Understanding the Role of Elastic Modulus in the Relationship Between Second Harmonic Generation Scattering and Tumor Cell Motility

Background: Second harmonic generation (SHG) is an intrinsic optical property of fibrillar collagen. SHG directionality is quantified by F/B, the ratio of forward- to backward-propagating signal, which is affected by collagen fiber internal structure, specifically the diameter, spacing, and disorder of fibrils within a collagen fiber. We have previously shown that F/B of primary invasive ductal carcinoma sections is prognostic of metastatic outcome. One possible cause of this relationship was revealed by our observation that tumor cells’ motility on collagen I gels varied when collagen fiber internal structure in those gels was manipulated. The mechanism by which tumor cells sense changes in collagen fiber internal structure remains unknown: here we evaluate the role of elastic modulus in the relationship between collagen fiber internal structure (as reported by F/B) and tumor cell motility. Methods: The 4T1 murine mammary adenocarcinoma, a model of metastatic triple negative breast cancer, (TNBC) and the 67NR line, a non-metastatic luminal phenotype, were introduced to a series of collagen-polyacrylamide mixed gels wherein collagen fiber internal structure and gel elastic modulus were independently controlled. F/B was measured with SHG, while elastic modulus was measured globally via rheometry and locally via atomic force microscopy (AFM). Tumor cell motility was quantified over three hours. Results: The motility of both cell lines varied with F/B while elastic modulus was held constant, and did so at two physiological modulus values. Interestingly, 4T1 cell motility increased as F/B increased, while 67NR cell motility decreased. Conclusions: Our results suggest that elastic modulus does not play a significant role in the observed relationship between collagen fiber internal structure (as reported by F/B) and tumor cell motility, for two cell lines that are models of TNBC and luminal-like breast

3 cancer. Our observation that the two lines exhibit opposite motility trends as F/B increases is consistent with the trends in metastatic outcome versus F/B observed in our published clinical data for ER+ (i.e. containing the luminal subtypes) and ER-(i.e. containing the basal subtypes) cohorts, and suggests that a tumor's subtype may play a role in their response to collagen fiber internal structure.

Background
Breast cancer is one of the most common cancers with approximately 12.8% of women being diagnosed within their lifetime (1). Between 2009 and 2015, women diagnosed with localized, or stage 1, breast cancer had a 98.8% 5-year survival rate (1). However, women diagnosed with distant metastases had a significantly lower 5-year survival rate of 27.4% (1). Metastasis to a secondary location is an onerous journey for a cancer cell. Once the primary tumor is established, cells begin to migrate within their microenvironment and may reach a blood or lymphatic vessel. Once the cell reaches the vessel it can intravasate into the lumen and, if it survives, reach a distant organ where it may lodge and/or extravasate and possibly develop into a metastasis (2).
One of the earliest steps in the metastatic process is migration through the tumor extracellular matrix (ECM). The ECM is made up of various proteins including fibrillar collagen type I, which can be imaged with an intrinsic optical signal caused by the scattering phenomenon known as second-harmonic generation (SHG) (3)(4)(5). SHG is observed when two incoming photons scatter off a noncentrosymmetric structure to produce one photon at twice the energy and half the wavelength of the individual incoming photons. In tumors the only significant source of SHG signal is fibrillar collagen (6). SHG imaging has revealed that tumor cells can move along collagen fibers, and that the orientation of collagen fibers with respect to the border between breast tumor and host tissue can predict patient outcomes (7). This suggests that collagen fibers may act as 'roads' facilitating tumor cell escape from the primary tumor. When an excitation laser is focused on one point along an individual collagen fiber, SHG photons can scatter in the "forwards" direction, i.e. the direction of propagation of the laser, or in the "backwards" direction, i.e. in the opposite direction. This directionality can be quantified by collecting photons in both directions using two detectors and calculating the forwards-to-backwards scattering ratio, or "F/B". F/B is affected by properties of the internal structure of the collagen fiber including the diameter and spacing of the component fibrils that make up a fiber, as well as the order versus disorder in fibril packing (8)(9)(10). This internal structure is not the same as the direction of the fiber, but to extend the 'roads' analogy, F/B may provide information about road quality, as distinct from road direction.
Previously, we have shown that the F/B ratio of primary invasive ductal carcinoma (IDC) tumor biopsies is an independent prognostic indicator of patients' metastasis-free survival time in 10-year follow-up data (11). This suggests that F/B may be an additional indicator to assist in identifying which patients will metastasize and therefore who requires adjuvant chemotherapy. Hence the predictive ability of the F/B ratio of primary tumors may be useful in reducing the recognized clinical problem of "overtreatment" (12). To begin to understand why collagen fiber internal structure predicts metastatic outcome, in a previous study we determined the effect of varying collagen fiber internal structure on tumor cell motility in pure collagen gels (13). Collagen fiber internal structure was varied by varying gel polymerization conditions, and reported with F/B. We found that tumor cell motility was statistically significantly affected by varying collagen fiber internal structure (i.e. varying F/B) (13). This suggested that in patients, excised tumor F/B may be prognostic of metastatic outcome because the collagen fiber internal structure which dictates F/B also affects the efficiency with which cells escape the tumor. However, the underlying mechanisms of the relationship are still unidentified.

