“Viscotaxis”- directed migration of mesenchymal stem cells in response to loss modulus gradient

Abstract

Directed cell migration plays a crucial role in physiological and pathological conditions. One important mechanical cue, known to influence cell migration, is the gradient of substrate elastic modulus (E). However, the cellular microenvironment is viscoelastic and hence the elastic property alone is not sufficient to define its material characteristics. To bridge this gap, in this study, we investigated the influence of the gradient of viscous property of the substrate, as defined by loss modulus (G″) on cell migration. We cultured human mesenchymal stem cells (hMSCs) on a collagen-coated polyacrylamide gel with constant storage modulus (G′) but with a gradient in the loss modulus (G″). We found hMSCs to migrate from high to low loss modulus. We have termed this form of directional cellular migration as “Viscotaxis”. We hypothesize that the high loss modulus regime deforms more due to creep in the long timescale when subjected to cellular traction. Such differential deformation drives the observed Viscotaxis. To verify our hypothesis, we disrupted the actomyosin contractility with myosin inhibitor blebbistatin and ROCK inhibitor Y27632, and found the directional migration to disappear. Further, such time-dependent creep of the high loss material should lead to lower traction, shorter lifetime of the focal adhesions, and dynamic cell morphology, which was indeed found to be the case. Together, findings in this paper highlight the importance of considering the viscous modulus while preparing stiffness-based substrates for the field of tissue engineering.

1. Introduction

The directed cell migration or “taxis” in response to different microenvironment cues, is crucial during development [1], wound repair [2], and immune response [3]. Depending on the cue that is responsible for directed migration, several different types of “taxis” have been reported in the literature such as chemotaxis [4], haptotaxis [5], rheotaxis [6], curvotaxis [7], topotaxis [8], and mechanotaxis [9]. Several of these reported “taxis” behaviors are based on mechanical cues [10,11]. In 2000, Lo et al. demonstrated that cells migrate from high to low Young’s modulus region on a substrate with a rigidity gradient. This process is known as “durotaxis” [12]. However, the Young’s modulus alone does not completely describe the mechanical properties of biological materials such as cells, matrices and tissues, all of which are known to be viscoelastic [13–16]. Yet surprisingly, only a handful of literature have studied the effect of both storage modulus G′ and loss modulus G″, on cell functions. Those studies demonstrated that viscoelasticity of the substrate influences cellular phenotype, differentiation, and migration [17–19]. For example, substrates with high loss modulus influence mesenchymal stem cells (MSCs) to differentiate into the myogenic lineage whereas elastic substrate directs them towards osteogenic differentiation [17]. Also, stress relaxation of the substrate was shown to enhance cell spreading [20]. Substrate viscoelasticity has been shown to influence cellular migration as well. On a high loss modulus substrate, the velocity of MSCs is significantly higher than on a low loss modulus substrate [21]. Substrate viscoelasticity also enhances the correlation between the movement of cells in an epithelial sheet [19]. A recent study has shown that fibroblast cells show amoeboid migration on high loss modulus substrate due to weak substrate adhesion and low stress fiber formation. However, on more elastic substrates they adhere strongly with more stress fibers leading to the mesenchymal mode of migration [18].

While the reported literature discusses the effect of uniform viscoelasticity on cell migration, the in vivo microenvironment is rarely uniform. To address how cells respond to a gradient of loss modulus, in this paper we created substrates with a gradient of loss modulus and observed the migration of human mesenchymal stem cells (hMSCs) on them. First, we extensively explored the rheological properties of polyacrylamide gels (PAA gels) made from different combinations of acrylamide and bisacrylamide. Based on the results, we selected two gel compositions with the same storage modulus but different loss moduli. Using these two combinations we created gels with a loss modulus gradient but uniform storage modulus. We found that cells preferentially migrate from high loss modulus to low modulus region. Further, an increase or decrease in the gradient strength resulted in an increase or decrease in migration bias respectively. Inhibition of actomyosin contractility by pharmacological inhibitors disrupted this preferential migration making cells nonresponsive to the loss modulus gradient. Also, higher membrane fluctuation of HeLa cells on high loss modulus substrate suggests dynamic nature of cells compared to stable cell on low loss modulus. In summary, our study demonstrates that cells respond to loss modulus gradient and migrate from high loss to low loss modulus region causing directed cell migration which we are terming as “Viscotaxis.”

2. Experimental section

2.1. Substrate preparation

Gels were formulated from base solutions of 40 wt.% Acryl (Sigma-Aldrich) and 2 wt.% Bis (Sigma-Aldrich). After mixing the solutions at different ratios in deionized water, Low Loss gels were fabricated by crosslinking 1 mL of solution with 1 μL of tetramethylethylenediamine (TEMED) (Sigma-Aldrich) and 10 μL of 10 wt.% ammonium persulphate (APS) (Sigma-Aldrich). High Loss gels were fabricated by crosslinking 1 mL of solution with 1.5 μL of TEMED and 5 μL of 10 wt.% APS. Gel with G″ = 150 Pa was created by mixing Low Loss and High Loss gel composition in the ratio 50:50. The gradient gels were prepared using two drop diffusion technique as described earlier [22]. Briefly, we made gradient gels by placing two drops (100 μl each) of High Loss and Low Loss solutions on a 22 mm x 22 mm square coverslip coated with di-chlorodimethylsilane (DCDMS) of Sigma-Aldrich make. FluoSpheres (Invitrogen) 0.2 μm in diameter were added into the High Loss solution at 0.1% by weight of the gel solution. For shallow gradient gel preparation, hydrophilic cover slip functionalized with 3-(Mercaptopropyl) trimethoxysilane (MPTS) (Sigma-Aldrich) was placed immediately on top of the drops, allowing the solutions to diffuse. For step gradient generation, gel solutions were allowed to partially polymerize for 5 min before placing the hydrophilic functionalized coverslip. In all cases, gels were allowed to polymerize for 15 min, which was sufficient for complete polymerization and crosslinking reactions. To note, for all the experiments, gels of 400 μm thickness, which is much higher than the limit of depth sensing, were used to ensure that the effect of the rigid supporting glass layer is not felt by the cells at the gel surface [23].

