Quantitative comparison of plasmodial migration and oscillatory properties across different slime molds

The investigated myxomycete strains, their origin (see table A1) and taxonomic as well as phylogenetic identification can be found in appendix A. All specimens were cultured in the dark at room temperature on 1.2% agar filled Petri dishes and fed with oat flakes (Kölln Flocken). The Badhamia utricularis and Physarum polycephalum cell cultures were renewed every 1–2 d. Fuligo septica could be cultured on the same Petri dish for longer intervals (2–4 weeks). Sclerotia were created for each strain of B. utricularis and P. polycephalum by drying plasmodia carrying wet filter paper [24]. Each B. utricularis and P. polycephalum cell culture was restarted once per month by regrowing plasmodia from sclerotia. Preparation of an experiment with these strains could be handled in the same way for both: One day prior to an experiment a sufficient amount of plasmodia was transferred to a large (9  ×  9 cm) Petri dish filled with 1.2% agar. The pieces of plasmodia were aligned along one side, fed with oatflakes and incubated as described above in order to create a large plasmodial front. On the contrary, plasmodia of F. septica had to be harvested directly from the cell culture.

An agar piece (approximately 2  ×  2 cm), carrying a part of the growing plasmodial front, was transferred to a new Petri dish containing 1.2% agar. The dish was placed into the experimental set-up (see appendix B.1 for a detailed description) and the recording was started immediately afterwards. Images were recorded once per minute and each image was recorded 3 times (total recording time approximately 1 s) and averaged afterwards in order to reduce noise.

The growth assay could be extended to include faster recording of images (1 frame per second, 1000 frames, no frame averaging). These episodes of fast recording were triggered once the plasmodium reached a pre-defined region (see appendix B.1 and figure B2). This could include the application of  ∼1.5 ml 0.1 M glucose, once the plasmodium reached the vicinity of the inlet (figure B2(b)).

The experiments were carried out in a glass culture chamber (24  ×  12 cm) filled with 1.2% agar (detailed description of the experimental set-up in appendix B.2). 24 h prior to the experiment, 300 μl of the respective sugar solution were filled into pre-punched wells (figure B3(C)). The culture chamber was covered and kept for 24 h to allow for diffusion of the sugars (see figures B4 and B5 for the evaluation of the sugar gradients). Four pieces of agar (1  ×  1 cm), carrying a plasmodial front, were placed onto the agar in approximately 1.5 cm distance to the sugar source (figure B3(C)). The agar pieces were placed such that the plasmodia on top faced different directions. The culture chamber was sealed with transparent foil and the recording was started right afterwards. Images were recorded once per minute. Similar to the growth assay each image was recorded three times (total duration approximately 1 s) and averaged afterwards. The maximal duration of an experiment was limited to 24 h due to the constant diffusion of the sugar solutions.

The first frame in each time series (i.e. recorded directly after transferring the plasmodium) is defined as the background frame. This frame is subtracted from every consecutive frame. In order to reduce noise growth, each frame and the background frame itself are median filtered prior to subtraction. Furthermore, the background intensity may not remain stable over a 1–2 d experiment. Each current frame's background level is therefore estimated by maximum filtering (the slime mold network is darker than the background and as such removed from the image). The average of the maximum filtered image describes the offset of the current frame's background intensity to the first frame and is thus subtracted as well. The resulting image serves as the input for all intensity based analysis.

The initial threshold for binarizing the background corrected image was defined as follows: a Gaussian distribution was fitted to the histogram of the background corrected image and subtracted of that histogram. The binary threshold is defined close to the point at which this difference turns positive (a bias away from a Gaussian distribution is caused by the dark pixels of the network). The binarized image unavoidably still contains noise and is therefore filtered such that only pixels remain which occur in five consecutive frames. Finally, the time series was filtered sequentially by labeling connected components. This left only pixels which were either connected to the start region or connected to the detected network of the previous frame.

The area of the plasmodium is calculated by MATLAB's bwarea function on the binary mask. Additionally, the explored area at time t is defined by the area at which the plasmodium was detected at least once until this time. The signal was counted as oscillatory, if a section of at least 4 full oscillation cycles was present. The explored area timeseries was then detrended by filtering it with a Savitzky–Golay filter [25] (MATLAB, signal processing toolbox) and subtracting the filtered signal from the original one. The oscillatory part was cut in phase and the dominant frequency was obtained from the FFT.

