Dynamics of 3D carcinoma cell invasion into aligned collagen

Engineering 3D environments to image focal invasion in vitro

To develop a novel 3D invasion assay that captures tumor relevant ECM architecture, we first generated aligned collagen matrices using our previously reported method²¹. In this method, collagen matrices seeded with carcinoma-associated fibroblasts are constrained along one axis, inducing anisotropic contraction and collagen alignment along that axis (Fig.1a)²¹. Such collagen matrices have previously been shown to have a tensile elastic modulus on the order of 25 kPa²², which may be further enhanced by the anisotropic fiber distribution. Label-free visualization of the collagen structure within the decellularized construct was performed with second harmonic generation (SHG) microscopy (Fig. 1b) and subsequent analysis of the matrix was performed using the curvelet transform coupled to a fiber extraction algorithm²³ (CT-FIRE) (Fig. 1b) to quantify the extent and quality of fiber alignment in each construct. To quantify alignment we developed an alignment index, defined as the spread of the angular distribution of fibers normalized to that of a uniform distribution, which allows us to robustly capture the degree of anisotropy in the matrix²¹. Using this metric, we observed that aligned matrices have alignment indices greater than 1.3, with high alignment observed at ≥1.5 and very highly aligned regions giving indices >2 (Fig.1b, c). The alignment indices of the constructs used here for the invasion assays were around 1.5 or greater.

To develop a tumor invasion platform where cells invade into, and migrate through, aligned matrices that mimic aligned stromal collagen observed in carcinomas^{6, 11}, we sought to generate a 3D interface between an ECM plug containing a high-concentration bolus of cancer cells with one end of the pre-aligned collagen matrix. We initially observed that seamlessly interfacing pre-formed aligned collagen matrices with a polymerizing ECM plug is challenging on several counts, which likely explains, in part, the lack of existing methods in the current literature to develop such interfaces for 3D cell invasion. First, the highly hydrophilic and water-retaining properties of collagen matrices make it extremely difficult to prevent “wicking” of the polymerizing plug onto the entire bulk surface of the pre-aligned matrix (Supplementary Fig.1a). Second, on a standard tissue culture dish, the polymerizing plug, even if localized to one end, tends to connect entirely on top of the pre-aligned matrix, thus creating a nearly 2D-like interface (Supplementary Fig.1b). We overcame these hurdles by introducing a few key modifications to the simple idea of pipetting a cell-seeded tumor-like plug suspension at one end of the pre-aligned matrix. We first partially air dried the pre-aligned matrix to decrease the amount of aqueous fluid at its surface, while retaining enough hydration to maintain its structural integrity (Supplementary Fig. 1b, c). Next while pipetting the cell-seeded collagen plug, the plate is tilted at an angle so that the surface tension-induced wicking is counteracted by gravity (Supplementary Fig. 1b, c). Lastly, we allow the plug and the end of the pre-aligned matrix to connect on a hydrophobic surface so that their mutual hydrophilicity spontaneously forces a 3D interface (Supplementary Fig. 1c).

To assemble the invasion assay, we first place a pre-aligned matrix on a tissue culture dish with a short overhang onto a parafilm-coated hydrophobic region, which is bounded on the other three sides by impermeable hydrophobic barriers (Fig.1d). Next, after having let the matrix partially air dry, we tilt the entire setup and pipette the cell-seeded collagen plug onto the hydrophobic region enclosed by the barriers and the pre-aligned matrix (Fig. 1d). The partially dried matrix, barriers, gravity, and the hydrophobic layer together confine the plug to the region where it is pipetted (Fig. 1d). In addition, the strong hydrophilic interaction between the plug and the overhang of the pre-made matrix on a hydrophobic surface forces the overhang to shift slightly upward into the polymerizing plug, thus allowing the latter to form a thin layer underneath the matrix, creating a 3D interface (Fig. 1d).

