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Computational Universality of Fungal Sandpile Automata

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Fungal Machines

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 47))

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Abstract

Hyphae within the mycelia of the ascomycetous fungi are compartmentalised by septa. Each septum has a pore that allows for inter-compartmental and inter-hyphal streaming of cytosol and even organelles. The compartments, however, have special organelles, Woronin bodies, that can plug the pores. When the pores are blocked, no flow of cytoplasm takes place. Inspired by the controllable compartmentalisation within the mycelium of the ascomycetous fungi we designed two-dimensional fungal automata. A fungal automaton is a cellular automaton where communication between neighbouring cells can be blocked on demand. We demonstrate computational universality of the fungal automata by implementing sandpile cellular automata circuits there. We reduce the Monotone Circuit Value Problem to the Fungal Automaton Prediction Problem. We construct families of wires, cross-overs and gates to prove that the fungal automata are P-complete.

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References

  1. Smith, M.L., Bruhn, J.N., Anderson, J.B.: The fungus Armillaria bulbosa is among the largest and oldest living organisms. Nat. 356(6368), 428 (1992)

    Google Scholar 

  2. Ferguson, B.A., Dreisbach, T.A., Parks, C.G., Filip, G.M., Schmitt, C.L.: Coarse-scale population structure of pathogenic armillaria species in a mixed-conifer forest in the blue mountains of northeast Oregon. Can. J. For. Res. 33(4), 612–623 (2003)

    Article  Google Scholar 

  3. Jaffe, M.J., Leopold, A.C., Staples, R.C.: Thigmo responses in plants and fungi. Am. J. Bot. 89(3), 375–382 (2002)

    Google Scholar 

  4. Kung, C.: A possible unifying principle for mechanosensation. Nat. 436(7051), 647 (2005)

    Google Scholar 

  5. Van Aarle, I.M., Olsson, P.A., Söderström, B.: Arbuscular mycorrhizal fungi respond to the substrate ph of their extraradical mycelium by altered growth and root colonization. New Phytol. 155(1), 173–182 (2002)

    Google Scholar 

  6. Fomina, M., Ritz, K., Gadd G.M.: Negative fungal chemotropism to toxic metals. FEMS Microbiol. Lett. 193(2), 207–211 (2000)

    Google Scholar 

  7. Howitz, K.T., Sinclair, D.A.: Xenohormesis: sensing the chemical cues of other species. Cell. 133(3), 387–391 (2008)

    Google Scholar 

  8. Purschwitz, J., Müller, S., Kastner, C., Fischer, R.: Seeing the rainbow: light sensing in fungi. Curr. Opin. Microbiol. 9(6), 566–571 (2006)

    Article  Google Scholar 

  9. Moore, D.: Perception and response to gravity in higher fungi-a critical appraisal. New Phytol. 117(1), 3–23 (1991)

    Article  MathSciNet  Google Scholar 

  10. Slayman, C.L., Long, W.S., Gradmann, D.: “Action potentials” in Neurospora crassa, a mycelial fungus. Biochimica et Biophysica Acta (BBA)—Biomembranes. 426(4), 732–744 (1976)

    Google Scholar 

  11. Olsson, S., Hansson, B.S.: Action potential-like activity found in fungal mycelia is sensitive to stimulation. Naturwissenschaften 82(1), 30–31 (1995)

    Article  Google Scholar 

  12. Adamatzky, A.: On spiking behaviour of oyster fungi Pleurotus djamor. Sci. Rep. 7873 (2018)

    Google Scholar 

  13. Adamatzky, A., Tuszynski, J., Pieper, J., Nicolau, D.V., Rinalndi, R., Sirakoulis, G., Erokhin, V., Schnauss, J., Smith, D.M.: Towards cytoskeleton computers. A proposal. In: Adamatzky, A., Akl, S., Sirakoulis, G. (eds.) From Parallel to Emergent Computing. CRC Group/Taylor & Francis (2019)

    Google Scholar 

  14. Adamatzky, A., Tegelaar, M., Wosten, H.A.B., Powell, A.L., Beasley, A.E., Mayne, R.: On Boolean gates in fungal colony. Biosyst. 193, 104138 (2020)

    Google Scholar 

  15. Adamatzky, A., Goles, E., Martinez, G., Tsompanas, M.-A., Tegelaar, M., Wosten, H.A.B.: Fungal automata (2020). ar**v:2003.08168

