Morphogenesis and dynamics of slime molds in various environments

Cells, including unicellulars, are highly sensitive to external constraints from their environment. Amoeboid cells change their cell shape during locomotion and in response to external stimuli. Physarum polycephalum is a large multinucleated amoeboid cell that extends and develops pseudopods. In this paper, changes in cell behavior and shape were measured during the exploration of homogenous and non-homogenous environments that presented neutral, and nutritive and/or adverse substances. In the first place, we developed a fully automated image analysis method to measure quantitatively changes in both migration and shape. Then we measured various metrics that describe the area covered, the exploration dynamics, the migration rate and the slime mold shape. Our results show that: 1) Not only the nature, but also the spatial distribution of chemical substances affect the exploration behavior of slime molds; 2) Nutritive and adverse substances both slow down the exploration and prevent the formation of pseudopods; and 3) Slime mold placed in an adverse environment preferentially occupies previously explored areas rather than unexplored areas using mucus secretion as a buffer. Our results also show that slime molds migrate at a rate governed by the substrate up until they get within a critical distance to chemical substances. Author summary Physarum polycephalum, also called slime mold, is a giant single-celled organism that can grow to cover several square meters, forming search fronts that are connected to a system of intersecting veins. An original experimental protocol allowed tracking the shape of slime mold placed in homogenous substrates containing an attractant (glucose) or a repellent (salt), or inhomogeneous substrates that contained an attractive spot (glucose), an eccentric slime mold and a repulsive spot (salt) in between. For the first time, the rate of exploration of unexplored areas (primary growth) and the rate of extension in previously explored areas (secondary growth) were rigorously measured, by means of a sophisticated image analysis program. This paper shows that the chemical composition of the substrate has more influence on the morphology and growth dynamics of slime mold than that of concentrated spots of chemicals. It was also found that on a repulsive substrate, slime mold exhibits a bias towards secondary growth, which suggests that the mucus produced during slime mold migration acts as a protective shell in adverse environments.


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Large-scale spatial patterns in biology are common and knowing how these patterns 73 evolve and what are their functional role, enables us to understand the evolution of 74 biocomplexity (see e.g. (1-4)). Morphogenesis has been studied in length at the cell 75 level (see e.g (5-8)); cells are highly sensitive to geometrical and mechanical 76 constraints from their microenvironment and respond to these conditions by 77

141
In a neutral (control) and slightly nutritive environment (glucose at 100 mM), the 142 slime molds started to spread from the very beginning of the experiment (Fig 1; 143 Table 1   At the end of the experiment (after 35 hours), the slime molds reached a similar 152 surface in a control environment and in an adverse environment (Table 3 and Fig 7  153 in S1 Appendix , P>0.05 when compared to the control). Interestingly, after reaching 154 a plateau at 18 hours, the area covered by the slime molds in an adverse 155 environment oscillated with seemingly cyclic fluctuations (Fig 1). In both a slightly 156 and a highly nutritive environment, the slime molds reached a higher final surface 157 than the slime molds placed in a control environment (P<0.001 in both comparisons) 158 and covered approximately 30% of arena at the end experiment. It is worth noting 159 that in a highly nutritive environment, the surface covered by the slime molds never 160 reached a plateau after 35 hours, suggesting that the slime molds did not reach its 161 maximum surface (Fig 1). 162 163 Refinement i.e. appearance of mucus, was observed after 5 hours in the control 164 environment. In all other environments, mucus appeared later (Table 4 and Fig 8 in 165 S1 Appendix: P<0.001 for all treatments when compared to the control). In a highly 166 nutritive environment, mucus was only observed after 10 hours, which marked the 167 strongest delay in the refinement process. Once the mucus started to be apparent, 168 its surface grew quicker in the control environment than in the other three treatments 169 (Table 5 and Fig 9 in S1 Appendix; P<0.001 for all treatments when compared to the 170 control). Thus the surface covered by mucus at the end of the experiment was the 171 largest in the control environment where it reached 75% of the arena against 55%, 172 40% and 35% for the slightly nutritive, the adverse and the highly nutritive 173 environments respectively (Table 6 and  leaving only 5% of the arena unexplored while in the other treatments the surface 178 unexplored were significant: 15%, 35% and 38% for the slightly nutritive, the highly 179 nutritive and the adverse environments respectively. Interestingly, although the 180 growth rate dynamics differed between highly nutritive and adverse environments, 181 the final unexplored surfaces were similar. In a highly nutritive environment the slime 182 molds grew slowly and steadily while in an adverse environment slime molds grew 183 rather quickly but after a long delay. 184 185 Next, we analyzed the evolution of the cumulative areas covered by primary growth, 186 refinement and secondary growth (Fig 2). The cumulative area covered by 187 secondary growth, which reveals the cyclic nature of the exploration process, was 9 the highest in the adverse environment (480% coverage) followed by the control 189 environment (380%), the slightly nutritive environment (250%) and the highly 190 nutritive environment (180%). All comparisons lead to significant differences P<0.05, 191 except control vs. adverse environment (Table 7 and    In accordance with the previous results, the migration rate was higher for the control 202 treatment than for the other treatments (Table 8 and Fig 12 in S1 Appendix: P<0.001  203 for each pairwise comparison). While slime molds exploring the highly nutritive 204 environment were slower than slime molds exploring the slightly nutritive or the 205 adverse environment (P<0.001 each), these two showed no significant differences 206 (P>0.05).