2.2. Gel mechanical testing

The viscoelastic spectrum (storage modulus, G′ and loss modulus, G″), as a function of frequency, of each of the resulting gels, were measured using an Anton Paar MCR 301 rheometer. Solutions containing varying compositions of Bis and Acryl monomers were cross-linked between the plates of the rheometer. The stainless steel top and bottom of 50 mm diameter were roughened by sticking polish paper (3M safety walk). Gap distance was fixed at 1 mm. For each composition, a time sweep test was conducted during the reaction to confirm that cross-linking had come to completion (Fig. S1). The duration of the time sweep was 25 min with a controlled absolute strain of 1% and at an angular frequency of 1 Hz. Next, a frequency test was performed on the gels where the angular frequency was increased from 0.01 rad/s to 100 rad/s at a fixed strain of 1%.

2.3. Gel functionalization for cell seeding

The substrates were functionalized with 100 μl of 5 μg/ml N-sulfosuccinimidyl-6-(4azido-2-nitrophenyl amino) hexanoate (Sulfo-SANPAH) (G-Bioscience) in HEPES buffer (pH=8.5) using UV cross-linker (Genetix) (312 nm) for 20 min. PAA gel substrates were then washed with Dulbecco’s Phosphate Buffer Solution (DPBS) twice to remove free molecules of sulfo-SANPAH and submerged in the collagen (25 μg/ml) or laminin (50 μg/ml) solution and incubated overnight at 4°C. Finally, before cell seeding, the substrates were kept in laminar hood under UV for 20 min following the washing with DPBS.

2.3.1. Cell culture

Umbilical cord human Mesenchymal stem cells (UC-hMSCs) were cultured in Dulbecco’s Modified Eagle Medium (DMEM) (Himedia) supplemented with 16% fetal bovine serum (FBS) (Himdeia), 1X Antibacterial-Antimycotic (Himedia) solution and 1X Glutamax (Invitrogen). Cells were passaged at around 70% confluency using 0.5% Trypsin-EDTA (Invitrogen) for 3 min at 37°C to detach the cells and centrifuged at 1000 rpm for 5 min. All experiments are performed with UC-hMSCs between passages 4 and 7. UC-hMSCs were seeded on the gels at a seeding density of 1000 cells per cm². The cells were allowed to adhere to the gel and spread for a period of 4-5 h before time lapse microscopy.

2.4. Time lapse microscopy

The time-lapse microscopy was performed using the Evos FL-Auto microscope (Life Technologies) attached with controlled environment on-stage incubator. Time-lapse imaging was started after 4 h of cell seeding and continued for 18 h duration with 30 min time interval between two consecutive images. The images were taken in two modes, first ‘PHASE’ mode to observe the cells, second in RFP mode to observe red fluorescent beads that determine the gradient boundary (Supplementary Fig. S3).

2.5. Cell migration analysis

ImageJ software (National Institutes of Health, Bethesda, USA) plugin with manual tracking (Fabrice Cordelières, Institut Curie, Or-say, France) was used to track the path of the cells from the images obtained over an 18 h period. During analysis on average 50-60 cells were tracked per substrate. Exported ASCII from manual tracking was imported to the software tool and the cell trajectories were all extrapolated to (X,Y) = (0,0) at time 0 h. Cell migration images were taken by setting up multiple sequential beacons that cover the gel along the gradient length. To analyze the Tactic Index, we needed to distinguish the cells migrating towards left and cells migrating towards right. This distinction was performed using plugin “Chemotaxis and Migration Tool” (IBIDI Software) [24].

2.6. Atomic force microscopy (AFM)

In Bio-AFM (MF3D, Asylum research), the probe of cantilever consists of micron sized tip. Cantilever deflection is used to calculate the indentation force. When the sample is indented by the probe, cantilever deflection is measured as a function of the probe’s z position. Thermal fluctuation was done in order to get the actual spring constant of the probe. To calculate the elastic modulus of the substrate, the indentation force was fitted to the Hertz model.

2.7. Inhibitor studies

hMSC cells were cultured on Low Loss and High Loss substrates at a density of 10,000 cells/cm². Cells were allowed to spread for 4 h and then inhibitors such as blebbistatin (20 μM, Sigma) and Y27632 (10 μM, Sigma) were added and it was maintained for the entire duration of the respective studies.

2.8. Traction force microscopy (TFM)

Gels for Traction Force Microscopy were prepared in a two-step process. High Loss substrate and Low loss substrate were made on 22 mm ^∗ 22 mm coverslips. Gels were allowed to solidify, then 25 μl of High Loss and Low Loss solution having 1μm fluorescent beads (Fluka with a final concentration of 1:50) along with APS and TEMED was added on the hydrophobic plate, and then the corresponding solidified gel was inverted onto the top of it and allowed to solidify. The gels were then treated with sulfo-SANPAH and coated with Collagen type-I as mentioned above. After 24 h of cell seeding, cells were lysed using Triton-X (1:100) without disturbing the gels, images of cells in a phase were taken before adding Triton-X, and the images of fluorescent beads were taken before and after Triton-X using EVOS FL Auto cell imaging system (Life Technologies). The code from J. P. Butler was used to calculate the bead displacement and traction force.

