Abstract
Endosymbiosis is a type of symbiosis where one species inhabits another species, and both are benefited. It is not trivial to develop models of endosymbiosis because the interaction might involve complex mechanisms, consisting of various steps, and occurring at different levels of the organisms activity. Reaction networks can be applied to model complex ecological interaction mechanisms that can hardly be represented by traditional network approaches. Namely, entities of the reaction network represent either ecological species, resources, or conditions for the ecological interactions to happen, and ecological interaction mechanisms are represented by sequences of reactions (processes) in the reaction network. Hence, an ecological interaction is modeled as a reaction pathway. In this article, we present a mechanistic model of an endosymbiotic interaction using reaction networks. The model includes three representation layers at different timescales (intracellular, intercellular and organismic) model of the interaction. As an example, We provide a numerical analysis of the effects of the endosymbiotic interaction at the intracellular layer.
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Notes
We omit the mathematical formulation of this property for simplicity.
References
Allemand D, Tambutté É, Zoccola D, Tambutté S (2011) Coral calcification, cells to reefs. In: Dubinsky Z, Stambler N (eds) Coral reefs: an ecosystem in transition, pp 119–150. Springer, Dordrecht
Angeli D (2009) A tutorial on chemical reaction network dynamics. Eur J Control 15(3):398–406
Antonelli PL, Rutz SF, Sammarco PW, Strychar KB (2016) Evolution of symbiosis in hermatypic corals: a model of the past, present, and future. Nonlinear Anal Real World Appl 32:389–402
Archibald JM (2015) Endosymbiosis and eukaryotic cell evolution. Curr Biol 25(19):R911–R921
Babcock RC, Bull GD, Harrison PL, Heyward AJ, Oliver JK, Wallace CC, Willis BL (1986) Synchronous spawnings of 105 scleractinian coral species on the Great Barrier Reef. Mar Biol 90(3):379–394
Baker AC (2004) Symbiont diversity on coral reefs and its relationship to bleaching resistance and resilience. In: Rosenberg E, Loya Y (eds) Coral health and disease, pp 177–194. Springer, Berlin, Heidelberg
Benkö G, Centler F, Dittrich D, Flamm C, Stadler BMR, Stadler PF (2009) A topological approach to chemical organizations. Artif Life 15(1):71–88
Black AJ, McKane AJ (2012) Stochastic formulation of ecological models and their applications. Trends Ecol Evol 27(6):337–345
Cunning R, Muller EB, Gates RD, Nisbet RM (2017) A dynamic bioenergetic model for coral-symbiodinium symbioses and coral bleaching as an alternate stable state. J Theor Biol 431:49–62
Davy SK, Allemand D, Weis VM (2012) Cell biology of cnidarian–dinoflagellate symbiosis. Microbiol Mol Biol Rev 76(2):229–261
Detournay O, Weis VM (2011) Role of the sphingosine rheostat in the regulation of cnidarian–dinoflagellate symbioses. Biol Bull 221(3):261–269
Dittrich P, Speroni Di Fenizio P (2007) Chemical organisation theory. Bull Math Biol 69(4):1199–1231
Dittrich P, Winter L (2005) Reaction networks as a formal mechanism to explain social phenomena. In: Proceedings of fourth international workshop on agent-based approaches in economics and social complex systems, pp 9–13
Dittrich P, Winter L (2008) Chemical organizations in a toy model of the political system. Adv Complex Syst 11(04):609–627
Douglas A, Smith DC (1984) The green hydra symbiosis. VIII. Mechanisms in symbiont regulation. Proc R Soc Lond Ser B Biol Sci 221(1224):291–319
