Integrated in silico and 3D in vitro model of macrophage migration in response to physical and chemical factors in the tumor microenvironment

Abstract

Macrophages are abundant in the tumor microenvironment (TME), serving as accomplices to cancer cells for their invasion. Studies have explored the biochemical mechanisms that drive pro-tumor macrophage functions; however the role of TME interstitial flow (IF) is often disregarded. Therefore, we developed a three-dimensional microfluidic-based model with tumor cells and macrophages to study how IF affects macrophage migration and its potential contribution to cancer invasion. The presence of either tumor cells or IF individually increased macrophage migration directedness and speed. Interestingly, there was no additive effect on macrophage migration directedness and speed under the simultaneous presence of tumor cells and IF. Further, we present an in silico model that couples chemokine-mediated signaling with mechanosensing networks to explain our in vitro observations. In our model design, we propose IL-8, CCL2, and β-integrin as key pathways that commonly regulate various Rho GTPases. In agreement, in vitro macrophage migration remained elevated when exposed to a saturating concentration of recombinant IL-8 or CCL2 or to the co-addition of a sub-saturating concentration of both cytokines. Moreover, antibody blockade against IL-8 and/or CCL2 inhibited migration that could be restored by IF, indicating cytokine-independent mechanisms of migration induction. Importantly, we demonstrate the utility of an integrated in silico and 3D in vitro approach to aid the design of tumor-associated macrophage-based immunotherapeutic strategies.

Insight

Macrophages and interstitial flow (IF) have emerged as important characteristics of the complex tumor microenvironment (TME). However, little is understood about the interactions of these variables. Therefore, we developed an integrated mathematical–experimental approach to probe the interplay of tumor cells, macrophages, and IF. The experiments utilize a novel three-dimensional microfluidic in vitro model where tumor cells can be co-cultured with primary macrophages with IF present. Employing this platform and our mathematical model, we show how key tumor-secreted factors (TSF) and IF are integrated by macrophages, which consequently migrate with increased directedness and speed, thus enhancing potential interactions with cancer cells to support their invasiveness. Therefore, we deduce that IF, additionally or complementary to TSF, importantly drives macrophage migration in the TME.

INTRODUCTION

Interstitial flow (IF) is an important, yet underappreciated, biophysical force that drives cancer progression [1]. It is derived from an elevated interstitial fluid pressure (IFP) in the solid tumor (~10–40 mmHg) [2, 3], due to highly permeable tumor vessels and the lack of functional lymphatic vessels [4, 5]. This abnormal pressure results in a steep pressure gradient near the tumor margin with escape of interstitial fluid from the tumor mass into the surrounding tissues [6–8], where IFP then drops rapidly to normal tissue values (~0 mmHg) [4, 9]. Because this fluid contains tumor-secreted cytokines and growth factors and can influence tumor cell migration, IF essentially fuels tumor metastasis [9, 10].

Clinical data across different solid cancers have shown that higher IFP at the tumor site strongly correlates with poorer patient survival [11–14]. Accordingly, IFP has been viewed as a strong prognostic factor that is independent of other clinical parameters [11, 15], with ongoing effort to develop strategies to decrease IFP, and hence IF, in patients [16–21]. However, given the complexity of cancer pathology, current findings have only begun to explain the multiple interacting facets of IF’s role in cancer, including its regulation of pivotal immune cell players in the tumor microenvironment (TME). This scenario motivates the need for additional studies that investigate the role of IF on multiple cell types in the TME.

Macrophages are highly abundant at the tumor-stromal boundary [22–24], where there are high levels of IF [25, 26]. Interestingly, this is also where there are high rates of tumor cell invasion [25, 26]. Clinical and experimental evidence report that macrophages crucially support tumor metastasis [27], with a meta-analysis showing that over 80% of studies correlate poor patient outcomes and macrophage density [28]. Moreover, intravital imaging of fluorescently labeled cells in mammary tumors has shown that tumor cells and macrophages move concordantly [24]. Indeed, growing evidence suggests that macrophages could be importantly involved in IF-based tumor cell invasion [25, 29]. Therefore, interfering with the signaling pathways associated with IF, tumor cells and macrophages could potentially inhibit the pro-tumor function of macrophages and also tumor cell metastasis [30].

Macrophages remodel extracellular matrix (ECM) through matrix metalloproteinases (MMP), which degrade collagen and create tracks for tumor cells to migrate [31, 32]. Such tracks also enable macrophages to migrate toward and interact with other cells in the TME to support tumor progression, for example, by their contact-dependent support of the epithelial-to-mesenchymal transition (EMT) of tumor cell aggregates [33] or their contact with the endothelium to increase its permeability to intravasating tumor cells [34]. Therefore, macrophage migration in the TME is an important parameter that reflects their ability to support tumor cell invasion through the ECM in the process of metastasis [35]. Current understanding of macrophage migration has been confined to the regulation by biological cues in the TME, including tumor-secreted factors (TSF), which have been identified as key regulators of macrophage motility [36–40].

The study of cell migration requires suitable experimental models that allow cells to migrate with spatial and temporal freedom while allowing for real-time measurements. A classical setup is the transwell migration assay, where cell motility is assessed by the number of cells that migrate across a two-dimensional (2D) porous membrane between upper and lower chambers [41, 42]. While the use of such platforms contributes insight toward cell motility, they lack a 3D ECM and fail to accurately mimic the physiological setting [43, 44]. Specifically, recent studies have reported differences in protein expression when cells migrate through a 3D matrix compared to their migration on a 2D substrate [42, 44–46]. For example, focal adhesion kinase (FAK) is crucial for migration through a 3D matrix, but in 2D, FAK-null cells can compensate for migration defects by overexpressing other cell migration machineries [46]. Moreover, matrix degradation, an important factor in 3D migration, is not required for migration on a 2D surface. Indeed, there is evidence that 3D measurements of migration directedness (ability to maintain direction of motion) and speed do not correlate with migration in 2D [45]. Finally, these classical assays present end point readouts of the number of transmigrated cells, failing to capture the temporal dynamics of cell motility.