To image invasion dynamics we employ nonlinear imaging to simultaneously image cells and the collagen matrix. Using combined multiphoton excitation (MPE) of fluorescence signals in cells and SHG imaging of collagen, we visualized the initial stages of invasion from the plug into the aligned collagen (Fig. 1e, f). Three-dimensional image reconstruction of the interface clearly demonstrates MDA-MB-231 breast carcinoma cells within the 3D volume as they advanced into the aligned matrix (Fig. 1e, f), confirming the successful interface and assembly of the invasion assay. Furthermore, the simple and robust principles utilized in this protocol suggested to us that the approach could be extended to other hydrophilic ECMs and cell types. We evaluated the ability to interface with alternate ECMs by using the same methods to interface Matrigel plugs containing primary murine mammary carcinoma cells with the aligned collagen matrices. Consistent with our rationale, the ECMs composing Matrigel matrix effectively interfaced with the anisotropic collagen construct. Time-lapse imaging with combined MPE and SHG revealed that these primary cells invade as a collective, often forming strands of advancing cells into the aligned matrix, in contrast to the single cell dissemination of MDA-MB-231 cells (Supplementary Movie 1, Fig. 1e, f), suggesting that the invasion platform presented here may be sufficient to capture and parse out distinct invasion behaviors and multiple invasion and migration modes, which are known to be present during cancer progression³.

Spatio-temporal evolution of invasion into aligned collagen

To capture and quantify invasion over time, we focused on quantifying cell dynamics using the highly invasive triple-negative MDA-MB-231 cell line. After the interface is generated between the cell-dense plug and the aligned ECM, MDA-MB-231 cells begin to spontaneously invade into the aligned matrix through an invasive front that develops, matures, and advances over time (Fig. 2a). This in effect advances the boundary of the tumor-like plug into the stromal collagen over time, much like a malignant lesion would expand into the surrounding tissue. Indeed, we can monitor these changes by imaging the engineered construct periodically using simultaneous MPE and SHG to visualize both cells and collagen, respectively (Fig. 2a, Supplementary Fig. 2a, c, e). To quantify the percentage of cells embedded within the matrix versus on top of it, we calculated the matrix and cell layer thicknesses and the fractional overlap between them at various time points using the three-dimensional image reconstructions. (Supplementary Fig. 2b, d, f). On an average, ~75–80% of the cell fluorescence signal overlaps with the SHG signal, indicating that the majority of the invasion front advances through the aligned matrix, although some cells migrate on top of the aligned matrix (Supplementary Fig. 2a-f). Furthermore, there were some notable variations of the collagen layer thickness and the percent overlap along the length of the gel. Behind the interface, the fraction overlap was lower with the thickness of the cell layer being larger than that of the collagen layer in the region where the highly cell dense plug interfaces with the pre-aligned matrix (Supplementary Fig. 2b,d,f). The thickness of the layers as well as the overlap tend to assume lower values close to the interface for earlier time points, owing to the local contraction resulting from the attachment of the plug and the partial drying of the pre-aligned matrix overhang on the hydrophobic layer (Supplementary Fig. 2b,d,f). Note that this effect is not as pronounced in all cases, as the example interface shown in Fig. 1e demonstrates a much smoother interface with more consistent cell, matrix layer thickness and overlap near the interface. Nevertheless, we primarily focused our analyses further along the invasion front, where the overlap is high, ranging between 0.8 and 1 and the collagen layer thickness remains largely constant, with SHG imaging measured thickness around 150–200µm (Supplementary Fig. 2b,d,f). This is considerably lower than the native pre-aligned matrices (700–1000µm) before integration into this assay, largely due to the partial drying of the matrix during assembly, which therefore suggests the matrix is it at least 4–5 times more dense than its original state. Overall, these results indicate the formation and maintenance of a 3D invasion interface over time. Although some cells near the interface are forced to the surface of the matrix due to the very high cell density, the large majority of cells remain embedded and invade through the matrix, thus enabling tracking and analysis of 3D invasion over time.

