Impact of elastic substrate on the dynamic heterogeneity of WC256 Walker carcinosarcoma cells

Cellular heterogeneity is a phenomenon in which cell populations are composed of subpopulations that vary in their behavior. Heterogeneity is particularly pronounced in cancer cells and can affect the efficacy of oncological therapies. Previous studies have considered heterogeneity dynamics to be indicative of evolutionary changes within subpopulations; however, these studies do not consider the short-time morphological plasticity of cells. Physical properties of the microenvironment elasticity have also been poorly investigated within the context of cellular heterogeneity, despite its role in determining cellular behavior. This article demonstrates that cellular heterogeneity can be highly dynamic and dependent on the micromechanical properties of the substrate. During observation, migrating Walker carcinosarcoma WC256 cells were observed to belong to different subpopulations, in which their morphologies and migration strategies differed. Furthermore, the application of an elastic substrate (E = 40 kPa) modified three aspects of cellular heterogeneity: the occurrence of subpopulations, the occurrence of transitions between subpopulations, and cellular migration and morphology. These findings provide a new perspective in the analysis of cellular heterogeneity, whereby it may not be a static feature of cancer cell populations, instead varying over time. This helps further the understanding of cancer cell behavior, including their phenotype and migration strategy, which may help to improve cancer therapies by extending their suitability to investigate tumor heterogeneity.

assessed at each time point according to the criteria discussed in the "Materials and methods" section.Figure 1 provides examples of cells from the different subpopulations, described by cell type and dynamics.The migration of these cells is presented in Supplementary Video S1.In addition, preliminary analysis showed that the mesenchymal subpopulation of the WC256 line is comprised of cells that behave differently from each other, even if they meet the criteria to be considered part of the same subpopulation.These cells differed in the presence of a retraction tail, small protrusions, the shape of the leading edge, or migration velocity.Although investigating the diversity of the mesenchymal subpopulation was not the aim of this study, this is a possible avenue for

Dynamic heterogeneity of WC256 cells.
A single cell of the WC256 line may exhibit properties of more than one subpopulation over time.During the 4h observation, subpopulation transitions were seen to occur without any external chemical or physical stimulation.However, not every cell underwent such transitions; cells with persistent morphology always remained.The types of observed transitions are shown in Fig. 2A.Transitions marked by solid arrows were the most common.A standard mesenchymal cell could transition into a polygonal/bigonal cell, while the bigonal and polygonal cells could transition to mesenchymal and amoeboid cells.The amoeboid cells primarily transitioned to polygonal/bigonal cells.Only a few cells performed a "full transition" from mesenchymal to polygonal/bigonal (non-polarized) and then amoeboid (or in reverse).There was also a very small fraction (3 out of 100) of cells that performed a direct transition between the mesenchymal and amoeboid subpopulations.Cells performing the two main transitions (mesenchymal ↔ polygonal/bigonal; polygonal/ bigonal ↔ amoeboid) are shown in Fig. 2B, C and Supplementary Video S3.