2.9. Collagen staining

The 25 μg/ml collagen coated on uniform and gradient gels substrates were washed with DPBS for 3 times. These gels were incubated in custom made anti-collagen antibody/serum (gifted by Prof. Shamik Sen, IIT Bombay) (1:50) raised in rabbit for 4 h at room temperature. After incubation, gels were washed with DPBS twice, 10 min each and incubated with Alexa fluor 488 goat anti rabbit (1:500) secondary antibody for 3 h at room temperature.

2.10. Cell boundary identification

Image segmentation techniques in MATLAB were used to obtain cell periphery from phase contrast microscopy images. Each grayscale image was cropped around the target cell, and the contrast was enhanced using contrast-limited adaptive histogram equalization (CLAHE) [25] to increase edge-detection accuracy. Edge detection was performed using the Sobel algorithm, a gradient-based edge detection method [26]. The Boolean output consisting of image edges was then dilated by two pixels in each of the 4 cardinal directions and a hole-filling algorithm was applied to obtain a closed region over the cell. Next, image cleaning algorithms were implemented to remove all objects not pertaining to the target cell. Finally, the region was eroded by two pixels to compensate for the dilation step performed earlier, thus giving us the segmented region consisting of the cell. The periphery of this region overlapped well with the cell membrane and was used for statistical analysis. The centroid of the cell was obtained by averaging the x and y coordinates of the segmented region.

2.11. HeLa cell culture for fluorescence experiments

HeLa cells were cultured in phenol free DMEM-HG media (Hi-Media) supplemented with PenStrep and L-Glutamine. For transfection, cells were cultured in tissue culture plastic dishes, and were transfected with GFP-Vinculin (WT), developed in Dr.Clare Waterman’s lab (NHLBI,NIH,USA) [27] overnight before the experiment using Fugene6 transfection reagent (Promega) according to the manufacturers protocol. Gels were equilibrated in M1-imaging buffer supplemented with 0.5% serum for 1 h prior to plating. Cells were deadhered using TrypLE (GIBCO, Invitrogen) according to the manufactures protocol and plated on equilibrated gels. These were allowed to spread for 4 h in M1₊0.5% serum at 37˚c/5%CO₂. Cells were then imaged for 30 min at 30s intervals at room temperature.

2.12. Kymograph analysis

Kymographs were made in ImageJ by analysing 30 min long movies of vinculin positive HeLa cells. A 55px line was drawn at the cell edge through vinculin positive punctae. The ImageJ plugin, Multikymograph, was used for making kymographs.

2.13. Immature FA persistence time analysis

Immature FA were identified the initial frame and its persistence is monitored from frame to frame. To calculate the immature FA persistence time, number of frames where immature FA is persistence is measured and then converted to time. Each frame is in interval of 30 sec.

2.14. Statistical analysis

Data are presented as means ± standard error of the mean and were analyzed using the Microsoft Excel software. Unpaired student t-test was for two samples and the one-way ANOVA for three samples. All tests were performed assuming non-Gaussian distribution of the sample values. Statistically significant differences were defined as: ^∗ = p < 0.05, ^∗∗∗ = p < 0.001, unless otherwise stated.

3. Results

3.1. Rheological characterization of polyacrylamide gel

To study the effect of the gradient of loss modulus on cell migration, the primary challenge was to find acrylamide and bis-acrylamide concentrations that would produce polyacrylamide (PAA) gels with similar storage moduli but different loss moduli. While many published literatures estimate Young’s modulus of PAA gel with certain predefined acrylamide and bis-acrylamide ratios, only limited data are available in the public domain describing the complete rheological characterization [17,20] of PAA gels. To bridge this gap, we prepared PAA gels with varying acrylamide and bisacrylamide concentrations and measured their rheological properties (Table S1). From this table, we selected two compositions that generate gels with the same storage modulus (G′) but widely different loss moduli (G″) (Table 1). Frequency sweep measurements performed from 100 to 0.01 Hz for these two gels are shown in Fig. 1a. In this paper, we will call the gel with high loss modulus as High Loss and the gel with low loss modulus as Low Loss.

Table 1. Polyacrylamide (PAA) gel samples selected for the study along with their composition and mechanical properties.

Sr. No.	Acrylamide	Bis-acrylamide	G′ (at ω = 0.01Hz)	G″ (at ω = 0.01Hz)	Sample
	wt.%	wt.%	kPa	Pa
1	6.68	0.06	1.1 ± 0.06	45.00 ± 6	Low Loss
2	8	0.26	1.6 ± 0.1	300.62 ± 18	High Loss

Fig. 1.

(a) Frequency sweep: experimental and predicted moduli (G′, G″) for Low Loss and High Loss gels versus frequency, ω. (b) Compliance, J observed for Low Loss (σ₀ = 10 and 400 Pa) and High Loss gels (σ₀ = 10 and 100 Pa) during creep test. Solid blue and dashed blue lines are fits for Low Loss and High Loss gels, respectively given by the eq.1. (c) Schematic of three Kelvin-Voigt (KV) modes in series. (d) Schematic of the loss modulus gradient generation procedure. (e) Fluorescent red polystyrene bead intensity measured along the shallow loss modulus gradient and step loss modulus gradient gels with respective fluorescent intensity plotted against the gel length.

