Enhancing cell motility via non-contact capacitively coupled electrostatic field

Abstract

Cellular motility is essential for making and maintaining multicellular organisms throughout their lifespan. Migrating cells can move either individually or collectively by a crawling movement that links the cytoskeletal activity to the adhesion surface. In vitro stimulation by electric fields can be achieved by direct, capacitive or inductive coupled setups. We tested the effects of electrical stimulation provided by capacitive coupling on glioma cells, using a capacitive-coupled system powered by a potential difference of 35 V between two electrodes placed outside the culture dish. Numerical dosimetry identified two different fields: (i) in the order of 10³ V/m at the level of the dielectric substrates, with almost uniform distribution; (ii) in the order of 10⁻¹ V/m at the level of the culture medium, with spatial and material-dependent distribution. The scratch assay and the tracking of single-cell movement showed a boosted motility when crawling occurs on polystyrene surfaces, demonstrating the feasibility of this peculiar exposure system to generate forces capable of influencing cell behavior.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-77384-9.

Introduction

The architecture of multicellular organisms is ensured by cellular motility both during development and throughout lifespan. This process is not only essential for tissue formation during the morphogenesis phase, but is also preserved for maintenance, regeneration and restoration of integrity, as well as for stem cell mobilization and immune defense^1–3. Migrating cells can move individually or collectively. The deformation and movement (crawling) of an individual cell are mediated by cytoskeletal activity that relies on actin polymerization and dynamics of adhesion complexes at the extracellular matrix (ECM) interface: cells apply traction forces to the substrate through the formation of adhesive structures and the transmission of internal forces produced within their cytoskeleton^4,5. Collective movement, to cell-ECM coupling, adds a layer of complexity with intercellular junctions between neighboring cells allowing them to coordinate cytoskeletal activity and act as a cohesive group¹. Collective and single-cell movements underlie distinct molecular programs that can be modulated by numerous external factors such as physical properties of the matrix, external forces and biochemical factors^2,6–10. Therefore, it is important to take into account the mechanical forces exerted by individual cells on the underlying substrate and the physical properties of the cellular environment, including its stiffness, topography and porosity⁴. Among other factors that can trigger cellular responses, electric fields (E-fields) can override most chemical gradients and bias the underlying signaling networks, influencing cell migration^11,12. This intimate connection between cellular function and electric potentials suggests that cellular behavior may be modulated by the application of an external E-field, offering as a possible application, design and engineering principles for the rational manipulation of the cellular network^13–15.

The 3D topological organization and constant remodeling of the ECM make in vivo analysis of cell movement difficult, therefore in vitro approaches are particularly useful for multiscale analysis from the molecular to the multicellular level. Standard disposable specimens on which cells are cultured for motility studies are 2D surfaces of polystyrene or borosilicate glass. The physical properties of these materials can strongly influence adhesion and crawling capability: cells attach more to plastic than glass, as indicated by the higher plating efficiency observed on plastic surfaces compared to glass surfaces¹⁶. Furthermore, companies often perform physical pretreatments, for example with plasmas, gamma rays or electrical stimuli, aimed at changing the surface free energy and thus increasing cell adhesion.

In vitro cell stimulation by exogenous E-fields can be accomplished by three different setups: (i) direct or conductive coupled (D-Coupled): two parallel metal electrodes are placed in direct contact (or indirectly through agar or salt bridges) with the culture medium; (ii) capacitive coupled (C-Coupled): two typically parallel flat metal electrodes are separated from the culture medium by an insulating layer and no electron transfer reactions occur at the insulator-electrolyte interface; (iii) inductive coupled (I-Coupled): a current flowing in the coil creates a magnetic field, which in turn induces an E-field (electromagnetic induction)^17,18.

In the vast majority of experiments aimed at capturing the mechanism of action underlying the driving effects of E-fields stimuli on cell migration (electrotaxis), D-Coupled (i) systems have been mainly employed^19,20 and have used direct current (DC) signals or low frequency AC potentials. In this case, the energy transferred to the culture medium is a current density (J) induced by electrophoresis which in turn induces a different charge distribution on the two sides of the cultured cells^21–26. However, the noble metals used as electrodes inserted into the physiological saline solution generate at the interface the electrolysis of water, the oxidation of the saline solution, the dissolution of the metal and the oxidation-reduction of organic materials, with the formation of unwanted electrochemical species and consequent toxic effects on the cells^27,28. In contrast, a C-Coupled system does not require contact electrodes and does not inject charges into the cell culture medium. Despite the generated E-field is small and screened on fast timescales a small number of studies uses the method as a powerful tool for mitigating unwanted physical-chemical interactions between the exposure system (metal electrodes) and the biological environment. The successful application of the C-Coupled system paired to AC potentials has been reported mainly for tissue engineering and particularly for bone, or hyaline cartilage regeneration^{22,23,29–32}, based on the seminal study by Rodan and coauthors³³. Only recently, it has been reported that capacitive stimulation using non-contact electrodes powered by a very low continuous stimulation (DC) delivered to a commercial titanium disk-based bioreactor increases the rate of cell proliferation and differentiated morphology of cultured human mesenchymal stem cells³⁴.

Among the computational modeling approaches aimed at numerically describing the effect of C-Coupled electrical stimulation on cells^26,35, the work of Taghian et al. also takes into account electrical stimulations at very low frequencies up to DC. The study claims that, although the E-field is shielded by the electrolytic compartments of the cell (the cytoplasm and the culture medium), if even only a portion of the cell membrane is adhered to the dielectric substrate, a direct voltage produced by the electrodes not in contact with the extracellular medium can exert an effect on the bioelectrical properties of the plasma membrane³⁶. The same research group, more recently, has reported in two experimental proceedings significant changes in the level of the plasma membrane lipid component (phosphatidylserine) of glioma cells following low-amplitude DC E-field exposure delivered by an external non-contact parallel-plate capacitor system³⁷.

In the present work, we designed a very simple C-Coupled exposure system which is based on the generation of an electrostatic field by the onset of a potential difference between two parallel-plate (positive and ground electrodes) placed outside the cell culture dish. Additionally, the C-Coupled system consists of ground components, which include a central ring surrounding the dielectric support (Petri dish) and a metal plate located at the bottom of the entire exposure system. The potential difference set in the presented exposure system gives rise to the generation of an E-field which enables the investigation of the role of an externally applied E-field on the migration of tissue-forming cells.