Examining invasion over 7 days, we observed that cells at the leading edge of the invasive front can advance greater than a millimeter from the interface, with many cells traveling several millimeters into the collagen matrix (Fig. 2a). To quantify invasion over time we utilized the average cell fluorescence intensity along the direction of invasion from maximum intensity projection images as a measure of the number of cells at each position along the front (Fig. 2b). Interestingly, the distribution of invading cells conform quite well to a Gaussian distribution centered at the interface between the cell-dense plug and the aligned matrix at early time points, but tend to shift to a more sigmoidal nature at later time points (Fig. 2b). This shift arises mainly due to the emergence of a new region of spatially unvarying high cell density close to the initial interface as the front invades further into the matrix. In the developing front at early time points, this region of high density exists within the plug (i.e., behind the tumor boundary/interface) and hence is excluded from the analysis. Thus, when taken in its entirety, the cell density profile from the bulk of the cell dense tumor-like plug to the edge remains similar in shape in both early and late stages as the entire front advances into the stroma over time (Fig. 1f, Fig. 2b). Consequently, at any given time point, the half width at half maximum of the fitted Gaussian can be employed as a representative metric of the distance of the invasion front from the tumor-stromal interface. Using this metric, we calculated the average velocity of the advancing fronts to be 117.4 ± 59.3µm/d (n=3). However, a remarkable feature of the invasion patterns is the distant dispersal of a small fraction of cells far away from the bulk of the invasive front at later time points (Fig. 2a). For instance, some of the more invasive cells are >1–2mm ahead of the leading edge of the invasive front at day 7 and many millimeters beyond the initial plug boundary (Fig. 2a), consistent with recent findings by us²¹ and others^{24, 25} on heterogeneously invasive subpopulations of carcinoma cells, and suggests that analysis of the distinct heterogeneous behavior of highly migratory cells may provide important insights into invasion dynamics that influence metastatic dissemination. Furthermore, the nonlinear nature of the front is typical of cancer cell invasion and reaction-diffusion models have been reported to explain such behavior in glioma^{26, 27}. However, it is not well understood whether heterogeneity exists in the diffusive behavior of cells across the invasive front, which prompted us to probe the spatio-temporal variations in cell alignment and migration.

Cell and collagen morphology along the invasive front

At the onset of invasion, cells in the plug that have not encountered the anisotropic collagen are randomly oriented while cells at the invasive front interacting with aligned collagen, not surprisingly, tend to align along the direction of ECM alignment (Fig. 1e). Once robust invasion has developed, there are three distinct regions of interest at any given time point, namely the bulk region representing a segment of very high densities of cells that are within the advancing tumor boundary at its current location; the leading edge of the invasive front that is a 0.3–0.5mm region capturing the sharpest drop in cell density located at the transition from highly crowded to single dispersed cells (i.e., cells at the edge and just beyond the tumor boundary); and cells invading well beyond (>0.5mm) the leading edge of the invasive front (Fig. 3a). It is important to reiterate that taking into account the bulk region within the initial cell-dense plug, the shape of the invasion fronts in the early (Fig.1f) or the late stages (Fig. 2b, 3a) remains similar, and the transition from the former to the latter is associated with an expansion of the bulk region as the boundary of the tumor-like plug extends into the stroma-like collagen.

To facilitate analysis of cell and collagen fiber alignment at various points in the developed front, we imaged stained cells and the matrix after several days of invasion using simultaneous MPE and SHG to visualize F-actin, nuclei and collagen fibers (Fig. 3b). Since it was difficult to delineate between individual cell boundaries in the densely packed bulk region, we employed nuclear orientation as a metric of cell alignment as has been previously done in several contact guidance studies^{28, 29}. Using alignment indices that we described previously²¹, we quantified the bias in cell orientation and surrounding ECM anisotropy at different locations along the invasion front and at distant regions beyond the front. Not surprisingly, collagen fiber alignment index is largely constant throughout the entirety of the invasive front, which is consistent with the objective of the assay to provide a largely uniform aligned ECM for carcinoma cell invasion (Fig. 3a, b). However, while cells in all regions display some bias in orientation due the response to contact guidance, cells at and beyond the edge of the invasive front show a greater degree of orientation in the direction of ECM alignment. When examining regions beyond the leading edge of the invasive front, it is clear that cells in that zone should behave like sparsely populated single cells in an aligned collagen matrix, a behavior we have extensively characterized previously using MDA-MB-231 cells²¹. Consistent with our previous work^{11, 21}, carcinoma cells beyond the leading edge are highly aligned to the direction of collagen alignment (Fig. 3b, c). Likewise, at the leading edge of the invasive front, carcinoma cells are also highly oriented even though the cell density is substantially higher (Fig. 3b, c). This is certainly in agreement with the contact guidance response of single carcinoma cells, and those that have undergone an epithelial-to-mesenchymal transition and therefore do not form strong force-transmitting cell-cell junctions that can compete with ECM guidance cues, even when higher cell densities result in adjacent placement of these cells¹¹. However, at the bulk region of the invasive front, while cells remain aligned, the degree of alignment is significantly less, even as the underlying matrix remained equally anisotropic (Fig. 3b, c). This is most likely due to crowding and cell-cell interactions at the very high cell densities, with a number of cells growing on top of each other at these locations, thereby diminishing responsiveness to the underlying matrix architecture. Indeed, evidence of cells stacking on top of each other to generate cell layers >100µm thick can be observed from 3D reconstructions of the invasive front in the aligned matrix at later time points (Supplementary Fig. 2c, e). Therefore, there may be cell density-dependent spatial variations in contact guidance-directed invasion along the front.