Influence of cellular substrate on subpopulation transitions of the WC256 line.
To analyze the influence of substrate micromechanics on the WC256 line, its impact on the number of cells exhibiting properties of a certain subpopulation or subpopulation transitions was first assessed (Fig. 3).Then, the occurrence of particular subpopulations was calculated throughout the length of the observation (Fig. 4).Finally, the basic biophysical parameters of migration and morphology were analyzed to determine the influence of the applied substrate on WC256 subpopulation behaviors compared to the entire cell line (Fig. 5).
The calculation of morphologies duration in each cell was performed for the entire observation period (4 h).For each substrate, 50 cells from 5 experiments were analyzed and pooled together.The histograms in Fig. 3A demonstrate the time cells spent in specific subpopulations, depending on the cellular substrate.As some observed cells transitioned between subpopulations and, therefore, belonged to two or three subpopulations over time, the total number of cells in Fig. 3A is larger than 50 for each substrate.Fewer cells belonged to the mesenchymal subpopulation on the PA substrate compared to the glass substrate (19 vs. 35 cells, respectively).For both substrates, long mesenchymal states (4 h) were preferred; however, on the PA substrate, there were more cells that belonged to this subpopulation for a shorter period of time (< 1 h).The number of cells in the polygonal/ bigonal subpopulation was similar between the PA and glass substrates (34 and 29 cells, respectively).The duration of this subpopulation was distributed evenly throughout the observation period on the PA substrate.On the glass substrate, there was a slight dominance of polygonal/bigonal states that lasted between 1-2 h; however, the remaining time intervals were also distributed evenly.The largest difference between the substrates in terms of the number of cells was in the amoeboid subpopulation; there were 3 times fewer cells on the glass substrate.Cells seeded on the PA substrate primarily spent a very short amount of time in the amoeboid subpopulation, although long occurrences (4 h) were also observed.Among the cells seeded on the glass substrate, a similar number of cells spent a very short (< 1 h) and long (4 h) time in the amoeboid subpopulation.Intermediate times were either rarely observed or not observed at all.However, it is hard to determine whether these differences were caused by the cellular substrate or due to a low occurrence of the amoeboid subpopulation on the glass substrate.Further analysis determined how many transitions could be performed during the entire 4h experiment for the two most common subpopulation transitions (Fig. 3B).The highest number of transitions performed by a single cell was observed between polygonal/bigonal and amoeboid state (up to 6 transitions), however most cells transitioned between those subpopulations only once or twice.The maximum number of transitions between mesenchymal and polygonal/bigonal subpopulation was 4, nevertheless, most of the cells performed such action only once or twice as well.However, the influence of substrate properties on the number of transitions remains still unclear, as the number of most common transitions differed between the glass and PA substrates.Therefore, it was not possible to determine whether the visible differences shown in Fig. 3B resulted due to the difference between substrates or due to different occurrences of this phenomena.Interestingly, full transitions from the mesenchymal to the amoeboid subpopulation occurred spontaneously without additional stimulation.In total, 4 cells (2 cells per substrate) performed this transition by passing through the polygonal/bigonal subpopulation, and 3 cells (2 on the glass substrate and 1 on the PA substrate) accomplished this transition directly.
Influence of cellular substrate on subpopulation distribution of the WC256 line.The occurrence of all subpopulations during the entire observation time was calculated.All frames of cells exhibiting properties of particular subpopulations were summed and divided by the number of registered time frames.There were several time frames (< 5% in total) that had unidentified morphology.The occurrence of each subpopulation is shown in Fig. 4A.The PA substrate had a clear impact on the appearance of WC256 subpopulations.On the glass substrate, the mesenchymal subpopulation was observed in over 55% of the time frames, while it was observed in less than 25% of PA substrate time frames.On the PA substrate, an increase in the occurrence of the polygonal/bigonal (from 31.87% on glass to 44.38% on PA) and amoeboid (from 8.89% on glass to 23.17% on PA) subpopulations was observed.Substrate properties had an impact on the number of time frames that fit a defined morphology and performed transitions between subpopulations, as well as on subpopulation occurrence.
Figure 4B gives a better insight into the dynamics of WC256 subpopulations in time.For the cells seeded on glass substrate, the slight decrease of mesenchymal subpopulation occurrence paired with the slight increase of polygonal and bigonal cells over the course of experiment can be observed.It is in line with the fact, that transition between those two populations were most commonly observed on glass substrate and is confirmed by the significant anticorrelation of these subpopulations in time (Pearson's r = −0.8616*,p < 0.0001) as presented in Table 1.At the same time, the occurrences of amoeboid and undefined cells remained low and stable.On the other hand, the occurrence of mesenchymal subpopulation on PA substrate does not change much over time.However, the temporal fluctuations of polygonal or bigonal as well as amoeboid subpopulations can be observed.Those subpopulations are significantly anticorrelated (Pearson's r = −0.8274*;p < 0.0001), which also confirms the fact, that transitions between those two subpopulations were observed most frequently on PA substrates.It is important to mention, that very low p-values come from the transitions between subpopulations, which means that they should be treated as dependent variables.In Table 1 we can also observe other statistically significant correlations occurring on glass substrate, however due to the low occurrence of amoeboid subpopulation, this result should not be considered reliable.Similarly, the correlation between mesenchymal and polygonal or bigonal  www.nature.com/scientificreports/cells on polyacrylamide substrate is statistically significant, however the Pearson's r = 0.5151 shows that correlation between those two subpopulations is definitely weaker than between polygonal or bigonal and amoeboid cells described above.

