Migration and 3D Traction Force Measurements inside Compliant Microchannels

Abstract

Cells in vivo migrate through channel-like tracks. While polydimethylsiloxane devices emulate such tracks in vitro, their channel walls are impermeable and of supraphysiological stiffness. Existing hydrogel-based platforms address these issues but cannot provide high throughput analysis of cell motility in independently controllable stiffness and confinement. We herein develop polyacrylamide (PA)-based microchannels of physiological stiffness and prescribed dimensions for high-throughput analysis of cell migration, and identify a biphasic dependence of speed upon confinement and stiffness. By utilizing novel 4-walled microchannels with heterogeneous stiffness, we reveal the distinct contributions of apicolateral versus basal microchannel wall stiffness to confined versus unconfined migration. While the basal wall stiffness dictates unconfined migration, apicolateral stiffness controls confined migration. By tracking nanobeads embedded within channel walls, we innovate 3-dimensional traction force measurements around spatially confining cells at subcellular-resolution. Our unique and highly customizable device fabrication strategy provides a physiologically relevant in vitro platform to study confined cells.

Graphical Abstract

Physical cues, such as confinement^{1, 2} and the stiffness³ of the local tissue microenvironment, are critical to diverse (patho)physiological processes, including proliferation, migration and differentiation. During cancer metastasis, tumor cells navigate through interstitial tissues via pre-established open paths or by generating such openings via remodeling of their surrounding extracellular matrix (ECM)^{4, 5}. Three-dimensional (3D) longitudinal channel-like tracks are either intrinsically present in various native anatomical structures like those at the perivascular and peri-muscular spaces, fat tissue and brain milieus⁶ or created by cancer-associated fibroblasts or migratory cancer cells themselves¹. As the human body consists of a plethora of microenvironments, cells adapt and respond to each environment differently. The development of in vitro systems that recapitulate key aspects of the in vivo setting will enable a comprehensive understanding of how cells respond to complex physiologically-relevant microenvironments where different physical and biochemical cues are present.

Over the years, researchers have emulated different aspects of the in vivo microenvironment to interrogate cell function in highly controlled experiments in vitro. The dimensionality of the ECM resulted in the production of 2D, 1D and 3D platforms^{7, 8}, and the intrinsic properties of the ECM led to development of model systems using distinct proteins⁹, substrate stiffness³, porosities¹⁰, protein fiber thicknesses¹¹ and alignments¹². A widely-used technique to emulate 3D micro-topographies in vitro relies on soft lithography of Polydimethylsiloxane (PDMS) to create 3D microchannels of prescribed dimensions^13-15 which are coated with the desired ECM protein. While such model systems have immensely contributed to the understanding of how physical confinement regulates motility, the channel stiffness is not physiologically relevant. Altering the degree of PDMS crosslinking during the curing process can produce substrates of lower stiffness¹⁶, but channel imprinting and maintaining integrity of channel dimensions post device assembly becomes a challenge. Moreover, PDMS is not permeable to water or small molecules and thus does not accurately recapitulate the exchange of soluble factors in the living tissues. Native PDMS also provides inconsistent and non-uniform cell adhesion due to the hydrophobicity and the fouling properties of its surface¹⁷. While oxygen plasma treatment and adsorption of ECM proteins facilitate cell spreading, the relationship between cell mechanics and ECM proteins can be confounded by the fact that native PDMS allows attachment but not spreading. To address the issues of supraphysiological stiffness and water permeability, non-cell degradable polymers, such as poly(ethylene glycol) (PEG)¹⁸, polyacrylamide (PA)¹⁹ and alginate²⁰ or reconstituted ECM proteins (e.g., collagen²¹) have been employed. Soft lithography of hydrogels has led to the generation of either non-confining channels²² or narrow 3-walled troughs¹⁹, which fail to confine cells in all directions. Although application of two-photon microscopy has the potential of creating fully-confining microchannels in 3D¹⁸, it does not allow high-throughput analysis of cell motility.

