Microfluidic devices fitted with “flowver” paper pumps generate steady, tunable gradients for extended observation of chemotactic cell migration

Chemotaxis is the directed migration of cells toward soluble biochemical cues called chemoattractants. Directed migration of mesenchymal cells supports normal physiological processes, such as tissue development,¹ angiogenesis,² and wound healing,³ while improper migration of such cells contributes to cancer metastasis,⁴ chronic wounds,⁵ and cardiac fibrosis.⁶ Therefore, understanding the regulation of mesenchymal chemotaxis is critical to inform medical innovations such as anti-metastasis pharmaceuticals⁷ and fibrosis treatments.⁶ 

Immortalized fibroblasts, such as the murine NIH/3T3 cell line, have served as prototypical mesenchymal cells in chemotaxis research for decades. However, the bulk of the prior literature is based on the Boyden chamber/transwell assay,^8–10 which obscures various aspects of fibroblast chemotaxis.^11–13 The transwell chamber generates transient chemoattractant gradients that last for only 1 h,¹⁴ confounds chemotaxis with other modes of invasion,¹⁵ and provides no information about spatiotemporal dynamics or individual cell behavior.¹³ Therefore, the need remains to evaluate the chemotaxis of individual fibroblasts responding to stable chemoattractant gradients with controlled properties (steepness, midpoint concentration).

Microfluidics has emerged as the most promising approach to generate gradients in chemotaxis assays.^16–18 Although such devices may be designed for predictable gradient control, generating sufficiently stable gradients in practice is a challenge.^19–21 Failure modes include the introduction of bubbles,^22,23 hydrostatic imbalances,^19,20 differences in tubing resistance,²¹ stretching of tubing during microscope stage movement,^24,25 and pulsatile syringe pump flows.^26–28 These failure modes are particularly deleterious in the study of fibroblast chemotaxis because of these cells’ protracted and heterogeneous chemotactic response.²⁹ 

To overcome these challenges, we have developed a new microfluidic system and experimental workflow, suitable for long-duration experiments^30,31 required to study chemotaxis of slow-moving mesenchymal cells. The requisite gradient stability is enabled by the combination of microfluidics and a novel paper pump design (a “flowver”), which differs from others^32–37 in that it produces steady flows that are principally determined by the dimensions and wetting properties of the paper; although steady flow requires the evaporation of water, the flow rate is insensitive to drying conditions. This approach obviates the use of syringe pumps and tubing, thereby mitigating bubble formation and reducing the experimental footprint.^38,39 The portability and tunability of flowvers allow them to be integrated with numerous microfluidic designs. For chemotaxis experiments, we selected a modified version of the Y-junction micromixer;⁴⁰ when fitted with a flowver, the system produces stable gradients that predictably vary with the channel position. We also demonstrate its robustness against pressure imbalances.

With this system, and using prism-based, total internal reflection fluorescence (TIRF) microscopy and semi-automated image analysis, we achieved high-throughput tracking of cell centroid trajectories (∼300 cells per experiment) and simultaneously quantified the pattern of intracellular signal transduction via the phosphoinositide 3-kinase (PI3K) pathway.^41,42 To the best of our knowledge, this is the first publication to report the use of a passive pumping system to generate stable chemoattractant gradients during a long-term chemotaxis experiment with TIRF microscopy or with flow rates >0.1 μl/min. The complete workflow reveals that NIH/3T3 fibroblasts chemotax in a preferred platelet derived growth factor-BB (PDGF-BB) gradient regime that aligns with a previous model.⁴³ Our results also corroborate prior work showing that fibroblast migration behavior—whether chemotactically biased or not—correlates with the asymmetry of PI3K signaling.⁴⁴ A deeper analysis of the high-throughput data set showed that the sensitivity of chemotaxis to the preferred PDGF gradient conditions depended on the alignment of PI3K signaling with the gradient; cells without aligned PI3K signaling did not exhibit significant chemotaxis, regardless of the PDGF gradient conditions.