  16. Dhar, D.: Self-organized critical state of sandpile automaton models. Phys. Rev. Lett. 64(14), 1613 (1990)

    Google Scholar 

  17. Goles, E.: Sand pile automata. In Annales de l’IHP Physique théorique 56, 75–90 (1992)

    MathSciNet  MATH  Google Scholar 

  18. Christensen, K., Fogedby, H.C., Jensen, H.J.: Dynamical and spatial aspects of sandpile cellular automata. J. Stat. Phys. 63(3–4), 653–684 (1991)

    Google Scholar 

  19. Bitar, J., Goles, E.: Parallel chip firing games on graphs. Theor. Comput. Sci. 92(2), 291–300 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  20. Goles, E.: Sand piles, combinatorial games and cellular automata. In: Instabilities and Nonequilibrium Structures III, pp. 101–121. Springer (1991)

    Google Scholar 

  21. Moore, R.T., McAlear, J.H.: Fine structure of Mycota. 7. observations on septa of ascomycetes and basidiomycetes. Am. J. Bot. 49(1), 86–94 (1962)

    Google Scholar 

  22. Lew, R.R.: Mass flow and pressure-driven hyphal extension in neurospora crassa. Microbiol. 151(8), 2685–2692 (2005)

    Google Scholar 

  23. Bleichrodt, R.-J., van Veluw, G.J., Recter, B., Maruyama, J.-I., Kitamoto, K., Wösten, H.A.B.: Hyphal heterogeneity in a spergillus oryzae is the result of dynamic closure of septa by Woronin bodies. Mol. Microbiol. 86(6), 1334–1344 (2012)

    Google Scholar 

  24. Bleichrodt, R.-J., Hulsman, M., Wösten, H.A.B., Reinders, M.J.T.: Switching from a unicellular to multicellular organization in an aspergillus niger hypha. MBio. 6(2), e00111–15 (2015)

    Google Scholar 

  25. Tegelaar, M., Bleichrodt, R.-J., Nitsche, B., Ram, A.F.J., Wösten, H.A.B.: Subpopulations of hyphae secrete proteins or resist heat stress in aspergillus oryzae colonies. Environ. Microbiol. 22(1), 447–455 (2020)

    Google Scholar 

  26. Goles, E., Margenstern, M.: Sand pile as a universal computer. Int. J. Mod. Phys. C 7(02), 113–122 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  27. Goles, E., Margenstern, M.: Universality of the chip-firing game. Theor. Comput. Sci. 172(1–2), 121–134 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  28. Chessa, A., Stanley, H.E., Vespignani, A., Zapperi, S.: Universality in sandpiles. Phys. Rev. E. 59(1), R12 (1999)

    Google Scholar 

  29. Moore, C., Nilsson, M.: The computational complexity of sandpiles. J. Stat. Phys. 96(1–2), 205–224 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  30. Gajardo, A., Goles, E.: Crossing information in two-dimensional sandpiles. Theor. Comput. Sci. 369(1–3), 463–469 (2006)

    Google Scholar 

  31. Martin, B.: On Goles’ universal machines: a computational point of view. Theor. Comput. Sci. 504, 83–88 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  32. Tenney, K., Hunt, I., Sweigard, J., Pounder, J.I., McClain, C., Bowman, E.J., Bowman, B.J.: Hex-1, a gene unique to filamentous fungi, encodes the major protein of the Woronin body and functions as a plug for septal pores. Fungal Genet. Biol. 31(3), 205–217 (2000)

    Google Scholar 

  33. Reichle, R.E., Alexander, J.V.: Multiperforate septations, Woronin bodies, and septal plugs in fusarium. J. Cell Biol. 24(3), 489 (1965)

    Google Scholar 

  34. Tey, W.K., North, A.J., Reyes, J.L., Lu, Y.F., Jedd, G.: Polarized gene expression determines Woronin body formation at the leading edge of the fungal colony. Mol. Biol. Cell. 16(6), 2651–2659 (2005)

    Google Scholar 

  35. Jedd, G., Chua, N.-H.: A new self-assembled peroxisomal vesicle required for efficient resealing of the plasma membrane. Nat. Cell Biol. 2(4), 226–231 (2000)

    Article  Google Scholar 

  36. Steinberg, G., Harmer, N.J., Schuster, M., Kilaru, S.: Woronin body-based sealing of septal pores. Fungal Genet. Biol. 109, 53–55 (2017)