To investigate how physical confinement alters motility at physiologically-relevant stiffnesses, we developed a soft lithography-based compliant microfluidic device with independently tunable stiffness and degree of confinement, which we call Hydrogel Encapsulated Micro-Channel Array (HEMICA). Specifically, we fabricated a mold with microchannels of prescribed dimensions, which were imprinted in a PA hydrogel of physiologically relevant stiffness ranging from 5 to 21 kPa. Subsequently, we created a flat PA gel with the same or different stiffness than the gel with the imprinted design and bonded the two gels together, thereby generating channels of homogeneous or heterogeneous stiffness, respectively. We herein demonstrate different applications of HEMICA for high-throughput analysis of cell motility, including single cell migration through 2D-like unconfined and confining channels of different stiffness in the absence and presence of a chemotactic stimulus as well as collective migration. By embedding nano-beads in the HEMICA gels of prescribed Young’s modulus, we utilized the confining microchannels to measure spatiotemporally-resolved 3D traction forces. While prior work with 3-walled hydrogel troughs revealed the dependence of cell morphology and migration on stiffness and channel width¹⁹, our 4-walled HEMICA device not only confirms these previous findings but also provides an enhanced multifaceted tool, which allows independent control of apicobasal substrate stiffness and measurement of 3D forces exerted by cells to their surrounding microenvironment.

Fabrication of HEMICA-

To decouple the effects of stiffness and degree of confinement on cell migration, we used photolithography to generate microchannels of prescribed dimensions made of PA gels whose stiffness can be highly tuned within physiological levels. Microchannels were first fabricated on a silicon wafer which was used as a mold for PA polymerization (Fig. 1Ai). As a result, the microchannel design was imprinted on the lower surface of the gel, termed “imprinted gel”. Next, a thin (~60-100 μm) flat layer of PA (called “flat-gel”) with the same or different stiffness than the imprinted-gel was polymerized on glutaraldehyde-activated coverslips (Fig. 1Aii). Both the flat-gel and the imprinted-gel were allowed to swell in PBS at 37 °C to reach their maximum volume. The volume of PA, its stiffness and the temperature in which the gels are kept are critical to determining the time required for maximal uptake of PBS²³. Depending on the stiffness of the gels, different final gel volume maxima were detected (Fig. 1B), with stiffer gels reaching a lower swelling ratio than softer ones. Because the flat-gels contained a smaller volume of liquid, the rate of drying is much faster than that of the imprinted gels (Fig. 1B), thereby requiring the minimization of the amount of time for gels outside a hydrating medium. Once the maximal swelling ratio is achieved, the excess PBS from the gel surfaces was removed by compressed air, inlet/outlet holes were punched on the imprinted gel whereas the surface of the flat-gel was coated with bis(sulfosuccinimidyl)suberate (BS3) (Fig. 1Aiii). Subsequently, the imprinted gel was positioned on top of the flat-gel and allowed to adhere, as BS3, an N-Hydroxysuccimide (NHS)-ester, formed amide bonds with the primary amines of the PA gels at a slightly basic pH (Supporting Information Fig. S1A). The two bonded gels created an array of four-walled microchannels in which the flat- and imprinted- gels had either the same (homogeneous) or distinct (heterogeneous) elastic moduli (Fig. 1C, Supporting Information Fig. S1B). Furthermore, imprinting microchannels of different dimensions enables the study of cell migration under various degrees of confinement (Supporting Information Fig. S1C-E) in the presence or absence of chemotactic or osmotic gradients. To coat the device with ECM proteins, microchannels were first incubated under UV light with sulfosuccinimidyl 6-(4’-azido-2’-nitrophenylamino)hexanoate (Sulfo-SANPAH)²⁴ followed by addition of the desired ECM protein (e.g., collagen type I) and overnight incubation (Fig. 1Aiv). The uniform coating of collagen type I across all channels of different stiffnesses was confirmed by using FITC-labeled collagen (Supporting Information Fig. S1F). After cell seeding, the device was immediately submerged in media to preserve the volume of the flat-gel, thus avoiding loss of gel-to-gel adhesion. To mimic tissue tracks of pathologically relevant stiffness encountered in the breast microenvironment^{3, 25, 26}, HEMICA devices were fabricated with a Young’s modulus of 8, 15 and 21 kPa (low, intermediate and high stiffness), as confirmed by atomic force microscopy (Fig. 1D). Although the use of profilometer was used to verify the desired dimensions of the mold, the swelling of the gels during the fabrication process necessitated the quantification of channel’s dimensions after device assembly. Channel dimensions were measured using confocal microscopy of microchannels filled with fluorescently labeled dextran solution (Supporting Information Fig. S1C) or microscopy of gels with suspended beads (Supporting Information Fig. S1D, E). Interestingly, cell entry and migration in confining channels caused the local expansion of the channel width, which was attenuated with increasing channel stiffness (Supporting Information Fig. S1E).

