
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. María Luz Cárdenas
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Francisco Montero
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Athel Cornish-Bowden.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cornish-Bowden, A., Piedrafita, G., Morán, F. et al. Simulating a Model of Metabolic Closure. Biol Theory 8, 383–390 (2013). https://doi.org/10.1007/s13752-013-0132-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13752-013-0132-0

Keywords

Search

Navigation