Conference publications


XXVI conference

Modeling the growth of fungal mycelium using a cellular automaton

Shumilov A.S.

Institute of Physicochemical and Biological Problems of Soil Science Russian Academy of Sciences Pushchino, Moscow Region, Russian Federation

1 pp. (accepted)

The fungus grows in the direction of a larger resource (chemotropism). If the resource is low, the fungus slows down their absorption and searches for resources through rapid unidirectional (apical) growth. Having found a resource, the fungus begins to branch out, which would increase the area of resource absorption and use it faster.

Resources are spent on the life and growth of new cells.

Mycelium can grow linearly or branch out depending on resources (Szabo and Štofanıkova 2002, Gbolagade, Fasidi et al. 2006).

To illustrate the capabilities of the general model, which we visualize in Figure 1, we will assume that there is an excess of carbon in the soil. An excess of carbon must get from the soil to the fungus. At the macro level, the decision is made to increase the absorption of external apical hyphae.

The mushroom absorbs new resources with its external parts. The area of the outer part grows with an increase in radius slower than the volume of the entire colony. After some time, the growth of resources that will be obtained by the external part of the fungus will not be enough for the whole colony. If there is still a lack of resources, then mature hyphae can encapsulate - they will be covered with a hard shell. With a lack of resources, theoretically, the absorption capacity of external hyphae can also be further increased.

The growth rate of the hyphae, the degree of branching and the parameters of the absorption of resources depend on the geometry and scale of growth of the fungus. So, old gifs can be encapsulated to reduce energy consumption (Cazelles, Otten et al. 2013). If the degree of encapsulation is large enough, then it turns out that with a spherical distribution, the mass of cells that absorb resources (i.e. the external surface area of the ball) is smaller than the mass of the colony (that is, the volume of the ball). Then the fungus has two choices.

1. The absorption of resources by external hyphae should be strengthened to an even greater extent.

2. To reduce energy consumption in these conditions, death can be observed internally (“death of hyphae” in Figure 1). At the death of the hyphae, the substances that were stored in them. Can be released to the outside. But they can not be used immediately by mushrooms, they must be converted to an accessible form for them. In the model, this is expressed through an increase in the “time of humification” or through a decrease in the mineralization constant of chitin-containing substance.

Let us try to show how growth is modeled using the example of a gradient resource field (Figure 2).

Take a field in which from left to right along the gradient increases the resource, for example, from one to ten. The field is labeled as a collection of cells (the Cell Borders table does not exist in reality; this is a model assumption for easy tracking of changes in the geometry of the fungus).

In the case of growth in agar, the model can repeat the pattern of growth of Trichoderma observed in the experiment (Ritz 1995).

Mushroom sucks resources actively and passively. The apical part sucks up resources five orders of magnitude faster. This is due to the encapsulation of mature hyphae. The mushroom can consume more resources than it needs at the moment. They can be transformed by moving from an external resource to an internal one, or they are transported to a daughter cell in need.

The substrate can enter non-encapsulated or encapsulated (part of the hypha. In the right part of the hypha, in addition to passive suction (through the channels), there is also active suction (using pumps, energy is wasted), and in the left part of the hypha only the passive one. Substrate, which enters the hypha cell, becomes the so-called transported biomass bt, it can transform in the right part into non - encapsulated biomass bn in the left part into encapsulated bi. Non-encapsulated hyphae can turn into encapsulated, which can be compared with hibernation in animals - a decrease in metabolism occurs, it is energetically beneficial. Activation in this model is not considered, since the probability of this process going on is much lower (Cazelles, Otten et al. 2013)

The formula for the resource transported to the mother cell is obtained.

m_transpInToMather = ({(p (Q_step * L_step) ^ 2-2p (Q_step * L_step)}} (s- 〖s * s〗 _invert) * (1- £ 〖) K〗 _res * V_max) / ((Km + s ) 〖/ K_min〗 ) (1)

Formula 1.

Table 1 - Model Parameters

Parameter P N References Notes

£ - encapsulation factor 0.1 - (Ames, Reid et al. 1983, Gow and Gadd 2007)

Vm maximum speed of the enzyme 0.018 - (Cazelles, Otten et al. 2013)

Km - Michaelis constant 1.1 * 10-12 - Cazelles, Otten et al. 2013)

Kres –– insulin level 1 - Ames, Reid et al. 1983

Kminer –mineralization 1 - (Schimel and Bennett 2004, Maslov 2014)

sinvert –reverse element outflow 0 0.5 (Kaiser, Franklin et al. 2014)

Qstep - Number of model steps

Lstep - length of a step of model of 0,1 mm -

substrate s-concentration, percent by weight of soil 0.00125 0.005 (Ames, Reid et al. 1983).

When recalculated, we obtain that for three days the transported phosphorus was 0.003489 per one tenth of a mm hypha of the fungus as a percentage of the soil mass (0.1% ms) under the assumption that 10% of the hyphae were encapsulated. when calculating according to the above formula, we obtain the amount of nitrogen transferred equal to 0.0032 0.1% ms. 35 and 32 are comparable values. When calculating the nitrogen transport, we assumed that its transfer to the plant from the soil is difficult for two reasons: mineralization and reverse nitrogen release in the form of enzymes for digesting the substrate — the Kminer and Sinvert parameters, which did not play a role in calculating phosphorus transport. Indeed, the article (Kaiser, Franklin et al. 2014) states that the flow of phosphorus through the plant is so fast that it cannot be the limiting factor in the root – mycelium interaction model in mycorrhiza. As for the sufficiently strong effect of mineralization on nitrogen availability, which follows from model calculations, there is an assumption in the literature that the more nitrogen is available and the less competition, the higher the value of nitrogen mineralization before it is consumed by the plant (Schimel and Bennett 2004). The experimental data of the transport is 0.0039 0.1% ms, and in the model 0.0037 0.1% ms, which is also similar to each other..

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