On the other hand, microfluidic models present suitable 3D environments for real-time measurements of migration directedness and speed. However, current microfluidic models of IF comprise a gel-based monoculture of cells including tumor cells [47, 48], fibroblasts [49, 50], or macrophages [51]. The most cellularly complex model has tumor cells seeded in a central microchannel with an additional endothelial monolayer in the adjacent microchannel [52]. Recently, Li et al. report evidence that IF increased the migration directedness and speed of mouse macrophages using a single-gel microfluidic platform [51]. However, there remain open questions such as how IF which specifically arises from tumor cells can dynamically modulate macrophage migration, and whether IF or TSF is the stronger determinant of macrophage migration behavior. To this end, the in silico modeling of in vitro data can yield quantitative insight into the biological signaling and biomechanics of macrophage migration in a 3D TME setting [53, 54].

The present work seeks to address the effect of tumor-derived IF and TSF on macrophage migration by developing a human-based microfluidic model comprising a co-culture of tumor cells and primary monocyte-derived macrophages, designed to impart the effect of tumor-derived IF and TSF on macrophages. Specifically, we will contribute insight toward the dynamic IF-associated interplay that exists between tumor cells and macrophages. Further, we will clarify if IF and TSF are functionally redundant or additive in regulating macrophage migration, thus identifying their relative importance as potential therapeutic targets. Moreover, we explore how our in vitro data contributes toward the development of a refined in silico signaling network model that associates TSF, IF, and the migration activity of macrophages.

MATERIALS AND METHODS

Generation and culture of GFP stable cell lines

A human pancreatic ductal adenocarcinoma (PDAC) cell line, Panc1 (ATCC® CRL-1469), and normal pancreatic epithelial cell line hTERT-HPNE (‘HPNE’) (ATCC® CRL-4023) were transfected to stably express green fluorescent protein (GFP). GFP gene was amplified from pGreenPuro shRNA Cloning and Expression Lentivector (CMV; System biosciences, SI505A-1) and sub-cloned into ITR-CAG-DEST-IRES-Neomycin-ITR plasmid (generous gift from Marc Supprian Schmidt). ITR-CAG-DEST-IRES-Neomycin-ITR (control plasmid) (Supplementary Fig. S1a) or ITR-CAG-GFP-IRES-Neomycin-ITR (GFP plasmid) (Supplementary Fig. S1b) was mixed with SB100x transposase (1:1 ratio), and the mixture was transiently transfected into the cell line using Lipofectamine 2000 (Thermo Fisher Scientific, 11668027). Three days post-transfection, transfected cells were selected with 300 μg/ml G418 for 10 days. To validate the stable and constitutive expression of GFP, selected cells were analyzed by flow cytometry. GFP-expressing Panc1 and HPNE were cultured in Iscove’s Modified Dulbecco’s Media (IMDM; GE Healthcare HyClone, SH30228.01) supplemented with 5% human serum (Innovative Research, IPLA-SER) and 1% 1X Penicillin–Streptomycin (hereafter referred to as ‘cIMDM’). Cells were maintained in a humidified CO₂ incubator at 37°C and 5% CO₂.

Multiplex array

Conditioned media were generated from either the 2D culture of Panc1 and HPNE cells using a previously described method [55] or the 3D culture of these cell lines. Briefly, in the 2D culture, 1 × 10⁶ cells were seeded in 30 ml of cIMDM in a T175 flask and allowed to grow to 70–80% confluency. Media were then removed from the flasks, centrifuged for 10 min at 15 000 rpm, sterile filtered (0.2 μm pore size), and stored at −20°C until use. For the 3D culture, cells were seeded at equal densities in the microfluidic device for at least 24 h, before collecting media from all media reservoirs of each device. Cell media were centrifuged at 14 000 rpm for 10 min at 4°C, and all supernatants were stored in −20°C until use. 2D and 3D culture media cytokines were, respectively, analyzed by the Proteome Profiler™ antibody array (R&D Systems) and the MILLIPLEX 38 Cytokine kit (Millipore, HCYTMAG-60K-PX38).

Isolation of monocytes and differentiation into macrophages

Blood samples and procedures used in this study have been approved by the Centralized Institutional Review Board, SingHealth (reference no: 2017/2512), and the Committee on the Use of Humans as Experimental Subjects (COUHES). All protocols are in accordance with The Code of Ethics of the World Medical Association. Written informed consent was given according to the principles expressed in the Declaration of Helsinki. Peripheral blood mononuclear cells (PBMCs) were isolated from whole blood of healthy donors by Ficoll–Paque (GE Healthcare, 17-1440-02) density gradient centrifugation, and monocytes were positively isolated using CD14 microbeads (Miltenyi Biotec, Auburn, CA). Monocytes were maintained in Petri dishes in cIMDM and 100 ng/ml recombinant human M-CSF (ImmunoTools, Friesoythe, Germany) over 7 days to generate macrophages. Cell viability was assessed by Trypan blue exclusion and was consistently > 90% viable.