The velocity was calculated for both the expanding and the retracting regions. The growth/migratory speed was only calculated on the expanding plasmodial front, while all regions, which were larger than 10 px, were considered for calculating the retraction velocity. The velocity at a certain point $B(x_{i}, y_{i}, t_{i})$ of the boundary was defined as $(\Delta(x_{i}, y_{i}, t_{i-5}) + \Delta(x_{i}, y_{i}, t_{i+5}))/2\Delta t$, where $\Delta t = 5$ min, $(\Delta(x_{i}, y_{i}, t_{i+5}))$ is the distance of $B(x_{i}, y_{i}, t_{i})$ to the closest point of the boundary B(x, y, t_i+5) and vice versa $(\Delta(x_{i}, y_{i}, t_{i-5}))$ the shortest distance to any point of B(x, y, t_i−5). Distances were calculated using MATLAB's internal bwdist routine. To investigate the growth of Fuligo septica the time profile of each pixel, which was visited by the network at least once, was scanned for strong changes by findchangepts (MATLAB, signal processing toolbox). Such a changing point reflects a network passing by and thereby decreasing / increasing the intensity. The binary masks for image series, recorded at 1 Hz, were created as described above. Additionally, the intensity profile over time of each pixel, which is present over the entire 1000 frames, was used to compute a periodogram. All periodograms were then averaged and the two dominant peaks were used to compare the intensity oscillations.

Prior to the quantification of the different plasmodial growth patterns, Badhamia utricularis Isolate 1 and Fuligo septica Isolate 1 were tested for their response towards gradients of different mono- and di-saccharides. These are either known to be attractants or repellents to Physarum polycephalum, which therefore served as a control [22, 23]. Figure B6(b) shows all recorded responses with their directionality over time color coded. A direct comparison of the different species is shown in figure B6(c). Each data point marks the directionality at the end of an experiment, or if reached, the directionality at t  =  800 min.

Badhamia utricularis responds to the same chemoattractants (glucose, galactose, maltose) as P. polycephalum, while the response towards the repellents of P. polycephalum is less clear. 0.1 M ribose acted five times as repellent and three times as attractant (out of eight experiments). Based on the average (directionality  =  −0.3  ±  0.26), 0.1 M sucrose acts as chemorepellent on B. utricularis as well. F. septica, however, did not show an average response towards or against most of the respective sugar gradients. Only 0.1 M lactose appears to act as a weak attractant causing a directionality of 0.1  ±  0.07.

The growth/migration of the phaneroplasmodium from the initial transferred culture is first characterized by the evolution of its area as a function of time. Two exemplary growth patterns, resolved in space, are shown in figure 2 for P. polycephalum (a) and B. utricularis (b). The outlines (plotted every 10 min) of both examples indicate an oscillatory expansion. A similar behavior was observed during the growth under the influence of an external sugar gradient (see figure 2(c)) for an exemplary evaluation of B. utricularis on a gradient towards 0.1 M glucose).

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The growth of all investigated species is displayed in figure 3. (a) shows the averaged area over time for four different isolates and (b) the averaged explored area over time for the same data sets. Clearly, P. polycephalum (Strain Japan) increases its area fastest ((a), linear growth rate between t  =  200 and t  =  600 min equals 1.1 mm² min⁻¹), while the two B. utricularis strains grow at a slower rate (0.57 and 0.6 mm² min⁻¹ between t  =  200 and t  =  600 min). Each plasmodium eventually reaches a state of nearly constant covered area, but the point at which this transition occurs varies strongly within and between the different isolates (figure 3(c)). If the timeseries of the explored area are plotted individually, see figure 3(d), it becomes evident that even though growing at a similar rate, only the Isolate 1 of B. utricularis shows the oscillatory expansion (in 5 out of 5 growth and 46 out of 57 chemotaxis assays), while all samples of Isolate 2 grow steady (23 assays in total).