5
The elastic modulus of the extracellular matrix is known to have an impact on tumor cell behavior, including cell motility (14,15). Therefore we hypothesized that cells could be reacting to modifications of collagen fiber internal structure because they are sensing matrix elastic modulus changes that may result from those modifications (15). To test this hypothesis, herein we characterized the motility of tumor cell lines in a series of collagen/polyacrylamide mixed gels in which we independently varied the collagen fiber internal structure and the elastic modulus (16)(17)(18). These gels provide an in vitro environment to study tumor cell motility and its relationship to ECM properties in the absence of other cellular actors, and their secreted factors, that may be present in an in vivo model. The two cell lines chosen were the metastatic 4T1 and nonmetastatic 67NR lines. The 4T1 murine mammary adenocarcinoma cells are a common model of basal-like TNBC and were used in our previous studies (19,20). For the non-metastatic cell line, 67NR was chosen since it is a paired sister cell line to the 4T1 cells (i.e. derived from the same tumor) and has a contrasting luminal phenotype (21,22  Mattek petri dishes (Ashland, MA) with 14-mm diameter coverslip-bottomed wells were coated with 2.5M NaOH and allowed to air dry. 200 µL of 97% 3-aminopropyltrimethoxy silane (APTES) was added to the coverslip bottom for 5 minutes and then rinsed three times with distilled water and gently dried with Kim Wipes. Each dish was flooded with 0.5% glutaraldehyde for 30 minutes and then rinsed three times with distilled water and 7 allowed to air dry. Separate 12 mm glass coverslips were treated with RainX and allowed to air dry. Each coverslip was wiped to ensure an even coating and then sprayed again.
Collagen gels were made of human type I collagen solution at a concentration of 3 mg/mL (Advanced Biomatrix, San Diego, CA). With all solutions kept at 4 °C to minimize gelation, 810 µL of collagen type I was combined in a conical tube with 108 µL of RPMI 1640 media, and 50 µL of distilled water. The solution was vortexed at the lowest speed for 5 seconds to ensure the solution was evenly mixed. The pH of the solution was measured with a Mettler Toledo Micro Pro pH meter (Columbus, OH). The acceptable pH range for this solution was 7.5-7.7 (see below). In a petri dish, 6 droplets of 125 µL each of the solution was pipetted, making sure the droplets did not touch or spread and that all droplets were equal in size to ensure equal gelation. The petri dish was placed in an incubator for 2 hours at 37 °C and 5% CO 2 .
Polyacrylamide is an easily manipulated polymer that can produce a wide range of elastic moduli, and when mixed with collagen will independently influence overall gel elastic modulus (16)(17)(18). Two polyacrylamide precursor solutions were made with different concentrations of acrylamide and bis-acrylamide. The first solution was 5% acrylamide: 0.1% bis-acrylamide and the second solution was 12% acrylamide: 0.25% bis-acrylamide; these combinations are known to produce polyacrylamide gels of significantly different elastic moduli (17). 375 µL of the desired polyacrylamide precursor was added to a conical tube. Once the collagen gel droplets gelled, they were added to the polyacrylamide precursor solution. This solution was vortexed on medium speed for 20 seconds to break up the collagen gels and mix thoroughly with the polyacrylamide. Next, 0.5 µL of N,N,N',N'-tetramethylethylenediamine was added to the solution and followed by 5 µL of 10% w/v ammonium persulfate, for a final concentration of 0.5% and 5%, respectively; to minimize premature polymerization, this step was completed within 2 minutes. The  Free FITC emits isotopically, which means the F/B ratio of a FITC calibration sample should be 1.0; any variation in the imaging system is reported by a variation in this measured ratio. To account for any day-to-day variation in the system, the background-subtracted SHG F/B ratios of the imaged samples on a given day (discussed below) are divided by the background-subtracted F/B ratio of the FITC calibration taken on that day. For each image pair, an F and B image was taken with the laser shutter closed and the average pixel counts for each image provided the background.
