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Growth and function of fungal mycelia in heterogeneous environments

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Abstract

As decomposer organisms, pathogens, plant symbionts and nutrient cyclers, fungi are of fundamental importance in the terrestrial environment. Moreover, in addition to their well-known applications in industry, many species also have great potential in environmental biotechnology. The study of this important class of organisms is difficult through experimental means alone due to the heterogeneity of their natural growth habitat and the microscopic scale of growth. In this work we present a mathematical model for colony expansion that is derived through consideration of the growth characteristics on the microscale. The model equations are of mixed hyperbolic-parabolic type and are treated with a numerical scheme that preserves positivity and conserves mass. The numerical solutions are compared against experimental results in a variety of environments. Thus the effect of different translocation mechanisms on fungal growth and function are identified. The derivation and analysis of an approximation to the full model yields further results concerning basic properties of mycelial growth. Finally, the acidification of the growth habitat is considered and the model thus provides important predictions on the functional consequences of the redistribution of internally-located material.

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References

  • Alexander, M. (1994). Biodegradation and Bioremediation, London: Academic Press.

    Google Scholar 

  • Alexopolous, C. J., C. W. Mims and M. Blackwell (1996). Introductory Mycology, 4th edn, New York: John Wiley and Sons.

    Google Scholar 

  • Bailey, D. J., W. Otten and C. A. Gilligan (2000). Saprophytic invasion by the soil-borne fungal plant pathogen Rhizoctonia solani and percolation thresholds. New Phytologist 146, 535–544.

    Article  Google Scholar 

  • Boddy, L. (1999). Saprotrophic cord-forming fungi: meeting the challenge of heterogeneous environments. Mycologia 91, 13–32.

    Google Scholar 

  • Boswell, G. P., H. Jacobs, F. A. Davidson, G. M. Gadd and K. Ritz (2002). Functional consequences of nutrient translocation in mycelial fungi. J. Theor. Biol. 217, 459–477.

    Article  MathSciNet  Google Scholar 

  • Boswell, G. P., H. Jacobs, F. A. Davidson, G. M. Gadd and K. Ritz (2003). A positive numerical scheme for a mixed-type partial differential equationmodel for fungal growth. Appl. Math. Comput. 138, 41–60.

    Article  MathSciNet  Google Scholar 

  • Britton, N. F. (1986). Reaction Diffusion Equations and their Application to Biology, New York: Academic Press.

    Google Scholar 

  • Burgstaller, W. and F. Schinner (1993). Leaching of metals with fungi. J. Biotechnol. 27, 91–116.

    Article  Google Scholar 

  • Cartwright, D. K. and H. W. Spurr (1998). Biological control of Phytophthora parasitica var. nicotianae on tobacco seedling with non-pathogenic binucleate Rhizoctonia fungi. Soil Biol. Biochem. 30, 1879–1884.

    Article  Google Scholar 

  • Davidson, F. A. (1998). Modelling the qualitative response of fungal mycelia to heterogeneous environments. J. Theor. Biol. 195, 281–292.

    Article  Google Scholar 

  • Davidson, F. A. and S. Olsson (2000). Translocation induced outgrowth of fungi in nutrient-free environments. J. Theor. Biol. 205, 73–84.

    Article  Google Scholar 

  • Davidson, F. A., B. D. Sleeman, A. D. M. Rayner, J. W. Crawford and K. Ritz (1996). Context-dependent macroscopic patterns in growing and interacting mycelial networks. Proc. R. Soc. Lond., Biol. Sci. 263, 873–880.

    Google Scholar 

  • Dix, N. J. and J. Webster (1995). Fungal Ecology, London: Chapman and Hall.

    Google Scholar 

  • Edelstein, L. (1982). The propagation of fungal colonies: a model for tissue growth. J. Theor. Biol. 98, 679–701.

    Article  MathSciNet  Google Scholar 

  • Edelstein, L. and L. A. Segel (1983). Growth and metabolism in mycelial fungi. J. Theor. Biol. 104, 187–210.

    Article  Google Scholar 

  • Edelstein-Keshet, L. and B. Ermentrout (1989). Models for branching networks in two dimensions. SIAM J. Appl. Math. 49, 1136–1157.

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Gadd, G. M. (1992). Microbial control of heavy metal pollution, in Microbial Control of Pollution, J. C. Fry, G. M. Gadd, R. A. Herbert, C. W. Jones and I. Watson-Craik (Eds), Cambridge: Cambridge University Press, pp. 59–88.

    Google Scholar 

  • Gadd, G. M. (1993). Interactions of fungi with toxic metals. New Phytologist 124, 25–60.

    Article  Google Scholar 

  • Gadd, G. M. (1999). Fungal production of citric and oxalic acid: importance in metal speciation, physiology and biogeochemical processes. Adv. Microb. Physiol. 41, 47–92.