During live imaging of fibroblast chemotaxis, chemoattractant gradients should persist for at least 6 h to allow appreciable translocation and changes in the direction of the slow-moving cells.^42,45–47 Therefore, gradient stability is paramount. In microfluidic gradient generators, two primary causes of gradient instability are pressure imbalances and the introduction of bubbles.^22,23 Bubbles, which readily form when foamable cell-culture media (that should not be degassed) is heated during transit through tubing into a microfluidic device, perturb device performance and cause cell death, ruining a high fraction of experiments. To all but eliminate bubbles, we devised a novel, passive pumping approach driven by capillary forces^34,37,48 coupled to evaporation-driven flow.^{32,33,35,49,50} Unlike previous paper pump designs, ours provides a steady flow rate that is insensitive to the evaporation conditions. The result is a compact, portable paper pump that we call a “flowver” (flow + clover), reflecting its biomimicry of transpiration in plants⁵¹ and its clover geometry (Fig. 1).

The flowver design builds on the concept of hydraulic batteries,³⁴ which are made of laminated filter paper cut into a stem-and-pad shape. By analogy to flow through a conduit, the resistance to flow is proportional to the wetted length, $L(t)$⁠, along the stem region [Fig. 1(a)]. Accordingly, we confirmed that the volumetric flow rate is inversely proportional to $L(t)$⁠, following the Lucas–Washburn equation [Fig. 1(b)].^52,53 Although hydraulic batteries drive flows that ultimately cease, and evaporative-area based designs drive flow that decelerates, flowvers drive flow that is both predictable and steady in principle (Fig. S1 in the supplementary material). In the flowver, resistance to flow is determined by the fully wetted length of the (laminated) stem, while stable flows are achieved by allowing water to evaporate from the leaves, which collectively have ample surface area [Fig. 1(b), inset].³³ With evaporation distributed over three leaves with six exposed surfaces, the leaves impose relatively little resistance to flow, and therefore the flow rate is insensitive to the humidity of the environment.

Given the flowver's tunability of flow resistance and simplicity of construction (ease and low cost), it can be readily designed to drive steady flow through various microfluidic devices. We tested three gradient-generating devices that were available to us (Fig. 2). Inlet ports were fitted/retrofitted with media reservoirs, and the flowver was installed at the outlet port. We confirmed that the flowver-retrofitted branched, pre-mixed micromixer (sometimes called the “Christmas tree” design) produces the expected gradient patterns [Fig. 2(a)], even though this device is typically operated with a pump-driven flow. Another retrofit device is a modified version of a ladder chamber^54,55 that produces several distinct gradient slopes⁵⁶ [Fig. 2(b)]. Gradients form across the ladder “rungs,” which are observation chambers bordered by taller channels that continuously replenish the chemoattractant source and buffer sink media. The third device that we evaluated is the Y-junction micromixer [Fig. 2(c)],⁴⁰ which is similar to the branched, pre-mixed micromixer but with only two streams entering the observation channel. With flowver-driven flow, this device generates a region with a sharp gradient at the centerline where the inlet streams converge [Fig. 2(c)]. For the remainder of this paper, we focus on the integration of a flowver pump with the Y-junction micromixer to generate and maintain chemotactic gradients.

The hydraulic circuit⁵⁷ of a microfluidic device is altered when it is retrofit with a flowver. Specifically, the conversion of inlet ports into reservoirs adds hydrostatic pressure at the inlets, while the installation of a flowver at the outlet introduces both a capillary pressure driving force and the resistance of the flowver stem [Fig. 3(a)]. With those alterations, the volumetric flow rate Q through the device is given by Eq. (1),

where $Ph$ is hydrostatic pressure at the inlet(s), $Pc$ is the capillary pressure (≈700 mm H₂O), $Rdevice$ is the resistance of the device, and $Rstem$ is the resistance of the flowver stem. Based on the characterization of hydraulic batteries,^34,38 it is typical for $Pc≫Ph$ and $Rstem≫Rdevice$⁠. Under those conditions, Q is about the same as $Qflowver=Pc/Rstem$⁠, greatly simplifying the design of the integrated system once the flowver has been calibrated.