    Google Scholar 

  37. Bleichrodt, R.-J., Vinck, A., Read, N.D., Wösten, H.A.B.: Selective transport between heterogeneous hyphal compartments via the plasma membrane lining septal walls of aspergillus niger. Fungal Genet. Biol. 82, 193–200 (2015)

    Google Scholar 

  38. Wolfram, S.: Cellular Automata and Complexity: Collected Papers. Addison-Wesley Pub. Co. (1994)

    Google Scholar 

  39. Goles, E., Margenstern, M.: Universality of the chip-firing game. Theor. Comput. Sci. 172(1–2), 121–134 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  40. Moore, C., Nilsson, M.: The computational complexity of sandpiles. J. Stat. Phys. 96(1–2), 205–224 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  41. Greenlaw, R., Hoover, H.J., Ruzzo, W.L., et al.: Limits to Parallel Computation: P-Completeness Theory. Oxford University Press on Demand (1995)

    Google Scholar 

  42. Margolus, N.: Physics-like models of computation. Phys. D Nonlinear Phenom. 10(1), 81–95 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  43. Margolus, N.: Universal cellular automata based on the collisions of soft spheres. In: Adamatzky, A (ed.) Collision-Based Computing, pp. 107–134. Springer (2002)

    Google Scholar 

  44. Morita, K., Harao, M.: Computation universality of one-dimensional reversible (injective) cellular automata. IEICE Trans. (1976–1990), 72(6), 758–762 (1989)

    Google Scholar 

  45. Durand-Lose, J.O.: Reversible space–time simulation of cellular automata. Theor. Comput. Sci. 246(1–2), 117–129 (2000)

    Google Scholar 

  46. Imai, K., Morita, K.: A computation-universal two-dimensional 8-state triangular reversible cellular automaton. Theor. Comput. Sci. 231(2), 181–191 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  47. Durand-Lose, J.: Representing reversible cellular automata with reversible block cellular automata. Discret. Math. Theor. Comput. Sci. 145, 154 (2001)

    MATH  Google Scholar 

  48. Tegelaar, M., Wösten, H.A.B.: Functional distinction of hyphal compartments. Sci. Rep. 7(1), 1–6 (2017)

    Article  Google Scholar 

  49. Soundararajan, S., Jedd, G., Li, X., Ramos-Pamploña, M., Chua, N.H., Naqvi, N.I.: Woronin body function in magnaporthe grisea is essential for efficient pathogenesis and for survival during nitrogen starvation stress. Plant Cell. 16(6), 1564–1574 (2004)

    Google Scholar 

  50. Jedd, G.: Fungal evo-devo: organelles and multicellular complexity. Trends Cell Biol. 21(1), 12–19 (2011)

    Article  Google Scholar 

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Acknowledgements

AA, MT, HABW have received funding from the European Union’s Horizon 2020 research and innovation programme FET OPEN “Challenging current thinking” under grant agreement No 858132. EG residency in UWE has been supported by funding from the Leverhulme Trust under the Visiting Research Professorship grant VP2-2018-001 and from the project the project 1200006, FONDECYT-Chile.

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Authors and Affiliations

  1. Faculty of Engineering and Science, University of Adolfo Ibáñez, Santiago, Chile

    Eric Goles & Michail-Antisthenis Tsompanas

  2. Unconventional Computing Laboratory, UWE, Bristol, UK

    Andrew Adamatzky & Genaro J. Martínez

  3. Microbiology Department, University of Utrecht, Utrecht, The Netherlands

    Martin Tegelaar & Han A. B. Wosten

  4. High School of Computer Science, National Polytechnic Institute, Mexico City, Mexico

    Genaro J. Martínez

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  1. Eric Goles
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  2. Michail-Antisthenis Tsompanas
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  3. Andrew Adamatzky
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  5. Han A. B. Wosten
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  6. Genaro J. Martínez
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Correspondence to Andrew Adamatzky .

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  1. Unconventional Computing Laboratory, University of the West of England, Bristol, UK

    Andrew Adamatzky

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Goles, E., Tsompanas, MA., Adamatzky, A., Tegelaar, M., Wosten, H.A.B., Martínez, G.J. (2023). Computational Universality of Fungal Sandpile Automata. In: Adamatzky, A. (eds) Fungal Machines. Emergence, Complexity and Computation, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-031-38336-6_24

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