Figure 1. HEMICA fabrication and characterization.

(A) Schematic representation of the production of PA gels with microfluidic tracks, assembly of HEMICA devices and ECM protein coating. (B) Swelling ratios of the imprinted-gel and the flat-gel. The weight of the gels was measured daily as they were swelling in PBS at 37°C. The weight of the gels undergoing drying at ambient air was measured at 0, 2, 4, 6, 8 and 24 h after having reached their maximum swelling in PBS. Dry weight was measured after lyophilization at the end of the experiment. Data represent the mean ± S.D. from 3 independent experiments for each stiffness. Two-way ANOVA followed by Tukey’s multiple comparison was performed. *p<0.05 relative to each of the other two stiffnesses for each time point. (C) Picture of assembled HEMICA (dimensions of coverslip: WxL=22x40 mm). (D) The Young’s modulus of gels with three different stiffness, as calculated by atomic force microscopy. Data represent the mean ± S.D. of ≥41 measurements from two independent experiments for each gel formulation. One-way non-parametric ANOVA (Kruskal-Wallis test) followed by Dunn’s multiple comparisons was performed.

The effects of channel stiffness and degree of confinement on cell morphology and migration-

Cells in vivo can migrate through tissue tracks ranging from 3 to 30 μm wide^{1, 27} and occasionally on 2D-like surfaces²⁸. To decipher the interplay between channel stiffness and degree of confinement on cell motility, we examined the behavior of human MDA-MB-231 breast cancer cells migrating inside collagen I-coated microchannels of prescribed dimensions and stiffness (Supporting Information Fig. S2A). 4-walled microchannels of uniform stiffness ranging from 8, 15 to 21 kPa, and of constant height (H=10 μm) and length (L=200 μm) yet different widths varying from ~4-60 μm were used, thereby enabling us to investigate cell morphological and migratory responses in a range of physical microenvironments spanning from highly confining (W=~4 μm) (Supporting Movie M1) to 2D-like (W=~60 μm) (Supporting Movie M2 and M3). Cell circularity and roundness were used as quantitative indices of cell morphology in channels of different widths and stiffness. For each channel width, cell circularity was the highest in low stiffness (8 kPa) channels, which is indicative of a less elongated morphology relative to that at higher stiffnesses (Fig. 2A). This is further substantiated by measurements of cell roundness, which is defined as the inverse of aspect ratio, and is highest for low stiffness channels (Fig. 2B). The circularity variance as well as the cell area variance are elevated in the low stiffness channels (Supporting Information Fig. S2B,C) suggesting that cells undergo more extensive morphological changes in compliant microenvironments (Supporting Movie M1).

Figure 2. The effects of channel stiffness and degree of confinement on cell morphology, migration speed and contact guidance.

