Part III | Results 40
3.5 Results| Simulation outcomes 87
3.5.3 Results| Fungi Simulation – ‘Kernel’ Mode 103
Similarly to the simulation modes presented in the previous sections, here, in silico fungus is also modeled as a line that extends from the tip and branches with a given probability. The probability of sending a branch depends both on satisfying basic logical conditions implemented in the program and on the probability distributions of the key growth parameters: apical extension velocity, branching angle, and branching distance.
The parametric values are withdrawn from the area under the normal curve as the program is executed. Importantly, customized kernel curves are produced for each of the key growth parameters separately. Moreover, different kernel curves are drawn for various sub- populations of hyphae, including parents, daughters, and further generation hyphae. If the value withdrawn from the area under the kernel curve does not meet the logical conditions, such as basic kinetic equations of movement, then the next value is withdrawn and checked against the same criteria. The process repeats as long as all three parameters: velocity, branching angle, and branching distance meet the logical criteria and satisfy kinetic equations. On this basis, the consecutive positions of every hyphal tip are calculated and visualized. Importantly, no more than two hyphae can grow on top of each other. Also, branches and further generation hyphae also extend from the tip and have to meet the same logical conditions as the parent hypha. Every animation consists of 150 consecutive frames and starts with the parent hypha that sends daughter branches. Daughter branches start sending further generation branches. As the parameters for various hyphae generations have different data distributions, their values in the simulation are withdrawn separately from parents and other generation hyphae. This way the program simulates forming the colony
Neurospora crassa (wild type) network.
The same seeds were used to generate the numbers at random. Therefore, the outcomes of the independent simulations that represents the small field of view (100x100 MATLAB cells) and large field of view (300x300 MATLAB cells) perfectly match each other regarding the outcome patterns. One can see that the animation in Figure 87 is a part of the same animation in Figure 86. Importantly, this is an additional validation of the simulation results. In this section, intentionally I give an example of the fungus animation run in the ‘Kernel’ mode, followed by the two series of 25 consecutive computer experiments. Figures 86-91 are complemented with the hyperlinks to the ‘avi’ files with the full simulations.
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Neurospora crassa (wt) Simulation in the 'Kernel' mode
Neurospora crassa (wt) Simulation in the 'Kernel' mode
Figure 86 Simulation of Neurospora crassa (wild type) growing on agar.
Parametric values were generated by withdrawing numbers from the area under the kernel curve constructed on the basis of the laboratory measurements. Kernel curves for different parameters and different hyphae sub-populations were calculated
individually. It is expected that the ‘Kernel’’ algorithm
used here should generate both precise parametric values and real-world based data distributions. Estimated real time of the animation is about 2 hours and 30 minutes. Animation consists of 150 consecutive time steps. It starts with the parent hypha growing in the middle of the field of view. The parent hypha extends from the tip and starts sending daughter branches that also extend from the tips. The daughter branches start sending further generation branches simultaneously. In this case fungus seem to form a structure that reminds the shape of real-world Neurospora crassa colony. Presented image is based on 300x300 MATLAB numerical matrix with encoded properties – “geographical” zones visualised here a
blue lines that are used in a further analysis of the dynamics of the colony growth. The picture here is the final frame of the animation
Figure 87 Simulation of Neurospora crassa (wild type) growing on agar.
Parametric values were generated by withdrawing numbers from the area under the kernel curve constructed on the basis of the laboratory measurements. Normal curves for different parameters and different hyphae sub-populations were calculated individually. It is expected that the
‘Kernel’ algorithm used here should generate both
precise parametric values and a real-world based data distributions. Estimated real time of the animation is about 2 hours and 30 minutes. Animation consists of 150 consecutive time steps. It starts with the parent hypha growing in the middle of the field of view. The parent hypha extends from the tip and starts sending daughter branches that also extend from the tips. The daughter branches start sending further generation branches simultaneously. In this case fungus seems to form a structure that reminds the shape of Neurospora crassa colony in the interior part. Presented image is based on 100x100 MATLAB numerical matrix with encoded properties –“geographical” zones visualised
here a blue lines that are used in a further analysis of the dynamics of the colony growth. The picture here is the final frame of the animation.
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In Figure 88 above one can notice slightly different patterns in the pictures 4 and 25, compared to the remaining ones. This variation in the behavior is displayed not only by in silico fungus presented here but also by its real world counterpart, Neurospora crassa (wt). The outcomes shown here are analogical to the ones obtained by the simulations run in ‘Actual Data’ mode. However, ‘Kernel’ mode simulates Neurospora crassa behavior much more accurately and precisely thanks to the improved procedures for ‘imitating’ the real-world data. According to the visual data, in the central part of the colony the surface is occupied very densely and that eventually all of the colonies converge to the ‘round’ shape, characteristic for the Neurospora crassa (wt) colonies grown in the laboratory conditions.
