2.1.12

GROWTH OF SOIL-BORNE FUNGI IN RESPONSE TO CARBON AND NITROGEN - A MODELLING APPROACH

A LAMOUR^{1}, F VAN DEN BOSCH^{2}, AJ TERMORSHUIZEN^{1} and MJ JEGER^{1}

^{1} Wageningen Agricultural University, Department of Phytopathology, PO Box 8025, 6700 EE Wageningen, The Netherlands; ^{2} Wageningen Agricultural University, Department of Mathematics, Dreyenlaan 4, 6703 HA Wageningen, The Netherlands

**Background and objectives**

Growth of soil-borne fungi is much studied *in vitro*. Several mathematical models have been developed to address fungal growth characteristics [1]. However, growth of fungi in soil is poorly understood, largely because the difficulties in observing hyphae. But here also, mathematical models might be of use to explain simple growth characteristics. Growth models can be based on biological assumptions regarding mechanisms controlling particular aspects of fungal growth and generate predictions which may be tested experimentally.

The objective of this study is to model growth of hyphae for a range of soil-borne fungal species with different growth potentials. Qualitative and numerical analysis of the model will be used to indicate directions for future experimental research.

**Materials and methods**

A model was developed to describe growth of soil-borne fungi. Substrate with a certain carbon nitrogen ratio is broken down and then taken up by fungal mycelium. The nutrients are first stored in internal pools and then incorporated into fungal tissues. Two fungal biomass components, cell walls and cytoplasm, are considered, differing in their nutrient demands, as previously described [2]. Eight differential equations describe the rates of change of substrate, nutrient concentrations and fungal density. All model parameters have a biological or physical description.

Standard mathematical procedures were used to obtain overall steady states of the variables. The conditions for existence of the steady states were derived. Numerical simulations were used to produce time plots for the variables.

**Results and conclusions**

The model analysis showed that the steady-state value of the substrate (@) follows implicitly from a cubic equation. The steady-state values of the other model variables are directly related to @. The cubic equation has three roots, resulting in three values for @, and thus three steady-state values for each of the other model variables. However, not all roots are biologically meaningful, as negative or complex values for densities are not possible. The conditions for existence of the steady states show that of the three solutions of @ one, at most, is biologically meaningful. The conditions specify a constraint with a biological meaning, namely that the energy invested in breakdown of substrate should be less than the energy resulting from breakdown of substrate.

The expression for the steady-state value of fungal cytoplasm gives values showing an inverse relationship with @, indicating a high sensitivity to the efficiency of substrate utilization. Numerical simulations show that the densities of all model variables stabilize at single-point steady states.

In summary, the analysis of a complicated fungal growth model gave results with biological interpretation. Additional assumptions may lead to a simplified model.

**References**

1. Prosser Ji, 1979. In: Fungal Walls and Hyphal Growth (Burnett JH and Trinci APJ, eds), pp.359-401.

2. Paustian K, Schnorer J, 1987. Soil Biology and Biochemistry Vol. 19, No.5, 613-620.