Influence of cellular substrate on migration and morphology of WC256 subpopulations.
As the application of 40 kPa substrate was found to impact the occurrence of subpopulations, a consecutive step was made to examine whether it also had an impact on cellular shape and migration by comparing biophysical such as velocities, turning angles, cellular elongations, areas and perimeter/area ratios.These parameters were analyzed for each subpopulation separately, as well as for the entire WC256 population.
As shown in Table 2 and Fig. 5A, WC256 subpopulations have different velocities.The median velocity of the entire cell line was mostly influenced by the predominant share of mesenchymal and polygonal/bigonal cells.These cells exhibited similar velocities, despite mesenchymal cells typically being migratory polarized cells, while polygonal/bigonal cells are more chaotic, sometimes exhibiting Lévy flights.The greatest impact of www.nature.com/scientificreports/applied substrate was observed in amoeboid cells.Although the median velocity of amoeboid cells was moderately affected (increased from 1.325 µm/min to 1.536 µm/min), the difference between the 3rd quartile was 0.531 µm/min, indicating that amoeboid cells migrated faster on the PA substrate.The velocities of polygonal/ bigonal cells were not affected by substrate micromechanics, which was expected due to their chaotic movement.Mesenchymal cells migrated on the PA substrate slightly slower than on the glass substrate (Δ = 0.096 µm/min).median velocity for the entire WC256 population was almost unaffected by 40 kPa substrate; however, a significant increase was observed in the 3rd quartile (from 0.988 µm/min to 1.287 µm/min).This indicates that the increases in amoeboid subpopulation velocity paired and occurrence had a significant impact on the velocity of the entire WC256 population.The significance of a velocity difference between glass and PA substrate registered for the mesenchymal cells and the entire population could be due to the large number of measurements taken rather than a practical implication of this result.
The widest distribution of turning angles on both substrates (> 160°) was observed in polygonal/bigonal cells, as shown in Table 2 and Fig. 5B.This was expected due to their chaotic movement and was not altered by the substrate type.The mesenchymal subpopulation was characterized by a narrower distribution of turning angles on both substrates (< 105°), indicating more directed movement that was not altered by application of 40 kPa substrate.It only impacted the distribution of turning angles in the amoeboid subpopulation, which migrated more straightly on the PA substrate (IQRs on the glass and PA substrates were 70.9 and 46.2, respectively).The distribution width for the entire WC256 population was 18 degrees narrower on the PA substrate; which could be due to the higher occurrence of the amoeboid subpopulation on this substrate.However, this statistical significance was rather caused again by the large sample size rather than practical differences in turning angles.
The morphologies of WC256 subpopulations were remarkably different from each other (Table 2, Fig. 5C-E).Mesenchymal and amoeboid cells seeded on the glass substrate had similar elongation factors (0.365 and 0.357, respectively); however, polygonal/bigonal cells were the most elongated ones.The elongation of the mesenchymal subpopulation was visibly affected on 40 kPa substrate, appearing significantly rounder there.The elongation of the polygonal/bigonal and amoeboid subpopulations was significantly different between the glass and PA substrates; however, it appears that this difference was again caused by the large sample size.The impact of substrate micromechanics on the elongation of the entire WC256 population was small (only a 0.009 difference between substrates), which poorly reflects the variety of subpopulations morphologies.Cells observed on elastic substrate had also significantly smaller area (Table 2 and Fig. 5D), which is applicable to all subpopulations.The impact of substrate type on cell area was however the highest among mesenchymal cells (478.9 µm 2 on glass compared to 338.3 µm 2 on elastic substrate).In contrary, the ratio of cell perimeter to its area (Table 2 and Fig. 5E) increased on elastic substrates, with the greatest increase for amoeboid subpopulation (from 0.163 to 0.180 1/µm).All three parameters of cell shape described here show that cellular shapes of WC256 cells significantly changed, when polyacrylamide elastic substrates were applied.