Spatio-temporal variations in carcinoma cell invasion dynamics

In order to gain insight into the dynamics of anisotropic stromal invasion by carcinoma cells from a confined lesion, we investigated the migration dynamics of invading cells at different locations of the front at various time points. As discussed above, the developing invasive front at early time points is comprised of cells within the bulk tumor boundary embedded in isotropic ECM and pioneer invading cells at the leading edge interacting with aligned collagen. In the mature front, however, both the bulk and leading edge of the invasive front regions encounter the anisotropic matrix. To study 3D cell migration behavior, we utilized time lapse two-photon microscopy of migrating cells in the engineered construct and analyzed their movement by fitting cell trajectories to a persistent random walk model along each axis, which enables comparison of parameters of cell migration between the orthogonal directions^{30, 31}. Owing to the complexity of 3D tracking of densely packed cells and our previous work²¹ demonstrating that ~90% of the motility of single MDA-MB-231 cells migrating through aligned collagen matrices is confined to the XY plane, we analyze and present data from projected tracks on the XY plane, i.e., from 2D cell tracking (Supplementary Movie 2, 3).

Cell dispersal, as expected, is largely anisotropic due the well-defined aligned ECM tracks. The directionality of migration, which is the percentage of total motility directed along a given axis²¹, is significantly higher for cells in regions with anisotropic collagen, viz. the leading edge of the developing invasive front and both the bulk and leading edge of the mature front (Fig. 4a, b). Note that cells behind the leading edge (bulk) in a developing front are still within the initial tumor-plug boundary and have yet to encounter the aligned collagen and that is certainly reflected in their directionality of migration (Fig. 4a, b). Moreover, the cells at the leading edge in the mature front are significantly more directional than the pioneer invading cells in the developing front that appear at the plug boundary in the initial stages of invasion (Fig. 4a, b). While the latter group of cells do exhibit directional movement, the isotropic forces exerted on the local matrix by the cell-dense plug behind them is likely a counteracting factor.

Interestingly, both in the developing and mature fronts, cell motility at the leading edge is greater than that in the bulk (Fig. 4a, c, Supplementary Movie 2, 3). The increase in total motility at the edge over the bulk is also mirrored by the enhanced motility along the direction of alignment (Fig. 4d). The enhanced motility observed in a persistent random walk may be due to increases in either speed or persistence time, or both. In this case, the differences in motility between the leading edge and bulk are largely due to changes in speed along the direction of alignment, while the persistence times are less variable (Supplementary Fig. 3a, b). There is, however, a significant difference in persistence between cells in the bulk and leading edge of the developing front, likely owing to the differences in underlying matrix alignment, as well as a trend (p<0.06) of increased persistence times in the mature front (Supplementary Fig. 3b). Moreover, it is important to note that along the direction of ECM anisotropy, both the speed and persistence times for all the individual groups are respectively higher than those in the orthogonal direction (Supplementary Fig. 3a-d). Apart from cells in the bulk of the developing front that show largely random movement and comparable numbers between the speeds and persistence times along the orthogonal axes, up to 50% greater speed and persistence times are present along the direction of alignment for the other three groups (Supplementary Fig. 3a-d). This is certainly congruent with the finding that in an anisotropic matrix, the majority of total cell motility (~70%) is directed along the orientation of the ECM fibers²¹.