Fabrication of microfluidic device

Microfluidic devices were fabricated following previously reported protocols [56, 57]. Polydimethylsiloxane (PDMS; Sylgard 184 silicone elastomer kit, Dow Corning, Midland, MI, USA) were fabricated by standard soft lithography methods from a patterned SU-8 silicon wafer. Silicone elastomer and curing agent were mixed at a 10:1 weight ratio, degassed in a desiccator, poured onto the photolithographically patterned SU-8 structures, and cured overnight at 37°C. Devices were cut from the PDMS replica, and inlet and outlet ports were created by biopsy punches before autoclave sterilization. After drying the devices overnight at 80°C, PDMS layers were plasma bonded to the glass cover slips to create channels of approximately 190 μm in height. Each device consists of four connected channels (4.36 mm in length), with two for injecting hydrogels (580 μm wide) and two for culture media (920 μm wide) (Fig. 1a). Each gel channel contains nine trapezoidal structures (base lengths of 290 μm and 120 μm, height of 140 μm) [33, 55, 56].

Figure 1.

(A) Design of microfluidic co-culture model of tumor cells (Panc1) and macrophages with the incorporation of interstitial flow (IF). Representative confocal image of cell-seeded gel channels at 0 h (B) with tumor cells or (C) without tumor cells.

Cell seeding

All channels were coated with 1 mg/ml poly-D-lysine (PDL) solution (Sigma-Aldrich, St. Louis, MO) to prevent the detachment of collagen gels from the channel walls and left at 80°C for at least 24 h to restore hydrophobicity [43]. GFP-Panc1 were trypsinized, counted, and resuspended in 2.5 mg/ml type I rat tail collagen gel (354236, Corning) solution. Macrophages were harvested by rinsing with D-PBS, incubating with PBS/EDTA (PBS; 2 mM EDTA; Axil Scientific, BUF-1052) for 10–15 min at 37°C, 5% CO₂, before adding cIMDM and gently scraping. Harvested macrophages were fluorescently stained with 2 μM CellTracker Orange, CMRA (Invitrogen), and resuspended separately in the same type of hydrogel. Cell seeding was performed using a protocol that was previously described [33, 55, 56]. Briefly, the GFP-Panc1 hydrogel suspension was injected into one gel channel and allowed to polymerize for 20 min in the incubator (37°C, 5% CO₂), followed by injection of the macrophage hydrogel suspension in the other gel channel and then gentle addition of cIMDM into the lateral fluidic channel adjacent to the GFP-Panc1 gel channel. The device was returned to the incubator for 40 min for the second injected hydrogel to polymerize before gentle addition of cIMDM to the media channel adjacent to the macrophage gel channel (Fig. 1b). In some devices, collagen hydrogel without GFP-Panc1 (herein referred to as ‘blank hydrogel’) was used as the first hydrogel being injected (Fig. 1c). Devices containing cells were left to stabilize overnight in the in-cubator.

3D assay and quantification of macrophage migration

After overnight incubation, the cell-containing PDMS chamber was sealed against another PDMS layer that contained a large media reservoir (Fig. 1a). To achieve a flow velocity of ~ 3 μm/s through the 3D collagen hydrogel, a media-height difference of 2.5 mm was established at the inlet ports connecting the media reservoir with the channels containing GFP-Panc1 or blank hydrogel. Through this setup, media flowed from the media reservoir, through the GFP-Panc1 cells (or blank hydrogel), and then finally to the macrophages. Darcy’s law was used to calculate the required media-height difference across the gel channels (refer to ‘Calculation and verification of interstitial flow’). In some devices, respective concentrations (ranging from 25 to 100 ng/ml) of recombinant human IL-8 (BioLegend, 715404) and/or recombinant human CCL2 (PeproTech, 300-04) reconstituted in cIMDM was added. In other devices, 0.4 μg/ml of anti-IL-8 antibody (R&D, MAB208) and/or 1 μg/ml of anti-CCL2 antibody (R&D, MAB279) was added.

Devices were transferred onto a confocal microscope (Olympus model FV1000) fit with a humidified environmental chamber, which maintained a temperature of 37°C and 5% CO₂. Macrophages were exposed for 24 h to the various stimuli, including IF, recombinant cytokines and anti-IL-8/anti-CCL2 antibodies, where their migration in 3D was tracked by time-lapse confocal microscopy, with 3D image stacks taken every 25 min at a 20× magnification (800 × 800 pixel density). As the cross-sectional area of the reservoirs was approximately 1500 times that of the hydrogel region, there was a negligible decrease in the media-height difference during the 24 h duration. IMARIS 9.2 was used to track and quantify the migration directedness and speed of macrophages in 3D and to produce the cell trajectory plots of macrophage migration.

Calculation and verification of interstitial flow

The hydraulic permeability, K, of the 2.5 mg/ml collagen gel used in this study was previously determined by Darcy’s law to be ~ 7 × 10⁻¹⁴ m² [51]. Darcy’s law was also used to determine the media-height difference that was required to establish a desirable IF velocity, v, through the microfluidic device, as represented by Equation (1):

(1)

where ρ is the density and μ is the viscosity of cIMDM media, W is the width of the chamber, and Δh is the initial media-height difference of the reservoir [58]. Based on the geometry of the total hydrogel matrix in the microfluidic device and the estimated hydraulic permeability, a media-height difference of 2.5 mm was needed to generate an IF velocity of approximately 3 μm/s in the hydrogel.

To quantify and confirm the velocity of IF through the hydrogel at the start and end of the IF treatment, fluorescence recovery after photobleaching (FRAP) was used following a previously reported protocol [59]. Here, 100 μg/ml of 70 kDa FITC-dextran in cIMDM was added, and a spot of 30 μm diameter of the hydrogel was bleached using the highest intensity of the laser, according to the microscope guidelines. After the bleaching step, time-lapse images in short intervals (~1.6 s) were recorded to monitor the recovery in fluorescence. Photobleaching was performed for the hydrogels in both gel microchannels. ImageJ and MATLAB were used to quantify the change in fluorescence after the bleaching step.