Glioma cells’ line is an appropriate model for both single and collective behavior since: (i) in vivo can invade both individually or as a group the brain parenchyma; (ii) in vitro, adhering easily on very stiff substrates, can produce their own ECM; (iii) make gap junction and when cultured express a cobblestone-like structure characteristic of epithelial monolayer; (iv) have a mesenchymal migration strategy instead of ameboid; (v) are sensitive to E-field both in vivo, such as that generated endogenously around fibers in white matter tracts or unmyelinated axons stimulating invasion³⁸ and in vitro, such as externally applied direct current inducing migration to the cathode³⁹. Furthermore, gliomas are anchorage dependent, meaning that to be viable they need to adhere to a solid therefore the physical features and mechanical properties, such as viscosity and elasticity of the surrounding environment⁴⁰ are interactively engaged in the process of movement. T98G cell line, derived from a human glioblastoma multiform tumor, is commonly used in brain cancer research and drug development. T98G cells are known for having high expression of the ACTA2 gene (actin alpha 2 is a globular multi-functional protein that forms microfilaments), which is involved in cell motility and structure⁴¹.

Thus, we tracked the motion of living T98G glioma cells cultured in vitro on standard surface and pushed to restore a confluent layer by mechanical scratch or single-cell movement in any direction exposed to the non-contact static E-field generated by the C-Coupled system. The exposure system is modeled by a capacitor-resistor (C-R) circuit in which a capacitive coupling generates a displacement current upon the application of a voltage difference across externally placed plates and metallic parts of the system all around the Petri dish containing the cells. Numerical simulations on the exposure system were performed to provide the E-field distribution generated in the Petri dish, using 3D detailed CAD models of the system in the COMSOL Multiphysics software and solving the simulations with a finite elements method approach.

Results

Numerical dosimetry

Numerical dosimetry provides the distribution of the electrical quantities inside the exposure system adopted for this study, enabling a rigorous and quantitative description of the electrical characterization of the environment. The key components of the exposure system have been recreated and studied using a three-dimensional CAD model. The system consists of a modified capacitor, where there are two electrodes arranged in parallel (set as ground and positive electrode). Adjacent to these electrodes are two ground components: a central ring surrounding the dielectric Petri dish containing the cells; and a metal plate situated at the bottom of the entire exposure system. The CAD model was built for the two exposure configurations and used for subsequent simulations and analysed using a Multiphysics software, as described in detail in the Numerical dosimetry setup section of the Methods.

The system has been simulated by the 3D models on two different cell sample holders: (i) a plastic Petri dish and (ii) a plastic Petri dish with a central glass-well. The E-field distribution for the two configurations is shown in Fig. 1A and B, in terms of spatial distribution on the ZX-cut plane crossing the center of the exposure system (log₁₀ scale), together with the E-field lines reported as blue arrows. From Fig. 1 it is evident how the highest values (in the order of tens of kV/m) of the E-fields remain within the insulating materials, such as plastic, glass, and air (mainly near the positive electrode), while in the conductive cell medium, the orders of magnitudes are in the range of tenths of mV/m (at the periphery of the system) to tenths of V/m in most part of the system. Moreover, as expected, the E-field arrows tend to be perpendicular at the two interfaces between the air-conductive culture medium and the conductive culture medium-plastic/glass, although a small parallel component is observed at the interface between air and conductive culture medium due to an ionization current building-up caused by the humid air environment. Figure 1C and D report the current density module and arrows on the ZX-plane crossing the center of the exposure system for the two configurations. Data show higher current density values in the medium, than in the plastic and glass of the sample holder, as expected.

Figure 1.

E-field (A, B) and J (C, D) distribution on the XY-cut plane passing through the center of the two configurations: (A, C) plastic Petri dish and (B, D) the Petri dish with the glass well sample holders. The E-field arrows on the selected plane are reported in light blue (A, B). The J arrows on the selected plane are reported in magenta (C, D).

These data are confirmed by the E-field spatial distribution on the XY-cut planes at different Z-quotes (see Fig. 2), crossing the plastic (Fig. 2A) and the glass (Fig. 2B) of the sample holders, where the values are about 6 kV/m, dropping down to 0.12 V/m (Fig. 2C) and 0.09 V/m (Fig. 2D) on the culture medium of the two configurations. The details on the values distribution of the E-field on the culture medium planes where the cells are placed are reported in terms of boxplots for the two configurations in Supplementary Fig. S3. From the numerical dosimetry of the two different configurations of the exposure system, it emerges that the first configuration, with the plastic Petri dish as the cell sample holder, gives higher E-field values, with a high non-uniformity of their distribution, and this feature of the E-field environment can resemble endogenous E-fields detected in vitro⁴². The differences in terms of induced E-field distribution between the two sample holders can be attributed mainly to the position of the adherent cells’ plane in these two cases, with a 0.5 mm shift of the plane for the Petri dish with glass configuration, compared with the plastic Petri dish (as shown in Supplementary Fig. S1, where the CAD models’ details are reported). For these reasons, we can assume that the first configuration is more suitable for performing in vitro studies, thus for the following results we will focus on this plastic Petri dish configuration.

Figure 2.

The E-field distribution evaluated on the XY-cut plane passing through the inner interface of the support for the plastic Petri dish (A) and the Petri dish with the glass well (B). The induced E-field distribution evaluated on the XY-cut plane where the cells are placed for the two configurations in panels C and D. Adherent cell planes at Z = -1 mm (C) and Z = -1.5 mm (D).

E-field effects on collective cell’s migration

Exposure of in vitro biological systems to E-fields could cause a thermal effect that would invalidate the interpretation of the results. To exclude thermal effects a preliminary test was carried out on the temperatures reached by the culture medium following exposure to the field generated by the non-contact C-Coupled, as described in Supplementary Information. The results indicate that there is no induction of temperature changes (Supplementary Fig. S9).

The scratch assay is a widely used test for studying the migration of adherent and tissue-forming cells. The most important information it provides is the capability of cells to move collectively, filling up the empty space created by the mechanical scratch. Considering the E-field distribution difference numerically evaluated of environments (Fig. 1) and surfaces (Fig. 2) due to the Petri dish geometry and materials, we studied the collective migration of cells when the scratch is parallel (vertical scratch) (Figs. 3 and 4) or perpendicular to the electrodes (horizontal scratch) (Figs. 5 and 6). The details of the numerical E-field data along the vertical and horizontal scratches are described in the Supplementary Information and reported in Supplementary Fig. S5. Despite the number of cells seeded is carefully standardized, the experimental procedure could introduce minor variations, such as the scratches dimension or the density population distribution on the Petri dish surface. Therefore, only those experiments in which the average gap between the leading edges was similar among controls and exposed right after scratching, i.e. at time 0 (T = 0 h), were selected. The effects of the E-field exposure on the collective migration of cells adhering to a polystyrene or a glass surface were tested by measuring the percentage of closure over time of a vertical scratch (parallel to the electrodes) as the Binary Area Fraction of each visual field (an example in Fig. 3A, B) normalized to the value obtained at T = 0 h following the formula reported in Methods, averaged and graphed in Fig. 3C and D as a function of time.