For SHG F/B ratio analysis of the gels, two xyz stacks of simultaneously collected forward and backwards images were taken at a given xy region on the gel; three different regions of each gel were imaged. The forward and backward image pairs were taken at 50 µm steps through the depth of the gel. Each image was 660 µm x 660 µm.
ImageJ was used for all image analysis (23). The forward and backward images were 9 background subtracted with the average background value for the corresponding direction. For each matched image pair, two masks of both the forward and the backwardscattered SHG signals were created, in which all collagen pixels were set to 1 and background pixels were set to 0 by applying a predetermined threshold to each of the two images. One forward threshold and one backward threshold was used for each imaging session and applied to all images. These thresholds were determined by surveying random background-subtracted images and adjusting the image's look-up tables until only collagen fibers are highlighted, and all other pixels were rejected. The two resultant masks for each matched image pair were then multiplied together to create a single mask that identifies pixels with SHG emission above the threshold in both the forward and backwards direction. A single F/B ratio image was calculated from the F and B image pair and then multiplied by the mask to set all non-fiber pixels to zero, thereby excluding these pixels from the analysis. The average pixel value of fiber pixels (i.e. non-zero pixels) for that region was then calculated for the masked F/B ratio image. This process was repeated in a for loop for each image pair in the stack for a single region. The average pixel value of each slice in the stack was then averaged to give a single F/B ratio for that region of the gel. The F/B ratio from all three regions were then averaged to produce a single F/B ratio to represent the entire gel.
To confirm that the measured F/B ratio was not affected by the thickness of the gel (i.e. that each gel was 'optically thin'), F/B was plotted as a function of imaging depth and a linear regression was performed. To exclude top and bottom edge effects, the middle 50% of the stack was used for analysis. Gels were only used if the slope of the line of best fit through the middle 50% of the stack was not significantly different from zero, thus ensuring that the measured F/B ratio was not affected by imaging depth. The F/B ratio of the gels was altered by manipulating the pH of the collagen gel in the initial stage of making the mixed collagen-polyacrylamide gels as previously described (13). The pH was altered by using increasing amounts of 2.5M NaOH in the collagen gel solution to bring the final pH to 8.5-8.7 or 9.5-9.7, measured with a Mettler Toledo Micro Pro pH meter (Columbus, OH). The collagen gels were gelled and incorporated into the polyacrylamide as stated above. To verify that F/B varied with collagen gelation pH, the F/B of each gel was then plotted as a function the collagen pH during synthesis. A linear regression was performed to yield a p-value which would indicate whether the slope of the line of best fit was significantly different from zero or not.