Signaling network model construction

A simplified version of the hypothesized signaling network model linking IL-8-based and CCL2-based signaling and IF-induced macrophage migration was constructed by analyzing literature-established signaling pathways associated with each of these extracellular stimuli. Relevant networks were analyzed for intersections (which indicate the presence of key signaling species), and using these intersections, these networks were combined into a single, unified signaling network. Our in vitro experimental data showed that similar trends are exhibited by both macrophage migration directedness and speed, suggesting the presence of a common regulator. Moreover, in the absence of a specific molecular output node in our in vitro data, we did not model complex downstream signaling and elected to keep the model as simple as possible. As such, we simplified this unified network by removing non-receptor, nonintersecting, intermediate reactions and unifying the various Rho GTPases that are regulated by the three extracellular stimuli, into a single ‘common regulator’ signaling node. Then, we combined the downstream signaling activity of Rho GTPases into a single regulatory node that regulated both migration directedness and speed.

Mathematical model development

A mathematical model was constructed from the aforementioned hypothesized signaling network model. Specifically, an ordinary differential equation (ODE) model tracked the concentration of each signaling element in its active form and its interactions with other signaling elements [60, 61]. The concentrations of activated receptors CXCR1/CXCR2 and CCR2 were defined in relation to the concentrations of their respective ligands IL-8 and CCL2 using steady-state approximations and the ligand-receptor dissociation constant (Equations [2 and 3]) [62]. The concentration of activated FAK in response to integrin-mediated, IF-induced signaling was calculated using a Hill function. Here, IF speed was correlated with the steady-state concentration of activated FAK, and constants were calculated to reproduce in vitro experimental observations (Equation [4]) [51]. Next, the concentration of active G proteins dissociating from G protein-coupled receptors CXCR1/CXCR2 and CCR2 in response to IL-8 and CCL2 binding, respectively, was calculated by integrating the two receptor signals in an additive manner through Hill functions with corresponding dissociation constants (Equation [6]). Then, we calculated the concentration of active common regulator (Equation [8]). Here, the concentrations of IL-8, FAK, and CCL2 additively contributed to common regulator activation through Hill functions with corresponding dissociation constants. Finally, migration directedness and speed were modeled as Hill functions that exhibit basal activity when no active common regulator is present and increase asymptotically to a maximum value as the concentration of active common regulator increases (Equations [9 and 10]). Table 1 defines the signaling species being tracked by the model.

Table 1.

Species variable abbreviations, definitions, initial steady-state values, and units.

Species	Abbreviation	Definition	Initial value	Units
S1	IL-8	Interleukin-8	9.01*	nM
S2	CCL2	C-C motif chemokine ligand 2	9.07*	nM
S3	IF	Interstitial flow	3000	nm/s
S4	CXCR1/2	C-X-C motif chemokine receptor 1 or 2; receptor for IL-8	0	nM
S5	CCR2	C-C chemokine receptor type 2; receptor for CCL2	0	nM
S6	FAK	Focal adhesion kinase; activated in response to interstitial flow	9.49	nM
S7	G proteins	Family of signaling G proteins (associated with G protein-coupled receptors CXCR1/2 and CCR2)	0	nM
S8	Common regulator	Downstream common regulator of migration directedness and speed. Potentially one or more Rho GTPases such as CDC42, Rac1, and/or RhoA	103	nM
MD	Directedness	Migration directedness relative to control	1.00	-
MS	Speed	Migration speed relative to control	1.00	-

^*Equivalent to 100 ng/ml.

The mathematical modeling framework is as follows (Equations [2–10]):

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

To simulate experiments involving the treatment of macrophages with TSF, or co-culture with cancer cells without IF, the following relationship was used to simulate TSF composition (Equation [11]):

(11)

where [IL-8]_TSF and r_TSF are free parameters fit to experimental data.

Furthermore, to simulate experiments where TSF-treated macrophages are exposed to anti-IL-8 and/or anti-CCL2 antibodies, the following functions were used to determine the uninhibited concentrations of each cytokine (Equations [12 and 13]):

(12)

(13)

Model parameter estimation

The mathematical model was implemented as a purpose-constructed code in Python 2.7 and solved at 50 000 time points over 48 h of simulated experimental time via the odeint solver found in the scipy.integrate module using the default settings. The model contained 36 parameters, 13 of which were assigned to experimentally derived values taken from the literature (Table 2), 2 of which were assigned based on manufacturer provided protocols for antibody blockade, and 2 of which were directly calculated from in vitro directedness and speed data. Here, the kinetics of each upstream interaction between IL-8, CCL2, and IF speed with downstream signaling elements of the model were taken from the literature. Also, initial conditions of each parameter were determined by running the model without the stimuli until it reached steady state. In addition, the total concentration of each intermediate signaling species (assumed here to be the total concentration of each species at steady state, including both its active and inactive forms) was assigned to a known benchmark value from the literature. The remaining 19 free parameters were fit to our in vitro experimental results using a gradient descent least-squares error minimization approach that minimized the error function (Equation [14]):

(14)

where and are the simulated migration directedness and speed for each stimulus, respectively, and and are the experimentally measured migration directedness and speed for each stimulus, respectively. Table 2 shows all model parameters, including those generated from the model fitting process. All free parameters were allowed to fit to any positive value, with the exception of δ, the fold increase in FAK activation associated with IF at a speed of S_3,data, which was constrained to within 50% of the in vitro experimentally observed value [48]. Determining the free parameter values by this approach allowed for an accurate fit that was able to capture the trends across all 58 experimental data points.

Table 2.

Parameter values used in simulations.