(A) Circularity, (B) roundness, (C) migration speed, (D) solidity and (E) persistence of individual MDA-MB-231 cells inside HEMICA microchannels of 8, 15 and 21 kPa stiffness having fixed height and length (H=10 μm, L=200 μm) with widths spanning from ~4 μm to ~60 μm (2D-like). Data represent the mean ± S.D. (A, B, D, E) or mean ± S.E.M. (C) for n≥23 cells from 6 independent experiments. Two-way ANOVA followed by Tukey’s multiple comparison test was performed. (F) Average number of jumps (number of times cells crossed the center line of a microchannel) for single MDA-MB-231 cells inside HEMICA microchannels of 8, 15 and 21 kPa stiffness having fixed height and length (H=10 μm, L=200 μm) with widths of 22-27 μm or ~60 μm (2D-like). (G) Average probability of single MDA-MB-231 cells migrating along the central portion of a wide microchannel (W=22-27 μm or ~60 μm (2D-like). Central portion is defined as being at least 7 μm away from each of the lateral channel walls. Data represent the mean ± S.D. for ≥24 cells (F) or ≥39 cells (G) from 6 independent experiments. Two-way ANOVA followed by Tukey’s multiple comparison test was performed.

For each stiffness, migration speed displayed a biphasic distribution as a function of channel width reaching a maximum at W=~12 μm, which was more prominent at 8 kPa (Fig. 2C). For every channel width, migration speed varied in a biphasic manner with channel stiffness, showing a maximum at 15 kPa (Supporting Information Fig. S2D). While the optimal stiffness and channel dimension can vary depending upon cell type and their morphology, a similar response was also observed with another triple-negative breast cancer cell line SUM159 (Supporting Information Fig. S2E). Prior work has shown that cells displaying a protrusive/mesenchymal morphology move faster^{29, 30}. As such, we examined how channel stiffness alters cell morphology by quantifying cell solidity, which is an index of cell protrusiveness. Interestingly, the stiffness (15 kPa), which promoted the fastest cell motility, also supported a more protrusive phenotype, as quantified from reduced cell solidity measurements (Fig. 2D). Along these lines, cell locomotion in unconfined channels (W≥17 μm) was more persistent at intermediate (15 kPa) relative to low (8 kPa) stiffness (Fig. 2E) due to their faster migration speed and protrusive phenotype. Cell persistence was also elevated at high (21 kPa) compared to low (8 kPa) stiffness channels, which is attributed to more coordinated protrusion/shrinkage cycles as evidenced by reduced fluctuations in cell area and circularity (Supporting Information Fig. S2B,C).

Prior work using supraphysiologically stiff PDMS-based devices revealed that the vast majority of MDA-MB-231 cells become elongated and move preferentially along the lateral-basal surface interface of 20 μm-wide channel³¹. Cells that do not switch lateral walls during their locomotion are termed as contact guided. Using HEMICA, we tested how channel stiffness influences contact guidance by quantifying two key parameters: i) the number of times cells crossed the centerline (defined as “jumps”) of wide (W≥22 μm) microchannels, and ii) the probability of a cell following a path within the central region of the microchannel without touching any of the lateral walls. Data analysis reveals that cells migrating inside compliant (8 kPa) microchannels are less susceptible to contact guidance (Fig. 2F, G).