For our modified Y-junction/flowver system, another operational target is that the flow rates from the two reservoirs should be approximately equal, even when the hydrostatic pressures of the reservoirs are not. In S1 in the supplementary material, we show that the key criterion is

In Eq. (2), $ΔPh$ is the difference in hydrostatic pressure between the reservoirs and $Rresistor$ is the resistance of each of the feed channels, which have a serpentine geometry and act as hydraulic resistors.¹⁹ For our design, we estimated that $Rresistor≈0.1Rstem$⁠, and therefore we can expect robust performance as long as $ΔPh≪0.1Pc≈70mm$ H₂O, a large difference in liquid heights. Indeed, when we set up an easily visible liquid height difference of ∼7.5 mm, there was only a mild bowing of the gradient at the junction of the two streams [Fig. 3(b)]. The robustness of this design to pressure imbalances is further supported by finite-element modeling, which allowed us to rapidly compare scenarios with various pressure differences, with or without the resistors that are critical for buffering them (Fig. S2 in the supplementary material).

Having devised and tested a robust strategy for steady flow through microfluidic devices, we sought to use the modified Y-junction/flowver system to generate gradients in a controlled manner and monitor gradient profiles over time by fluorescence microscopy using FITC-labeled, 20-kDa dextran [Fig. 4(a)]. As the laminar flow of the fluid progresses through the length of the channel, the gradient in the direction across the channel (with dimension $W=750μm$⁠) naturally flattens because of molecular diffusion. Based on the scaling analysis, a dynamic length scale, $λ$⁠, associated with this flattening may be defined as follows:^58,59

In Eq. (3), h is the height of the channel (80 μm) and D is the diffusivity of the chemical (estimated as ≈105.5 μm²/s = 0.00633 mm²/min for both the dye-labeled dextran⁶⁰ and PDGF-BB). Substantial flattening is expected when $z∼0.1λ$ (∼100 mm for our system) or larger, where z is the position in the direction of flow. This is tunable based on the flow rate Q, which is controlled primarily by the design of the flowver. Thus, both steep and shallow gradients may be formed within the same device/experiment [Figs. 4(b) and 4(c)]. Importantly, we reproducibly and predictably generate this gradient landscape. In the plot shown in Fig. 4(c), the dotted lines show 95% confidence intervals of experimentally measured gradients after 6 h, and the solid lines show the gradient profiles along a surface slice (y = 0 μm) from a three-dimensional, finite-element numerical solution of the device with $Q=0.58μl/min$ (flow rate corrected for temperature; see S1 in the supplementary material). The gradient formed at position “2” closely matches the gradients formed by actively pulling liquid out of, or pushing flow into, the device using a syringe pump with programmed flow rate (Fig. S3 in the supplementary material).

We also evaluated the stability of the gradients over time [Fig. 4(d) and Movie 1 in the supplementary material]. Here, the normalized gradient slope at position “2” is plotted over time for six independent experiments. The gradients were persistently within ±20% of the 6-h mean as a criterion for stability. One experiment was allowed to run over multiple days; in that case, a serviceable gradient persisted for 40 h, although it did not meet the 20% stability criterion throughout (Movie 1 in the supplementary material). Over the course of more than 150 h of collective operation in these experiments, no bubbles were observed.

The ability to accurately model the concentration field in the device, by numerically solving the conservation equations for total mass, linear momentum, and the chemical species in three dimensions, allows us to predict the full gradient landscape for a particular flow rate [Fig. 4(e)]. Here, the heat map shows the frequency of distinct gradient conditions, characterized by the point concentration, C, and relative gradient, RG,

In Eq. (4), the x dimension points across the width of the channel toward the source side. The gradient properties are “measured” at the centroids of 1 × 1 μm² areas of the channel footprint (within the first 100 mm of the channel length). For example, for a dimensionless concentration of 0.1 and RG = 12/mm, the heat map shows that there are ∼3 × 10⁴ such locations in the device (for comparison, a cell's contact area of ∼10³μm²), including regions observed in position “2” (squares). Other channel positions may be selected to access different gradient conditions with high/low concentration and high/low steepness. By varying the source concentration across experiments, the point concentration variable scales accordingly.