Another remarkable feature of the spatial variation in migration of cells during invasion can be observed by studying the trajectories of cells at the leading edge versus the bulk of a mature front. While the directionality is significantly, yet modestly, different between the groups (Fig. 4b), the cells at the leading edge tend to move in a unidirectional fashion, i.e., away from the interface while those in the bulk show bidirectional migration (Fig. 4a,e, Supplementary Movie 2, 3). This is quantitatively captured using the ratio of the total step-wise displacement of each cell along the invasion axis to the total step-wise distance (unsigned displacement) covered to metricize unidirectional bias. This ratio would assume a value of -1 for cells moving perfectly towards the interface, 0 for bidirectional cells and 1 for cells moving perfectly in the direction of invasion. We note that while both groups on average have positive unidirectional bias, it is significantly higher for cells at the leading edge compared to those in the bulk (Fig. 4e). In other words, regions in the bulk surrounded by high density of cells on both ends do not as effectively “perceive” differences in their environment with one side largely appearing the same as the other.

Overall, the preceding results confirm and characterize the effect of contact guidance due to the aligned collagen fibers as a strong local regulating factor in the dynamics of cell migration during invasion. However, contact guidance alone is insufficient to fully explain why the cells at the leading edge tend to move faster and more frequently in the direction of invasion than the cells in the bulk. We postulated that such differences could be explained simply by considering the enhanced crowding of cells in the bulk and its influence on cell movement by contact inhibition³². To test this hypothesis, we employed a Brownian dynamics simulation for cell proliferation and migration with single cell values of cell motility and growth obtained from published experimental data by us²¹ and others (NIH Physical Sciences in Oncology Network Bioresource Core Facility, Protocol NCI-PBCF-HTB26). In the simulation, cells are allowed to grow, divide, and migrate while maintaining non-overlapping boundaries along a one-dimensional track, mimicking guided invasion along the direction of collagen alignment. Previously, it was shown that under some conditions the model predicts the existence of a “jammed” state, where an advancing front of tumor cells is propelled quasi-ballistically through synergistic interaction between proliferation and migration, an effect not captured with reaction-diffusion models using realistic single cell migration speeds³³. Over several days, the simulated cells dispersing along the invasion axis produce a similar cell density versus distance curve as observed experimentally in mature invasion fronts with clearly distinguishable bulk and leading edge regions (Fig. 4f). Indeed, the model predicts that the motility of cells increases dramatically along the front from the crowded bulk region to the leading edge, where cells have free space to allow for largely unhindered migration (Fig. 4f). Consistent with the experimental data, the free leading edge cells thus display a significantly higher motility than those in the bulk (Fig. 4f, g). In addition, unidirectional bias for the simulated cells in the bulk is highly variable, spanning both positive and negative values but settled to a positive value of ~0.25 at the leading edge (Fig. 4h). Therefore, cells at the leading edge, owing to the unoccupied space available for migration in the direction of invasion, display a consistent positive unidirectional bias, in agreement with our experimental results (Fig. 4e, g, h). Thus, in addition to contact guidance, physical contact inhibition, manifested as a crowded state, plays an important role in the invasion dynamics observed here. Furthermore, it is important to note the key difference from a purely diffusive dispersal, where the fundamental input growth and movement parameters of individual cells in high and low density regions is assumed to be independent of their concentration or of position. Overall, our experimental and simulation results suggest that the phenomenon of physical crowding acts in concert with random diffusive behavior leading to the emergent invasion into less populated regions from an overgrown lesion when a physical barrier is not in place to constrain cell distribution. Indeed, our combined experimental and modeling results demonstrate the lack of uniformity in migration both spatially and temporally during invasion, where local cues dominated by contact guidance and physical contact inhibition together contribute to the emergence of the advancing invasion front.

Cell culture

Validated MDA-MB-231 cells were freshly obtained from ATCC (2013) and used at low passage relative to the original culture. Cells were grown in high glucose DMEM (HyClone) supplemented with 10% fetal bovine serum (FBS; HyClone). Stable GFP expression was induced in MDA-MB-231 cells using GFP-lentivirus particles (Gentarget) and subsequent positive selection using puromycin (Invivogen). Primary breast cancer cells and primary carcinoma-associated fibroblasts were derived from invasive mammary carcinomas from MMTV-PyMT mice as described⁴⁵ using differential trypsinization and selective outgrowth. These cell lines were grown and maintained in DMEM supplemented with 10% Fetal Bovine Serum (FBS). All animal work was approved by the University of Minnesota Institutional Animal Care and Use Committee (IACUC) and all animal and experimental work followed institutional and NIH guidelines.

