Team:DTU-Denmark/StructuralIntegrity
Structural Integrity
Modelling in the biological sciences provides a great tool for investigating and predicting outcomes based on a multiple of parameters.
From studying the fungal behaviour in details to the structural behaviour of the mycelium-based structures, we’ve been applying four different approaches to solve some of the problems and increase our understanding of the processes involved in the project.
The whole idea of basing structures on fungal mycelium relies on the growth and the optimization of the basic physical and mechanical properties of the fungus. We have therefore developed two different approaches to simulating the biomass growth; a detailed model following the location of hyphae and locations [LINK TO SECTION] and another one involving applying a system of partial differential equations (PDE) that models the biomass movement [LINK TO SECTION].
When you change the characteristics of the mycelium, the structural properties will most likely also be influenced. The study of this have therefore been carried out by both designing the building [LINK TO SECTION] and testing out whether the mycelium can withstand the pressure needed [LINK TO SECTION].
Under the lens
Filamentous fungi have a very characteristic growth pattern on solid medium, as they appear as a large network of interwoven filaments [link to figure of fungi network] [3]. If we can accurately predict how a fungus will grow over time, it will allow us to determine the optimal growth conditions to gain the best end product. Therefore, we have investigated how the fungal morphology changes over time at two level of details.
Microscopic view
One of our models focuses on the morphology at the hyphal level by simulating the movement of hyphal tips, branching rates, extension rates and the density levels during a growth period in two dimensions. All of the code scripts can be found on our GitHub repository.
The mycelium of a fungi consists of many interwoven hyphae, and the density depends on how many filaments there are in the location. In figure 1 below, it is possible to see microscopic pictures of fungal mycelium. Three different levels of zoom illustrate how the network looks, where it can be observed how they interlink and how a fungal filament can branch into more.
Fig. 1: - Snapshots of mycelium development of Aspergillus oryzae. These are representative microscopic images of how a network of intertwined hyphal filaments could look in a microscope.
Simulation of the mycelium development
Fungal growth is initiated by $n$ number of spores, and a branch will start to extend from each of the spores added to the space. Following along one of these branches originating from a single spore, the hyphae will grow in a direction $\theta$ with a tip extension $r_{tip, i}$. A branching event, in which a new branch is formed from the first branch, can occur with a probability $q$.
Tip extension rate is calculated by using the equation below, which considers growth kinetics for the fungi and the amount of substrate available. It essentially outputs the accelerated growth dependent on the amount of substrate available, where the accelerated growth equation depends on fungal kinetics and branch lengths [1, 3].
\begin{equation}
r_{tip, i} = \bigg(k_{tip,1} + k_{tip,2}\cdot \frac{l_{br,i}}{l_{br, i} + K_t}\bigg)\cdot\bigg(\frac{S}{S+K_s}\bigg)
\end{equation}
$k_{tip,1}$ is the initial tip extension rate of the branch and $k_{tip,2}$ is the difference between the maximum extension rate and $k_{tip,1}$ [1, 3]. The length of branch $i$ described by $l_{br,i}$. $S$ is the substrate concentration and $K_S$ corresponds to the substrate concentration to reach half of the maximum growth level [4].
As the starting coordinates of this simulation are $(x_0, y_0)$ and end coordinates $(x, y)$, the length of branch $i$ can be calculated as the distance between two points:
\begin{equation}
l_{br, i} = \sqrt{(x-x_0)^2 + (y-y_0)^2}
\end{equation}
By dividing the growth area into a grid of $w\cdot h$ areas, it is possible to investigate the uptake of substrate, hyphal movement and the development of biomass through the simulation.
At the start of the simulation, it can be assumed that the initial substrate concentration $S_0$ will be distributed evenly across the grid. When the spores are placed randomly, the branches start to develop by using the substrate available around the hyphal tip. So for each branch, it is checked which tip is in which grid and whether there is any substrate available. That means that one can track the substrate depletion in each grid, and when there is no more substrate in one of the areas of the grid, the hyphal tips located there can no longer grow and can be considered as inactive hyphae. If the total area around the mycelium no longer contains substrate, the growth will simply stop.
In the same way as tracking substrate depletion, biomass production can also be viewed in a grid. But instead of calculating a loss of substrate, each new branch extension is considered a gain in biomass or the density $d$. It should show the same mechanics as the substrate depletion, as these two are directly related to each other by the equation $l_{br,i}$.
Results
The simulation ran with the parameters listed in table 1 [below], which painted a detailed picture of the time history of growth from the spore to the densely branched network of hyphal filaments. The parameters are based on growth of Aspergillus oryzae originates from 10 spores added to the medium.
More to come!