Discussion
Current research indicates that heterogeneity is an inherent property of biological populations.This carries profound consequences for the biological sciences, as the fact that biological objects (in this case, cells) differ from one another has to be considered when analyzing experimental data.The current study has characterized the time evolution of morphology and migration parameters in adherent WC256 sublines for the first time.Previous studies 41,43 have characterized the entire WC256 population, including adherent and non-adherent sublines.Such studies demonstrated the complexity of WC256 cell morphology involving mesenchymal, polygonal/bigonal, and amoeboid (blebbing) cells.In the current study, based on time-lapse observations, cellular migration strategy and morphology were considered as two interrelated dynamic features that influence cell behavior.This approach enabled the construction of behavioral, dynamic criteria for the classification of WC256 subpopulations.This improves upon previous classifications, which were based on static images at specific time points.Previous classifications of WC256 subtypes are easily comparable with the approach presented in Fig. 1 and Supplementary Video S1.
The current study found a significantly larger number of mesenchymal (lamellipodia-creating) cells compared to polygonal/bigonal (nonpolar) cells on the glass substrate.This is in clear opposition to previous findings 41 and is thought to be due to several factors, including the way cellular subtypes were classified.During static analysis, mesenchymal cells could be classified as nonpolar due to their heterogenous morphology, as lamellipodia may not be clearly distinguishable (Supplementary Videos S1 and S2).Therefore, the analysis of time-lapse sequences is required to properly classify WC256 cell types in bright-field microscopy.The reversed proportion between mesenchymal and nonpolar subpopulations might also be a result of fibronectin coating, which was not present in previous work 41 but can significantly influence cell adhesion and morphology 44,45 .
The current analysis of time-lapse experiments revealed that the morphology and migration strategy of cells were unstable.WC256 cells were found to be capable of transitioning from one subpopulation to another, with 40% of cells seeded on the glass substrate exhibiting spontaneous transitions that occurred during the experiment without any external physical or chemical stimulation.The transitions observed were dynamic and reversible and could occur several times in a single cell.Current literature presents numerous examples of cells transitioning from mesenchymal to amoeboid (MAT) subpopulations and from amoeboid to mesenchymal (AMT) subpopulations.However, these examples were triggered by various physical, chemical, and biological factors, including the local ECM environment 46 , surface coating and confinement introduction 47 , perturbation of actin polymerization and actomyosin contractility 43,48 , and integrin receptor blocking 49 .Previous research has stated that a more pronounced shift between ameboid and mesenchymal morphology requires long-term culture under specified conditions and is likely due to epigenetic changes 41 .The most common transitions observed in the current study occurred between mesenchymal and polygonal/bigonal subpopulations, as well as between www.nature.com/scientificreports/ the polygonal/bigonal and amoeboid subpopulations.Even if they did not undergo MAT/AMT transitions, the observed cells could change their morphology significantly by losing or establishing polarization.A small number of cells underwent a full MAT/AMT transition, passing through the intermediate polygonal/bigonal state.
To the authors' knowledge, there are no other reports of transitions similar to these.The spontaneous nature of these transitions in any 2D in vitro culture has also not been previously observed.This may be due to the long migration observations in the current study, which were densely sampled.The time-lapse observation of cancerous cells used in the current study may be the key to improving further research by providing greater insights into cellular functioning.The velocity of mesenchymal subpopulation seeded on the glass substrate was similar to the velocity of "lamellipodia-forming cells" distinguished in previous work 42 , while the amoeboid subpopulation was significantly slower.Such differences may stem from the fact that in previous studies, amoeboid cells were directly derived from a non-adherent subline and had weak substrate adhesion that promoted effective migration due to bleb formation.In contrast, the amoeboid cells in the current study were part of an adherent subline and were present in approximately 10% of all observed glass substrate frames.The epigenetic differences between non-adherent and adherent sublines and, consequently, differences in adhesion levels might explain this velocity difference.It also highlights the lack of difference between well-spread cells that are similar to each other in the current study and previous studies.
In the current study, mechanical microenvironment impacted WC256 cells in several ways, one of which was the distribution of subpopulations.The glass substrate had more mesenchymal cells but fewer amoeboid cells compared to the PA substrate.Only the polygonal/bigonal cells were similarly abundant on both substrates.The differences in occurrence and duration of subpopulations and their durations were clearly visible.On the glass substrate, mesenchymal cells were the predominant subpopulation, while on the PA substrate, it was the polygonal/bigonal subpopulation.The amoeboid subpopulation had a low presence on the glass substrate, being more abundant on the PA substrate.This 'shift' from a well-spread mesenchymal to a poorly-spread amoeboid subpopulation may be due to the possible presence of obstacles in substrate-cell interactions on the PA substrate, which is in line with previous models that state that softer substrates promote blebbing and pseudopodial morphology over mesenchymal morphology 50 .The influence of elastic substrates on cell morphology and migration has been widely discussed in previous literature 15,30,[51][52][53][54] , as well as their role in tumor progression 19,55 .Many different factors have been discussed within the context of tumor heterogeneity, including epigenetic and genetic alterations 56 .The current work provides important evidence that substrate properties, especially mechanical ones, can significantly impact the distribution of cell subpopulations and, therefore, cancer heterogeneity.This result is significant within the context of cancer development, as the mode of migration is a crucial aspect of metastasis.