Fabrication of aligned collagen matrices

Aligned collagen matrices were generated as previously described²¹. Briefly, 3mg/ml collagen matrices seeded with mammary carcinoma-associated fibroblasts were prepared in a modified 6-well plate to form rectangular constructs connected at the long ends to a pair of porous polyethylene anchors. Following overnight incubation, the matrices were detached from the bottom of the plate and incubated for an additional 1–2 days while attached only to the anchors at its two ends. Fibroblast-mediated contraction during this time compacts the construct into a dog-bone shape with concomitant collagen fiber alignment along the axis joining the two anchors. Subsequently, these matrices are decellularized using a two-step cell lysis and nuclease treatment protocol and stored at 4°C until further use. High-density rat tail collagen-I (Corning) (purity of >90%, according to the manufacturer’s specifications) was used as the collagen stock and polymerized by neutralizing in HEPES buffer solution, as previously described^{8, 21}. Note that since the aligned constructs are generated by compaction of the original gel, the final density can be higher than the starting density of 3mg/ml, as is the case for any compacted matrix (isotropic, anisotropic etc.). The thickness of these anisotropic, decellularized constructs was measured by calipers while maintaining the gel flat in a bath of PBS by clamping the polyethylene spacers at the two ends of the gel onto the opposite arms of a uniaxial stretcher.

Constructing the 3D invasion assay

First, 4mL of 1.5–2% agarose in 1X Tris-buffered saline was poured onto a 35mm tissue culture dish and let solidify to form a uniform layer on the plate. This cylindrical layer of agarose was then cut along a straight line ~1.5–2cm from the edge of the plate with a scalpel blade and the larger portion removed. The remaining portion provides a straight barrier against which the plug can be pipetted while keeping the plate tilted and retaining lower height as compared to the walls of the plate to provide better access to a microscope objective for imaging. Next, a small piece of Parafilm “M” laboratory film (Bemis) ~1.5 cm in width is cut out and fixed onto the plate and onto the directly adjacent agarose layer. Then an aligned collagen matrix, generated as described above²¹, is detached from its two polyethylene anchors (Interstate) and placed carefully with its long axis perpendicular to the agarose barrier and one end of it overhanging marginally onto the piece of Parafilm. The two polyethylene anchors were then glued on either side of the short axis of the aligned matrix near the agarose layer as hydrophobic barriers (See Fig. 1d). In theory, any hydrophobic solid material such as PDMS could be utilized as barriers. This creates a small rectangular Parafilm-coated region bounded by the agarose and barriers on three sides and the overhang of the pre-aligned matrix on the other. The setup was left to air dry for several minutes while preparing the cell-seeded collagen plug.

To prepare a cell-seeded collagen plug, high-density rat tail collagen (Corning) was neutralized by a HEPES buffer and cells in suspension were mixed with it to achieve a final concentration of 4mg/ml collagen with 6.7 X 10⁶ cells/ml. The matrix was allowed to start polymerizing for 6–7mins before 75µl of this collagen mixture was pipetted into the rectangular nook at the edge of the aligned matrix, making sure the edge just overlapped with the pipetted plug. While pipetting the plug, the plate was maintained in a tilted position at an angle of ~30° (usually done by balancing it against the lid of a 50ml conical tube or a 35mm plate) so that gravity can counteract the forces from surface tension that may cause the plug to spill over to the bulk of the aligned matrix as it is polymerizing. The gel was allowed to polymerize for 15mins further at room temperature before moving the setup to a 37°C incubator in a humidified chamber maintaining the slanted position. After another 1.5h, a small amount of media was carefully added to soak the pre-aligned matrix, not disturbing the polymerizing plug, and incubated overnight in the humidified chamber for the matrix to fully polymerize. The next day, the assay was fed with cell culture media and henceforth incubated in a flat position without the need for a humidified chamber. Subsequently, within a day or two, the plug was detached from the barriers and subsequently contracts away from them, integrating into the aligned matrix as one single piece of tissue. This could then be removed from the entire setup and placed by itself in a 35mm tissue culture plate for subsequent invasion.