Given that the elastic modulus is expected to scale with the crosslink density, it is surprising that despite having more than four times higher concentration of bis-acrylamide, the High Loss gel exhibits a similar elastic modulus as the Low Loss gel. This can be attributed to the different concentrations of initiator and activator used for the two gels. The molecular weight of the acrylamide chains, the cross-link densities and the resulting elastic and viscous moduli of the gels are known to be non-linear functions of not only the concentrations of monomer and cross-linker, but also the concentrations of initiator and activator [28,29]. The High Loss gel has 5x the crosslinker bis-acrylamide concentration, 0.5x the initiator (APS) concentration and 1.5x the activator (TEMED) concentration as compared to the Low Loss gel. For such variations, it is expected that for High Loss composition, gelation would be slower, (as seen with gelation kinetics in figure S1) that the acrylamide chains would be longer and that the cross-links would be non-uniformly distributed. The work of Adibnia and Hill on PAA gels [28] indicates the existence of an optimum ratio of crosslinker to monomer concentration beyond which the elastic modulus is lower than that expected from its linear dependence on crosslink density. This is attributed to the lack of monomer molecules to connect all the cross-links yielding a non-uniformly distributed crosslinks and leading to the creation of a weaker than expected network.

To study the deformation of these substrates under a constant shear force, creep measurements were performed with both PAA gels (refer to the Creep test protocol in Supplementary). A constant shear stress, σ₀, was applied and deformation of PAA gels (strain, γ) was measured for up to an hour. The compliances (J = γ (t)/σ₀) for High Loss and Low Loss gels are plotted in Fig. 1b. Both the gels were tested for two applied stresses, one below (10 Pa) and the other close to the yield stress of the gels (400 Pa for Low Loss and 100 Pa for High Loss). We observed that at short time scales (t < 2 s) both gels deform equally by $~\frac{{\sigma }_0}{G^{\prime }}$, indicating that the short time compliance is, J ~ G^′−1 for both gels. At long time, however, compliance of the gels plateau at different values, with the High Loss gel showing ten times higher deformation. Next, we explored the relationship between high loss modulus of this gel and higher deformation under creep.

3.2. Relationship between substrate loss modulus and substrate deformation

High Loss gel exhibits higher deformation than the Low Loss gel. To ascertain the relationship between the moduli and compliances as a function of frequency and time, we model the substrates using three Kelvin-Voigt (KV) modes arranged in series as shown in Fig. 1c. Each mode i consists of a spring of modulus, G_i, and a dashpot of viscosity, η_i, connected in parallel. When a constant stress (σ₀) is applied, the cumulative compliance will be:

$$J(t)=\frac{\gamma (t)}{{\sigma }_0}=\sum _{i=1}^3\frac{1}{G_i}(1-e^{-t/{\tau }_i}),$$ (1)

where, ${\tau }_i={\eta }_{i/G_i}$ is the relaxation time scale for that mode. G_i and η_i were obtained as best fit parameters from the data of compliance versus time for each gel in Fig. 1.b. These are tabulated in Table S2. The relaxation times τ_i are similar for both gels. The moduli of the first two modes are also similar. However, the third and the longest mode (τ₃ > 1000 s) of High Loss gel is around fifty times softer (G₃ = 0.12 kPa) that the Low Loss gel (G₃ = 5.0 kPa). It is therefore expected that this third mode contributes to the larger deformation observed for the High Loss gel at long times and is confirmed from the plots of mode-wise compliance for Low Loss and High Loss gels, in Supplementary Fig. S2a and S2b, respectively.

Additionally, we use the parameters obtained above to estimate the viscoelastic moduli (G′, G″) as a function of frequency. The model estimates match experimental data in Fig. 1a. Here also, by plotting the contribution of each KV mode to the moduli it is seen that the same third KV mode leads to relatively higher G″ value of High Loss gel at low frequencies. We thus established that a higher value loss modulus would lead to a larger deformation under creep. We next established a method to create a substrate with a gradient of loss modulus, to explore how the resulting non uniform creep of substrate will affect the migration of hMSCs.

3.3. Preparation of substrates with loss modulus gradient

To prepare the gel with a gradient of loss modulus, we used the two drop technique as reported earlier [12,27], which is a well-established technique for creating rigidity gradient in PAA gels. In short, we placed two drops of pre-polymer solutions with two different compositions, HLC and LLC, at proximity on a hydrophobic coverslip (Fig. 1d). Here, HLC and LLC stands for the compositions that give rise to High Loss and Low Loss gels respectively. Next, we placed a hydrophilic plate on top to make the drops coalesce and diffuse into each other. Two competing processes run here in parallel; diffusion and polymerization. Depending on the relative dominance of these two processes, the strength of the gradient is established. Depending on whether we coalesce the drops and start the diffusion simultaneously with polymerization, or allow the polymerization to go for 5 min before coalescence, we get gels with two different gradient strength (Fig. 1.e). Here, the gradient was visualized by adding red fluorescent polystyrene beads of 0.2 μm into High Loss solution (Supplementary Fig. S3). The change in this gradient was estimated by measuring the intensity of fluorescence along the gel length (dashed line in Fig. 1e). This measurement is only indicative as the gradient strength in the actual gel would be governed by diffusivity of bis-acrylamide and not the beads and would therefore be weaker than seen in Fig. 1e. However, this estimate gives us a reasonable basis to compare among substrates.

Further, to confirm that such mixing leads to only the change in loss modulus and not in storage modulus, we have measured the elastic and viscous moduli for different mixing ratios of the Low Loss and High Loss solutions. As can be seen from the chart in supplementary figure S4, the viscous modulus is seen to vary as expected with the mixing ratio. Since Figure S4 shows small variations in elastic moduli, we performed a secondary check by measuring E′ all along the gradient direction on an actual gel created by the two-drop technique. As seen in Figure S5, E′ = 3G′, varied insignificantly along the gradient direction.