The ratio of mesenchymal to amoeboid cells within a population, as well as the plasticity of transitions between them, can determine the probability of cancer dissemination.A significant change in subpopulation distribution, as observed in the current study, can significantly impact the results of migratory experiments due to the involvement of a completely different set of signaling pathways 57 .This becomes particularly important when considering potential antimetastatic agents.One of the most important results in the current study was the observed shift towards the amoeboid mode of migration on the PA substrate.The significance of the amoeboid mode of cancer cell migration was recently summarized 57,58 .It is connected to an improved ability of cancer cells to disseminate and cancer cell stemness.There is indirect evidence that the dependence of MDA-MB-231 and A375M2 cell lines (human breast cancer and melanoma cells, respectively) on PKCα amoeboid migration correlates with their invasiveness 59 .Cancer cells that easily change their mode of migration from mesenchymal to amoeboid can avoid proteolytic enzyme inhibitor-based therapy 60 .The ability of the adherent WC256 subline used in the current study to switch from a mesenchymal to amoeboid mode of migration without external stimulation, particularly on the PA substrate, is an important finding due to its potential use in cancer therapy.
Novel computational models predict that particular modes of migration are advantageous within homogeneous conditions of low or high resistance (amoeboid and mesenchymal migration, respectively) 61 .The same models demonstrate that high plasticity of mesenchymal to amoeboid transitions is beneficial in heterogeneous microenvironments, which are typically in vivo 61 .The current study considered direct MAT/AMT transitions, as well as the intermediate stages.It revealed a high plasticity on both substrates, with cells rapidly adapted to them.A mathematical model of cancer cell migration in extreme modes in a maze-like 2D environment revealed an additional advantage of heterogeneity within populations, as the proteolytic activity of mesenchymal cells paved the way for amoeboid cells 62 .In the current study, the PA substrate led to a substantially higher proportion of amoeboid cells and cells that could dynamically change their mode of migration to amoeboid, however there was a small population of mesenchymal cells that could turn into amoeboid.The amoeboid mode of migration was underestimated for a long time due to its rare occurrence and difficult characteristics on rigid 2D substrates.It has drawn wider attention since migration research has begun using 3D conditions 63 .Although the current study model does not simulate a 3D microenvironment, it is still able to reflect in vivo conditions while maintaining the convenience of 2D in vitro migration models.As tumor heterogeneity is an important factor in cancer diagnosis and treatment 3,4,56 , further studies are needed to elucidate the effects of the mechanical interactions between a tumor and its microenvironment.
In addition to subpopulation duration, transition, and distribution, substrate micromechanical properties impacted the morphology and migration parameters of some WC256 subpopulations.Mesenchymal cells were rounder on the PA substrate, but other parameters in this subpopulation were poorly influenced by the type of substrate.No practical differences were observed in polygonal/bigonal cells as their velocity and turning angles did not change; however, they became slightly rounder on PA substrate.In the amoeboid subpopulation, cellular velocity visibly differed, with faster cells seen on the PA substrate.The current data consisted of a large number of samples; therefore, even very small changes appeared statistically significant.Therefore, even in parameters where statistically significant differences were reported (e.g., mesenchymal cell velocity, polygonal/bigonal, and www.nature.com/scientificreports/amoeboid cell elongation), the practical implications in some cases could be minimal.However, the elastic substrate did impact the subpopulations differently in the context of migration and morphology parameters.The existing literature demonstrates that cell properties, for example, cell growth, can depend on substrate rigidity 17 , although this impact differs for particular cell lines.The current study clearly demonstrates that even in one cell line, distinct subpopulations are present and respond differently to the mechanical properties of the microenvironment.
The current data highlights the significance of unitary analyses of heterogenous cell lines.Across all analyzed parameters of cell migration and morphology, the results obtained across the entire WC256 population differed from those obtained for each subpopulation.It is crucial that heterogeneous cell lines are analyzed in the context of their subpopulations, as averaging parameters may significantly change the final results 2 .
Two different cellular substrates were employed in these studies-glass and polyacrylamide-based hydrogel with Young modulus of 40 kPa.It is known that the mechanical properties of the microenvironment significantly impact many biological processes in physiological and cancerous cell lines, including stem cells.One of them is substrate elasticity which can alter cell proliferation 17,51,55,64 , spreading 30,64 , morphology 15,51,52 , F-actin organization 30,54,65 , migration velocity 30,53 and directionality 53,54 .However, other substrate properties such as substrate adhesiveness, porosity, ECM patterning or dimensionality can influence the cell behavior.In this study, the mechanism of ECM binding on glass and PA substrates differed, so even if the similar concentration of protein solution during biofunctionalization of the substrates was provided, the resulting density of extracellular matrix proteins might differ.Current literature shows, that ligand density interplays with substrate elasticity, resulting in the modified cell spreading 44 .Another aspect in which glass and PA substrate differ is the porosity.While generally glass is smooth, the PA gels exhibit pores that in substrates that are softer (30 kPa) than the one used in this study, reach up to 45 nm 34 .However, the porosity does not need to impact cellular functioning in subject of their differentiation or magnitude of traction forces, while regardless of the porosity, those processes were regulated predominantly by the substrate elasticity 34 .Taking all of this into consideration, we expect the substrate elasticity to be the major factor causing changes in the dynamic heterogeneity of WC256 Walker carcinosarcoma cells.Nonetheless, further investigation of the interplay of different aspects of substrate micromechanics on cellular heterogeneity is necessary to give a better insight into mechanisms of cancer biology.

