Below, I present animations for in silico fungus that follows the ‘Gauss’ mode (statistical algorithm). Analogically to the ‘Actual Data’ mode, here, the fungus also is 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. In the ‘Gauss’ mode, parametric values instead of being withdrawn from the sets of observed values (with replacement) are withdrawn from the area under the normal curve defined by the mean and standard deviation. Analogically to the ‘Actual Data’ mode, if the value withdrawn does not meet the logical conditions, such as basic kinetic equations of movement, and then the next value is withdrawn and checked against the same criteria.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. The same as for to the previous simulation mode, no more than two hyphae can grow on top of each other. Also, branches and further generation hyphae extend from the tip and have to meet the same logical conditions as the parent hypha. Parametric values for daughter and further generation branches are withdrawn from the areas under the normal curves different for those for the parents. Normal curves at all times are based on the mean and standard deviation for the particular parameter in certain sub-population (parent, daughter, or further generation). 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As the parameters for various hyphae generations have different data distributions, their values in the simulation are withdrawn separately from parents and other generation hyphae.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 analogically to the program in the previous section, however, it uses a different statistical algorithm for generating simulation values. Similarly to the previous case, the same seeds were used to generate the numbers at random. Independent simulations run with the application of MATLAB numerical matrices about different sizes – 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 76 is a part of the same animation in Figure 77. Importantly, this is an additional validation of the simulation results.
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Neurospora crassa (wt) Simulation in the 'Gauss' mode
Neurospora crassa (wt) Simulation in the 'Gauss' mode
Figure 77 Simulation of Neurospora crassa (wild type) growing on agar (300x300pix).
Parametric values were generated by withdrawing numbers from the area under the normal curve defined by the mean and standard deviation value calculated from the laboratory measurements. Normal curves for different parameters and different hyphae sub- populations were calculated individually. It is expected
that the ‘Gauss’ algorithm used here neither generates
precise parametric values, nor 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 in the fungus does not seem to form a structure that reminds the shape of 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 78 Simulation of Neurospora crassa (wild type) growing on agar (100x100pix).
Parametric values were generated by withdrawing numbers from the area under the normal curve defined by the mean and standard deviation value calculated from the laboratory measurements. Normal curves for different parameters and different hyphae sub- populations were calculated individually. It is expected
that the ‘Gauss’ algorithm used here neither generates
precise parametric values, nor 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 the fungus does not seem to form a structure that would remind the shape of Neurospora crassa colony. 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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Figure 79 above shows the outcomes of the first 25 computer experiments run in consecutive order. All simulations are run in a ‘Gauss’ mode. ‘Gauss’ statistical algorithm uses mean and standard deviation values to produce normal (Gauss) curves. The simulation values are generated at random, by withdrawing the numbers from the area under the normal curves. The number of the experiment is also the number of the MATLAB seed. As expected, this statistical description in reality is not feasible for a description of the growth of Neurospora crassa, although it has been used to characterize laboratory results achieved by others (Held, 2011b). Obtained geometrical patterns do not resemble the typical shape of
Neurospora crassa (wt) formed in the laboratory conditions, although to some degree reflects the branching angles.
Figure 79 Gauss’ 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 84&85 is available here: Biomass Distribution Pictures.
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Figure 80 is a continuation of the experiment series introduced in Figure 79. It shows the outcomes of 25 independent computer simulations run in consecutive order, whereas the number of the experiment is also the number of the MATLAB seed used to generate random values. Any of the geometrical patterns obtained in this series does not resemble the shape of Neurospora crassa in a real world, although branching angles reflect well those are occurring in a real world setting.
Figure 80 ‘Gauss’ 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 84&85 is available here: Biomass Distribution Pictures
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Figure 81 displays the outcome of 25 consecutive simulations and is associated with the Figure 79. Every image shown here is a part of the image with the same number from the Figure 79 (large field of view 300x300 versus small field of view 100x100). Results show that the area that is supposed to be fully occupied by the central part of the colony of Neurospora crassa, in most of the cases, is not fully covered. Interestingly, it is striking in the picture that the fungus branches mainly at the angles 90°, which is in good agreement with the real- world measurements. In the ‘Exploratory data analysis- branching angles’ section, it is said that the mean branching angle value for daughter branches is 83°, for the further generations 78° and that the overall mode value for the parents, daughters and further generations considered altogether is 94°.
Figure 81 ‘Gauss’ 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 86&87 is available here: Biomass Distribution Pictures.
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Figure 82 displays the outcome of 25 consecutive simulations and is associated with the Figure 80. Every image shown here is a part of the image with the same number from the Figure 80 (large field of view 300x300 versus small field of view 100x100). Results shown here, are the replication of the results from the Figure 86 and the only difference comes from the variability of stochastic components and generating numbers at random.
Figure 82 ‘Gauss’ 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 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 86&87 is available here: Biomass Distribution Pictures.
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Consecutive images 1-50 from the Figures 79 and 80 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 81 and 82 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 83 In Silico Fungus - Normalised Biomass Distribution for the ‘Gauss’’ mode. Large Field of View (300x300 matrix).
The maximum recorded value for the most frequently visited cells (pixels) is 100 hyphae (cumulative number from the 50 consecutive experiments, each of the consisting of 150 time steps.
The colour map shows the general tendency of the fungus to occupy certain regions of the surface, based on the simulation values
generated according to the ‘Gauss’’ mode that
relies on withdrawing numbers from the area under the normal curve, that is determined by the mean and standard deviation values. The central line in the middle of the picture represents parent hypha, while the rest of the visualised biomass are daughter and further generation hyphae. Similarity of the colony shape between in silico fungus and its real world counterpart is much less apparent for the
‘Gauss’ mode compared to the ‘Actual Data’ and ‘Kernel’ geometrical outcomes.
Figure 85 Neurospora crassa wild type colony formation. The picture is the final frame of the laboratory movie introducing Neurospora crassa that is a kind gift of prof. Roger Lew (University of York, Canada). The colony growth time in the movie is 1h 3 minutes and 31 seconds
Figure 84 In Silico Fungus - Normalised Biomass Distribution for the ‘Gauss’ mode. Small Field of View (100x100 matrix). The picture is a part of the geometrical distribution displayed in the Figure 88 above. This 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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