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The oscillatory expansion of the plasmodial front can be compared between the two species for both the growth and the chemotaxis assay (figure 3(e)). Interestingly, for B. utricularis the measured period of oscillation decreases from 60  ±  8.6 min (undisturbed growth, GA—growth assay, Wat—water control of chemotaxis assay) to 41  ±  2.8 min in the presence of a gradient of 0.1 M glucose, to 39  ±  3.3 min in the presence of 0.1 M galactose, and to 41  ±  7.1 min for 0.1 M maltose, which all act as chemoattractants to B. utricularis.

The growth of the plasmodial front as well as the retraction of the plasmodium elsewhere, can be further characterized by their velocities. Figures 4(a) and (b) show two spatially resolved examples of the growth velocity for P. polycephalum (Strain Japan) and B. utricularis (Isolate 2). The color scale represents the respective velocity at each point of the plasmodial front. In accordance with the growth patterns, the velocity maps show also oscillating patterns. This is more evident for P. polycephalum, but also the Isolate 2 strain of B. utricularis grows in an oscillatory manner. The dense outlines of the B. utricularis plasmodium indicate an oscillation of a shorter period, which gives the apparent steady growth pattern also seen in figure 3(d). This is best displayed and investigated in detail by drawing the velocity histograms (i.e. the histogram of all velocities at a certain time t) for both growth and retraction as a function of time (figures 4(c) and (d)). For P. polycephalum the phases of fast growth and rest are clearly visible in the histograms over time. The retraction shows a similar oscillatory pattern. Phases of stronger retraction go along with phases of growing the plasmodial front, but are shorter compared to those. Regarding the B. utricularis Isolate 2, the velocity histograms over time show that neither the growth nor the retraction drop to zero during the expansion and migration (the only exception is the plasmodial front reaching the boundary of the Petri dish at t  =  970 min). Yet, the periodicity in the growth of Isolate 2 is visible in both histograms and can be calculated using the time profile of the median growth velocity (i.e. number of counts of that velocity over time). It results in a period of  ∼20 min, which is considerably shorter compared to the other isolate of B. utricularis (60  ±  8.6 min, see section 3.2).

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Finally to compare all different species, the mean of all detected velocities per experiment is plotted in figure 4(d) (small dots) with respect to the experimental condition (i.e. growth with or without an external sugar gradient). The average over all experiments of one strain and one external condition is given by the larger symbols. In five out of eight cases P. polycephalum shows the largest average velocity (above 0.08 mm min⁻¹), while both isolates of B. utricularis as well as F. septica extend their plasmodial front with a similar velocity (0.05–0.07 mm min⁻¹). Interestingly, F. septica expands its plasmodium at the same rate while the net growth rate of the covered area is much slower (0.14 mm² min⁻¹, figure 3(a), yellow squares). This is due to the expansion pattern of F. septica. It lacks self-avoidance, but consists of multiple re-growths and retractions along previously visited areas.

The pattern of multiple re-growths and retractions of F. septica, required a different analysis approach to quantify its plasmodial expansion. First, all pixels at which the plasmodium was at least detected once are displayed in figures 5(a) and (b) with their color indicating the relative time the plasmodium spent at the particular position. This relative time is computed by the fraction of time the plasmodium was detected at the evaluated pixel divided by the total duration from the first detection to the end of the experiment. The resulting images show that F. septica forms a plasmodial network with major and interconnected veins over time. However, even the major veins may fully retract several times, before becoming stable. Furthermore, with each re-growth along the existing routes, the plasmodium extends its explored area, as shown in figure 5(c). Here, each outline represents the maximal extension reached during one particular re-growth cycle. In (d) and (e), the intensity profiles of each pixel, at which the plasmodium was at least detected once, are plotted over time. The y-axis is given by the linear indexing of the binary mask, meaning that neighboring indices are likely but not necessarily neighbors in the binary mask. The re-growth/retraction behavior is visible for practically every part of the plasmodium (see the supplementary materials for a movie of this experiment (stacks.iop.org/JPhysD/51/344001/mmedia)). The first stable veins form after 2000 min (straight darker horizontal lines with no further interruption). In the particular experiment shown in (a), (c) and (d), the plasmodium forms two parts, which remain fully connected, but their re-growth and retraction cycle are anticorrelated.