Parameter	Value	Units	Definition	Source
p4	4.27 × 10−5	1/s 1/nM	Activation rate constant for CXCR1/2 activating G proteins	Fit to in vitro experimental data
p5	1.28 × 10−4	1/s 1/nM	Activation rate constant for CCR2 activating G proteins	Fit to in vitro experimental data
p6	7.67 × 10−3	1/s 1/nM	Activation rate constant for G proteins activating common regulator	Fit to in vitro experimental data
p7	2.32 × 10−3	1/s 1/nM	Activation rate constant for active FAK activating common regulator	Fit to in vitro experimental data
k1	1.9	nM	Dissociation constant for IL-8 binding to CXCR1/2	[63]
k2	0.77	nM	Dissociation constant for CCL2 binding to CCR2	[64]
k4	410	nM	Apparent dissociation constant for active CXCR1/2 activating G proteins	Fit to in vitro experimental data
k5	937	nM	Apparent dissociation constant for active CCR2 activating G proteins	Fit to in vitro experimental data
k6	166	nM	Apparent dissociation constant for G proteins activating common regulator	Fit to in vitro experimental data
k7	175	nM	Apparent dissociation constant for active FAK activating common regulator	Fit to in vitro experimental data
n4	1.15	-	Hill coefficient for active CXCR1/2 activating G proteins	Fit to in vitro experimental data
n5	2.09	-	Hill coefficient for active CCR2 activating G proteins	Fit to in vitro experimental data
n6	5.60	-	Hill coefficient for G proteins activating common regulator	Fit to in vitro experimental data
n7	1.38	-	Hill coefficient for active FAK activating common regulator	Fit to in vitro experimental data
b3	9.49	nM	Basal concentration of active FAK	Fit to in vitro experimental data
S4,tot	500	nM	Total concentration of active and inactive CXCR1/2	[65]
S5,tot	500	nM	Total concentration of active and inactive CCR2	[65]
S6,tot	500	nM	Total concentration of active and inactive FAK	[65]
S7,tot	500	nM	Total concentration of active and inactive G proteins	[65]
S8,tot	500	nM	Total concentration of active and inactive common regulator	[65]
c7	1.56 × 10−4	1/s	Combined degradation and dilution rate for G proteins	[66]
c8	1.56 × 10−4	1/s	Combined degradation and dilution rate for common regulator	[66]
S3,data	3.00 × 103	nm/s	Interstitial flow (IF) speed associated with δ-fold increased FAK activation	[48]
δ	1.43	-	Fold increase in FAK activation associated with IF at S3,data nm/s	[48]
rS	3.25	-	Ratio between highest and lowest observed migration speed	Calculated from in vitro experimental data
kS	131	nM	Half maximum constant for common regulator-induced migration speed	Fit to in vitro experimental data
nS	8.74	-	Hill coefficient for common regulator-induced migration speed	Fit to in vitro experimental data
rD	2.95	-	Ratio between highest and lowest observed migration directedness	Calculated from in vitro experimental data
kD	114	nM	Half maximum constant for common regulator-induced migration directedness	Fit to in vitro experimental data
nD	10.9	-	Hill coefficient for common regulator-induced migration directedness	Fit to in vitro experimental data
[IL-8]TSF	1.12	nM	-	Fit to in vitro experimental data
rTSF	1.18	-	-	Fit to in vitro experimental data
αIL8	2.67	nM	Concentration of anti-IL-8 antibody in antibody blockade experiments	Reflective of in vitro experimental conditions
kα,IL8	0.888	-	Molar ratio of antibody to IL-8 required for 50% inhibition	Based on manufacturer supplied datasheet
αCCL2	6.67	nM	Concentration of anti-CCL2 antibody in antibody blockade experiments	Reflective of in vitro experimental conditions
kα,CCL2	1.32	-	Molar ratio of antibody to CCL2 required for 50% inhibition	Based on manufacturer supplied datasheet

All activation rate constants, dissociation constants, hill coefficients, and basal activation constants are numbered such that they correspond to different signaling pathway reactions. All total species concentrations and degradation rates are numbered such that they correspond to the species numbers detailed in Table 1.

Sensitivity analysis

Stimulus sensitivity analysis was used to quantify the effect of each extracellular stimulus on the concentration of active common regulator. Here, the elasticity of the concentration of active common regulator was computed for the concentration of each stimulus using the following function (Equation [15]):

(15)

where the denominator represents a 20% change in the stimulus under study (centered at the default stimulus value given in Table 1) and the numerator represents the percent change in the concentration of active common regulator.

An additional stimulus sensitivity analysis was used to quantify the effect of each extracellular stimulus on the quality of the model fit against the in vitro experimental data, as quantified by the coefficient of determination (R²) value. This was done in order to determine the effect of changing the magnitude of each extracellular stimulus on the migration speed and directedness magnitudes induced by each stimulus relative to one another. This could also be conceptualized as quantifying the influence of each extracellular stimulus on the trends within the data across all extracellular stimuli. Here, the model R² elasticity was computed for each stimulus using the following function (Equation [16]):

(16)

where the denominator represents a 20% change in the stimulus under study (centered at the default stimulus value given in Table 1) and the numerator represents the percent change in the R² value between the model outputs and all in vitro experimental directedness and speed data.

Parameter sensitivity analysis was used to quantify the effect of each model parameter on the concentration of active common regulator. Here, the elasticity of the concentration of active common regulator was computed for each parameter using the following function (Equation [17]):

(17)

where the denominator represents a 20% change in the parameter under study (centered at the default parameter value given in Table 2) and the numerator represents the percent change in the concentration of active common regulator.

Finally, an additional parameter sensitivity analysis was used to quantify the effect of each model parameter on the quality of the model fit against in vitro experimental data, as quantified by the R² value. This was done in order to determine the effect of changing the magnitude of each reaction parameter on the migration speed and directedness magnitudes induced by each stimulus relative to one another. This could also be conceptualized as quantifying the influence of each parameter on the trends within the data across all extracellular stimuli. Here, the model R² elasticity was computed for each parameter using the following function (Equation [18]):

(18)

where the denominator represents a 20% change in the parameter under study (centered at the default parameter value given in Table 2) and the numerator represents the percent change in the R² value between the model outputs and all in vitro experimental directedness and speed data.