215
The slime molds exploring the adverse environment showed the highest probability 216 to explore a previously explored substrate than the other treatments as shown in Fig  217   4 and supplementary materials (Tendency for secondary growth: Table 9 and Fig 13  218 in S1 Appendix: P<0.001 for each pairwise comparison). When exploring a highly 219 nutritive environment, slime molds also displayed a significant positive tendency for 220 secondary growth (P<0.001 for each pairwise comparison) but significantly less 221 strong than on the adverse environment (P<0.001). For the others treatments, the 222 measured proportion of secondary growth was not different from the expected 223 proportion of secondary growth, indicating that the slime molds did not avoid 224 previously explored substrate and explored randomly (Fig 13 in S1 Appendix). The 225 peaks observed within the first 5 hours of the experiment correspond to an isotropic 226 extension immediately followed by a refinement process that occurred before the 227 slime mold started to explore continuously its environment. This behavior is often 228 observed when a slime mold is introduced in a new environment and is referred as 229 "contemplative" (49) i.e. the slime mold migrates, retracts and moves again. The 230 peak was larger for adverse environment.

237
We then analyzed the evolution of the shape of the slime molds contour. Note that 238 the experimental set ups in which slime molds were placed exhibited radial 239 symmetry. Hence, no preferential expansion direction was expected. We thus 240 focused on contour shape, not orientation. 241 As expected, circularity was initially one in all tests (circular slime mold spot), and 242 increased over time as the contour shape departed from a circle (Fig 2 in S1  243 Appendix). In the control and nutritive environments, circularity remained between 244 1.05 and 1.10, whereas it fluctuated between 1.05 and 1.30 in the adverse 245 environment. This observation suggests that, in an adverse environment, slime 246 molds explored the petri dish by spreading and thinning over larger areas than in the 247 other environments, which led to shape changes and a decrease of slime mold 248 circularity. However fluctuations among the 20 replicates were too high to identify 249 any trend in the evolution of slime mold circularity. Solidity decreased with the emergence of pseudopodia, since slime mold branching 259 disrupted the initially convex shape of the slime mold (Fig 5). In the control 260 environment, in which the exploration rate was the highest, the decrease of solidity 261 of the slime mold area was the highest (and the fastest) decreasing from 1 to 0.3 and 262 then becoming relatively stable, with fluctuations of +/-0.05 (Table 10 and

2) Spot experiments 297
In the spot experiments, we studied the influence of discrete distributions of nutrients 298 and repellents on exploration dynamics. When looking at the evolution of slime mold, 299 mucus and unexplored substrate over time (Fig 7), we only observed marginal 300 difference among the treatments, which all exhibited similar patterns of exploration, 301 e.g. similar percentage of non-explored area and similar mucus accumulation. The 302 presence of an adverse spot only delayed the appearance of the first pseudopod 303 (first movement: Table 12 and Fig 15 in S1 Appendix, P<0.05) but not the first 304 appearance of mucus (first appearance of mucus: Table 15 in S1 Appendix, not 305 significant). The only noticeable differences lie in the surface reached at the end of 306 the experiment: slime molds that were offered a highly nutritive spot grew larger 307 (final surface: Table 14 and Fig 17 in S1 Appendix; P < 0.01). By contrast, the 308 surface covered by mucus was lower (mucus final surface: Table 17   were also similar for all treatments (Table 18 in S1 Appendix, P >0.05), suggesting 333 again, that isolated spots with nutritive or adverse stimuli did not alter the overall 334 exploration of slime molds when growing on the same, control, substrate.  Table 19 in S1 Appendix. This 344 effect showed that the migration rate was slightly superior when slime molds were 345 offered a higher than a lower nutritive spot.   (Table 19 in S1 Appendix), which suggests that the growth type  The results obtained for the four different shape indexes (Fig 4 in S1 Appendix) for 365 the spot experiments support the hypothesis that discrete spots of nutrients or 366 repellents did not affect the overall expansion dynamics and exploration cycles. This   area not explored by the slime molds was 3 times larger (respectively 7 times larger) 414 than in the environment deprived of nutrient (control case) for a slightly nutritive 415 (respectively highly nutritive) environment. The exploration rate was almost linear for 416 highly nutritive environments, while for other treatments, the area covered by the 417 slime molds reached a plateau after a period of stretching, which indicates 418 secondary growth and slime mold displacement. This means that slime molds that 419 explored nutritive environments never exhibited a Phase (iii) in their exploration 420

