L-System model for the growth of arbuscular mycorrhizal fungi, both within and outside of their host roots

Appressorium is formed when root and hyphal surfaces meet leading to fungus penetration into the cortical cells. The fungus then develops a branched external hyphae network in soil serving as a medium for gathering and distributing soil resources to the same or neighboring plants. Hence, it can be said that root patterns and soil colonization are among the most important mycorrhizal traits related to plant nutrient acquisition.

In a recent article of Schnepf et al. (2016) and published in Journal of Royal Society, the collaborative research team developed a spatially explicit and dynamic three-dimensional model that predicts roots and soil colonization making use of new L-System model in order to improve the mechanistic understanding of root soil colonization by AM fungi.

The L-System model was developed by including the possibility of mycorrhizal fungi infection of root segments and considering the growth of external fungal hyphae from each infected root segment. This was achieved by assuming an average probability for primary infection of root segments caused by fungal propagules present in soil and by assuming a high probability that a root segment next to an already infected root segment gets infected through secondary infection.

The model was implemented by extending the L-System model for root growth, ROOTBOX written in MATLAB® with growth and infection alternately computed at each step set to be 1 day and each root flagged as either infected or not.

Root architectural parameters were directly measured by analyzing a total of seven previously published images of root systems of Medicago truncutula with ages ranging from 14 to 18 days using a software ‘Root System Analyzer’. Mycorrhizal infection in growing root system was mainly parametrized based on literature including different host fungus combination.

From model calibration and experimental results, first traces of arbuscular mycorrhizal root colonization were visible in individual pots five weeks from planting, whereas significant levels of arbuscular mycorrhizal root colonization and external hyphae were only observed at seven weeks after planting and onwards. Simulation time was adjusted according to an observed delayed plant development in the calibration experiment. The arbuscular mycorrhizal development was thus also delayed so that at stage 2 of the experiment, arbuscular mycorrhizal hyphae extending from the plants in stage 1 did not fill the whole volume of the mesh bags for stage 2 but only penetrated the mesh from each side to grow a certain distance inside the pot leaving the inner volume of the pots initially with no AM fungal inoculum.

Following model calibration, simulation experiments were performed. Results based on simulation of sample size of 100 realizations of a 21-day-old root system showed that an increasing speed of secondary infection has large effect on root system colonization in concentrated than dispersed inoculum placement. In the dispersed case, any root segment can become infected at any time.

Hyphal length density increased with increasing hyphal lifetime for both dispersed and placed inoculum. Doubling the hyphal lifetime led to fivefold increase in realized length density. Doubling the hyphal branching rate resulted in a fivefold increase in hyphal length density. Increase in distance between entry points decreased the simulated  hyphal length density.

This study gave the first model results that dynamically followed the infection within a root system in a spatially resolved way. It offers a framework for optimization of inoculum placement to achieve a predefined rate of root system infection.