3.4. hMSCs migrate in response to loss modulus gradient

We expect that gradient in loss modulus seen in Fig. 1e will be experienced by the hMSCs at cellular level as well. Careful experiments conducted by Buchanan et al. [30] show a perfect match between the elastic and viscous moduli obtained using conventional macrorheology as in Fig. 1, with those obtained using microrheological techniques, as would be experienced by individual hMSCs at the cellular level.

To address if the gradient of loss modulus induces directed cell migration, we recorded the movement of hMSCs on substrates with loss modulus gradient. We used uniform High Loss and Low Loss gels as controls. Movement of cells on these substrates was recorded using time-lapse microscopy for 18 h with 30 min time intervals. The videos were analyzed using “Chemotaxis Migration Tool” plug-in in ImageJ software. Fig. 2a-c show representative cell trajectories. In Fig. 2a, 18 cells (red lines) moved from High Loss to Low Loss region in the 18 h of observation, while only 4 cells (black lines) moved in the opposite direction. We term this so far unreported biased migration in response to the substrate Loss Modulus gradient as Viscotaxis. Such biased migration was absent on gels with uniform loss modulus, used as control (Fig. 2b-c) (Supplementary Video S1, S2 and S3).

Fig. 2. Viscotaxis, biased cell migration in response to the loss modulus (G″) gradient.

Representative plots depicting the trajectories of hMSCs migrating on (a) the gels with loss modulus gradient (b) gels of uniform Low Loss modulus, and (c) gels of uniform High Loss modulus. (Fig. a-c: Size of each box is 400 by 400 μm, scale bar 100 μm) (d) Tactic index at the end of 18 h for cells on gradient and uniform High Loss and Low Loss substrate. (n = 107 cells for Low loss, n = 98 cells for High loss, and n = 232 cells for loss modulus gradient from three independent experiments). (e-g) Evolution of x-displacement over time 18 h with 30 min interval for cells on (e) loss modulus gradient gel, (f) Uniform Low Loss gel, and (g) Uniform High Loss gel. (n for each of the figures: same as before) (h) Analysis of cell steps in viscotactic (positive) and non-viscotactic (negative) directions. Up and Down directions are taken as control. For this analysis, 27 viscotactic and 27 non-vistotactic cells were randomly chosen from the total 232 cells analyzed on loss modulus gradient. (i) The gradient region was further divided into three equal sections, as shown by the dashed lines. (j) Tactic index for the cells whose initial position falls in the three regions indicate no significant effect of the initial position on viscotaxis. (n = 62 cells) Error bar represents standard error of the mean (^∗ p< 0.05).

To further quantify the directional bias in cell migration, we estimated tactic index (TI), defined as the ratio of the difference in the number of cells moving in the two opposite directions to the total number of cells:

$$\text{TI}=(\text{L}-\text{R})/(\text{L}+\text{R}),$$

Where R and L are the numbers of cells migrated toward the right, the high loss modulus region, and to the left, the low loss modulus region, respectively. Cell population with no bias, i.e., with equal probability of going toward either direction, has TI = 0. We found (Fig. 2d) TI = 0.45 ± 0.05 on gradient substrate indicating that on an average 73% cells responded to the loss modulus gradient and migrated from High Loss to Low Loss region. It must be noted that, this fraction remains stable over time indicating that 30% of the cells are non-responsive. Cells on control gels, High Loss and Low Loss, had TI = (0.04 ± 0.05) and (-0.03 ± 0.05) respectively, indicating no preference for directional migration.

While TI captures the overall bias in migration as a ratio, it fails to estimate the strength of the bias. In other words, TI calculation only considers the relative shift from the initial position for a cell but does not take into account the extent of shift. To overcome this limitation, we calculated the average x displacement over time. An average x displacement close to zero indicates random migration while the width of the distribution estimates the randomness. Cells on substrates with a loss modulus gradient showed a steady increase in x direction displacement. Also, it can be seen that bias migration took approximately 6 h to get established (Fig. 2e).

Although, in the case of uniform Low Loss, the average x displacement shows a slight deviation from zero, the standard deviation (SD) is distributed in both +x and –x region. In contrast, average x displacement on gradient gel, SD are all within the +ve x direction indicating steady bias. It must be noted that, SD on uniform High Loss gel, is much larger compared to uniform Low Loss gel indicating more randomness in cell migration as compared to that on Low Loss (Fig. 2f-g).

From the TI data, we see that approximately 30% of the cells show negative viscotaxis, i.e., they migrate toward high loss region. However, the TI estimation is an end-point analysis where intermediate steps are not considered. As a result, this analysis cannot differentiate between a cell that ends in a final location which is in more High Loss region due to random walk from a cell that has the same outcome but due to more decisive motility. To answer the question if this is an outcome of random walk or a decision of individual cell at every time point, we classified the steps into +ve steps and –ve steps. When a cell takes a step in the direction of decreasing loss modulus i.e., in the direction of Viscotaxis, we consider that step as +ve and when the step is in the opposite direction, we consider that step as –ve step. For analysis, we randomly chose 27 out of cells of 232 cells that showed +ve displacement after 18 h in our TI study. We call this population as viscotactic cells (VisC). Similarly, we also randomly selected 27 cells which showed –ve displacement after 18 h in TI study. We call this population as non-viscotactic cells or NVisC.

We found that VisC took +ve steps in 77% of the cases (Fig. 2h). In contrast NVisC had no bias and took an almost equal number of +ve steps (55%) and -ve step (45%). To use as internal control, we analyzed the movement of the cells in the up down direction. For cells with net movement in up direction, +ve and -ve steps were 46% and 54% respectively. Cells with net downward migration took 49% +ve steps and 51% -ve steps. As expected, there was no bias in the up-down direction.