pattern. 421
Second, on substrates with higher nutrient concentrations, the slime molds grew in a 422 more compact fashion, i.e. slime molds presented the highest solidity index and the 423 lowest number of pseudopodia (clusters). Additionally, the appearance of mucus, 424 which indicates that the slime mold was withdrawing, occurred much later in nutritive 425 environments. As glucose is only aversive when only above 300mM (54), our results 426 suggest that nutritive media depressed migration due to feeding behavior. This 427 allows the organism to remain at a site until nutrients are exhausted (54,62,63). In 428 previous studies, it was shown that the area of substrate covered increases when 429 slime mold responds to nutrient dilution (54,64). Here, we confirmed these 430 observations and noted that slime mold tended to migrate and grow faster on 431 substrates with the lowest concentration of nutrients, thus maximizing nutrient intake 432 and optimizing the trade-off between nutrient foraging and nutrient intake.

1) Species 484
Physarum Polycephalum, also known as the true slime mold, belongs to the 485 Amoebozoa, the sister group to fungi and animals (50). Slime molds are found on 486 organic substrates like tree bark or forest soil where they feed on microorganisms 487 such as bacteria or fungi (50). The vegetative morph of P. polycephalum, the 27 plasmodium, is a vast multinucleate cell that can grow to cover up to a few square 489 meters and crawl at speeds from 0.1 to few centimeters per hour (29,30). When 490 hygrometry and food availability decrease, the plasmodium turns into an encysted 491 resting stage made of desiccated spherules called sclerotium (29). 492

2) Rearing conditions 493
Experiments were initiated with a total of 10 sclerotia per strain (Southern Biological, 494 Victoria, Australia). We cultivated slime molds on a 1% agar medium with rolled oat 495 flakes, slime molds were fed every day and the medium was replaced daily. Slime 496 molds were 2 weeks old when the experiment started. All experiments were carried 497 out in the dark at 25°C temperature and 70% humidity, and ran for 35 h. Pictures 498 were taken every 5 min with a Canon 70D digital camera. 499

3) Experimental setup 500
Initially we monitored the exploration movement evoked in slime molds in a 501 homogeneous environment. Each slime mold was placed in the center of a circular 502 arena (14.5cm in diameter) with a layer of agar (1% in water) mixed with non-503 nutritive cellulose (5%). Adding cellulose to the agar mix proved to be useful to 504 obtain a homogeneous pigmentation and to enhance the color contrast between the 505 substrate and slime mold, therefore improving the identification process. A circular 506 hole (2.5cm in diameter) was punched and replaced with a circular slime mold of the 507 same size sitting on oat. In the first and second treatments (nutritive environments) 508 we added glucose (100mM or 200mM) to the medium. In the third treatment 509 (adverse environment), we added a known repellent (NaCl 100mM (51)) to the 510 medium. Lastly, in the fourth treatment, the medium remained unchanged (neutral 511 environment i.e. control treatment). 512 28 513 Subsequently, to investigate how chemotaxis modified the exploration behavior, we 514 introduced discrete spots of attractants/repellants within a neutral substrate made of 515 plain agar. In these so-called "spot experiments", we followed a procedure similar to 516 that for the homogeneous environments. A circular slime mold (2.5 cm in diameter) 517 was placed diametrically opposite to a glucose (attractant) spot of same size placed

4) Image Processing 534
Time-lapse images were taken every 5 minutes for a total of 420 pictures for each 535 replicate. The images acquired initially belong to the RGB color space and their size 536 was 1200 by 1200 pixels. Image analysis followed three main steps. First, the edge 537 of the petri dish was identified by fitting its border to a circle of known diameter. 538 Second, the image was segmented using the clustering algorithm k-means (52), 539 which was applied to the images converted into the ab* color space, which is the 540 CLAB space without the L* (lighting) component; this choice corresponds to the 541 robustness of this color space against changes of lighting conditions between 542 images. By the end of this step, all the pixels inside petri dish, e.g. the region of 543 interest (ROI), are identified as either slime mold or not-slime mold. 544 545 After distinguishing slime mold and non-slime mold areas, we identified the mucus 546 by using a subtraction method. The mucus is left by slime after refinement; this 547 substance acts as a marker present on already explored areas of the domain, 548 serving as an external memory to the slime mold (36,53). The fact that this mucus is 549 transparent makes it very challenging to identify by sole color analysis. We thus 550 trinarized the image based on the history of a given pixel, since a pixel that is 551 classified as non-slime-mold at the current image will necessarily contain mucus if it 552 has ever been classified as slime mold in any of the previous images. Conversely, a 553 non-slime-mold pixel will be classified as unexplored substrate if it has never hosted 554 slime mold up to that point in time. 555