Figure 3.

E-field effects on collective migration of T98G monolayers adherent to polystyrene and glass surface tested by scratch assay parallel to the electrodes. Phase contrast micrographs of the same visual field acquired at 200× magnification right after scratching (T = 0 h; left) and after 6 h of EF exposure (T = 6 h; right) at the level of the scratch on the specimen of polystyrene (A) and glass (B). The yellow area represents the Binary Area Fraction. Scale bars are 250 μm. The black arrow above each micrograph represents the E-field direction from the positive pole to the ground. Mean of the Binary Area Fractions measured from the images scanned along the scratch carried out in six independent experiments (CTL n = 75; EF n = 99) for polystyrene (C) and four experiments (CTL n = 36; EF n = 32) for glass (D). Blue and red solid lines show the percentage of closure of the scratch along time (20 h) for CTL and EF experiments, respectively. Blue and red transparencies are the relative confidence interval (95%). The inserts on the right side of each graph show the area of data collection relative to the scratch made on monolayers (C and D).

Figure 4.

E-field effects on collective migration of T98G monolayers adherent to polystyrene and glass surface tested by scratch assay parallel to the electrodes. Phase contrast micrographs of the same visual field acquired at 200× magnification right after scratching (T = 0 h; left) and after 6 h of EF exposure (T = 6 h; right) at the level of the scratch on the specimen of polystyrene (A) and glass (B). The two leading edges are highlighted by solid red lines for the ground side and dashed lines for the positive pole side. Scale bars are 250 μm. The black arrow above each micrograph represents the E-field direction from the positive pole to the ground. Mean Distance (µm) performed by the leading edges on the Ground (Edges 1, blue for CTL and red for EF solid lines) and Positive Pole side (Edge 2, blue for CTL and red for EF dashed lines) during the first four hours on the polystyrene (CTL n = 75; EF n = 99) (C) and glass (CTL n = 36; EF n = 32) (D) surface. Blue and red transparencies are the relative confidence interval (95%). The inserts on the left side of each graph show the area of data collection relative to the scratch made on monolayers (C and D). Mean velocity (µm/hours) performed by the leading edges on the Ground (Edges 1, blue for CTL and red for EF solid lines) and Positive Pole side (Edge 2, blue for CTL and red for EF dashed lines) during the first four hours on the polystyrene (CTL n = 75; EF n = 99) (E) and glass (CTL n = 36; EF n = 32) (F) surface. Blue and red transparencies are the relative confidence interval (95%).

Figure 5.

E-field effects on collective migration of T98G monolayers adherent to polystyrene surface tested by scratch assay perpendicular to the electrodes. Phase contrast micrographs of the same visual field acquired at 200× magnification right after scratching (T = 0 h; above) and after 6 h of EF exposure (T = 6 h; bottom) at the level of the scratch near the ground electrode (A), the center (B) and the positive pole (C). The colored areas represent the Binary Area Fraction. Scale bars are 250 μm. The black arrow above each micrograph represents the E-field direction from the positive pole to the ground. D) Mean of the Binary Area Fractions calculated from the images scanned near the Ground (black, n = 16), the Center (green, n = 16) and the Positive (red, n = 16) regions along the scratch carried out perpendicular to the electrodes and during 20 h of EF exposure in three independent experiments. Green, black and red transparencies are the relative confidence interval (95%). Blue solid line shows the percentage of closure of the scratch along time for CTL (n = 75) in the six independent experiments showed in Fig. 3C, blue transparency is the relative confidence interval (95%). E) Mean of the Binary Area Fractions measured during EF exposure from the images scanned along the entire scratch carried out perpendicular to the electrodes in the three independent experiments showed in Fig. 5D (red dashed line, n = 48) and parallel to the electrodes in the six independent experiments showed in Fig. 3C (red solid line n = 99). Red transparencies are the relative confidence interval (95%). The inserts on the right side of each graph show the area of data collection relative to the scratch made on monolayers (D and E).

Figure 6.

E-field effects on collective migration of T98G monolayers adherent to polystyrene tested by scratch assay perpendicular to the electrodes. A) Phase contrast micrographs of the same visual field acquired at 200× magnification right after scratching (T = 0 h; left) and after 6 h of EF exposure (T = 6 h; right) at the level of the scratch near the ground electrode. The two leading edges are highlighted by solid black lines for the upper side and dashed lines for the lower side. Scale bars are 250 μm. The black arrow above each micrograph represents the E-field direction from the positive pole to the ground. B) Mean of the Distance (µm) performed by the leading edges on the Ground (Edge 1, black solid line and Edge 2, black dashed line) and Positive Pole side (Edge 1, red solid line and Edge 2, red dashed line) during the first two hours. Black and red transparencies are the relative confidence interval (95%). The insert on the left side of the graph shows the area of data collection relative to the scratch in the positive (red dashed ellipse) and ground (black dashed ellipse) sides (B). C) Mean velocity (µm/hours) performed by the leading edges on the Ground (Edges 1, black solid line and Edge 2, black dashed line) and Positive Pole side (Edge 2, red solid line and Edge 2, red dashed line) during the first two hours. Black and red transparencies are the relative confidence interval (95%).

The population of cells adhering to the polystyrene surface, under the effect of the E-field, filled the scratch significantly faster compared to the control, as indicated by the non-overlap of the confidence interval in Fig. 3C. In contrast, no significant difference is observed in the data from experiments performed on the glass-well Petri dish (Fig. 3D). Moreover, the statistical comparison (two-tailed T-test) between the means of the Binary Area Fraction values (% ± SEM) obtained from the polystyrene CTL group (23.5 ± 4.1, n = 75, exp = 6) and the EF one after six hours (T = 6 h) of exposure (57.8 ± 4.8, n = 99, exp = 6), gave a P = 0.0003, while the same comparison between the glass CTL group (24.5 ± 7.7, n = 36, exp = 4) and the EF one (27.9 ± 3.8, n = 32, exp = 4), gave a P = 0.6996.

The closing speed can also be expressed as the Mean Distance (mm ± SEM), which is defined as the average of the movement of all captured pixels along the edge, calculated with respect to the position of each pixel at T = 0 h (1); and Mean Velocity (µm/hours ± SEM) which is defined as the average of the rate of change of the Distance over time (2). This calculation quantifies how far each edge has moved from its initial position and at what speed. In Fig. 4 these values are reported as a function of time showing that, only on the polystyrene surface both Edges (1, closer to the ground and 2 closers to the positive electrode) increase Mean Distance (Fig. 4C, D) and Velocity (Fig. 4E, F) after exposure to the E-field, as expected. Interestingly, the movement of the leading edges appears to be symmetrical, considering the similar values ​​expressed by Edges 1 vs. Edges 2. All these results indicate that the collective migration of cells adhering to a polystyrene surface is boosted by the E-field already within a few hours from the beginning of the exposure, while this effect does not occur on glass. The increase in the distance covered by the leading edges depends on the acceleration of their movement. An example movie of the time-lapse experiments of up to 15 h for each group is shown in Supplementary Video 1 (polystyrene CTL), Video 2 (polystyrene EF), Video 3 (glass CTL) and Video 4 (glass EF).