HEMICA applications-

During the HEMICA assembly process, bonding between the imprinted- and flat-gels of the same or distinct stiffnesses results in generation of homogeneous or heterogeneous 4-walled microchannels, respectively. Heterogeneous microchannels enable us to emulate aspects of the in vivo microenvironment where cells are sandwiched by distinct longitudinal tissue interfaces bearing different stiffnesses. For instance, tumor cells migrate in vivo by preferentially polarizing their perceived basal and apical surfaces towards myofibers and relatively softer collagen fibers, respectively³⁰. Cells also migrate on basement membranes and muscle fibers interfacing with the ECM, which enclose them in a microenvironment of nonuniform stiffness on different sides. Because confined migration inside homogeneous microchannels of intermediate (15 kPa) stiffness is faster than in low (8 kPa) stiffness ones (Fig. 2C), we wished to examine the relative contributions of apicolateral versus basal wall stiffness on cell motility. To this end, we fabricated 4 different HEMICA devices with the following apicolateral and basal wall stiffness combinations: 8 kPa on 8 kPa, 8 kPa on 15 kPa, 15 kPa on 8 kPa and 15 kPa on 15 kPa (Fig. 3A). We first confirmed that the speed and velocity of migration inside homogeneous confining (WxH: ~4x10 μm²) microchannels of intermediate (15 kPa) stiffness were markedly elevated relative to those in low (8 kPa) stiffness (Fig. 3A and Supporting Information Fig. S3A). Increasing the stiffness of the basal wall to 15 kPa while retaining a stiffness of 8 kPa for the apicolateral walls led to a modest increase of migration speeds and velocities relative to those in homogeneous low stiffness microchannels (Fig. 3A and Supporting Information Fig. S3A). Interestingly, the reverse configuration, in which the apicolateral walls had a stiffness of 15 kPa whereas the base was kept at 8 kPa, resulted in a marked increase of migration, which nearly approached the levels observed in homogeneous 15 kPa microchannels (Fig. 3A and Supporting Information Fig. S3A). The individual contributions of apicolateral and basal channel wall stiffness to migration persistence were less evident with maximal persistence requiring both apicolateral and basal channel walls of 15 kPa (Fig. 3B). Taken together, our data reveal that the stiffness of apicolateral walls has a more pronounced effect than that of basal wall on confined migration. As a control, we measured the speed of non-contact guided MDA-MB-231 cells inside unconfined (W=~60 μm; 2D-like) heterogeneous microchannels, which is expected to be independent of the imprinted gel stiffness (Supporting Information Fig. S3B).

Figure 3. HEMICA as a multifaceted tool for generating microchannels with heterogeneous wall stiffness as well as chemotactic gradients to study single cell, collective and single cell-file migration.

(A) Confined migration speed and (B) persistence of individual MDA-MB-231 cells inside homogeneous and heterogeneous HEMICA microchannels of fixed height (H=10 μm), length (L=200 μm) and width (W=~4 μm). Microchannels of prescribed imprinted (apicolateral) and flat (basal) PA gel stiffness combinations were fabricated: 8 on 8 kPa, 18 on 15 kPa, 15 on 8 kPa, 15 on 15 kPa. Data represent the mean ± S.D. for ≥170 cells from 3 independent experiments. One-way non-parametric ANOVA (Kruskal-Wallis test) followed by Dunn’s multiple comparisons was performed. (C) Phase contrast image (left) and FITC image (right) of 15 kPa HEMICA microchannels (H=10 μm, L=200 μm and W=~4 μm) with 1% wt/vol FITC-Dextran added to the top (cell exit) channel and PBS on the bottom (cell seeding) channel for chemotactic gradient quantification. Orange, green and blue boxes depict the cell exit channel at the top, the cell seeding channel at the bottom, and the microchannel ROIs, respectively, used for fluorescence measurements. Scale bars: 100 μm. (D) Representative moving average of mean FITC-Dextran fluorescence intensity over time for all three ROIs. Images were acquired every 10 min, and moving average was calculated over 3 frames. (E) Mean FITC-Dextran fluorescence intensity of the three aforementioned ROIs at every timepoint normalized to the initial value at the upper ROI (orange box). Data are mean ± S.D. representative of two independent experiments. One-way non-parametric ANOVA (Kruskal-Wallis test) followed by Dunn’s multiple comparisons was performed. (F) Confined migration speed and (G) persistence of single MDA-MB-231 cells migrating through microchannels of prescribed dimensions (H=10 μm, L=200 μm, W=~4 μm) and stiffness (15 kPa) in the absence of FBS (Control (−) FBS) or presence of a 10% FBS in the cell exit channel to create chemotactic gradient (Gradient 10% FBS). Data represent mean ± S.D. for ≥199 cells from 3 independent experiments. Mann-Whitney (non-parametric) test was performed. (H, I) Images of collectively migrating A431 cells through ~60 μm (2D-like) (H) or ~25 μm (I) in width microchannels of 21 kPa stiffness. (J) Image of single cell and single cell-file migration of A431 cells through ~13 μm-wide microchannels of 21 kPa stiffness. Scale bars: 50 μm for (H-J).