Limitations and further issues
The current study involved the 4-h observation of transitions between different subpopulations of an adherent WC256 subline.To find prospective longer transitions and investigate this uncommon phenomenon in greater depth, future studies should extend the observation time while maintaining a similar degree of sampling to capture all significant information.In this study, the 40 kPa substrate was used to mechanically mimic breast parenchymal tissue, which has elasticity between 30 and 50 kPa 66 and to create a biomimetic microenvironment for the rat breast carcinosarcoma cells.However, the breast also consists of fat tissue that has a Young modulus of approximately 7 kPa, and the elasticity of cancerous breast tissues can vary from 20 to 100 kPa depending on their malignancy 66,67 .Furthermore, the composition and concentration of the ECM is not typically even within the whole breast.The dimensionality of the experimental setup could also have influenced the results, as cells in 2D, 3D, and sandwich-like environments can exhibit different migration modes 50,57 .Therefore, the comparison of cellular transitions and morphologies on softer and stiffer substrates, combined with different types of ECM and substrate dimensionality, will provide deeper insights into the biophysical and biochemical mechanisms of this phenomenon.However, future studies will require the invention of new quantitative methods for analyzing cellular morphology and migration properties since such datasets will contain tens to hundreds of thousands of frames that each need to be assigned to their proper subpopulation.