Having established the function of the Y-junction/flowver system for generating and maintaining chemical gradients, we used it to study fibroblast chemotaxis to PDGF.^11,12,42,46 The channel of the device has ∼75 mm² of usable gradient space for cell tracking, or ∼300 cells per experiment. We developed a computer vision workflow for semi-automated tracking and analysis of the cells [Fig. 5(a)]. In the experiments shown here, NIH/3T3 cells expressing EGFP-AktPH, a biomarker for PI3K signaling,^41,44 were imaged by TIRF microscopy.⁴¹ Thus, we can track each cell's centroid position⁶¹ and analyze the pattern of PI3K signaling as the cells migrate^42,62 [Fig. 5(a) and Movie 2 in the supplementary material]. Each centroid is mapped onto a directory of PDGF concentration profiles (estimated by including Cascade Blue-dextran in the PDGF source solution) for each position and time point in the experiment [Fig. 5(b)], and thus each cell track is mapped to a local midpoint concentration and RG value. Cell trajectories were partitioned into 3-h, non-overlapping trajectory intervals to capture the cellular response as a function of the average local stimulus conditions. The forward migration index (FMI), a common metric of chemotactic fidelity, was used.

For each trajectory, the FMI, PDGF concentration, and RG coordinates are plotted to construct a chemotaxis response diagram [Fig. 5(c)], with data from experiments with PDGF source concentrations of 1 and 10 nM. By inspection, it appears that as RG increases, the trajectories tend to exhibit more positive FMI values (warm-colored circles), but there is apparently some dependence on PDGF concentration. We further elucidate this trend by overlaying a previous model of NIH/3T3 PDGF gradient sensing,⁴³ with two fit parameters (S1 in the supplementary material),

In Eq. (5), $RG¯$ and $C¯$ are the time-averaged RG and concentration values taken at the cell centroid, and A and $C∗$ are fitted scaling parameters. The best-fit model is overlaid in Fig. 5(c) (dashed curves), with A = 0.06 mm and C* = 0.7 nM. Using this model, we find that the local gradient conditions satisfying $FMIpredicted>0.05$ produce statistically greater chemotactic responses than those outside this “chemo-conducive” region of the gradient landscape (p = 1 × 10⁻⁴). Furthermore, chemo-conducive regions support significant chemotaxis, whereas non-chemo-conducive regions do not, with chemotaxis defined as the exclusion of FMI = 0 in the 95% confidence interval [Fig. 5(d)].

We next asked whether or not the fidelity of chemotaxis is correlated with the orientation of PI3K signaling. To address this, we applied signaling vector (SV) analysis^42,62 and defined the alignment of the signaling vector with the PDGF gradient as the signaling index (SI), which is constructed in the same way that the vector of cell centroid movement determines the FMI [Fig. 6(a)]. SI or FMI = 1 corresponds to a signaling vector/cell movement vector that is perfectly and persistently aligned with the PDGF gradient, whereas SI or FMI = −1 corresponds to an alignment opposite to the gradient. SI values were fit to the same function of time-averaged PDGF concentration and RG values as done for FMI, with different fit parameters; we found that the predicted SI > 0.05 region is similar to the predicted FMI > 0.05 region, but the former includes more trajectories, closer to the bottom right corner of the response diagram [Fig. 6(b)]. Analogous to the FMI > 0.05 (chemo-conducive) region, trajectories in the SI > 0.05 region have a mean SI statistically greater than those outside of this region (p = 1 × 10⁻⁴), and only the 95% confidence interval of trajectories from the SI > 0.05 trajectories exclude SI = 0 (Fig. S4 in the supplementary material).

Consistent with a previous study, but supported here by an order-of-magnitude more data, FMI is positively correlated with SI (n = 744, slope = 0.53, R²= 0.45) [Fig. 6(c)]. Another way to appreciate the correlation is to note the frequencies of the data in the four quadrants of the plot [Fig. 6(c)]: quadrants I (42.2%) and III (32.1%) are the regions where FMI and SI share the same sign (positive and negative, respectively), as compared with quadrants II (12.2%) and IV (13.4%). Quadrant I contains the trajectories that apparently exhibit both chemotactic migration and alignment of PI3K signaling with the PDGF gradient.

Furthermore, the statistical power of the data set allows a more nuanced relationship to be revealed [Fig. 6(d)]. Considering the subset of trajectories with positive SI (quadrants I and IV), the mean FMI of trajectories in the chemo-conducive region [dots in Fig. 6(c)] is 0.31 ± 0.07 (95% CI), significantly greater (p = 0.002) than the mean FMI of trajectories outside the chemo-conducive region (0.19 ± 0.03). This distinction does not hold when SI is negative [Fig. 6(d)]. This suggests that alignment of PI3K signaling with the PDGF gradient is not only generally predictive of chemotactic behavior, it also predicts the sensitivity of the response to gradient conditions.