. 6 A n a l y s i s o f T u m o r C e l l M o t i l i t y
The following preparation and imaging were performed one gel at a time. An hour prior to imaging, all media was removed from the gel and 1 × 10 4 cells were resuspended in their respective media and added to the surface of the gel in a droplet. The gel was placed in the incubator for an hour to allow the cells to adhere to the surface before all excess media was removed to minimize motion during the imaging session. Live cell images were taken on a Nikon Eclipse Ti microscope, using a Nikon MRH201201 air lens (20x, 0.45 N.A.). Cells were quickly transferred to a microscope stage incubator (Pathology Devices, Westminster, MD), at 37 °C, 5% CO 2 , and 85% relative humidity. One phase contrast image was taken every 2 minutes for 3 hours and saved as a tiff file.
All image analysis was performed in ImageJ (23). For each gel, every cell in the field of view was tracked using the "Manual Tracking" ImageJ plugin, which tabulates the XY location of each cell at each time point (23). From this data, the total distance was calculated for each cell by summing the distance traveled between each time point. From this data, the five most motile and five least motile cells were identified and used for 11 further analysis. To confirm that the gels did not significantly move during the imaging session, a fiducial artifact on each gel was identified and tracked in the same manner; total distance traveled by fiducial artifacts did not exceed 4.37 µm per imaging session and averaged 2.17 µm ± 1.62 µm, significantly less than the motion of all cells in all conditions. For comparison with previous literature (13), imaging sessions did not exceed three hours to ensure that there was no significant penetration of the cells into the gels and hence that the analysis remained two-dimensional. The methods described above produced mixed collagen/polyacrylamide gels with a uniform distribution of collagen fibers throughout (Fig. 1). To perform SHG imaging and obtain a single representative F/B value, the sample being imaged must be optically thin, which means that the measured F/B must not be affected by the imaging depth into the sample. When plotting F/B versus imaging depth, non-optically thin samples would have a slope significantly different than zero. The linear regression was only applied to the middle 50% of the image stack to exclude any edge effects. Thus, to confirm that the collagen polyacrylamide gels were optically thin, F/B was plotted against imaging depth and a linear regression was performed to determine the slope, as seen in Fig. 2. For each line, the p-value was much greater than 0.05, which indicates that F/B is not significantly affected by depth and the samples are optically thin. The gels used in this study were consistently 'optically thin'.