Materials and methods
Cell culture.Walker carcinosarcoma cells were obtained from Professor H. Keller (University of Bern, Bern, Switzerland).The adherent subline of WC256 cells was derived from the initially non-adherent cells grown in a suspension by Dr. Jolanta Sroka 41 .The WC256 cells were cultured in an RPMI-1640 medium (EuroClone) supplemented with 5% fetal bovine serum (Gibco), 100 IU/mL penicillin, and 10 μg/mL streptomycin (Sigma-Aldrich).Cells were maintained in a humidified 37 °C incubator with 5% CO 2 42 .

Substrate preparation.
Two types of substrates were used: glass-bottom dishes for control samples and elastic PA substrates for experimental samples.The dishes were silanized via treatment with an acetic acid solution of 3-(trimethoxysilyl) propyl methacrylate (Sigma-Aldrich) and 96% ethyl alcohol in a 1:1:14 proportion for 20 min.They were subsequently rinsed three times using 96% ethyl alcohol 68 .These procedures were performed to increase the affinity of the PA substrate for glass 69,70 .The PA substrates with a Young modulus of E = 40 kPa were prepared according to standard procedure, using a 40% aqueous solution of acrylamide (Bio-Rad), a 2% aqueous solution of Bis-Acrylamide (Bio-Rad), and red fluorescent beads (Invitrogen) diluted in a 10 mM aqueous solution of HEPES (Sigma-Aldrich) 11,25,69,70 .As the WC256 cells came from rat carcinosarcoma, the 40 kPa elasticity was chosen to mimic the elasticity of breast parenchymal tissue 66 .The mixture was polymerized using 10% ammonium persulfate (Bio-Rad) and tetramethylethylenediamine (BioShop) in ratios of 1/200 and 1/2000 to the total volume of the mixture.Then, 23 μl of the solution was applied to the silanized glass bottom plates.Each drop was covered with an 18 mm (diameter) coverslip.Polymerized substrates were activated by applying the Sulfo-SANPAH solution (Thermo Scientific) and 5 min of ultraviolet light.The substrates were then washed three times with sterile PBS.The hydrogels were incubated with a 15 μg/ml fibronectin solution at 4 °C for 12 h 69,70 .The glass-bottom dishes used in the control experiments were incubated with the same fibronectin solution.www.nature.com/scientificreports/Time-lapse registration of cell migration.WC256 cell migration was recorded using the time-lapse method and an inverted Axio Observer.Z1 microscope (Zeiss), AxioCam camera (Zeiss), and a Plan Apochromat 10×/0.45objective (Zeiss).Data acquisition was carried out for the duration of 4-h observation at 90-s intervals.Cell migration registration started 1 h after seeding (30 min after cell adhesion was observed).A temperature of 37 °C and a CO 2 concentration of 5% were maintained during image acquisition.The definite focus component (Zeiss) was used to maintain the proper plane.

Image analysis.
During the image analysis, 50 cells from five control and five experimental samples were analyzed.Binary masks were obtained from the brightfield images.Cells with sharp boundaries and regular shapes were analyzed automatically using cell migration software that produced binary masks 71 .Cells that were not appropriately identified by the software were analyzed manually using the ROI Tracker plugin 72 in the ImageJ software.The perimeters were converted to binary masks using ImageJ.The binary masks were analyzed using a custom script in MATLAB.From each binary mask, the centroid and elongation were calculated.The velocity in each frame was calculated by dividing the displacement in the current (n) and following (n + 1) frames by the time interval.Turning angles were calculated as the angle between two subsequent displacement vectors (i.e., between frames n − 1 → n and n → n + 1).Elongation was defined as ε = 1 − (a/b), whereby a and b represent the major and minor axis of the ellipse fitted to binary shape, respectively (ε = 0 for circular shapes and ε = 1 for infinitely elongated ellipse).Cell area and perimeter were obtained from binary masks and recalculated to the pixel size.Quantitative descriptors of migration and morphology are presented in Fig. 6.
Inclusion criteria.This study aimed to analyze single migrating cells that did not visibly interact with each other.Therefore, only cells that met certain criteria were analyzed: (1) the cell had to be an individual; (2) the analyzed cell could not be in contact with another cell; and (3) the cell could not be undergoing division in current or neighboring frames.In most cases, cell division starts with cell rounding, followed by spreading on the substrate.However, before and after this process, WC256 cells maintained a similar morphology.Thus, only those frames in which cells were not rounded or were already spread after the division process were analyzed.Frames where a cell was interacting with another cell either by direct collision or visible changes in shape or migration direction that occurred only near a neighboring cell were excluded from the analysis.