Next, we asked whether the initial location of a cell on a gradient determines its decision. In other words, we asked how the loss modulus gradient experienced by a cell at an initial time period influenced the migratory decision. To do that, we divided our field of observation into three parallel rectangular regions, each of width 130 μm (Fig. 2i).

The regions close to the Low Loss side was named as zone 1. Similarly, the middle section was named as zone 2, and the region towards High Loss side was named as zone 3.

We found that in the zone 2, TI was 0.62 ± 0.25. In zone 1 and 3, TI = 0.45 ± 0.32 and 0.36 ± 0.62, respectively (Fig. 2j). Though not statistically significant, the difference in mean TI for these three zones indicates that the observed TI might be dependent on the gradient of G″ at the initial positions of the cells. Together, these results highlight the possibility that whether a cell will respond to the loss modulus gradient or not depends on the local gradient strength.

3.5. Viscotaxis depends on the loss modulus gradient strength

Next, to investigate the influence of the strength of loss modulus gradient on migration bias, we prepared two sets of gels. In the first case, we increased the loss modulus gradient strength by creating a step increase from G″ = 45 Pa to G″ = 300 Pa (Fig. 3a-b). Whereas in the second case, we reduced the strength of the loss modulus gradient to 0.06 Pa/μm from 0.12 Pa/μm as used in the previous section. This was achieved by using two pre-polymer solutions, one that gives rise to a gel of G″ = 30 Pa and the other that gives rise to a gel of G″ = 150 Pa.

Fig. 3.

Effect of gradient strength on viscotaxis: We classify the events at the border of two loss moduli as positive and negative events. If the cell crosses from High loss side to Low loss side, or, refuses to cross from Low loss side to High loss side, we termed the event as Positive response. The two opposite events are termed as negative response. (a) Representative images for each event (as in our experiments, no event 4 was observed, we represented the situation with an imaginery ellipse with dotted line. (b) As high as 85% of the cells show Positive Response. (c) TI reduces to 0.28 when the gradient strength is reduced to ~half of the original. The figure shows representative cell trajectories.

In case of a step increase in loss modulus, the cells can take four probable trajectories, as shown in Fig. 3a. Here, the top panel shows the possible event 1, in which the cell starts from the High Loss modulus region and crosses the boundary to reach the Low Loss modulus region (Supplementary Video S3). In the possible event 2 (2^nd panel), the cell starts from the Low Loss modulus region, tries to cross the border but eventually takes a U-turn and returns to the Low Loss modulus region (Supplementary Video S5). We group these two events as a positive response because the movement follows the expected Viscotaxis direction (preferred movement from High Loss to Low Loss modulus region).

The negative events, i.e., in which cellular movements contradict the predicted Viscotaxis direction are shown in panels 3 and 4 The third panel shows event 3 where a cell crosses over from Low Loss to High Loss modulus region (Supplementary Video S6). The last panel shows the possible event 4 where a cell starts from High Loss modulus, approaches the Low Loss region but takes a U-turn from the boundary. In the time-lapse videos, for four independent experiments, recorded over 18 h, we could find 14 incidents of event 1, 23 incidents of event 2, and 9 incidents of event Interestingly, we could not find any incident of event four. That is why, in Fig. 3a, event 4 is presented with an imaginary cell with a dotted circle. Overall, we found that 85% of the cells show positive response demonstrating Viscotaxis (Fig. 3b). In terms of TI, this percentage corresponds to as high as 0.7. In contrast, with gradient strength reduced to half of the original, we found that the bias of cellular migration goes down, as shown in Fig. 3c (Supplementary Video S7). Correspondingly, the average TI also significantly reduced to 0.28 ± 0.08 from the earlier TI of 0.44 ± 0.06 (Fig. 2d).

To confirm that the observed migration is not caused by a rigidity gradient, we measured the elastic modulus (E) of the substrate along the gradient using atomic force microscopy (AFM). We found no gradient in elastic modulus (Supplementary Fig. S5). We confirmed the uniformity of collagen density on the gel by immunostaining, thus eliminating the possibility of haptotaxis (Supplementary Fig. S6). Further, to check if viscotaxis is ECM specific, we analyzed cell migration on another ECM i.e., laminin coated gel and found no significant difference (Supplementary Fig. S7 and Video S8).

3.6. Acto-myosin contractility is essential for Viscotaxis

To understand the mechanism of viscotaxis, we first measured cellular traction on uniform Low Loss and High Loss substrates using Traction force microscopy (TFM). We found that the cells on a Low Loss substrate apply ~5 times more force than they do on a High Loss substrate (Fig. 4a-c). This difference in traction may result in a force asymmetry on a substrate with loss modulus gradient leading to viscotaxis.

Fig. 4.

Viscotaxis is mediated through actomyosin contractility: Traction force applied by hMSCs on (a-c) High Loss substrate was lower than that on Low Loss substrate. Representative stress heat maps are shown for (a) Low Loss substrate, and (b) High Loss substrate, (c) Corresponding average Traction Stress (n = 10 cells, ^∗∗∗ p< 0.001). (d-g) Effect of contractility inhibitors on viscotaxis. Representative cell trajectories of migrating cells for (d) without inhibitor, (e) with blebbistatin, myosin inhibitor (20 μM), and (f) with Y-27632, ROCK inhibitor (10 μM). (g) Tactic index without inhibitor (n = 106 cells), with blebbistatin (n = 56 cells), and with Y-27632 (n = 62 cells). (h) Average cell velocity after treating with blebbistatin and Y27632 compared with a cell with no drug treatment to ensure that the drug doses used do not hinder the migration.