In all experiments so far, HEMICAs were submerged in FBS-containing media for two reasons: first, to ensure that the hydrogels will not shrink over time; and second, to study migration in the absence of a chemotactic gradient. To study chemotactically-driven migration, different media need to be added at the cell seeding (FBS-free medium) and cell exit (FBS-containing medium) channels. To this end, after HEMICA assembly and cell seeding, the medium in which HEMICAs were submerged was aspirated out and replaced with two distinct media at the cell seeding and cell exit channels. During this process, we had to maintain the bonding of the flat and imprinted gels and prevent gel shrinkage by increasing the humidity in the live-microscopy incubator chamber. As a control to ensure the generation and maintenance of a gradient, 1% FITC-Dextran in PBS was introduced to the cell exit channel, whereas PBS was added to the cell seeding one. Under static conditions, a gradient was established through the microchannels (blue), in-between the cell exit channel (orange color Region Of Interest (ROI)) and the cell seeding side (green color ROI) of the device (Fig. 3C). A stable gradient was maintained for at least 15 h (Fig. 3D). By normalizing the fluorescence intensity of the ROIs over time to the maximum intensity of the upper (cell exit) ROI, we observed that the microchannel ROI average intensity was at intermediate levels between the upper and lower (cell seeding) ROIs (Fig. 3E). We next examined the migratory potential of MDA-MB-231 cells in confining (WxH: ~4x10 μm) microchannels of 15 kPa stiffness in the absence and presence of a 10% FBS gradient. The presence of chemotactic stimulus increased the speed, velocity and persistence of migration (Fig. 3F, G, Supporting Information Fig. S3C).

In addition to single cell migration, HEMICA can be used to study collective or single cell-file migration, which are prevalent in vivo⁵. To illustrate the utility of HEMICA in these applications, we used a multichannel design with microchannels of fixed stiffness (21 kPa), height and length (H=10 μm, L=200 μm), with widths ranging from ~4 μm to ~55 μm. Subsequently, a confluent monolayer of A431 squamous cell carcinoma cells was allowed to form at the cell seeding channels of HEMICAs. Cells entering the larger (~55 μm and ~22μm) width channels used a collective mode of migration (Fig. 3H, I), while cells in smaller width channels migrated as single cells or single cell-files (Fig. 3J).