    Article  Google Scholar 

  • Gadd, G. M. (Ed.) (2001). Fungi in Bioremediation, Cambridge: Cambridge University Press, p. 481, ISBN: 0-521-78119-1.

    Google Scholar 

  • Gadd, G. M. and J. Sayer (2000). Fungal transformations of metals and metalloids, in Environmental Microbe-Metal Interactions, D. R. Lovley (Ed.), Washington: American Society for Microbiology, pp. 237–256.

    Google Scholar 

  • Gadd, G. M. and C. White (1993). Microbial treatment of metal pollution—a working biotechnology? Trends Biotechnol. 11, 353–359.

    Article  Google Scholar 

  • Garrill, A. (1995). Transport, in The Growing Fungus, N. A. R. Gow and G. M. Gadd (Eds), London: Chapman and Hall, pp. 163–181.

    Google Scholar 

  • Gerisch, A., D. F. Griffiths, R. Weiner and M. J. Chaplain (2001). A positive splitting method for mixed hyperbolic-parabolic systems. Numer. Methods Part. Diff. Eqns 17, 152–168.

    Article  MathSciNet  MATH  Google Scholar 

  • Gerisch, A. and R. Weiner (2003). On the positivity of low order explicit Runge-Kutta schemes applied in splitting methods. Comput. Math. Appl. (in press).

  • Gooday, G. W. (1975). Chemotaxis and chemotrophism in fungi and algae, in Primitive Sensory and Communication Systems, M. J. Carlile (Ed.), London: Academic Press, pp. 155–204.

    Google Scholar 

  • Gooday, G. W. (1995). The dynamics of hyphal growth. Mycol. Res. 99, 385–394.

    Google Scholar 

  • Gow, N. and G. M. Gadd (Eds.) (1995). The Growing Fungus, London: Chapman and Hall.

    Google Scholar 

  • Heath, I. B. (1990). Tip Growth in Plants and Fungi, London: Academic Press.

    Google Scholar 

  • Hundsdorfer, W., B. Koren, M. van Loon and J. G. Verwer (1995). A positive finite-difference advection scheme. J. Comput. Phys. 117, 35–46.

    Article  MathSciNet  MATH  Google Scholar 

  • Jacobs, H., G. P. Boswell, F. A. Harper, K. Ritz, F. A. Davidson and G. M. Gadd (2002a). Solubilization of metal phosphates by Rhizoctonia solani. Mycol. Res. 106, 1468–1479.

    Article  Google Scholar 

  • Jacobs, H., G. P. Boswell, K. Ritz, F. A. Davidson and G. M. Gadd (2002b). Solubilization of calcium phosphate as a consequence of carbon translocation by Rhizoctonia solani. FEMS Microbiol. Ecol. 40, 65–71.

    Google Scholar 

  • Jin, X., C. K. Hayes and G. E. Harmon (1992). Principles in the development of biological control systems employing Trichoderma species against soil-borne plant pathogenic fungi, in Frontiers in Industrial Mycology, G. F. Leatham (Ed.), London: Chapman and Hall, pp. 174–195.

    Google Scholar 

  • LeVeque, R. J. (1992). Numerical Methods for Conservation Laws, Lectures in Mathematics, ETH Zürich, Basel: Birkhäuser.

    MATH  Google Scholar 

  • LeVeque, R. J. (1996). High-resolution conservative algorithms for advection in incompressible flow. SIAM J. Numer. Anal. 33, 627–665.

    Article  MATH  MathSciNet  Google Scholar 

  • Littlefield, L. J., R. D. Wilcoxson and T. W. Sudia (1964). Translocation of Phosphorus-32 in Rhizoctonia solani. Phytopathology 55, 536–542.

    Google Scholar 

  • McCabe, P. M., M. P. Gallagher and J. W. Deacon (1999). Microscopic observation of perfect hyphal fusion in Rhizoctonia solani. Mycol. Res. 103, 487–490.

    Article  Google Scholar 

  • Metting, F. B. (1992). Structure and physiological ecology of soil microbial communities, in Soil Microbial Ecology, Applications and Environmental Management, F. B. Metting (Ed.), New York: Marcel Dekker, pp. 3–25.

    Google Scholar 

  • Morley, G. F., J. A. Sayer, S. C. Wilkinson, M. M. Gharieb and G. M. Gadd (1996). Fungal sequestration, solubilization and transformation of toxic metals, in Fungi and Environmental Change, J. C. Frankland, N. Magan and G. M. Gadd (Eds), Cambridge: Cambridge University Press, pp. 235–256.

    Google Scholar 

  • Murray, J. D. (1989). Mathematical Biology, 2nd edn, London: Springer.

    MATH  Google Scholar 

  • Ogoshi, A. (1987). Ecology and pathology of anastomosis and intraspecific groups of Rhizoctonia solani Kühn. Annu. Rev. Phytopathol. 25, 125–143.