We set out to design a chemotaxis assay that is suited to the protracted, heterogeneous mesenchymal motility phenotype. Previously, we evaluated the chemotactic response of NIH/3T3 cells to gradients generated from alginate beads; that approach, though facile, suffers from lack of control, low throughput, and inability to estimate the absolute chemoattractant concentration.⁴² Hence, our aims were to generate an extensive, tunable, and measurable gradient landscape; increase experimental throughput; and maintain gradient stability for more than 6 h. We adopted the Y-junction microfluidic device as it can generate gradients ranging from a step function to completely mixed; however, the greatest challenge proved to be the gradient stability criterion, which is increasingly more difficult to achieve as the required observation time increases. Particularly deleterious are the effects of bubbles in the device, which are readily introduced via tubing and forced flow associated with syringe pump systems. Such systems also affect the complexity of the experimental protocol and scalability of the assay.

To address the common shortcomings, we devised a method to achieve stable flows passively, without syringe pumps. We built on the method of hydraulic batteries³⁴ by adding evaporative “leaves” at the end of a flow rate-determining “stem” to make paper pumps that we call “flowvers” (flow + clover). An initial concern was that the flow rate might decrease over time due to residual salt caking on the evaporative surfaces.³³ This was mitigated by providing excess evaporative capacity, with three leaves providing six evaporative surfaces; however, pumping of biological media still showed a slight decline in the flow rate over the course of ∼10 h, which was modestly but noticeably greater when the device contained cells. We attribute the latter to fouling of the filter paper pores by cell debris. Steps to minimize debris prior to cell seeding might ameliorate that effect.

In addition to the aforementioned advantages, the flowver pump facilitates overall design once its capillary pressure and hydraulic resistance are known. This is particularly the case when hydrostatic driving forces and the hydraulic resistance of the microfluidic device are relatively small, which was true for the systems we tested. Importantly, the high capillary pressure allows one to use on-device reservoirs with ample volume for long-term experiments, effectively buffering both the change in liquid height with time and any difference in liquid height between reservoirs. Along those lines, one benefit of the Y-junction device relative to designs that require a static mixing region, such as the ladder design, is that even a microscopic difference in pressures between the source and sink channels is intolerable in static mixing region devices. In the Y-junction device, a pressure difference may cause the midpoint of the gradient to deviate from the midpoint of the channel, but the gradient will still form (Fig. S2 in the supplementary material). For designs with convection-suppressed observation channels, fluid mechanics calculations show that similar pressure differences are ruinous (Fig. S5 in the supplementary material).

We coupled our microfluidic design with TIRF microscopy to simultaneously track cell centroids and evaluate PI3K signaling. Previously, we modeled PDGF receptor activation of NIH/3T3 cells in the presence of PDGF gradients from a micropipette, resulting in an equation for receptor activation as a function of the PDGF concentration.⁴³ Here, we overlaid that model on the forward migration index (FMI) responses of cells over a broad range of PDGF midpoint concentrations and gradient steepness. The receptor activation model appears to extend to the chemotactic response, as a PDGF stimulus region defined by the model prediction at FMI > 0.05 delineated a subpopulation of trajectories with significantly greater chemotactic fidelity.

With the dramatic increase in throughput afforded by the present workflow, we readily reproduced the finding that each cell's chemotactic fidelity, whether robust or poor, correlates with the asymmetry of PI3K signaling,^42,44 and new insights were revealed. Under the conditions tested, PI3K signaling orientation predicted migration behavior far better than the external PDGF gradient conditions. Accordingly, the analysis showed that the tendency of chemo-conducive gradient conditions to favor chemotaxis was only significant among trajectories with properly oriented PI3K signaling; the corollary—that properly oriented PI3K signaling depends on PDGF gradient conditions—was also statistically significant. Taken together, these results suggest that chemotactic sensing competes with the spontaneous, dynamic patterns of signaling that arise during random migration on extracellular matrix,^44,47,62 subject to the known overlap of signaling components in growth factor receptor- and integrin-mediated signal transduction.^46,63,64