The numerical microdosimetry analyses indicated that the divergence of the E-field on the adherent cells plane of the polystyrene Petri dish (Supplementary Fig. S6A) rapidly increases from the positive pole (red region) to the ground (black region). However, no difference in movement speed is observed between the edge closer to the ground and the one closer to the positive pole. Therefore, we investigated the effects of the E-field exposure on collective migration of cells on this surface by measuring the percentage closure over time of a horizontal scratch (perpendicular to the electrodes) as the Binary Area Fraction of each visual field (one example in Fig. 5A, B) normalized to the value obtained at T = 0 h, averaged and graphed in Fig. 5D and E as a function of time.

In this case, to investigate a possible correlation with the E-field divergence, the data obtained are further divided into three groups, according to the regions where they are collected: Ground (black), Center (green) and Positive Pole (red). The three pools of data, under the effect of the E-field, filled the scratch significantly faster compared to the control but did not show an effect dependent on the proximity to the poles, as indicated by the overlap of the confidence interval in Fig. 5D. Moreover, the statistical comparison (two-tailed T-test) between the means of the Binary Area Fraction values (% ± SEM) obtained from the horizontal scratch closer to the Ground (76.8 ± 3.9, n = 16, exp = 3) and the Positive Pole (57.8 ± 8.0, n = 16, exp = 3) after six hours (T = 6 h) of exposure gave a P = 0.0992, indicating that there is no significant difference. The values of the Mean Distance (µm ± SEM) (Fig. 6B) and the Mean Velocity (µm/hours ± SEM) (Fig. 6C) are reported as a function of time showing that the movement of the leading Edges (1 upper and 2 lower) calculated for the Ground group, after exposure to the E-field, appears symmetrical to that of the Positive Pole group, considering the similar values ​​expressed by Edges 1 vs. Edges 2.

The mean of the three groups (Ground, Center and Positive Pole) is also similar to that obtained from the vertical scratch, as indicated by the overlap of the confidence interval in Fig. 5E. Moreover, the statistical comparison (two-tailed T-test) between the means of the Binary Area Fraction values (% ± SEM) obtained from the vertical scratch (57.8 ± 4.8, n = 99 exp = 6) and from the horizontal one (69.8 ± 6.0, ​​n = 48, exp = 3) after six hours (T = 6 h) of exposure gave a P value = 0.1782 indicating that there is no significant difference. All these results indicate that the direction of the E-field does not influence the increase exerted on collective migration and that this increase does not depend on the relative position of the population with respect to the divergence induced by the field itself. An example movie of the time-lapse experiments of up to 15 h for each group is shown in Supplementary Video 5 (EF Ground), Video 6 (EF Center) and Video 7 (EF Positive Pole).

E-field effects on single-cell movement

Although the analysis of scratch assays carried out with the scratch perpendicular to the electrodes did not show any evident correlation with proximity to the pole regions, in order to get a closer look, we have performed a specific test to answer the question of whether nearness to the poles can influence cell migration differently. Scanning by the microscope the polystyrene Petri dish along the middle axis perpendicular to the electrodes, time-lapse images of all the possible visual fields (frames) were acquired as described in Methods. The single cells were followed for 3 h for both control (Supplementary Video 8) and E-field exposure phases (Supplementary Video 9). The distances traveled by each selected cell (n = 280 collected form six independent experiments, see Methods) during the CTL phase (from T_CTL = 0 to T_CTL = 3 h) and the E-field exposure phase (from T_EF = 3 to T_EF = 6 h) are calculated as the sum of the segment from the first frame to the current frame obtaining a value named Path Length (Fig. 7A, B). The probability distributions of Path Length were fitted by a gamma function whose tail is heavier for EF group (mean = 82.0 μm and variance = 2041.6 μm² given by the shape and rate parameters A = 3.3 and B = 24.9 respectively) than for the CTL (mean = 65.8 μm and variance = 1194.1 μm² given by the shape and rate parameters A = 3.6 and B = 18.2 respectively), indicating that the E-field exposure increases the probability of cells traveling a longer distance (Fig. 7C, D). This is also confirmed by the Box Plot analysis and the non-parametric Kruskal-Wallis statistical test on the control compared to the E-field population which resulted in a H = 42.346 that gives a corresponding P < 0.00001 for a Chi-square distribution with 1 degree of freedom (Fig. 7E). Moreover, the Mean Square Displacement analysis showed that one hour after the start of exposure, there is no overlap between the confidence intervals related to the data collected during the control and E-field conditions (Fig. 7F).

Figure 7.

E-field effects on the movement of single cell adhering to the polystyrene surface tested by tracking along the entire line perpendicular to the electrodes their path for three hours of control and three hours of exposure. A) and B) Example of two visual fields acquired in phase contrast at 200× of magnification after 3 h of control conditions (T_CTL = 3 h), and after 3 h of E-field exposure (T_EF = 6 h). The sample cells and their tracked pathways are visualized in different colors. Scale bars are 200 μm. C) and D) Histograms of the Probability Density Function (PDF) for the Path Length (µm) performed by each cell (n = 280, collected form six independent experiments) monitored during T_CTL (Blue) and T_EF (Red). The PDF has been fitted by a gamma function (Solid lines). E) Box Plot of the Path Length (µm) analysis performed by each cell (n = 280) monitored during T_CTL (Blue) and T_EF (Red). The non-parametric Kruskal-Wallis statistical test indicated a Chi-square distribution with 1 degree of freedom H = 42.346 that give a corresponding P < 0.00001. F) Mean Square Displacement (MSD; µm²) performed by the cells population during T_CTL (Blue) and T_EF (Red) and the relative intervals of confidence (shadow areas).

Then we graphed the Probability Density Function (PDF) for the Path Length variation (3) of each single cell grouped according to regions proximity (Ground, Center, Positive Pole) (Fig. 8B), obtaining an information consistent with the motility performance of each cell relative to the spatial distribution of E-field divergence on the plane of the adherent cell obtained from the numerical dosimetry (Fig. 8A). Details of the results of the numerical simulations performed considering simplified cells on the plastic Petri dish configuration are described in the Supplementary Information and reported in Supplementary Fig. S6.