    Google Scholar 

  • Olsson, S. (1994). Uptake of glucose and phosphorus by growing colonies of Fusarium oxysporum as qualified by image analysis. Exp. Mycol. 18, 33–47.

    Article  Google Scholar 

  • Olsson, S. (1995). Mycelial density profiles of fungi on heterogeneous media and their interpretation in terms of nutrient reallocation patterns. Mycol. Res. 99, 143–183.

    Google Scholar 

  • Olsson, S. and D. H. Jennings (1991). A glass fibre filter technique for studying nutrient uptake by fungi: the technique used on colonies grown on nutrient gradients of carbon and phosphorus. Exp. Mycol. 15, 292–301.

    Article  Google Scholar 

  • Otten, W., C. A. Gilligan, C. W. Watts, A. R. Dexter and D. Hall (1999). Continuity of air-filled pores and invasion thresholds for a soil-borne fungal plant pathogen, Rhizoctonia solani. Soil Biol. Biochem. 31, 1803–1810.

    Article  Google Scholar 

  • Paustian, K. and J. Schnürer (1987). Fungal growth response to carbon and nitrogen limitation: a theoretical model. Soil Biol. Biochem. 19, 613–620.

    Article  Google Scholar 

  • Persson, C., S. Olsson and H.-B. Jansson (2000). Growth of Arthrobotrys superba from a birch wood food base into soil determined by radioactive tracing. FEMS Microbiol. Ecol. 31, 47–51.

    Google Scholar 

  • Prosser, J. I. (1995). Mathematical modelling of fungal growth, in The Growing Fungus, N. A. R. Gow and G. M. Gadd (Eds), London: Chapman and Hall, pp. 319–335.

    Google Scholar 

  • Prosser, J. I. and A. P. J. Trinci (1979). A model for hyphal growth and branching. J. General Microbiol. 111, 153–164.

    Google Scholar 

  • Ritz, K. (1995). Growth responses of some soil fungi to spatially heterogeneous nutrients. FEMS Microbiol. Ecol. 16, 269–280.

    Google Scholar 

  • Ritz, K. and J. W. Crawford (1990). Quantification of the fractal nature of colonies of Trichoderma viride. Mycol. Res. 94, 1138–1141.

    Article  Google Scholar 

  • Roe, P. L. (1986). Characteristic-based schemes for the Euler equations. Ann. Rev. Fluid Mechanics 18, 337–365.

    Article  MATH  MathSciNet  Google Scholar 

  • Segel, L. A. (Ed.) (1980). Mathematical Models in Molecular and Cellular Biology, Cambridge, U.K.: Cambridge University Press.

    MATH  Google Scholar 

  • Sietsma, J. H., H. A. B. Wosten and J. G. H. Wessels (1995). Cell wall growth and protein secretion in fungi. Can. J. Botany 73(Suppl. 1), S388–S395.

    Google Scholar 

  • Sweby, P. K. (1984). High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal. 21, 995–1011.

    Article  MATH  MathSciNet  Google Scholar 

  • Thornton, C. R. and C. A. Gilligan (1999). Quantification of the effect of the hyperparasite Trichoderma harzianum on the saprotrophic growth dynamics of Rhizoctonia solani in compost using a monoclonal antibody-based ELISA. Mycol. Res. 103, 443–448.

    Article  Google Scholar 

  • Tobin, J. M., C. White and G. M. Gadd (1994). Metal accumulation by fungi—applications in environmental biotechnology. J. Ind. Microbiol. 13, 126–130.

    Article  Google Scholar 

  • Trujillo, E. E. (1992). Bioherbicides, in Frontiers in Industrial Mycology, G. F. Leatham (Ed.), London: Chapman and Hall, pp. 196–211.

    Google Scholar 

  • Wainwright, M. (1988). Metabolic diversity of fungi in relation to growth and mineral cycling in soil—a review. Trans. British Mycol. Soc. 90, 159–170.

    Article  Google Scholar 

  • Watters, M. K. and A. J. F. Griffiths (2001). Tests of a cellular model for constant branch distribution in the filamentous fungus Neurospora crassa. Appl. Environ. Microbiol. 67, 1788–1792.

    Article  Google Scholar 

  • Wessels, J. G. H. (1993). Wall growth, protein excretion and morphogenesis in fungi. New Phytologist 123, 397–413.

    Article  Google Scholar 

  • Whipps, J. M. (2001). Microbial interactions and biocontrol in the rhizosphere. J. Exp. Botany 52, 487–511.

    Google Scholar 

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Correspondence to Fordyce A. Davidson.

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Boswell, G.P., Jacobs, H., Davidson, F.A. et al. Growth and function of fungal mycelia in heterogeneous environments. Bull. Math. Biol. 65, 447–477 (2003). https://doi.org/10.1016/S0092-8240(03)00003-X

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