. 2 M a n i p u l a t i o n o f F / B R a t i o a n d C o n f i r m a t i o n t h a t F / B w a s N o t A f f e c t e d b y A d d i t i o n o f P o l y a c r y l a m i d e
The F/B ratio of the gels was manipulated by altering the pH of the collagen gel during fibrillogenesis, and elastic modulus was manipulated by altering polyacrylamide polymerization, each as described above. The pH of the collagen was adjusted to either 7.5, 8.5 or 9.5. Figure 3 shows that F/B increases as pH of the collagen during synthesis increases, which is consistent with our previous studies (13). A two-way ANOVA was 13 performed to compare the F/B of the high and low elastic modulus gels within a single pH category. A p-value greater than 0.05 and a Bonferroni post-hoc test revealed that there is no statistically significant difference between the F/B of the high and low modulus gels within a single pH category. Lastly, a t-test was performed to compare the slopes of the two lines in Fig. 3 which yielded a p-value much greater than 0.05, which indicates that the linear relationship between F/B and pH of collagen during synthesis is not affected by the presence of polyacrylamide nor its elastic modulus.

. E v a l u a t i o n o f E l a s t i c M o d u l u s o f G e l s
The elastic modulus of the gels was manipulated by altering the acrylamide and bisacrylamide concentrations in the polyacrylamide precursor solution. The 'high modulus' gels were composed of 12% acrylamide and 0.25% bis-acrylamide and the 'low modulus' gels were composed of 5% acrylamide and 0.1% bis-acrylamide. Figure 4a shows the elastic modulus of gels produced with these procedures, as measured by both AFM and rheology. At each modulus value, a two-way ANOVA was performed with Bonferroni posthoc test to confirm that the AFM and rheology results were not statistically different. Figure 4b shows the elastic modulus results from AFM plotted as a function of F/B. A linear regression for both data sets yielded a p-value greater than 0.05. The same analysis was performed for rheology data, with the same outcome (graph not shown). Taken together this data demonstrates that the mixed gels had an elastic modulus that could be tuned between two desired values (confirmed with both bulk rheology measurements as well as local AFM measurements), that the average values of elastic modulus were 1.738 ± 0.168 kPa and 18.504 ± 0.685 kPa (values that are relevant to tumor physiology (28)), and that alteration of collagen gelation did not affect the elastic modulus of the mixed gel.  (Figures 5a and 5b), a linear regression fit of the total distance traveled versus F/B reveals that all four slopes have an F-test p-value <0.05, meaning that each slope is significantly different from zero. As the elastic modulus was held constant within each of the four combinations, this demonstrates that 4T1 cells can respond to variations in collagen fiber internal structure (as reported by F/B) independently of elastic modulus. The observation that motility of 4T1 cells increases with collagen gel F/B is consistent with our previous in vitro study (in which elastic modulus was not held constant) (13). Finally, cell motility was greater on gels of higher elastic modulus (2-way ANOVA, main effect of modulus p < 0.0001) (14,15). Interestingly, the trend for the most motile 67NR cells is negative (i.e. the slope of the distance traveled versus F/B plot is negative), whereas the trend is positive for the 4T1 cells. Finally, cell motility was not significantly different between gels of lower versus higher elastic modulus (2-way ANOVA, main effect of modulus p = 0.8583) (14,15).