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To further analyze similarities and differences between the two exemplary F. septica experiments, the time the plasmodium spent continuously at a certain position is counted in a histogram for all pixels and all individual visits of the plasmodium. Corresponding to experiments (d) and (e), the histograms are shown in (f) and (g) with the most occurring durations (peak) 191 min and 221 min, respectively. Yet, the time between visits of the plasmodium, detected on a particular pixel, differs (figures 5(h) and (i)). In the regular expanding case, see (a), (c) and (d), the histogram over all intervals in between visits also peaks at 191 min, indicating that the continuous presence of the plasmodium at a certain position was as long as the time the plasmodium was not detected. However, the distribution of this histogram is much broader. The second shown plasmodium, (b) and (e), regrows with an irregular pattern along the pre-existing routes, displayed by the histogram (i), which contains several different peaks and many intervals larger than 1000 min. Finally, figures 5(k) and (l) show the velocity histograms of the two displayed plasmodia. Similar to the other two investigated species, the plasmodium, shown in (a), (c) and (d), is almost continuously growing, migrating, and retracting its network (k). The velocity spikes (growth) are irregularly distributed and do not correlate with the very regular expansion pattern (d). The more irregular expanding plasmodium, (b) and (e), partially follows this observation. However, the velocity histogram shows several time intervals in which either growth or retraction were not detectable (l).

The tube oscillations in Physarum polycephalum, which generate the shuttle flow of intracellular material, can be connected to intensity oscillations of the plasmodium [20]. To study these oscillations, the growth assay (1 frame min⁻¹, see appendix B.1) was interspaced by faster recording (1 frame s⁻¹), once the plasmodium reached a pre-defined location (figure B2, orange outline). The resulting averaged periodogram contains multiple dominant frequencies, of which the two largest are shown in figures 6(a) and (b). The graph is plotted with respect to the area of the plasmodium at the point of recording and additionally shows the full width half maximum (FWHM) for each plotted peak position (indicated by the errorbars). Stronger variations in the oscillation frequency across the plasmodium would lead to a larger FWHM. The dominant frequency (a) of the intensity oscillations show both Badhamia utricularis strains oscillate on a shorter frequency, i.e. on a longer period (8.9  ±  1.30 mHz  ≈112 s, n  =  8) compared to the three investigated Physarum polycephalum strains (10.8  ±  1.70 mHz  ≈93 s, n  =  12). This holds true for the second most prominent frequency within the periodogram ((b), B. utricularis: 18.0  ±  2.46 mHz  ≈56 s, n  =  7, P. polycephalum: 21.4  ±  4.22 mHz  ≈47 s, n  =  11).

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The amplitude of the dominant and second dominant frequency in the averaged periodogram are shown in figures 6(c) and (d). A smaller variation (errorbars in (c) and (d) are the standard deviation) would hint to a tighter control of the oscillation within the plasmodium. However, the averages and their deviations remain in the same range among the different isolates and organisms. A small dependence of the oscillation frequency on the area, covered by the plasmodium, is measurable but not likely (Pearson correlation coefficient (PCC)  =  −0.27, P  =  0.24). Interestingly, there is a strong correlation between the frequency of oscillation and the mean velocity of the leading front across the different species and isolates (PCC  =  0.59, P  =  0.007, n  =  19, figure 6(e)). Here, the mean velocity was calculated as the mean of the respective velocity histogram at the time of recording the intensity oscillations.

Finally, experiments involving the application of a sudden stimulus of a chemoattractant or repellent, are a key to investigate the immediate response of the plasmodium. In a first set of experiments,  ∼1.5 ml 0.1 M glucose were applied to the two different isolates of B. utricularis. The stimulus induces a local response first [26] and therefore the histograms of the detected dominant periods within the individual periodograms are required, in addition to the averaged periodogram, to describe the stimulus response (figure 7: (a) Isolate 1, (b) Isolate 2). If applied directly, glucose at a concentration of 0.1 M can act as a repellent [23], thus decreasing the frequency of oscillation in P. polycephalum [27]. Both B. utricularis strains follow this observation. The exemplary case of Isolate 1 decreases the oscillation frequency from 9.5 mHz ((a) yellow) to 7 mHz ((a) blue), corresponding to an increase of the oscillation period from 105 s to 142 s. Accordingly, Isolate 2 responded with a decrease from 10.5 mHz to 9.5 mHz (b), equaling an oscillation period increase from 95 s to 105 s. Following the analysis displayed in figure 6, figures 7(c)–(f) show the analysis based on the averaged periodogram. Other recorded time series taken over the course of the experiment are displayed for the sake of completeness. The amplitude of the dominant frequency in the averaged periodogram remains in the same range, see (c) and (e), while the frequency drop after the application of a stimulus (red dashed line) is clearly visible, see (d) and (f).