556
The change of class from unexplored substrate to slime mold, defined as primary 557 growth, means that a new sprout of the slime mold reaches a point in space that it 558 had never explored before. Similarly, secondary growth is defined as the change 559 from mucus to slime mold, meaning that the slime mold is revisiting an already 560 explored location. Lastly, if the slime mold recedes from a point, e.g. a pixel goes 561 from slime mold to non-slime mold, it becomes mucus, and the process is defined as 562 refinement. By the end of these three steps, the images have been trinarized, 563 meaning that every pixel is classified as slime mold, unexplored substrate, or mucus 564 In order to quantify the differences of slime mold spreading dynamics on distinct 576 substrates, we first calculated the fraction of the petri dish area covered by slime 577 mold, mucus and unexplored substrate over time. The total area, the lighting 578 conditions and the test duration were the same for all treatments, both in the 579 homogeneous and spot experiments. Note that glucose only provides energy to 580 slime mold, which is not gaining significant mass during the experiments (54). In 581 other words, slime mold is changing its area by mostly by stretching and contracting, 582 therefore changing its area density. 583 In order to gain further insights about the exploration process we then computed the 585 cumulative area of primary growth, refinement, and secondary growth over the full 586 period of the experiments comparing two consecutive images at the time. The 587 cumulative area covered by primary growth is indicative of the total area of 588 exploration, therefore it is always smaller or equal to the total area of the dish. The primary plus secondary growth equals that covered by refinement, then slime mold 595 keeps the same density, whereas if it is superior, the slime mold stretches (e.g. 596 density decreases). If secondary growth is negligible and if the area covered by 597 primary growth equals the area covered by refinement, then slime mold displaces 598 mass. 599 600 We next measured the migration rate. To this aim, for two consecutive images, we 601 measured the distance from each pixel where growth occurred (both primary and 602 secondary) to the closest pixel classified as slime mold in the previous image. This 603 distance represents the extent of growth from one image to the next. We calculated 604 the migration rate as the ratio between the maximum distance traveled and the time 605 interval between two images (5 min). This maximum distance traveled was then 606 used to delineate the region explored by slime mold within the 5 min interval. In other 607 words, we defined an area of interest as the contour of the slime mold with an offset 608 corresponding to the maximum distance traveled (see Fig 1 in S1 Appendix for more 609 details). 610

611
We estimated the fraction of secondary growth as the ratio between the number of 612 pixels changing from mucus to slime mold and the total number of pixels in the 613 region of interest. We then calculated the fraction area of "expected secondary 614 growth", which would have occurred if secondary growth had happened randomly. If 615 the measured secondary growth fraction is higher (respectively, lower) than the 616 expected one, this means that slime mold has a bias towards mucus (respectively, 617 unexplored substrate). Where P and A are the perimeter and area of the shape of slime mold at a given 623 time; this index is equal to one when the contour of slime mold is circular, and 624 increases as the shape deviates from the circle. Eccentricity (E) is calculated as the 625 ratio between the distance between the foci and the major axis length, as follows: 626 = 1 − ! In which a and b are the lengths of the major and minor axes, respectively. When E 627 is equal to zero, the contour is a circle; when E is equal to one, the contour is 628 degenerated into a line. Solidity (S) is the ratio between the area of the slime mold 629 contour and the area of its convex hull, e.g. the smallest convex polygon that 630 encloses all the slime mold pixels. S is equal to unity when the contour shape is 631 convex. Lastly, we measured the number of clusters by performing an "erosion" 632 operation along the contour of the slime mold, consisting in removing the veins that 633 connect the regions of high concentration of slime mold. After this erosion process, 634 only the clusters of high concentration of slime mold remained, which provided the 635 number of pseudopodia at the given image. 636

637
For the spot experiments, we also determined the distance from the slime mold to 638 the glucose spot at every time step. This distance was calculated as the minimum 639 distance between the contour of the slime mold and the perimeter of the glucose 640 circular spot. The evolution of the distance to glucose over time was analyzed in a 641 way similar to a survival analysis, as described below. 642 643

5) Statistics 644 645
The full description of the statistics is provided as part of the supplementary 646 information; Appendix S1 includes the results of the complete statistical analyses, 647 while appendix S4 gives the necessary instructions to reproduce those analyses. 648 When dependent variables lasted until the occurrence of certain event, we 649 conducted survival analyses using the R package coxme (55). For the remaining 650 dependent variables, we did linear analyses using the R packages lme4 (56)