In a previous work, we found that PI3K signaling is not absolutely required for fibroblast chemotaxis,⁶³ but it plays a definite role in stabilizing nascent protrusions; thus, it can bias cell turning behavior for more efficient alignment with a chemotactic gradient.^44,64 The associated morphological dynamics are mechanically linked to adhesion-based processes, and thus PI3K signaling might be more integral to sensing of extracellular matrix gradients.^46,65 Dissection of requisite pathways for fibroblast chemotaxis revealed that the phospholipase C/protein kinase C pathway is essential and responsible for the negative regulation of non-muscle myosin II motor activity.⁶³ The associated conceptual model asserts that local inhibition of myosin contractility favors more frequent and/or persistent protrusion, consistent with studies of randomly migrating cells.^66,67 The present results support the notion that multiple signaling pathways synergize to promote efficient chemotaxis,²⁹ and we speculate that co-localization of those activities is critical for that synergy. The experimental workflow presented here offers a platform for such studies, with controlled variation of gradient conditions.

Flowvers with a 70 × 2 mm² stem and a 10 mm-radius semicircle evaporation pad were outlined in CorelDRAW®. The designs were cut out of Whatman #1 filter paper (Sigma Aldrich) using a Universal® Laser System VLS 3.5 laser cutter. The stem of the flowver was folded 5 mm from the bottom and threaded through a pipet tip. Then, two additional evaporation pads with 2 mm stems were attached using cleanroom tape, and the flowver stem was wrapped in multiple layers of parafilm. Finally, to minimize its footprint, the parafilm-wrapped stem was folded like an accordion and secured to the side of the pipet tip. We confirmed that folding the stem in this manner does not significantly alter the flow rate, relative to a straight stem (S1 in the supplementary material).

Flowvers with various stem lengths were installed in a microfluidic device, with a single channel ∼30 mm long and 600 μm wide. The device served to couple the flowver to a long (∼250 mm) segment of clear, Tygon® tubing with 0.51-mm inner diameter (Cole-Parmer). The linear displacement of the water (dyed with trace red food coloring) in the tubing was recorded over time. The volumetric flow rate was calculated as the product of the linear velocity and the cross-sectional area of the tubing.

AutoCAD 2018 (Autodesk) was used to draw the top view of the modified Y-junction micromixer. The resistor channels were ∼60 mm long and 50 μm wide. The gradient channel was ∼130 mm long and 750 μm wide. The photomask was ordered from Fineline Imaging (Colorado Springs, CO) with 50 K dpi. One-step photolithography⁶⁸ was used to prepare the positive relief master template. SU-8 2050 (Microchem) photoresist was cured on a 100 mm diameter silicon wafer (University Wafer), following the vendor's protocol for ∼80 μm tall channels. For this and other microfluidic devices, polydimethylsiloxane (PDMS, Sylgard 184 Fisher Scientific) was mixed with a curing agent (10:1 w/w), poured onto the master wafer, and cured overnight at 65 °C. Inlet reservoirs were cored out using 7-mm biopsy punches (World Precision Instruments), and the outlet reservoir (flowver connection port) was cored out using a 2-mm biopsy punch. Then, the PDMS device was bonded to a 50 × 75 × 1 mm³ plain microscope slide (Corning) after both the glass slide and the PDMS were treated with air plasma for 60 s (Harrick Plasma PDC-32G).

Using photolithography as previously described for the modified Y-junction device, our lab had previously prepared master templates of the “Christmas tree” and angled ladder microfluidic designs. The Christmas tree design had outlet dimensions of 980 μm width and 15 mm length; the serpentine mixing channels had a width of 70 μm, and all channel heights were 75 μm. The angled ladder design had source and sink side channels, with 250 μm height, 200 μm width, and 10.1 mm length, and cross channels with 200 μm width, 30 μm height, and lengths ranging from 500 to 2000 μm.