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For taxonomic identification the respective plasmodia were exposed to visible light and starvation conditions under room temperature to induce sporulation [36]. The fruiting bodies (shown in figures 1(e)–(g)) were identified following the key of [37]. For Fuligo septica, only an aethallium was observed, which is characteristic for the genus of Fuligo within the Physaraceae.

For phylogenetic identification, the plasmodia of all sampled strains were grown on 1.2% agar for 24 h at room temperature. Plasmodia were harvested with a pipet tip and resuspended in 50 μl ddH2O. DNA-extraction was done with QIAGENs Mini-Plant-Kit according to the manufacturers instructions and kept at  −20 °C after isolation.

Primers specific for regions in the genes for 18 s, 26 s rRNA and EF-1 were designed by identifying conserved regions of the respective genes by aligning [38] entries of the order of Myxogastria from the NCBI database (table A2)

PCR was done with Phusion Polymerase (ThermoScientific) with annealing temperatures of 60 °C and extension times of 45 s. PCR products were cleaned with E.Z.N.A cycle pure kit (Omega Bio-Tek) and sent for sequencing (Microsynth). Primers Phy26sF5 and Phy26sR8 gave rise to a 1,6 kb product aligning well with the respective 26 s rRNA gene for Physarum polycephalum, Badhamia utricularis and Fuligo septica in a BLAST search. Primerpairs 18sRNA-600-FW & 18sRNA-2300-rev, 18sRNA-2150-FW & 18sRNA-3500-rev and 18sRNA-3400-FW & 18sRNA-4300-rev produced sequences of 300–600 bp length that overlapped to produce contigs of 1,2 kb for P. polycephalum and B. utricularis. From F. septica template DNA, overlapping sequences were produced from primerpairs 18sRNA-600-FW & 18sRNA-2300-rev and 18sRNA-2150-FW & 18sRNA-3500-rev. The product from 18sRNA-3400-FW & 18sRNA-4300-rev did not overlap with the contig from the the two primerpairs upstream, but nevertheless was identified by BLAST to be part of the 18s rRNA gene of F. septica, therefore the sequence was pasted downstream in the F. septica-contig after the insertion of several Ns as separator. Finally, the primers for EF-1alpha did produce sequences when used in a Touchdown-PCR (58 °C–62° C), but sequencing showed that these were not specific products, probably because of the degenerate nature of these primers. Those sequences were dismissed.

Sequencing data from isolates were used to create alignments with publicly available Myxogastric 18 s and 26 s rDNA sequences using MAFFT [38]. A consensus tree was computed with IQ-Tree [39], based on 1000 ultrafast bootstrap approximations while automatically choosing the best DNA substitution model for the data [40]. Figtree (v1.4.3, [41]) was used to visualize the tree (figure A1).

An image and a corresponding sketch of the experimental set-up are shown in figure B1. The Petri dish containing the respective plasmodium to be imaged was placed without a lid into a larger chamber (a), which fully enclosed the Petri dish as well as a temperature humidity sensor (Seeed studio). The sensor was connected via a Grove Base Shield (V.2, Seeed Studio) to an Arduino Uno^TM (b) and recorded the temperature/humidity throughout the entire experiment (RT, humidity 80%–85%). The sample was either illuminated by transmitted light from a circular array of 5 green high power LED's (Cree^TM XP-E, Roschwege LSC-G) (c), or by incident light from the top (d). Most data was recorded with transmitted light, while incident light was preferable for special occasions. In both cases, diffusive material was placed within the light path. All images were recorded by an AVT Pike F505B camera (Allied vision) (e) operated through MATLAB and its image acquisition toolbox. Illumination was only turned on during camera exposure (to minimize light illumination). The only exception was the recording of intensity oscillations (at 1 frame per second). LEDs were triggered by MATLAB (Support package for Arduino) through an Arduino controlled transistor circuit.