3D traction force measurements using HEMICA-

HEMICA enables the measurement of 3D traction forces exerted by cells on their surrounding microenvironment during confined migration in microchannels of prescribed stiffness. For this purpose, we fabricated PA-based microchannels with fluorescent nanospheres embedded in the hydrogel mix. Traction stresses were evaluated by recording the displacement maps of the nanospheres as cells migrated inside the confining (WxH=~4 μm x10 μm) microchannels (Supporting Information Fig. S4A, B). In brief, from the displacement field maps, the microchannel wall deformation can be readily determined, which along with the Young’s modulus of the gels allows the estimation of the stress (σ) experienced by the microchannel wall using finite element analysis. Total stress exerted by cells increases with microchannel stiffness due to increases in both normal and shear traction forces (Fig. 4A-C). Interestingly, cells exerted higher forces in the normal directions than in the plane of cell motion. This observation further expands the understanding of confined migration, which exhibits distinct traction force profiles and actomyosin structures than those of unconfined migration³². Inhibition of cell contractility via para-nitroblebbistatin (20 μM) markedly reduced traction stresses during confined migration inside microchannels of 15 kPa stiffness, thereby validating the robustness of our measurements (Fig. 4D-F). Of note, blebbistatin-treated cells migrating in confining channels of 15 kPa stiffness exerted traction stresses similar to those of untreated cells inside microchannels of 8 kPa (Fig. 4A, D), which is in line with previously reported findings showing that the effect of blebbistatin treatment on actomyosin contractility is equivalent to that of plating cells on softer substrates^{33, 34}. In addition to computing the average 3D traction stress at the whole cell level, we spatially dissected the force fields corresponding to distinct regions along the cell body during locomotion inside microchannels. Consistent with the notion that the nucleus represents the stiffest component of the cell³⁵, the forces tended to be highest in the perinuclear region of migrating cells (Fig. 4G). This was likely due to the combination of cytoskeletal forces to position the nucleus forward³⁶ and the pushing forces transmitted from the nucleus onto the channel wall. Myosin II inhibition via blebbistatin reduced the magnitude of stresses along the entire cell length (Fig. 4D-F) including the perinuclear region (Supporting Information Fig. S3A). Taken together, we demonstrate the ability to measure spatiotemporally resolved traction forces of migrating cells in confinement using HEMICA.

Figure 4. 3D traction force microscopy at total cell level and subcellular resolution.

(A) Average total stress, (B) average normal stress, and (C) average shear stress exerted by individual MDA-MB-231 cells on confining (H=10 μm, L=200 μm, W=~4 μm) microchannel walls of 8, 15 and 21 kPa stiffness. Data represent mean ± S.D. for ≥13 cells from 2 independent experiments for each gel stiffness. One-way ANOVA with Tukey’s multiple comparison test was performed for A, B and Kruskal-Wallis test followed by Dunn’s multiple comparison was used for C. (D) Average total stress, (E) average normal stress and (F) average shear stress exerted by blebbistatin-treated single MDA-MB-231 cells on confining microchannel walls of 15 kPa stiffness. For visual comparison purposes, vehicle control data, shown in A-C, are also plotted here. Data represent mean ± S.D. for ≥16 cells from 2 independent experiments. Unpaired t test was performed on log transformed data. (G) Average total stress exerted by different cellular compartments of single MDA-MB-231 cells on confining microchannel walls of 8, 15 and 21 kPa stiffness: trailing edge, perinuclear and leading edge. Data represent mean ± S.D. for ≥9 cells from 2 independent experiments for each gel stiffness. One-way ANOVA with Tukey’s multiple comparisons was performed for cells at 8 and 15 kPa and after log transformation for cells at 21 kPa.

In summary, we establish the utility of HEMICA as a multifaceted tool that allows independent tuning of stiffness and degree of confinement for high-throughput cell migration studies. Using microchannels of heterogeneous stiffness, we demonstrate the relative contributions of the basal and apicolateral walls in confined migration. Although HEMICA is limited to fabrication of confining microchannels with Young’s moduli higher than 5 kPa, the unique, highly controlled, and physiologically relevant microenvironment generated in HEMICA can permit its usage in organ-on-a-chip applications. While 3D traction force microscopy of a 2D cell culture substrate has been instrumental in revealing novel mechanisms of epithelial morphogenesis^{37, 38}, our 3D spatial traction force measurement techniques can expand the understanding of single cell mechanics during cell entry into and exit from confining channels, which emulate aspects of extravasation and intravasation, respectively¹³. Additionally, the 4-walled confining channels can extend the understanding of migration mechanisms and path selection in response to hydraulic resistance in different microenvironments of physiologically-relevant stiffness. Of note, the dynamic mechanical behavior of PA gels is affected by their non-linear mechanical properties, which need to be considered for improved accuracy under large deformation³⁹.