Figure 8.

Path tracking of single-cell movement on the polystyrene surface as a function of their relative position with respect to the electrodes. A) Exposure system geometry and spatial distribution of the E-field divergence on the adherent cell plane (color scale) with T98G considered for the analysis (white square for Ground, n = 107; white triangle for Center, n = 94 and white circles for Positive, n = 79). B) Histograms of the Probability Density Function (PDF) for the Path Length Variation (%) performed by each cell. C) Box Plot of the Path Length Variation (%) analysis of the sub-populations performing above the threshold of 50% (Ground n = 35; Center n = 25; Positive Pole n = 27). The non-parametric Kruskal-Wallis statistical test indicated a Chi-square distribution with 2 degrees of freedom H = 2.09 that give a corresponding P = 0.35. D) Mean Path Speed (µm/h ± SEM) of the sub-populations performing above the threshold of 50% (black line, Ground n = 35; green line, Center n = 24; red line, Positive n = 29) along the time axis (3 h of CTL + 3 h of EF whose starting point is indicated by the grey dashed line) with an image-lapse acquisition frequency of 4/h. P < 0.05 for a two tailed t-Test performed on each time point of Ground (n = 35) vs. Positive (n = 29).

The sub-population of best performing cells (i.e. more than 50% of positive Path Length variation) is Box plotted in Fig. 8C for each of the three groups (Ground n = 35; Center n = 25; Positive Pole n = 27). The non-parametric Kruskal-Wallis statistical test did not detect a significant difference between the three groups but a P = 0.0745, the higher median value and 75° percentile of the Positive Pole group compared to the others suggest a trend indicating a better influence of this pole on cell motility performance during the E-field exposure.

Therefore, we asked how E-field exerts its effect over time plotting the average of the Path Speed values (the length of the path divided by the amount of time elapsed from the beginning to the current position) as a function of time (Fig. 8D). All three groups (Ground n = 35; Center n = 24; Positive Pole n = 29) showed a clear increase immediately after the beginning of the exposure phase and the achievement of a plateau after about 2 h which persisted during the entire exposure phase, indicating a very rapid (less than 15 min) effect of E-field on cell migration capacity followed by delayed but long-lasting saturation. Performing the parametric t-Test between the averaged time data points of the Positive and Ground groups a P < 0.05 is obtained 45 min after the start of the E-field exposure, indicating a different influence of the Poles on the temporal evolution of the boosting effect.

Each group can also be subdivided according to the performance shown during the exposure phase: cells with decreased motility (less than − 10%); cells with no variation (between − 10% and 10%) and cells with increased motility (greater than 10%) (Supplementary Fig. S7A). Interestingly, the majority (more than 50%) of the cell’s population increases the Path Length Variation after exposure and that near the ground (63.6%) this effect appears to be more relevant than in the center (56.4%) and at the positive pole (58.2) (Supplementary Fig. S7B).

Moreover, by tracking the path of each cell during the control and E-field phases and plotting the calculated vectors in polar graphs relative to the three regions (Fig. 9), we can conclude that their crawling is not influenced by the E-field in the directional component. This is also confirmed by statistical comparison of the averages of X and Y values of each cell reached at the end of the CTL vs. EF phases (Supplementary Fig. S8).

Figure 9.

Polar graph of single-cell movement on the polystyrene surface as a function of their relative position to the electrodes. The track of each T98G cell belonging to the sub-populations with performance above the threshold of 50% (black line, Ground n = 35; green line, Center n = 24; red line, Positive Pole n = 29) during the 3 h of control and the 3 h of E-field exposure are plotted as vectors describing the mean Segment Length (magnitude) and the mean Heading (direction). The yellow dots indicate the averages of X and Y values of each cell reached at the end of the of CTL and EF phases (see Supplementary Information File).

Discussion

Standard in vitro collective and single-cell migration assays were performed to test the capability of a capacitive coupled exposure system to affect the cell motility. The numerical dosimetry approach allowed to predict intensity and distribution of the E-field generated by applying a voltage difference of 35 V at one electrode plate (positive pole) and setting the other plate at 0 V (ground). In this setup the ground is enhanced by the other metallic parts of the exposure system, resulting in asymmetric exposure. The numerical dosimetry analyses revealed the E-field distribution and its divergence in the exposure system. Moreover, to provide a complete overview of the physical quantities involved during the exposure and their interaction, they are reported in Fig. 10. In particular, two possible effects result from the application of the voltage difference in the system: i) a strong capacitive coupled electric field (C-Coupled E-field) over the surface of the Petri dish. This E-field, with an approximate intensity of 10³ V/m as a function of the dielectric constant, is terminated in the extracellular medium and possible adhesion sites on the substrate surface. Given the salt concentration of the culture medium it is possible to calculate a screening length < 1 nm according to the Poisson-Boltzmann theory; ii) a lower E-fields at the level of the extracellular medium, with values at the adherent cell plane that range from 0.02 V/m (near the ground and positive pole) up to 0.12 and 0.09 V/m in the center region, for the polystyrene and glass-well Petri dishes, respectively, with an asymmetric distribution which tends to increase toward the positive pole (see Fig. 2C, D). A residual charge density through non-null conductivity of the humid air (conductivity 1 × 10 ⁻⁴ S/m) of the incubator causes a small continuous ion flux through the extracellular medium (electrolyte solution); this determines a redistribution of the charge density inside the cell which adheres to the dielectric substrate (Fig. 10).

Figure 10.

Scheme of three physical quantities built-up during the exposure on the XZ-cut plane view crossing the center of the cell. The induced current density (J) in the extracellular medium with the J arrows, and the induced E-field in the dielectric support (with the E-field arrows). Finally, the induced charge density distribution build-up inside the cell.

The experimental results obtained on the specific behavior of cell motility, once thermal effects have been ruled out, must be read in the light of both these hypothesized effects, which are determined by the physical quantities built-up and the spatial distribution. Based on current knowledge, it is not possible to predict which effects are most relevant and how each component of the system interacts to drive cell behavior.

The collective migration assay indicated that the boosting effect, measured as a faster restoration of the monolayer integrity, was only observed in the cell population performing on polystyrene surface, while no effects was detectable on glass (geometries described in Supplementary Fig. S1). Moreover, even when changing the orientation of the scratches from parallel to perpendicular to the electrode plates (numerical dosimetry observes for both median values above 0.1 V/m and maximum values of about 0.12 V/m Supplementary Fig. S5), no differences were observed between the displacement of the two edges.

These experimental evidences suggest that the capability of the E-field to enhance cell motility is strictly dependent on the material to which the cells adhere and that it does not exert any directional cues that influences the collective migration of cells.