Subpopulations analysis.
Different subpopulations were distinguished similarly to previous work 41 , with mesenchymal, polygonal/bigonal, and amoeboid classifications used.The current study focused on the qualitative identification of cell types as robust and universal quantitative descriptors for the discrimination of cell subpopulations do not exist.To be qualitatively identified as mesenchymal, cells had to meet several criteria: the one-way expansion of the cell border had to result in the directional displacement of the cell centroid in a short timeframe (several image frames); movement had to involve either a keratinocyte-like gliding motion or repeated cycles of protrusion and attachment of the cell leading edge, coordinated with the detachment and retraction of the cell rear 57,73,74 ; and a similar shape (mostly well spread) had to be maintained over time.To be qualitatively identified as polygonal/bigonal, cells had to meet different criteria: expansion of the cell border had to occur in more than one direction (cell stretching) and result in the non-directional displacement of the cell centroid in a short timeframe; there could only be limited moments in which the cell tore off from one adhesion site, which had to result in the displacement of the cell centroid; and similar morphology (mostly well spread) had to be maintained over time.To be qualitatively identified as amoeboid cells, several criteria had to be met: the one-way expansion of the cell border had to result in the directional displacement of the cell centroid in a short timeframe; they had to have an unstable shape (mostly poorly spread) with small dynamic protrusions (pseudopodial cells); or migration had to occur via spherical protrusions on the leading edge (blebbing cells) 43,47,57 .
The assignment of subpopulations was conducted within the context of cell dynamics rather than using a simple analysis of cell shape in a given frame.For each frame, the 2 previous and 2 ensuing frames were compared to determine cell behavior.This enabled the observation of membrane extension direction (uni-or multidirectional), which was an important criterion of subpopulation classification.Frames that were hard to classify using the criteria were designated as an "unidentified" subpopulation.This subpopulation was excluded from further analysis of migration and shape parameters.

Figure 2 .
Figure 2. (A) Subpopulations transitions observed in migrating cells of WC256 adherent subline.The main transition path marked with solid arrows starts from mesenchymal and goes through polygonal and bigonal to amoeboid subpopulation.Direct transition between mesenchymal and amoeboid subpopulation (marked with dashed arrows) was observed as well, although very rarely (3% of all observed cells).(B) Exemplary transition between mesenchymal and polygonal form.(C) Exemplary transition between amoeboid and polygonal form.Time scale in minutes:seconds, scalebar = 25 µm.Dynamic behaviors of the same cells are presented in Supplementary Video S3.

Figure 3 .
Figure 3.The influence of the mechanical properties of substrates on the dynamics of WC256 cells; (A) histograms of time spent in each subpopulation by WC256 cells; (B) histograms of number of transitions performed by dynamic cells, presented for two most common transitions (mesenchymal ↔ polygonal/bigonal; polygonal/bigonal ↔ amoeboid).

Figure 4 .
Figure 4. (A) The occurrence of different subpopulations in WC256 adherent subline plated on glass or elastic PA substrate.Each bar represents the share of frames of each subpopulation in the total number of registered frames; error bars represent the square root of counts.(B) Time evolution of total share of each subpopulation; error bars represent the square root of counts.

Figure 6 .
Figure 6.Selected quantitative parameters describing cell migration and morphology.