Fell DA (1992) Metabolic control analysis: a survey of its theoretical and experimental development. Biochem J 286(Pt 2):313
Fellermann H, Cardelli L (2014) Programming chemistry in DNA-addressable bioreactors. J R Soc Interface 11(99):20130987
Fitt WK (2000) Cellular growth of host and symbiont in a cnidarian–zooxanthellar symbiosis. Biol Bull 198(1):110–120
Gates RD, Muscatine L (1992) Three methods for isolating viable anthozoan endoderm cells with their intracellular symbiotic dinoflagellates. Coral Reefs 11(3):143–145
Gordon BR, Leggat W (2010) Symbiodinium-invertebrate symbioses and the role of metabolomics. Mar drugs 8(10):2546–2568
Hernandez-Agreda A, Gates RD, Ainsworth TD (2017) Defining the core microbiome in corals’ microbial soup. Trends Microbiol 25(2):125–140
Hordijk W, Hein J, Steel M (2010) Autocatalytic sets and the origin of life. Entropy 12(7):1733–1742
Hordijk W, Steel M, Dittrich P (2018) Autocatalytic sets and chemical organizations: modeling self-sustaining reaction networks at the origin of life. New J Phys 20(1):015011
Horn F, Jackson R (1972) General mass action kinetics. Arch Ration Mech Anal 47(2):81–116
Kreyssig P, Wozar C, Peter S, Veloz T, Ibrahim B, Dittrich P (2014) Effects of small particle numbers on long-term behaviour in discrete biochemical systems. Bioinformatics 30(17):i475–i481
Kutschera U, Niklas KJ (2005) Endosymbiosis, cell evolution, and speciation. Theory Biosci 124(1):1–24
Lipschultz F, Cook C (2002) Uptake and assimilation of 15 N-ammonium by the symbiotic sea anemones Bartholomea annulata and Aiptasiapallida: conservation versus recycling of nitrogen. Mar Biol 140(3):489–502
Mandel MJ, Dunn AK (2016) Impact and influence of the natural vibrio-squid symbiosis in understanding bacterial–animal interactions. Front Microbiol 7:1982
Matsumaru N, di Fenizio PS, Centler F, Dittrich P (2006) On the evolution of chemical organizations. In: Proceedings of the 7th German workshop of artificial life, pp 135–146
McAuley PJ (1985) The cell cycle of symbiotic Chlorella. I. The relationship between host feeding and algal cell growth and division. J Cell Sci 77(1):225–239
McAuley PJ, Darrah PR (1990) Regulation of numbers of symbiotic Chlorella by density-dependent division. Philos Trans R Soc Lond Ser B Biol Sci 329(1252):55–63
McAuley PJ (1985) The cell cycle of symbiotic Chlorella. II. The effect of continuous darkness. J Cell Sci 77(1):241–253
McAuley PJ (1982) Temporal relationships of host cell and algal mitosis in the green hydra symbiosis. J Cell Sci 58(1):423–431
McKane AJ, Newman TJ (2004) Stochastic models in population biology and their deterministic analogs. Phys Rev E 70(4):041902
Munzi S, Cruz C, Correa A (2019) When the exception becomes the rule: an integrative approach to symbiosis. Sci Total Environ 672:855–861
Muscatine L, Cernichiari E, Pool RR (1972) Some factors influencing selective release of soluble organic material by zooxanthellae from reef corals. Mar Biol 13:298–308
Muscatine L (1990) The role of symbiotic algae in carbon and energy flux in reef corals. Coral Reefs 25(1.29):75–87
Muscatine L, Ferrier-Pages C, Blackburn A, Gates RD, Baghdasarian G, Allemand D (1998) Cell-specific density of symbiotic dinoflagellates in tropical anthozoans. Coral Reefs 17(4):329–337
Neckelmann N, Muscatine L (1983) Regulatory mechanisms maintaining the Hydra-Chlorella symbiosis. Proc R Soc Lond Ser B Biol Sci 219(1215):193–210
Peter S, Veloz T, Dittrich, P (2011) Feasibility of Organizations—a refinement of chemical organization theory with application to P systems. In: Gheorghe M et al (eds) Membrane computing, pp 325–337. Springer, Berlin