Disposable Petri dishes of polystyrene, standardly used in vitro systems, have a structure of hydrophobic polymer chains with high electrical resistance. Pretreatment by oxygen or argon plasmas generates high energy reactive species that bind to the surface (–COOH and –CHO, respectively). This process increases the surface free energy of the polymers giving better adhesive properties by: reducing the wetting contact angle⁴³; increasing the surface polar component⁴⁴; modifying protein absorption⁴⁵. The glass-well of Petri dish, usually preferred for microscope optical applications, are made of borosilicate which generally has SiO₂ as the main component that form strong covalent bonds involving tetrahedra and triangles of oxides with several non-bridging oxygens (NBOs). Gamma irradiation, used for the sterilization of disposable devices, inducing a more compact and dense glass network by increasing the number of BO₄ tetrahedra and reducing the number of NBOs, causing a decrease in electrical conductivity, but also an increase of cell adhesion capability by activating the surface free energy⁴⁶. In general, when a dielectric material is placed in an E-field, the electric charges shift, only slightly, from their average equilibrium positions, causing the dielectric to become polarized. The weaker the bond between the molecules, the more they polarize and reorient themselves, aligning the axes of symmetry with the field⁴⁷. Numerical dosimetry revealed that the intensity of the C-Coupled E-fields generated across the polystyrene and glass substrates were similar. Therefore, the different results between the two materials could mainly attribute to the peculiar effects of treatments (vacuum plasma and gamma ray) on physical-chemical properties and to their reaction to C-Coupled E-field forces. Unfortunately, patent protection rules do not allow to predict the specific properties of the substrate, even more so after an E-field exposure. The processes of cell adhesion and motility are supported by the interaction and interfacing between all the components of the system, which in turn are subject to direct electrical stimuli or secondary interactions with other parts of the system. The ECM has been shown to modulate several cellular processes, including cell migration⁴⁸. The crucial aspect indicated as driving cell behavior is the structure of the matrix in terms of size, orientation and stiffness of the fibers^49,50. Very low static E-fields (in the order of mV/nm) have been shown to affect dimers of peptide forming amyloid⁵¹ and serum albumin fibrils⁵², indicating possible targets for the C-Coupled E-fields generated at the interface/substrate level and a specific role in remodeling the ECM structure. Moreover, literature data indicate that external electrostatic fields (EESF) can marginally influence the lipid matrix of plasma membranes, causing changes in the functional state of bilayer⁵³. Nevertheless, at this stage, it can only be assumed that the observed change in cell motility performance is related to the E-field stimulus in a substrate dependent way; a combination of causes deriving from the possible interaction and remodeling of the substrate, ECM and plasma membrane could be hypothesized.

Numerical dosimetry also evidenced a weak ionic current due to a residual charge density flowing through the non-null conductivity of humid air. The numerical data obtained for the two configurations showed a different distribution of the E-field values, with the plastic Petri dish exhibiting a highly non-uniform E-field distribution (in the range of 0.02 V/m to 0.12 V/m, depending on the relative position respect to the poles), compared to the configuration of the Petri dish with the glass well (from about 0.02 V/m up to 0.09 V/m), mainly attributable to the variation between the Petri dishes geometry. It was not possible to detect whether this current is able to exert an effect on cell motility with the scratch assay. Therefore, a test of the E-field effect on single-cell movement of T98G population on the polystyrene surface was performed. In this case, possible interferences on the migration of single cell due to the bulk behavior of the cell population, such as traction phenomena exerted by leader cells or recall by cell-to-cell signaling, were avoided, with the exception of the evidently forced directionality towards empty space, which may perturb the walk performance. In accordance with the results on collective cells migration, single cells movement is clearly boosted by the electrical stimulation but, even in this case, the migration seems to be not directionally oriented. Considering the position of the most affected cells with respect to the electrode plates and plotting the performance along the time axis, it is possible to notice that: (i) the booster effect occurs immediately after the start of the stimulation; (ii) it increases with time; (iii) it has reached a plateau that persists throughout the duration of the exposure; (iv) during the incremental phase, a significantly different trend of the increase in movement was detected for the population of cells near the positive pole, compared to those near the ground. The virtual microdosimetry data, based on a 3D cell modelled as a semi-ellipsoidal with a non-conducting membrane separating two conducting regions (culture medium and cytoplasm) in direct contact with a flat dielectric substrate, (Supplementary Fig. S5) suggest that redistribution of the E-field divergence occurs around each isolated cell, and it depends on two factors: (a) the position of the cell on the plane with respect to the positive pole and ground; (b) the orientation of the major length of the cell with respect to the E-field lines. Interestingly, the cell modelled near the positive pole showed the highest value of E-field divergence (around − 25 V/m²), suggesting a possible contribution of field divergence to greater increase in cell motility near the positive pole. Overall, the analysis performed on both scratch assays, such as the edge displacement in the parallel scratch, the closest performance in the perpendicular one and that one on the tracking in single-cell movement assay are aimed to overlap and correlate the effect of E-field gradients on cell behavior. All these results showed that no electrotaxis effect can be detected. Previous in vitro studies on human glioma cell lines described a clear phenomenon of electrotaxis induced by DC E-field generated by contact electrodes in an electrotactic chamber. In this case, the calculated intensity of the field at the cellular level (100–250 V/m), which is about two orders of magnitude higher than ours, is able to drive the cell migration toward the cathode³⁹. The lack of directional migration in the analyzed cell populations could be due either to a subthreshold field intensity or to a noisy movement of the cells due to their random orientation with respect to the direction of the ionic current before the stimulation is activated.

In conclusion, this work has demonstrated that, despite the widespread opinion that C-Coupled systems can generate forces capable of exerting a certain effectiveness on cellular behavior only if the electrical stimulus is alternating (AC)²⁴, the presence of dielectric materials whose molecules can be polarized and on which adherent cells are interfaced can also make a system coupled to a DC stimulus effective, as predicted by a computational model approach³⁶. This system, characterized by the delivery of an indirect stimulus generated by a low potential and through conductive electrodes not in contact with the culture medium, allows avoiding all the inconveniences deriving from reactive faradic by-products and the adsorption of proteins by agar salt bridges¹⁷, but at the same time it is able to provide an effective stimulus with a very homogeneous distribution throughout the sample. Therefore, polystyrene (or equivalent materials) devices based on C-Coupled systems and powered in DC, could be successfully used for further insights into in vitro basic research such as studying the mechanism of action of electrostatic fields on cell-interface interaction, or it could be leveraged in a new generation of in vivo implantable polymeric scaffolds where cell motility can be increased through C-Coupled stimulation, ensuring homogeneous effect and long-term use without unwanted disadvantageous reactions.