To verify this hypothesis, we inhibited actomyosin contractility by using two specific pharmacological inhibitors, blebbistatin and Y27632. Blebbistatin is known to inhibit myosin II [32] and Y27362 reduces the cellular contractility by inhibiting ROCK [33].

After 4 h of seeding on the substrate, hMSCs cells were treated with 20 μM blebbistatin and 10 μM Y27362. In the presence of the inhibitor, time lapse microscopy was performed for 18 h with 30 min interval. Fig. 4d-f represent cell trajectories for cell migration on substrate with loss modulus gradient in the presence of blebbistatin or Y27632. For control, only growth media and no inhibitor was used. We observed that the bias in migration significantly drops in the presence of traction inhibitors. The same is re-flected in the tactic index (TI) as shown in Fig. 4g. In the presence of contractility inhibitors, the TI came down to value 0.07 ± 0.03 for blebbistatin and 0.09 ± 0.08 for Y27362 signifying no preferred direction for migration (Supplementary Video S9, S10). As the cellular motility itself is dependent on contractility, we ensured that the concentration of the inhibitors used in this study reduced the cellular traction (supplementary table 3) but did not affect the net cell velocity (Fig. 4h).

3.7. Cells have less stable focal adhesions and more fluctuating boundary on High Loss substrate

As shown in Fig. 1B and discussed in the corresponding section, High Loss substrate creeps at a time scale of (τ₃ > 1000 s). Consequently, the material compliance increases and effective rigidity decreases (Supp Fig. S2). We predicted that the observed Viscotaxis is the result of this creep behavior of the substrate. We further predicted that the dynamic change in effective modulus will show its signature on the dynamics of cell spreading and focal adhesion (FA) assembly. However, testing this hypothesis with hMSCs is complex due to their inherent motility which causes a continuous fluctuation in cell shape and FA anyway. To simplify the situation, we performed the following experiments and analysis with less motile HeLa cells.

3.7.1. Focal adhesions are more dynamic on High Loss substrate

One of the primary sites of traction is at the focal adhesion, and there is evidence to suggest that the mechanosensitive protein vinculin is indispensable for traction [31,34]. There is also evidence to suggest that focal adhesion maturation takes place in a force dependent manner [35]. We hence decided to investigate vinculin enriched focal adhesions. We transfected HeLa cells with EGFP-Vinculin and observed vinculin positive focal adhesions. We performed kymograph analyses of time-lapse images of transfected cells on High Loss and Low Loss substrate (Fig. 5a). We observed that Kymographs of the cell edge indicate less stability of focal adhesions on High Loss substrates- FAs on High Loss substrates appear to assemble and disassemble much more frequently than on Low Loss substrates. This observation indicates that focal adhesions seem to be more stable on Low loss substrates.

Fig. 5. Focal adhesion (FA) and cell shape are more dynamic on High loss substrates.

(a) Time sequences of HeLa cells with GFP-tagged vinculin at time t = 0 min, 10 min, 20 min, 26 min on Low Loss and High Loss substrates. The first image in each row shows one complete cell. The next images are the time- sequenced ROI as shown by the yellow box. The bright spots are GFP tagged vinculin rich focal adhesion points. For kymograph analysis, 55 px line is drawn at vinculin position. The line position is kept constant and vinculin position is monitored with time. The resulting kymograph is presented as the last image of the sequence. In kymograph, y-axis represents time and x-axis represents the distance of the line drawn at vinculin position. scale bar 50 μm. (b) Immature FA persistence time on the High Loss and Low Loss substrate. ^∗∗∗p < 0.001. (c) Time lapse images of the Hela cell cultured on Low Loss and High Loss substrate. Boundaries are highlighted for easy visualization. scale bar 100 μm (d) Merged boundaries of cells on Low Loss and High Loss with equispaced radial lines drawn from a reference point (nucleus) intersecting the membrane boundaries. (e) Membrane fluctuation as measured by the standard deviation of the length of the radial line, as shown in fig. (d). ^∗p < 0.05.

Further to test whether difference in substrate loss modulus also regulates the persistence of FA formation and FA growth, we measured immature FA persistence time in HeLa expressing EGFP-vinculin as an FA marker. This revealed that persistence time of immature FA on High Loss substrates is significantly less than on Low Loss substrates (Fig. 5b).

3.7.2. Cells fail to attain a stable shape on High Loss substrate

To study the effect of substrate viscoelasticity on cell spreading, we imaged the cells over 4 h with 5 min time intervals. We found the cell boundaries more dynamic on High Loss substrate than on Low Loss substrate (Fig. 5c) (Supplementary Video S11, S12). To quantify this observation, cell boundaries were identified over time sequenced images and were overlapped. Any effect of cell migration was corrected by keeping the centroid of the cell stationary (Fig. 5d). Further in each image, the linear distance of the cell boundary from its centroid was measured for 8 equally spaced angular positions covering 360°, averaging over a ± 10° arc for each angular position. Variation of these radial distances with time is presented in supplementary Fig. S8. Standard deviations in these distances measured over time is the signature of cell area fluctuation. We found almost 2 times more fluctuation in cells on High Loss than the cells on Low Loss (Fig. 5e).

Overall, shorter persistence time of focal adhesions in conjunction with the unstable membrane boundary, indicates overall lack of mechanical stability on High Loss substrates.