Razeto-Barry P (2012) Autopoiesis 40 years later. A review and a reformulation. Orig Life Evol Biosph 42(6):543–567
Rowan R (1998) Diversity and ecology of zooxanthellae on coral reefs. J Phycol 34(3):407–417
Schnoerr D, Sanguinetti G, Grima R (2017) Approximation and inference methods for stochastic biochemical kinetics-a tutorial review. J Phys A Math Theor 50(9):093001
Sutton DC, Hoegh-Guldberg O (1990) Host-zooxanthella interactions in four temperate marine invertebrate symbioses: assessment of effect of host extracts on symbionts. Biol Bull 178(2):175–186
Varela F, Maturana HR, Uribe R (1974) Autopoiesis: the organization of living systems, its characterization and a model. Biosystems 5(4):187–196
Velegol D, Suhey P, Connolly J, Morrissey N, Cook L (2018) Chemical game theory. Ind Eng Chem Res 57(41):13593–13607
Tanaka Y, Grottoli AG, Matsui Y, Suzuki A, Sakai K (2015) Partitioning of nitrogen sources to algal endosymbionts of corals with long-term 15N-labelling and a mixing model. Ecol Model 309:163–169
Tanaka Y, Suzuki A, Sakai K (2018) The stoichiometry of coral-dinoflagellate symbiosis: carbon and nitrogen cycles are balanced in the recycling and double translocation system. ISME J 12(3):860–868
Taylor CE, Muscatine L, Jefferson DR (1989) Maintenance and breakdown of the Hydra-Chlorella symbiosis: a computer model. Proc R Soc Lond B Biol Sci 238(1292):277–289
Tambutté S, Holcomb M, Ferrier-Pagès C, Reynaud S, Tambuttè É, Zoccola D, Allemand D (2011) Coral biomineralization: from the gene to the environment. J Exp Mar Biol Ecol 408(1–2):58–78
Veloz T, Razeto-Barry P, Dittrich P, Fajardo A (2014) Reaction networks and evolutionary game theory. J Math Biol 68(1–2):181–206
Veloz T (2013) Teoría de organizaciones químicas: un lenguaje formal para la autopoiesis y el medio ambiente. In: Razeto-Barry P, Ramos-Jiliberto R Autopoiesis. Un concepto vivo. Editorial Nueva Civilización, pp 229–245. Santiago, Chile
Veloz T, Razeto-Barry P (2017) Reaction networks as a language for systemic modeling: fundamentals and examples. Systems 5(1):11
Veloz T, Razeto-Barry P (2017) Reaction networks as a language for systemic modeling: on the study of structural changes. Systems 5(1):11
Veloz T, Bassi A, Maldonado P, Razeto P (2018) On the existence of synergies and the separability of closed reaction networks. In: International symposium on molecular logic and computational synthetic biology, pp 105–120. Springer, Cham
Veloz T (2020) The complexity–stability debate, chemical organization theory, and the identification of non-classical structures in ecology. Found Sci 25(1):259–273
Weber MX, Medina M (2012) The role of microalgal symbionts (Symbiodinium) in holobiont physiology. Adv Bot Res 64:119–140
Wernegreen JJ (2004) Endosymbiosis: lessons in conflict resolution. PLoS Biol 2(3):e68
Wilkinson DM (2001) At cross purposes. Nature 412(6846):485
Wilkinson DJ (2011) Stochastic modelling for systems biology. CRC Press, Boca Raton
Yellowlees D, Rees TAV, Leggat W (2008) Metabolic interactions between algal symbionts and invertebrate hosts. Plant Cell Environ 31(5):679–694
Acknowledgements
This work was partially supported by Grant ID# 61733 John Templeton Foundation (Tomas Veloz) and ANID-PFCHA/Doctorado nacional/2019-21191885 (Daniela Flores)
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Veloz, T., Flores, D. Toward endosymbiosis modeling using reaction networks. Soft Comput 25, 6831–6840 (2021). https://doi.org/10.1007/s00500-020-05530-2
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DOI: https://doi.org/10.1007/s00500-020-05530-2