Statistical analysis

Statistical analysis of experimental data was performed using GraphPad Prism 8.2 (GraphPad Software) considering at least two regions of interest (ROIs) in the hydrogel per device. For each in vitro experiment, the average migration directedness or speed of macrophages in each ROI (~150 macrophages per ROI) was used to generate a data point. To quantify the agreement between the in vitro experimental data and the output values of the mathematical model, the R² values were calculated for (1) directedness data only, (2) speed data only, and (3) all data together. At each data point, statistical analysis was performed to determine if the population mean predicted by the model would be likely to produce the in vitro experimental data. Data were plotted as the mean ± standard error of the mean (SEM), where n.s. represents not significant, ^* represents P ≤ 0.05, ^** represents P ≤ 0.01, ^*** represents P ≤ 0.001, and ^**** represents P ≤ 0.0001. Statistical significance was determined using a Student’s t-test or, where appropriate, a one-way ANOVA with Holm–Sidak’s multiple comparison test. Only a P-value or adjusted P-value of ≤ 0.05 was taken as evidence of statistical significance.

RESULTS

Generation of an in vitro 3D co-culture model with tumor interstitial flow

Based on previously optimized protocols [51, 56], we designed a 3D in vitro microfluidic model of tumor IF to specifically study macrophage migration. In this platform, we cultured tumor cells in one channel and macrophages in the adjacent channel, thus allowing us to simulate and study the impact of tumor-originating IF on macrophage migration without the influence of physical cell contact (Fig. 1). In our setup, we confirmed that the velocity of IF through both gel channels was within the range reported for tumor tissues [25, 26]. FRAP analysis revealed a mean IF velocity of 3.9 ± 0.7 μm/s at the beginning of IF exposure and 4.4 ± 0.5 μm/s after 24 h (P > 0.05) (Supplementary Fig. S2). These results correspond with the height difference of 2.5 mm between the two media channels, which stayed relatively unchanged over the 24 h. Thus, it could be assumed that IF velocity was relatively constant throughout the duration of IF treatment.

Similar effect on macrophage migration by tumor-secreted factors and interstitial flow

In our first set of in vitro experiments, we observed that compared to the control macrophage monoculture without IF (Fig. 2a,i), 24 h of IF exposure appeared to increase macrophage motility (Fig. 2a,ii) as shown by the relatively increased spread of their x–y migration path trajectories. Interestingly, it appeared that the presence of tumor cells alone without IF (TSF) also increased the spread of migration path trajectories relatively (Fig. 2a,iii), suggesting that either IF or TSF alone could promote increased macrophage motility. Interestingly, combining IF and TSF (at the cell concentrations tested in Fig. 2) did not have an additive effect on the spread of macrophage migration (Fig. 2a,iv).

Figure 2.

(A) X–Y path trajectories of macrophage migration in the (i) control (Cntrl) monoculture of macrophages without interstitial flow (IF) or exposed to (ii) only IF, (iii) only tumor cells, tumor-secreted factors (TSF), or (iv) both IF and TSF. (B) Quantification method of macrophage migration directedness and speed. (C) Directedness and (D) speed of macrophage migration under the different conditions tested. Data are shown as the mean ± SEM (n = 3), where statistical significance was determined using a one-way ANOVA with Holm–Sidak’s multiple comparisons test with ^*P ≤ 0.05.

To ascertain the effect of each stimulus on macrophage motility, we quantified the directedness and speed of macrophage migration during the period of IF exposure following a previously reported approach (Fig. 2b) [36, 51]. Consistent with the observed increase in x–y migration path trajectories, IF, TSF, or the combination of both could substantially increase the directedness (Fig. 2c) and speed of macrophage migration (Fig. 2d). Compared to the untreated control where the directedness and speed of macrophage migration were D = 0.31 ± 0.04 and S = 8.3 ± 1.2 μm/h, respectively, a 2-fold increase in directedness and 3-fold increase in speed were observed for the conditions of IF (D = 0.57 ± 0.03, S = 19 ± 3 μm/h), TSF (D = 0.63 ± 0.04, S = 23 ± 3 μm/h), and the IF–TSF combination (D = 0.62 ± 0.06, S = 24 ± 3 μm/h), and these values are within the range reported in previous in vitro investigations [51].

Hypothesized signaling pathway linking key tumor-secreted factors and Rho GTPase-regulated migration

A multiplex cytokine array of culture supernatant of the tumor cell line (Panc1) and a normal control cell line (HPNE) was conducted to identify the main cytokines within TSF that drove the migration behavior that we observed in vitro of macrophages. Our analysis on 2D cell culture-derived supernatant revealed several cytokines secreted at higher levels by the Panc1 compared to the HPNE cell line (Fig. 3a). A review of known signaling networks revealed that the upregulation of CCL2 and IL-8 is highly associated with the regulation of cell migration [67, 68]. We also confirmed that Panc1 secreted higher levels of both cytokines than HPNE in the 3D in vitro culture environment (Fig. 3b), suggesting that IL-8 and CCL2 could mainly drive the migration we observed of macrophages in the 3D in vitro system.

Figure 3.

Multiplex array of cytokines in culture supernatant derived (A) from cells grown as a 2D monolayer using the Proteome Profiler^TM antibody array (R&D Systems) or (B) from cells grown in a 3D matrix environment using the Milliplex 38 Cytokine kit (Millipore). Data are shown as the mean ± SEM (n = 3), where statistical significance was determined using a Student’s t-test with ^*P ≤ 0.05 and ^****P ≤ 0.0001.