All microscopy experiments were performed at 37 °C. Our TIRF/epifluorescence microscopy rig⁴¹ uses an Axioskop 2 FS base stand (Zeiss) and is outfitted with automated multi-position stage control and CRISP autofocus system (Applied Scientific Instrumentation). Images were acquired at up to 50 stage positions every 10 min. Epifluorescence microscopy, using a pe-300lite LED light source (CoolLED), was employed to visualize the gradient in the device. For 20-kDa FITC-dextran (Sigma Aldrich) used during device characterization, 488/10-nm bandpass excitation and 525/50-nm bandpass emission filters were used (all spectral filters from Chroma); for Cascade Blue-dextran used in chemotaxis experiments, 350/50-nm bandpass excitation and 480/40-nm bandpass emission filters were used. For TIRF imaging of cells, a 60 mW, 488 nm sapphire laser line (Coherent) was used, with 1556 ms exposure time and 515/30-nm bandpass emission filter. For both microscopy modes, a 10× 0.30 NA water immersion Achroplan objective (Zeiss) was used. The camera was an ORCA ER cooled CCD (Hamamatsu), fitted with a 0.63× camera mount. Metamorph image acquisition software (Universal Imaging, West Chester, PA) was used.

To outfit a plasma-bonded microfluidic device for microscopy, it was placed back into the plasma cleaner along with a PDMS rectangular well (the objective reservoir, to accommodate the water-dipping objectives of our upright microscope) and a PDMS slab with three cylinders bored through (the media reservoirs). After 60-s treatment with air plasma, the objective reservoir was bonded to the glass, and the media reservoir slab was PDMS–PDMS bonded onto the microfluidic device. The device was then backfilled via the outlet port with sterile, de-ionized water, delivered by a syringe; care was taken to ensure that there were no bubbles after this step. For chemotaxis experiments, the device was backfilled with human fibronectin coating solution (∼400 μl, 10 μg/ml in water, Corning) and incubated for 1 h at 37 °C, and then the device was flushed with ∼1 ml imaging medium.

NIH/3T3 mouse fibroblasts (American Type Culture Collection) stably expressing the EGFP-AktPH biosensor⁶² were recovered from cryogenic storage and used between passages 6 and 30. Cells were subcultured in a 37 °C, 5% CO₂ incubator in Dulbecco's Modified Eagle's Medium supplemented with 10% v/v fetal bovine serum and 1% v/v penicillin–streptomycin–glutamine (all from Gibco). The imaging medium was Live Cell Imaging Buffer (Molecular Probes, Fisher Scientific) supplemented with 10 mM glucose, 1× Amino Acids (MEM AA and MEM NEAA from Invitrogen), 10% fetal bovine serum, and 1% penicillin–streptomycin–glutamine (pH = 7.4).

For chemotaxis experiments, cells were briefly trypsinized, resuspended in imaging medium at ∼5 × 10⁵/ml, backfilled into the device, and incubated in the microscope chamber (air, 37 °C) for 2 h to allow them to spread. The flowver was inserted at the outlet, and the device was mounted on the microscope. The source (chemoattractant) reservoir was evacuated using Kimwipe and refilled with imaging medium supplemented with 1 or 10 nM human recombinant PDGF-BB (Peprotech) and 5 μM of the fluorescent marker, 10-kDa Cascade Blue-dextran (Invitrogen/Molecular Probes), and both the chemoattractant and buffer reservoirs were capped with mineral oil (Millipore Sigma) to prevent evaporation. Finally, the objective reservoir was filled with the imaging medium, the objective was dipped into the medium, and the objective reservoir was capped with mineral oil.

To quantify PDGF concentration in the dye-dextran spectral channel, images of the source and sink channels (pre-Y-junction merge) were taken. These served as shading control and background images, respectively, for pixel-by-pixel operations. Shading-corrected gradient images were obtained by normalizing the background-subtracted gradient image by the background-subtracted shading control image.⁶⁹ The resulting image was cropped to include only the middle 610 μm (x dimension) of the channel. Then, to normalize for shading artifacts at different stage locations, a mass balance was imposed on the concentration profile. When there is equal flow of source (dimensionless concentration, C = 1) and buffer (C = 0) entering the Y-junction, the average concentration at each axial position z should be 0.5. As such, the mass balance criterion was applied using the following process to generate a correction factor.