In order to prepare cell-seeded Matrigel plugs, the same number of primary mammary carcinoma cells were mixed with growth factor reduced Matrigel (Corning) to a final concentration of 5mg/ml and the same 75µl total volume of the plug was interfaced with the aligned matrix. Due to the quick gelling properties of this matrix, the plate was removed from the tilted configuration and the humidified chamber and complete growth media added to it after 1.5h.

Imaging and analysis of invasive fronts

Invading carcinoma cells and surrounding collagen architectures were visualized using combined MPE and SHG imaging on a custom-built multi-photon laser scanning microscope ⁴⁶ (Prairie Technologies / Bruker) using a Mai Tai Ti:Sapphire laser (Spectra-Physics) at an excitation wavelength of 880nm. Multi-dimensional image acquisition involving Z-stacks at several adjacent fields of view starting from the interface to beyond the leading edge of the invasive front were captured, merged together and then projected along different axes (Fiji) to obtain the XY and XZ views shown in Figs. 1, 2, and Supplementary Fig. 2. Distinct changes in collagen density and structure were utilized to mark the location of the interface. The thickness of the cell and collagen layers were calculated by image analysis in Matlab by determining the width of the major peak (beyond a noise threshold) in intensity along each column of pixels. Data were smoothed by a moving average over 100 pixels to obtain profiles shown in Supplementary Fig. 2. Fractional overlap was calculated by dividing the thickness of the portion of the cell layer overlapping with the collagen layer by the total thickness of the cell layer.

From the XY projected images, average intensity profiles were measured along the X axis as a relative measure of cell density at each location (Fiji). The raw data was converted to a relative intensity scale, smoothened by moving averages and fitted to Gaussian curves centered at the interface (Matlab). The half-width at half maximum of the fitted Gaussian was taken to represent the distance of the corresponding front from the interface. If σ denotes the standard deviation of the fitted Gaussian, then the distance of the front from the interface was thus given by

This distance obtained from multiple measurements of an advancing front was used to calculate its average velocity.

Immunofluorescence staining and quantification of morphology

The plug and adjoining aligned matrix were fixed in 4% paraformaldehyde (Sigma) for 20mins, permeabilized with 0.1% Triton X-100 (Roche), quenched in 0.15M glycine (Sigma) for 10mins and blocked with a solution of 2% fatty acid free-BSA (Fisher Scientific) + 2.5% goat serum (Sigma), followed by incubation with rhodamine phalloidin (1:250; Life Technologies) and 1:40000 bisbenzamide (Sigma). Imaging was subsequently performed using multiphoton laser scanning microscopy to visualize F-actin, nuclei and collagen. The leading edge was defined as positions where the field of view contained partially confluent invading cells, whereas the bulk region was defined as a location in between the interface and invasive front, usually ~600–1000µm behind the leading edge of the invasive front with spatially invariant cell density.

Automated quantification of nuclear morphology was done using CellProfiler⁴⁷, with subsequent analysis in Matlab. Collagen fiber analysis and quantification of nuclear and collagen alignment indices were performed as previously described²¹. If σ denotes the standard deviation of a distribution of collagen fiber orientations, ranging from -90 to 90, 0 being the direction along the anisotropic axis, the alignment index is then given by

where the numerator denotes the standard deviation for a uniform distribution with the same range.

Live cell timelapse imaging and cell migration analysis

Live cell imaging of cell migration using simultaneous MPE of fluorescently labeled cells and SHG imaging of surrounding collagen fibers, was performed as described previously²¹. Briefly, cell migration was captured by taking 2-channel Z stacks of at 5–10µm intervals at each stage position at 20min intervals over 12–16h for cells in the bulk and the leading edge of a developing (early) or mature (late, 4–7 days after initial intrusion through the interface) invasion front in a custom temperature controlled chamber²¹. The definitions of the invasive front and bulk were the same as noted above.

For cell migration analysis, only the maximum intensity projection data on the XY plane were considered. 2D tracking of cell migration was performed after registration of stacks (StackReg⁴⁸, Fiji) using the Manual Tracking plugin (Fiji). The method of overlapping intervals⁴⁹ was used to fit the cell trajectories to a persistent random walk model (PRWM)^{30, 31} using Matlab (Mathworks) to interface with the cell tracking output, as described previously²¹. Mathematically, the PRWM can be written as

where MSD denotes the mean squared displacement, S is the migration speed, P is the persistence time, and n_d is the dimensionality of the random walk.. The motility coefficient is given as

We fit the model separately to the two orthogonal directions of motion, thus obtaining motility, speed and persistence times for×and y directions (therefore, n_d =1 in each case). Directionality of migration along any given axis was obtained by simply taking the ratio of the motility along that axis to the total motility of the cell, thus quantifying the fraction of total motility that is directed along that particular axis²¹.