Methods

Experimental setup

The experimental equipment consists of: (i) an inverted optical microscope Nikon Eclipse Ti (Nikon, Bologna, Italy) (Fig. 11A) capable to allocate a water jacket stage top incubator Fig. 11C); (ii) two CO₂-O₂-temperature control units (OKOlab s.r.l., Rovereto, TN, Italy) each connected to a thermocouple (not shown); (iii) a circulating heating water bath Lauda E200 Ecoline 003 StarEdition (LAUDA-Brinkmann, Marlton, NJ, USA) (Fig. 11A); a DC power supply TTi CPX200 DUAL 35 V 10 A (Thurlby Thandar Instruments Ltd., Huntingdon, Cambs., UK) (Fig. 11E); (iv) a homemade support platform that can allocate the culture Petri dishes of 35 (ø) mm and around it one pair of copper plates with a gap of 42 mm between them connected to the power supply (Fig. 11B). By applying 35.24 ± 0.28 V and 0.25 A to one copper plate (positive electrode) while the other is set to 0 V (ground) (Fig. 11D), a voltage difference can be generated between the two non-contact plates. This setting has been used in all the so-called EF groups. Control groups (CTL), defined as a group used to simulate the environmental conditions of exposed samples but in absence of exposure, were performed by setting the system as for the stimulus delivery, but with the out-put switched off.

Figure 11.

Experimental set up for scratch assay and single cells tracking. The microscope (A) allows to allocate a small incubator (B) for time-lapse imaging of living samples cultured on Petri dishes. The incubator (D) contains an aluminum board on which rests a plastic board that hold two rectangular copper plates positioned along the opposite side of the dish inserted in an aluminum ring. The electrodes are connected via cables to an externally placed DC power supply (C). E) Geometry and materials that compose the C-Coupled exposure system; see Supplementary Figure S1A for details.

The Petri dish and the electronic components useful to deliver the stimuli are placed in the microscope stage incubator by means of the homemade support platform. The incubator, connected to ii) and iii) is capable to provide standard culture conditions (37 °C in humidified atmosphere at 5% CO₂) and, once placed on the motorized table of the microscope, to perform the acquisition of time-lapse images of living cells for several days. The exposure setup has been modelled with a 3D CAD model as shown in Supplementary Figure S1.

Numerical dosimetry setup

The numerical dosimetry of the electrical quantities generated by the use of this non-contact exposure system has been performed by creating the CAD models of the system using the geometry section of COMSOL Multiphysics software v. 6.1. Two different models have been built to simulate the two configurations: (i) the first employing a polystyrene or plastic Petri dish as a cell sample holder; (ii) the second using a plastic Petri dish with a central glass well. Supplementary Figure S1 reports the 3D CAD models built, with a focus on the details of the two configurations. Supplementary Figure S1A shows the global exposure setup that resembles the experimental system where the sample holder, filled with a conductive culture medium, is placed between two electrodes (42 mm apart), on the top of two boards (with aluminium and plastic materials), and surrounded by an aluminium ring. The whole system is placed in a microscope stage incubator, that is represented as a parallelepiped conductive air box (26 mm in height, 60 mm in width and depth), not shown in Supplementary Figure S1. The two models have been built using the dimensions of the real configurations, where the main dimensions are reported (Supplementary Fig. S1F, S1G). Supplementary Figure S1B and S1C report the top view of the exposure system in the two configurations, while the Supplementary Figure S1D and S1E show the side view of the systems, in which the difference in terms of adherent cells plane quote is reported. In particular, for the plastic Petri dish the adherent cell plane is Z_p=-1 mm, while for the Petri dish with glass, the cells are placed on the glass well at Z_g=-1.5 mm (Supplementary Fig. S1).

A custom mesh has been setup for each simulation, and the details of the mesh elements are reported in the Supplementary Table S1 and an example of the mesh accuracy is shown in Supplementary Figure S2. After a first set of simulations considering the setup, the sample holder (plastic Petri dish) and the buffer (PBS), a second set of simulations has been carried out by adding 3D cell models adhered to the bottom surface of the holder. In particular, 3D cell models with a simplified shape obtained starting from an ellipsoidal one, and a size corresponding to glioblastoma multiforme cells⁵⁴ have been considered. These cell models have been manipulated by cutting the bottom of the cells to obtain a semi-ellipsoid shape, thus representing cells adhering to the Petri dish substrate, see Supplementary Figure S3 for the details. Such cell modelling is in line with previous preliminary studies on 2D cell model³⁶ and 2.5D cell representation²⁶, for electrical stimulation generated by capacitive coupling systems. The custom mesh used for simulation with cells required a number of tetrahedra and triangles that was 10 and almost 9 times higher, respectively, than that employed for the exposure system alone.

All the simulations are performed with COMSOL Multiphysics v. 6.1 software, using the Electric Currents Mode of the AC/DC physics module interface, and solving the problem with a time dependent study. In accordance with the experiments, the potential at the positive electrode (in red in the Supplementary Fig. S1) is set to increase from 0 to 35 V in a few milliseconds and kept constant at its maximum value, while the ground electrode is set to 0 V, together with the aluminium ring and the board to which it is in contact (the ground metallic parts are colored in dark blue in the Supplementary Fig. S1). Dielectric properties for known materials are taken from COMSOL library. Inside the incubation chamber of the microscope stage, where the sample and electrodes are located, the CO₂ gas concentration and temperature are controlled at 5% and 37 °C respectively, thus giving rise to a high humidity environment. The electrical conductivity of this environment has been set to approximately 1e⁻⁴ S/m⁵⁵. The properties of the culture cell medium have been measured. Dielectric properties of cells were taken from the literature⁵⁶. Details of the dielectric properties used in these simulations are reported in the Supplementary Table S2.

Cell culture

T98G (CRL-1690™) cell line it was purchased from ATCC (Manassas, VA, USA) and cultured in Minimum Essential Medium (MEM, Gibco™ 51200046, Thermo Fisher Scientific), supplemented with 10% fetal bovine serum, 1% L-glutamine, 10% sodium pyruvate and antibiotics (1% penicillin and 1% streptomycin) at 37 °C in 5% CO₂ incubator. When the cell population reached the sub-confluence (70–80%) was detached by 0.25% trypsin in 0.02% EDTA solution, re-suspended in fresh supplemented MEM and counted using the hemocytometric chamber. The cell culture has a population doubling time (PDT) approximately of 28 h, as reported by the ATCC Company, which provided the cell line. All chemicals were purchased from Merck.