First, an average gradient profile across the channel (x dimension) was obtained by averaging over a short (∼890 μm) segment in the axial dimension,

Then, the correction factor was defined by imposing the mass balance,

Finally, the correction factor was applied to the concentration profile,

Image segmentation of the cells’ spectral channel was executed using Matlab 2019b (Mathworks) with the following algorithm. First, a background-subtracted image is normalized by 95% of the maximum intensity value, with pixels greater than one redefined as one. Then, an adaptive threshold is applied using the Matlab function adaptthresh, with 0.05 sensitivity parameter. Regions of interest with more than 4000 pixels or fewer than 500 pixels (1 μm = 1.15 pixels), as well as those touching the image border, are excluded. Finally, the mask-overlaid image is passed to the user for manual quality control.⁷⁰ At this step, regions that apparently included multiple cells in contact were excluded, and proximal but apparently non-contacting cells were split and included.

To construct cell migration trajectories, the area centroids of the segmented cells were passed to the Simple Tracker algorithm (Matlab File Exchange⁶¹). Simple Tracker was augmented to scrub trajectories per the following criteria: exclude cells that traveled more than 60 pixels over a single frame (1 frame = 10 min), cells that did not contain at least six consecutive trackable frames, and cells that did not travel with a velocity greater than 1 pixel per frame on average.

Matlab was also used to calculate the forward migration index (FMI), the signaling vector, and the signaling index (SI). The FMI is a standard metric defined as the displacement of the centroid trajectory in the direction of the gradient divided by the total path length of the trajectory. The signaling vector for each cell image and the SI for each cell trajectory were calculated as described previously⁴² [Fig. 6(a)]. One modification was that the magnitude of the signaling vector for each image was normalized by the cell's total fluorescence volume (area times mean intensity).

To model bulk liquid flow and molecular transport in devices, COMSOL 5.4 Multiphysics software was used to solve the standard continuity, Navier–Stokes, and diffusion/advection equations appropriate for a dilute solute in incompressible liquid. The two-dimensional AutoCAD drawing of the device was imported into COMSOL and extended in the third dimension with a height of 80 μm. The normal boundary conditions for the laminar flow physics were 73.6 Pa (7.5 mm H₂O) pressure at the two inlets and a volumetric flow rate equivalent to 0.58 μl/min at the outlet. The boundary conditions for transport of dilute species physics were concentrations of 1 and 0 at the source and buffer inlets, and set to “outflow,” which imposes no axial diffusion, at the device outlet. The geometry was meshed using the “extremely fine” setting based on fluid dynamics physics.

To prepare the gradient landscape, it was beneficial to take advantage of a straight channel that could be easily interpolated onto a regular grid. In this case, only half of the device geometry is needed, with boundary conditions at the centerline of the channel set as symmetry for laminar flow physics and concentration = 0.5 for transport of dilute species physics. Concentration data were exported from COMSOL and interpolated onto a 1 × 1 μm² mesh of the first 100 mm of the mixing channel in Matlab using the griddata function. The interpolation was smoothed using a 30 μm moving average of the gradient.

Comparisons of FMI and SI distributions were performed in Matlab using a one-sided, two sample Student's t-test (ttest2), with statistical significance evaluated at $α=0.05$⁠.

See the supplementary material for S1: supplementary Methods; Fig. S1: comparison of paper-based pumping methods; Fig. S2: finite-element modeling calculations of gradients for various hydrostatic pressure imbalance scenarios in the Y-junction; Fig. S3: comparison of syringe pumps and flowvers for gradient generation; Fig. S4: signaling index (SI) is biased by PDGF gradient conditions; and Fig. S5: impact of hydrostatic pressure imbalance in the angled ladder device; Movie 1: time-lapse video of a long-term, stable FITC-dextran gradient in the Y-junction device; and Movie 2: time-lapse video of PI3K signaling (pseudocolor) during migration of NIH/3T3 cells (top) in a PDGF gradient indicated by Cascade Blue-dextran (bottom), as in Figs. 5(a) and 5(b).

The authors thank Professor Orlin Velev and Dr. Timothy Shay for helpful discussions about evaporative paper pumps. This work was supported by the National Science Foundation under Grant No. 1706087, by NIBIB of the National Institutes of Health under Award No. U01-EB018816, and by NIGMS of the National Institutes of Health under Award No. R35-GM130312. S.A.B. and R.A. were partially supported by the NC State Molecular Biotechnology Training Program, funded by NIGMS of the National Institutes of Health under Award No. T32-GM133366. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Science Foundation or of the National Institutes of Health.

The data that support the findings of this study are available from the corresponding author upon reasonable request.