To capture the tendency of leading edge cells to move more often in the direction of invasion, we used a metric called unidirectional bias. For each cell track, this was simply the ratio of the sum of all piece-wise displacements along the direction of invasion to the sum of all piece-wise distances covered along the same direction. Thus, if at each time step i, the movement of a cell along the direction of invasion is x_i, then its unidirectional bias would be given by

In our setup, positive values of x_i denotes movement in the direction of alignment. Thus, this metric assumes values of -1 (perfect unidirectional movement away from the direction of invasion), 0 (unbiased bidirectional migration) and +1 (perfect unidirectional movement towards the direction of invasion) for three distinct cases.

Brownian Dynamics Simulation of cancer cell invasion

A Brownian Dynamics Tumor Simulator that accounts for both cell proliferation and migration was adapted from previously published work⁵⁰ to test the hypothesis that physical crowding of cells influences the spatial variability in migration along the invasion front observed in our experiments. In the model, each cell is treated as a sphere with a starting diameter of 20µm and allowed to move one-dimensionally via Gaussian-distributed steps dictated by a random motility coefficient⁵¹ of 5µm²/min, which is of the same order of magnitude as our previous experimentally derived value of average single cell motility for MDA-MB-231 cells²¹. In addition, each cell was also allowed to grow and divide with a proliferation rate (1/day), obtained from publicly available data characterizing behavior of MDA-MB-231 cells.

Beginning with an initial value of 1min, time intervals were set such that each time interval was divided into equal timesteps dictated by the number of present cells at that instant, as previously described³³. At each timestep, a cell was selected from a uniform probability distribution function among the entire pool of cells, and either underwent movement in the form of random walk diffusion, growth, or both to the extent calculated for the length of the time interval. Importantly, only those movements would be allowed which do not lead to physical overlap among cells, thus simulating an idealized case of physical contact avoidance. Twenty initial cells with varying initial volume (correlated with the state of growth, imposes an asynchronous point in the cell cycle across the initial cells) were spaced uniformly 80µm away from each other centroid to centroid, and the entire simulated time was set to be seven days. During this timespan, cells were allowed to proliferate, divide, and move, hence occupy more space and exhibit a crowding effect that initiates a physical contact inhibition or jammed state in which the leading edge of the cell ensemble exhibits a linear advancement through time instead of a random walk’s purely diffusive behavior, i.e. becomes quasi-ballistic. We limited our analysis to a timespan in this crowded state, preceding the completely jammed configuration. In this timespan, the spatial distribution of cells resembled the experimental invasion fronts in that they could be divided into distinct bulk and leading edge regions, as defined previously.

For data analysis, the simulated values were sampled once every 100 timesteps, which amounted to a duration ranging from 83 to 93 mins and an average of 89 mins. We calculated the MSD of cells in that time period in the crowded regime by the method of overlapping intervals and subsequently obtained the motility coefficient by the slope of the MSD versus time curve. The axis of invasion was divided into 300µm segments (which were approximately the same as our field of view during live cell imaging experiments) and the motility of all cells within each segment was grouped together. For calculating unidirectional bias, similar segmentation was used. However, in the latter case, the total movement of all cells within a given segment were taken together to calculate the unidirectional bias of cells within that segment. The invasion front was divided into bulk and leading edge sections based on the cell density versus distance along the invasion axis curve according to definitions mentioned above. Results from 12 independent simulations were combined to obtain the reported data.

Statistical Analysis

Student’s t test was used to compare null hypotheses between two groups for large datasets. The non-parametric Mann Whitney test was employed for non-normal or small datasets. Multiple groups were compared by ANOVA and post-hoc tests. Unless otherwise mentioned, the data analyzed were pooled from many cells/field of view over several fields of view across n≥2 experiments. Number of data points for each group, the specific statistical tests, and significance levels are noted in the figure text.