Discussion
Previously, we have shown that the average F/B of primary IDC tumor biopsies is prognostic of metastatic outcome. Specifically, in ER + IDC tumors (i.e. including the luminal subtypes), patients whose tumors had higher F/B experienced fewer distant metastases in 10-year follow-up data (29,30). Conversely, in ER − IDC tumors (i.e. including the basal triple negative and HER2-enriched subtypes) the relationship was inverted and patients whose tumors had higher F/B experienced more distant metastases.
One possible explanation for the prognostic relationship is provided by observations that tumor cells move along SHG-emitting collagen fibers in murine tumor models, and that the tendency of those fibers to orient perpendicularly to the tumor/host interface in patient samples is prognostic of patient outcome (7). This suggests that collagen fiber internal structure (which dictates F/B) may influence the motility of tumor cells moving along a fiber and thereby alter the outflow of cells from a tumor, hence influencing metastatic outcome for the patient. Therefore, in previous work we examined the relationship between collagen fiber internal structure in pure collagen gels (as reported by F/B) and tumor cell motility of metastatic 4T1 cells, a model of basal-like triple negative breast cancer (TNBC), on those gels (13). We observed that motility increased as F/B of the collagen gels increased. That trend is consistent with the trend observed in the ER − cohort in patient samples (containing basal TNBC patients), and those results suggest that in patient tumors F/B may predict metastasis because the collagen fiber internal structure upon which it depends influences the ability of tumor cells to locomote along those fibers and escape the tumor (13). However, the mechanisms by which tumor cells sense differences in collagen fiber internal structure, in order to respond with differences in motility, remains unclear.
One such mechanism is suggested by the ample literature demonstrating that elastic modulus of a cell's environment influences its behavior (14,15). This suggests that cells may alter their motility by reacting to changes in elastic modulus that may result from changes in collagen fiber internal structure (15), or conversely that cells may directly sense changes in collagen fiber internal structure independently of elastic modulus. Therefore, herein we studied the role of elastic modulus in the relationship between collagen fiber internal structure, as reported by F/B, and tumor cell motility. To evaluate this relationship, we introduced metastatic and non-metastatic cell lines to mixed collagen/polyacrylamide gels of various F/B values and two different physiologically relevant values of elastic modulus. First, we created a series of in vitro gels with multiple values of F/B and elastic modulus. To develop these gels in our laboratory, we incorporated polyacrylamide into our previous pure collagen gel protocols (13). After developing this protocol, we first verified that the measured F/B was constant throughout each gel and was not affected by the presence of the polyacrylamide nor by variation of the elastic modulus (Fig. 3). Next, we confirmed that varying collagen fiber internal structure (as reported by F/B) by varying collagen polymerization conditions did not affect the measured elastic modulus and that all three F/B categories had the same elastic modulus (Fig. 4).
As demonstrated in Fig. 5a and 5b, in mixed collagen-polyacrylamide gels the motility of 4T1 cells increases as F/B of their microenvironment increases. These results confirm our previous study where we observed 4T1 motility increasing as F/B increased in pure collagen gels whose elastic modulus was not controlled (13). Furthermore, this specific trend of tumor cell motility increasing with F/B is consistent with the trend of metastasisfree survival time decreasing with F/B observed in patient tumor samples in the analogous (ER − , containing basal TNBC) cohort of human patients. This suggests that F/B may predict metastatic outcome in patient samples because changing collagen fiber internal structure (which affects F/B) alters the outflow of cells from a tumor. Importantly, 4T1 motility increased with F/B even as the elastic modulus was held constant, as evidenced by both local AFM and global rheometry measurements (Fig. 5). This suggests that the 4T1 model of TNBC can respond to changes in internal collagen structure with changes in motility independently of significant changes in elastic modulus. In the 67NR model of luminal breast cancer we again observed that tumor cell motility varies with F/B and does so even as the elastic modulus was held constant (Fig. 6). This suggests that the 67NR model of luminal breast cancer can also respond to changes in internal collagen structure with changes in motility independently of significant changes in elastic modulus. Interestingly, we observe the opposite trend between motility and F/B in the 67NR cells versus 4T1 cells, as seen in Fig. 6a and 6b, where 67NR tumor cell motility decreases as F/B of the microenvironment increases. This is again consistent with the data from patient samples where metastasis-free survival time increases with increasing F/B in the ER + cohort, which contains the luminal subtypes (11). This again suggests that F/B may predict metastatic outcome in patient samples because changing collagen fiber internal structure  (22). Taken together these results suggest that variations in collagen fiber internal structure do not modify tumor cell motility via any induced changes in elastic modulus. Furthermore, these results suggest that luminal and basal-type breast cancer reacts to changes in collagen fiber internal structure in different ways. In future work we hope to continue to explore the mechanism by which tumor cells sense changes in collagen fiber internal structure. Our observation that these cells are not sensing changes in collagen fiber internal structure through elastic modulus suggests that there may be cell surface receptors that are directly sensitive to variations in this property.

Availability of data and materials
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request

Competing interests
The authors declare that they have no competing interests DD. The funding bodies had no role in in the design of the study, data collection, data analysis, data interpretation of data, nor in writing the manuscript.

Authors' Contributions
TE designed the protocol for collagen-polyacrylamide gels in consultation with PN and CKK, and prepared all gels for experiments, imaged and analyzed F/B data from all gels, performed cell motility experiments, and completed statistical analyses. TE is responsible for writing the majority of the manuscript. DD contributed to the design of the experiment as well as data interpretation and troubleshooting. AG performed all rheometer measurements, as well as analyzed elastic modulus data. PN performed all AFM elastic modulus measurements and contributed to AFM analysis. CK provided consultation on making collagen-PA gels, access to AFM, as well as expertise and advice involving AFM and motility results. DB provided access to live cell imaging microscope, cell culture hoods, and incubators. MB provided access to rheometer as well as expertise in analyzing and comparing elastic modulus results. EB contributed to the design of the experiments, troubleshooting, data interpretation, and writing the manuscript.
All authors read and approved the final manuscript.