Mechanistically, IL-8 [67, 69, 70] and CCL2 [39, 68, 71–73] bind to G protein-coupled receptors CXCR1/CXCR2 and CCR2, respectively, resulting in the activation and subsequent dissociation of an associated G protein [74]. This releases the α subunit of the G protein to activate further intracellular signaling that results in the posttranslational regulation of regulatory proteins such as small monomeric GTPases of the Rho-family, leading to polymerization and retraction of the actin cytoskeleton, which are important processes for cells to migrate. Additionally, our in vitro experimental data support previous studies that have demonstrated a synergistic integration between these receptors, whereby downstream signals are significantly greater in response to the activation of both receptors than either receptor alone [75]. This synergy has been shown to depend on the activation of both receptors, suggesting that synergy is the result of intracellular signaling, as opposed to extracellular cytokine interactions or receptor–receptor associations [75]. Moreover, even in the presence of both receptors, certain cell types fail to demonstrate this synergy, suggesting this behavior arises from a characteristic intracellular signaling motif or protein that is unique to certain cell types such as macrophages [76]. G proteins represent a common element in the downstream signaling networks associated with both receptors [69, 73] and are upstream of migration-regulating Rho GTPases and extracellular signal-regulated kinases (ERK) (which also exhibit a synergistic activation in response to the activation of both receptors) [75]. Thus, we hypothesized that a subset of G proteins may represent the integration point and the source of the synergy between these signaling pathways. In addition, IF-modulated signaling, as mediated by integrin-β2 and FAK, is known to drive the activation and downstream migratory activity associated with Rho GTPases [51, 77]. Finally, because our in vitro experimental data show that IF and TSF induced a similar increase in directedness and speed, we hypothesized that IL-8, CCL2, and IF regulate one or more of the relevant Rho GTPases, namely, CDC42, Rac1, and/or RhoA [38–40].

Notably, the purpose of our model is to infer the logical structure of the network that integrates multiple molecular (IL-8 and CCL2) and mechanical (IF) stimuli, but not the intricate details of interactions associated with the downstream Rho GTPases. For this reason, we model the Rho GTPases collectively through a single representative concentration and hereafter denote this group of signaling species collectively as ‘common regulator’. Also, as downstream signaling (connecting Rho GTPase activity to migration-related processes) becomes increasingly complex, we recognize that there is no need to model all theoretical details of GTPase signaling. Moreover, the similar trends exhibited by both directedness and speed in response to all tested stimuli could be explained simply by a common regulator, as opposed to more complex interactions between largely independent signaling pathways. Thus, we depicted directedness and speed as phenomena that are indirectly induced by this common regulator, with intermediate signaling described by respective response functions that depend on the concentration of active common regulator. These considerations led to our proposed signaling network model (Fig. 4) [37].

Figure 4.

Hypothesized signaling model showing how signals associated with IL-8, CCL2, and interstitial flow (IF) activate a common regulator, both individually and in combination, to regulate macrophage migration directedness and speed. The input stimuli (IL-8, CCL2 and IF), associated cytokine receptors (CXCR1/2 and CCR2), and intermediary signaling species (S1–S8), including focal adhesion kinase (FAK) and heterotrimeric small G proteins, G(α, β, γ), are identified by their respective abbreviations and species variables (Table 1 and Equations [2–10] in section ‘Mathematical model development’). These elements contribute toward interconnected signaling pathway reactions (reaction numbers R1–R7).

Effect of varying IL-8, CCL2, and/or interstitial flow on macrophage migration

A second set of in vitro experiments was conducted to confirm the central roles of IL-8 and CCL2 proposed in the signaling network model. Compared to the non-treated control, where macrophage migration directedness and speed were D = 0.35 ± 0.06 and S = 8.4 ± 1.1 μm/h, respectively, the exogenous addition of saturating concentrations (100 ng/mL) of only IL-8 (D = 0.56 ± 0.03, S = 20 ± 2 μm/h) or only CCL2 (D = 0.60 ± 0.07, S = 22 ± 4 μm/h) to a macrophage monoculture substantially increased migration directedness and speed (Fig. 5a). These increases were comparable to those obtained by exposing the macrophage monoculture to only IF (D = 0.61 ± 0.05, S = 23 ± 4 μm/h). Moreover, simultaneously exposing macrophages to IF together with either IL-8 (D = 0.59 ± 0.01, S = 19 ± 4 μm/h) or CCL2 (D = 0.60 ± 0.08, S = 22 ± 3 μm/h) did not further increase macrophage migration (Fig. 5a), supporting the notion that IF and TSF can commonly regulate macrophage migration behavior.

Figure 5.

Directedness (top panel) and speed (bottom panel) of macrophage migration with the exogenous addition of a (A) saturating concentration (100 ng/ml) of IL-8 or CCL2 to a macrophage monoculture in the presence or absence of IF or (B) sub-saturating concentration (25 ng/ml) of IL-8 and/or CCL2 to a macrophage monoculture or the addition of (C) blocking antibodies against IL-8 and/or CCL2 to a macrophage-tumor cell co-culture in the presence or absence of IF. Data are shown as the mean ± SEM (n ≥ 3), where statistical significance was determined using a one-way ANOVA with Holm–Sidak’s multiple comparisons test with ^*P ≤ 0.05, ^**P ≤ 0.01, and ^***P ≤ 0.001. (Cntrl: control, IF: interstitial flow, Sub.: sub-saturating, Sub. Both: combined addition of sub-saturating concentrations of IL-8 and CCL2, TSF: tumor-secreted factors, αComb.: combined blockade of IL-8 and CCL2).