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Finally, the experimental set-up as well as the software could be modified, such that next to the growth of the plasmodium, the tube oscillations undisturbed and after the application of a chemical stimulus, could be recorded.

The enclosing chamber would therefore be equipped with an inlet and tubing connected to a peristaltic pump (f), through which a sugar solution could be applied. Exemplary images of such an experiment are shown in figure B2. While recording the growth (as described above) each recorded frame is evaluated. The faster recording of images is triggered as soon as the average intensity in a region lowers with respect to the first frame for at least three consecutive frames. Figure B2(b) (dark gray) shows the network growth (in this particular experiment) which triggered the fast recording of 1000 images at 1 Hz and figure B2(b) (light gray) the situation which triggered the release of 1.5 ml glucose. Sets of 1000 images were recorded before and after the application.

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The set-up for investigating the chemotaxis of the different plasmodial slime molds is displayed in figure B3. Four individual plasmodia were placed on 1.2% agar in a glass culture chamber (24  ×  12 cm) (a), which was covered by transparent foil throughout the experiment. Similar to the growth assay, a temperature/humidity sensor was was placed within the culture chamber and read out by an Arduino^TM (b) over the entire duration of an experiment (RT, humidity 95–100%). The chamber was illuminated by a 3  ×  2 array consisting of six green high power LEDs (specifications as above). A diffusor (d) was placed between the LED array and the glass culture chamber. All images were recorded by a DMK 23UP031 (The Imaging Source) camera, which itself was operated via MATLAB and its image acquisition toolbox. The illumination was only switched during camera exposure. LEDs were triggered by MATLAB through an Arduino^TM controlled transistor circuit. About 300 μl of the individual sugar was placed into pre-punched wells ($\varnothing \approx 1.6$ cm) (figure B3(C) (^*)) 1. Two wells were punched on the opposite side to rule out non-chemotactic effects on the migration. The 1  ×  1 cm agar pieces carrying the plasmodia (figure B3(C) (#)) were placed approximately 1.5 cm away from sugar source and with an approximate distance of 4.5 cm to each other.

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To estimate the diffusion of the different sugars in 1.2% agar the culture chamber including the punched wells were prepared as described above. The diffusion over time was evaluated on 0.1 M glucose after 24 h and 42 h, respectively. The piece of agar was excised, stained in 50 ml 0.01 M tetrazolium chloride (TTC, +1 ml 1 M NaOH) for 1 h [21] and imaged afterwards. The resulting images are shown in figures B4(a) and (b). Based on the diffusion profiles (figures B4(c) and (d)) the agar piece carrying the plasmodium was placed at 1.5 cm distance to the sugar containing well (figure B3(C)). Besides 0.1 M glucose, the chemotactic response of Fuligo septica Isolate 1 and Badhamia utricularis Isolate 1 was evaluated in response to 0.1 M galactose, 0.1 M maltose, 0.1 M ribose, 0.1 M lactose and 0.1 M sucrose. The TTC staining of the diffusion after 24 h of the different (reducing) sugars is shown in figures B5(a)–(d) and the respective diffusion profiles are shown in figures B5(e) and (f).

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To asses the chemotactic migration the binarized masks of each individual chemotaxis experiment were evaluated with respect to its location away from the source. A sketch of the analysis method is given in figure B6(a). First, the radial distance (indicated by white dashed lines) was normalized, such that the center of the source (^*) is equal to 1 and the center of the initial transferred culture (#) is equal to 0. Second, a binning of the surrounding area by means of the angle between the initial culture and the source is created (color coded background). A weighting factor weighs the parts of the area, which are located directly towards or away from the source by 1, whereas areas pointing in other directions are penalized by up to 1/2. Each pixel of a binarized mask (black) is then assigned with the product of the normalized distance and the weighting factor. The average over all pixels results in the directionality at time t. The time series is analyzed until the final frame, unless the plasmodium left the area or merged with a neighboring plasmodium.

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