4. Discussion

Tissue microenvironment, be it cell, ECM, or the whole organ, is viscoelastic in nature with characteristic storage moduli (G′) and loss moduli (G″) [36–40]. However, research in the field of mechanobiology is mostly limited to investigating the effect of rigidity but not the viscoelasticity of the microenvironment. In particular, no prior study has investigated the effect of viscoelasticity gradient on cellular migration. In this work, we have demonstrated that hMSCs migrate from high loss modulus region to low loss modulus region when exposed to a substrate with a gradient of G″ but nearly constant G′. The bias during migration, as defined by the tactic index (TI), increases with an increase in gradient strength. We have termed this, so far unreported, migration as “viscotaxis”. Viscotaxis is not a new term. This word was previously used to describe the preferential swimming behavior of non-mammalian cells in a liquid medium with viscosity gradient [41]. However, this is the first work to report the effect of solid viscoelasticity on the crawling migration of adherent cells. There are two other cellular migrations or “taxis” well reported in literature namely durotaxis and haptotaxis that depend on adherent cues such as the gradient of rigidity and ligand density, respectively [12,42]. To substantiate that the observed migration in this paper was not durotaxis or haptotaxis, we confirmed the uniformity of rigidity and the concentration of the ligand by AFM and immunostaining respectively (Fig. S5 and S6). Although there is a small stiffness gradient in elastic modulus, the gradient is in the opposite direction nullifying the possibility of the observed migration to be durotaxis.

We hypothesize that viscotaxis originates from the differential response of elastic and viscoelastic material to the same applied force. While an ideal elastic material attains a constant steady deformation instantaneously, a viscoelastic response is a time dependent phenomenon. If the same amount of stress is applied for the longer duration, the deformation increases with time (Fig. 1b); this phenomenon is known as creep. We have explained viscotaxis with the help of creep, as shown in Fig. 6. For an adherent cell located on a substrate with a gradient of G″, each focal adhesion that pulls the substrate would experience a local substrate deformation, commensurate with the local viscoelasticity of the substrate. Imagine a prototypical 2-D cell with focal adhesions at the left and right ends, FA_L and FA_R, respectively. Substrate at FA_L has higher viscoelastic nature (High Loss) than the substrate at FA_R (Low Loss)_. As we have shown using three KV modes in series, at shorter times (t₀) (< 10s), the mode 1 would contributed to the symmetric elastic response in both the gels (aka both ends of the cell). However, at longer times (t₁) (>100s), the third KV mode which is softer (with lower spring modulus) for High Loss gel would dominate (Fig. 1b and c). We observe that persistence time of FAs on High Loss and Low Loss gels are ~600s and ~1200s respectively (Fig. 5b). This duration is sufficient to invoke the creep in the material at High Loss end of the cell but not at Low Loss side. As a result, High Loss end should deform more than the Low Loss end resulting in a small shift in the cell’s position to the right. The process is further assisted by higher cellular traction (Fig. 4a) [43] and more stable FAs (Fig. 5a and b) at the Low Loss (elastic) end compared to the High Loss end, causing a break in symmetry, an essential condition for directed cell migration.

Fig. 6.

Schematic of the proposed mechanism for observed Viscotaxis: Adherent cells apply traction on the substrate on which they adhere. In response, the substrate deforms. When a cell applies traction on a substrate with gradient loss modulus but constant storage modulus, substrate at both the ends of the cell (FA_L and FA_R) deform equally on shorter timescale (t₀ < 2 sec), as shown using three KV modes in series in Fig. 1. However, at longer timescale (t₁ > 1000 sec), the third KV mode will dominate and hence High Loss end (FA_L) would deform more than the Low Loss end (FA_R). As a result of this symmetry breaking, the cell will shift to the right causing a directed migration from High Loss towards the Low Loss region.

Here in this manuscript, we have presented a so far unreported type of “-taxis” wherein migration of cells occurs due to gradient in viscous modulus, even though the substrate elastic modulus remains constant. These data do not challenge or contradict the known knowledge of durotaxis. Instead, our result opens one important question in the context of durotaxis. In all previous studies exploring durotaxis, researchers only considered the elastic modulus (E or G′). The changes in E or G′ were achieved by changing the polymer concentration or cross-linking density [44–46]. However, the same process may also change the substrate viscoelasticity and may have a pronounced effect on observed cellular migration. Our results suggest that any study probing the effect of substrate material properties on cellular migration must take the possible effect of substrate viscoelasticity into consideration. Our data also opens up the possibility to reexamine the published data on durotaxis and evaluate if the observed migration was the result of one or both the cues. Further study is needed to assess the combined effect of substrate storage and loss modulus on cellular migration.

5. Conclusion

In conclusion, we have demonstrated that a gradient in loss modulus (G″) is an important mechanical cue governing cell migration. We propose that viscoelasticity of the materials should be taken into account in the discussion of mechanotaxis. Further, its role in physiological and pathological conditions should be investigated in more detail.

Supplementary Material

Supplementary material associated with this article can be found, in the online version, at 10.1016/j.actbio.2021.08.039.

Statement of significance.

While the effect of substrate elastic modulus has been investigated extensively in the context of cell biology, the role of substrate viscoelasticity is poorly understood. This omission is surprising as our body is not elastic, but viscoelastic. Hence, the role of viscoelasticity needs to be investigated at depth in various cellular contexts. One such important context is cell migration. Cell migration is important in morphogenesis, immune response, wound healing, and cancer, to name a few. While it is known that cells migrate when presented with a substrate with a rigidity gradient, cellular behavior in response to viscoelastic gradient has never been investigated. The findings of this paper not only reveal a completely novel cellular taxis or directed migration, it also improves our understanding of cell mechanics significantly.