Scratch assay

An aliquot, calculated to have a final density of 1 × 10⁵ cells/cm², was diluted in 3 ml of supplemented MEM and plated on two different 35 (ø) mm Petri dishes for cell culture: (i) a polystyrene bottom (Falcon^® TC-treated Easy-Grip Style - #353001, Becton Dickinson Labware, USA) vacuum gas plasma treated; (ii) a polystyrene dish with a glass bottom microwell of 10 (ø) mm inserted in the center and gamma irradiated, suitable for fluorescence microscopy (MatTek Corporation, Ashland, MA, USA). When 48 h later, the population covered the entire surface as a monolayer of confluent and tightly contacting cells, the supplemented MEM was harvested and replaced with a fresh and pre-heated aliquot of 3 ml. One hour later a scratch along the middle axis was done using a sterile pipette tip for Gilson (10–200 µl) and right after the specimen was placed in the microscope stage incubator (Fig. 11) for automated imaging acquisition in culturing standard conditions.

The experimental protocol adopted was the follow: phase contrast micrographs of living cells were acquired in time-lapse configuration at 200× of magnification for up 24 h at the rate of 1 frame/15 minutes. For each time point, visual fields (1200 × 1600 pixels) of the size of 0.85 × 0.63 mm, were scanned along the parallel and perpendicular scratches to the electrodes with an approximate Y and X ranging from − 11.5 mm < y < + 11.5 mm and from − 14.0 mm < x < + 14.0 mm respectively and acquired for the off-line analysis. Data analysis was performed using the Wound Healing tool of the Bio Analysis module of NIS Elements AR 4.0 (Nikon, Bologna, Italy) analysis software. A Binary Area Fraction was generated from the measured parameters Binary Area (sum of area of all binary objects)/Measured Area (both expressed as number of pixels) for each time point. Scratch closure was calculated as the percentage difference of the wound area measured at t = Δh (hours) after scratching with respect to the wound area measured at time 0 (T = 0), averaged for all over the experimental sections and plotted as a function of time. The final number of data points observed was: in plastic parallel scratch assay 75 for CTL and 99 for EF, both carried out in six independent experiments; in glass parallel scratch assay 36 for CTL and 32 for EF, both carried out in four independent experiments; in plastic perpendicular scratch assay 48 for EF, carried out in three independent experiments.

The pixel position indexes of wound edges were also captured with the the Bio Analysis module of NIS Elements AR 4.0 software while calculations were performed using custom scripts developed in MATLAB, with the origin of the image set at the top-left corner (0,0). The Mean Distance (D̅) represents the average across all pixels along the edge points and is calculated using the formula:

1

where Ei is the position of each pixel along the edge at time i, Ei0 the initial position of that edge, and N the total number of pixels per edge, with ΔX converting pixel measurements to micrometers (µm). This calculation quantifies how far each edge has moved from its initial position. Velocity is then calculated using the MATLAB ‘gradient’ function, which approximates the first derivative of the displacement over time using a time interval ΔT of 15 min, equivalent to 0.25 h. The Mean Velocity (V̅) represents the average across all pixels and is determined by the formula:

2

employing the partial derivative ∂/∂t to determine the velocity of edge movement towards the center of the wound, measured in micrometers per unit time (µm/hours).

Tracking of single cells

An aliquot, calculated to have a final density in the range of 2.5-3.0 × 10³ cells/cm² was diluted in 3 ml of supplemented MEM and plated on the 35 (ø) mm polystyrene bottom Petri dish. At 24 h from seeding the specimen was placed into the microscope stage incubator and phase contrast micrographs were acquired along the central line (horizontal) of the Petri dish XY-plane, perpendicular to the electrodes, in a time-lapse configuration at 200× of magnification for up six hours at the rate of 1 frame/15 minutes. During the first 3 hours, a control exposure was performed, and control data were collected (CTL); during the next 3 hours, the out-put of the power supply system was switched on and a stimulus of ~ 35 V was applied to the positive copper electrode, allowing to collect the exposure data and compared it with control on the same cells. In each visual field (1200 × 1600 μm) single cells that were free to move (i.e. none other cells were present in a double cell radius around) and did not incurring in replication within the 6 h of recording were tracked. Statistical analysis was performed on a total number of 280 cells collected from six independent experiments, with a minimum of 23 and a maximum of 61 cells per replicate. The analysis of the frames sequence was performed using the Tracking module of NIS Elements AR 4.0 (Nikon, Bologna, Italy) analysis software. According to the manual, the Path parameter is defined as the portion of an object’s track made up of segments connecting successive object positions. Path Length is the sum of the segment distances. Path Speed is the Path Length divided by the amount of time elapsed from the beginning to the current position. The distribution of the number of cells relative to the Path Length performed has been compared by fitting it with a gamma function. According to the XY parameters of the visual fields recorded, 107 cells have been grouped as belonging to the Ground with a X range of − 10.5 mm < x < − 3.5 mm; 94 as belonging to the Center with a range from − 3.5 mm < x < + 3.5 mm and 79 as belonging to the Positive Pole with a range of + 3.5 mm < x < + 10.5 mm. The Path Length Variation of each cell has been calculated as follow:

3

Cells with a Path Length Variation greater than 50% are plotted in polar graphs, box plot and as a function of time up to six hours.

Statistical analysis

Data are expressed as mean ± standard error of the mean (SEM). Two-tailed Student’s t-tests were performed to determine significant differences between the study groups during the scratch assays. Both two-tailed Student’s t-tests and non-parametric Kruskal-Wallis statistical tests were performed to compare the study groups in most of the experiments related to the single-cell tracking assay. P < 0.05 was considered statistically significant. Statistical analyses were performed with Microsoft Excel (Microsoft Corporations, USA). Statistical significance is indicated in the figures by “ * ” (0.01 ≤ P < 0.05), “ ** ” (0.001 ≤ P < 0.01), and “ *** ” (P < 0.001).

Author contributions

Experimental design and conceptualization, I.Z. and G.C.; in vitro experiments performing I.Z. and M.Ca.; in silico modelling, L.C., M.L. and F.A.; data analysis and validation, A.F., G.Gi., M.Ca., L.C., M.L., F.A. and I.Z.; investigation, I.Z. and T.C.; resources, L.C., M.L., F.A. and I.Z.; data curation, M.Ci. and G.Gu.; writing—original draft preparation, I.Z., T.C., L.C., M.L. and F.A.; writing—review and editing, M.Ci., G.Gu., T.C., L.C., M.L., F.A., A.F., G.Gi., M.Ca., G.C., D.R. and I.Z.; visualization, A.F., L.C., and I.Z.; supervision, I.Z.; funding acquisition, G.C. and D.R. All authors have read and agreed to the published version of the manuscript.

Data availability

The datasets generated and analysed during the current study are available from the corresponding author on reasonable request. All data generated or analysed during this study are included in this published article and in its Supplementary files.

Declarations

Competing interests

The authors declare no competing interests.