Figure 88 ‘Kernel’ simulations of Neurospora crassa (part I). Final frames (300 x 300 pixel images) are given for the simulations consisting of 150 consecutive steps. Random generator seeds are set as 1 to 25 respectively. PSFis the number describing ‘proportion of the surface filled’ by in silico fungus within 150 time steps (~2h 30 min). Compilation of the pictures 1-50 from the Figures 92&93 is available here: Biomass Distribution Pictures.
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Figure 89 above is a continuation of the experiment series from the Figure 88. Analogically, one can observe the difference between the geometrical patterns between the pictures 27, 38, 39, 43-45, 47 and 26, 28-37,40-42,46, 48-50. Importantly, the simulations in the ‘Kernel’ and ‘Actual Data’ mode give patterns that are similar to each other, but the general tendency in a series of experiments are different. In silico fungus growing according to the ‘Kernel’ algorithm, colonizes the surface faster and more efficiently compared to the fungus growing according to the ‘Actual Data’ statistical algorithm. More details on the proportions of the surface filled with the fungi growing according to different statistical algorithms are available in the later section of this chapter.
Figure 89 ‘Kernel’ simulations of Neurospora crassa (part II). Final frames (300 x 300 pixel images) are given for the simulations consisting of 150 consecutive steps. Random generator seeds are set as 26 to 50 respectively. PSFis the number describing ‘proportion of the surface filled’ by in silico fungus within 150 time steps (~2h 30 min). Compilation of the pictures 1-50 from the Figures 92&93 is available here: Biomass Distribution Pictures.
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Figure 90 is correlated with the Figure 88, whereas, for every individual simulation, the small field of view (Figure 90) is a part of a bigger field of view (Figure 88). According to the visual results, in silico fungus efficiently covers the surface in the central region of the colony in most of the cases. This outcome is in good agreement with the anticipated results – the values generated for the simulations are withdrawn from the area under the kernel curve, therefore in silico fungus is expected to ‘imitate’ the behavior of Neurospora crassa growing in the laboratory conditions. Thus, the fungus is expected to cover the central region of the colony in a similar way to the one shown in the pictures above.
Figure 90 ‘Kernel’ simulations of Neurospora crassa (part I’). Final frames (100 x 100 pixel images) are given for the simulations consisting of 150 consecutive steps. Random generator seeds are set as 1 to 25 respectively. PSFis the number describing ‘proportion of the surface filled’ by in silico fungus within 150 time steps (~2h 30 min). Compilation of the pictures 1-50 from the Figures 94&95 is available here: Biomass Distribution Pictures.
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Results shown in Figure 91 are the continuation of the simulation series shown in Figure 90. Similarly, the individual experiments no 26-50 run with the application of 100x100 MATLAB matrices (small field of view) are a part of the bigger pictures (300x300) displayed in Figure 89. The results shown here support previous observations and conclusions: (1) fungus efficiently covers the surface in most of the cases, (2) surface coverage shape is similar, but much more efficient compared to the outcomes of the simulations based on the ‘Actual Data’ statistical algorithm.
Figure 91 Kernel’ simulations of Neurospora crassa (part II’). Final frames (100 x 100 pixel images) are given for the simulations consisting of 150 consecutive steps. Random generator seeds are set as 26 to 50 respectively. PSFis the number describing ‘proportion of the surface filled’ by in silico fungus within 150 time steps (~2h 30 min). Compilation of the pictures 1-50 from the Figures 94&95 is available here: Biomass Distribution Pictures.
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Consecutive images 1-50 from the Figures 88 and 89 were overlaid on top of each other as 300x300 MATLAB numerical matrices. The numbers of hyphae occupying particular cell (pixel) were added and on that basis the color maps were produced by the in silico program. Analogically, the consecutive images 1-50 from the Figures 90 and 91 were overlaid as 100x100 MATLAB numerical matrices, the numbers of hyphae occupying particular cell (pixel) were added, and the associated color maps were produced
Figure 92 In Silico Fungus - Normalised Biomass Distribution for the ‘Kernel’ mode. Large Field of View (300x300 matrix).
The maximum recorded value for the most frequently visited MATLAB cells (equivalents of the pixels in the images) is 100 hyphae (it is a cumulative number from the 50 consecutive experiments, consisting of 150 time steps.
The colour map shows the general tendency of the fungus to occupy specific regions of the surface. Results are based on the simulation values
generated according to the ‘Kernel’.
Central line in the middle of the picture represents parent hypha, while the rest of the visualised biomass consists of daughter and further generation hyphae. Overall, the biomass is shifted to the right with regards to the central, parent hypha.
Figure 94An example of a real-world laboratory grown colony of Neurospora crassa (wild type). Internet source:
http://www.fgsc.net/neurosimages/cul tureimages/CULTUREwild_type_FGSC9 88.jpg
Figure 93Distribution for the ‘Kernel’ mode. Small Field of View (100x100 matrix). The picture is a part of the geometrical pattern displayed in the Figure 96 above. The order of magnitude of the field of view matches the one for the laboratory samples (movies) that were used for the measurements of Neurospora crassa wild type and that are a kind gift of prof. Roger Lew (University of York, Canada). Results are for the growth time ~2h 30 min
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