Next, macrophages were exposed to sub-saturating concentrations of IL-8 and/or CCL2 to test if the same extent of increase in directedness and speed would be achieved as seen with either (1) a saturating concentration of individual cytokines or (2) the 3D co-culture of macrophages and tumor cells (TSF). Sub-saturating concentrations of 25 ng/ml of IL-8 and 25 ng/ml of CCL2 were identified based on prior titration experiments (Supplementary Fig. S3a and b). While exposure to the sub-saturating concentration of only IL-8 (D = 0.34 ± 0.03, S = 9.9 ± 1.3 μm/h) or only CCL2 (D = 0.35 ± 0.08, S = 11 ± 2 μm/h) did not result in an observable increase in directedness and speed, the combined exposure to sub-saturating concentrations of both cytokines promoted a comparable increase in directedness and speed (D = 0.54 ± 0.09, S = 21 ± 3 μm/h) to the TSF condition (D = 0.6 ± 0.1, S = 22 ± 2 μm/h) (Fig. 5b). Importantly, the data suggest a synergistic integration of the intracellular signals associated with these two cytokines.

Finally, the introduction of 0.4 μg/ml of anti-IL-8 and 1 μg/ml of anti-CCL2 blocking antibodies could inhibit the TSF-mediated increase in migration directedness and speed (Fig. 5c). Compared to the co-culture condition (TSF) (D = 0.56 ± 0.10, S = 25 ± 2 μm/h), both directedness and speed were substantially decreased upon treatment with anti-IL-8 (D = 0.35 ± 0.07, S = 13.0 ± 0.3 μm/h), anti-CCL2 (D = 0.33 ± 0.06, S = 13 ± 1 μm/h), or combined blockade of both cytokines (D = 0.27 ± 0.02, S = 11 ± 1 μm/h). Interestingly, IF could restore migration back to a level that was comparable to the TSF condition (D = 0.47 ± 0.09, S = 21 ± 2 μm/h) despite combined antibody blockade of IL-8 and CCL2.

Modeled signaling network captures fundamental migration behaviors

A mathematical model was developed based on the hypothesized signaling network (Fig. 4) using Hill functions: (1) to relate the concentration of active signaling proteins with the rate of activation of their downstream targets while capturing various nonlinear signaling behaviors of the system that are not explicitly modeled (Supplementary Fig. S4) and (2) to determine the steady-state concentrations of bound, active cytokine receptors using dissociation constants from the literature [60, 61]. Here, an ODE model tracked the concentration of each signaling element in its active form and its interactions with other signaling elements. The mathematical model exhibited similar trends between extracellular stimuli as those observed in in vitro measurements of migration directedness and speed (Fig. 6a–c). Specifically, the addition of individual or combined stimuli increased directedness and speed to approximately its maximum value, similar to in vitro observations. Also, the mathematical model results exhibited similar trends as in vitro experimentally observed migration responses to sub-saturating concentrations of IL-8 and/or CCL2 (Fig. 6b), to the antibody blockade of IL-8 and/or CCL2 when tumor cells were present (Fig. 6c), and to the titration of either cytokine concentration in the absence of IF (Supplementary Fig. S3c and d). Quantifying this model agreement across all data points yields a mean R² value of 0.71 for all directedness data, 0.92 for all speed data, and 0.85 for all directedness and speed data taken together. Therefore, our model could successfully capture 85% of the variation in the in vitro experimental data.

Figure 6.

Comparison between in vitro experimental data (white) and model simulations (grey) of normalized macrophage migration directedness (top panel) and speed (bottom panel) with the exogenous addition of a (A) saturating concentration (100 ng/ml) of IL-8 or CCL2 to a macrophage monoculture in the presence or absence of IF or (B) sub-saturating concentration (25 ng/ml) of IL-8 and/or CCL2 to a macrophage monoculture or the addition of (C) blocking antibodies against IL-8 and/or CCL2 to a macrophage-tumor cell co-culture in the presence or absence of IF (100% antibody blockade of cytokines assumed). Data are shown as the mean ± SEM (n ≥ 3). The coefficient of determination (R²) values was used to quantify the agreement between the simulated data and in vitro experimental data. (Cntrl: control, IF: interstitial flow, Sub.: sub-saturating, Sub. Both: combined addition of sub-saturating concentrations of IL-8 and CCL2, TSF: tumor-secreted factors, αComb.: combined blockade of IL-8 and CCL2).

Sensitivity analysis reveals most influential stimuli and parameters

Sensitivity analyses were conducted to identify the most influential extracellular stimuli and reaction parameters that impacted macrophage migration speed and directedness. Specifically, they determined the influence of changing the magnitudes of different stimuli and reaction parameters on the magnitude of the migration speed and directedness response. The analyses also determined the influence of these changes on the measurements of the speed and directedness response to each extracellular stimulus relative to one another.

First, we performed a stimulus sensitivity analysis to quantify the relative influence of each modeled stimulus on the concentration of active common regulator (Equation [15]) (Fig. 7a). Because directedness and speed were both regulated by the common regulator, these analyses captured the influence of each stimulus on both types of migration behaviors. IF had the greatest influence on the concentration of active common regulator, with approximately 1.5 times the influence of IL-8 and approximately 7 times that of CCL2.

Figure 7.

Sensitivity analysis that quantifies most influential stimuli and parameters on migration directedness and speed. The analysis considered (A) common regulator activation elasticity (Equation [15]) or (B) coefficient of determination (R²) elasticity (Equation [16]) in response to varying the magnitude of each extracellular stimulus. Also considered was (C) common regulator activation elasticity (Equation [17]) or (D) R² elasticity (Equation [18]) in response to varying the magnitude of each parameter. The denominators Δ%X and Δ%P, respectively, represent a 20% change in the stimulus or the parameter under study. The numerator Δ% [Common Reg.] and Δ%R², respectively, represent the resulting percent change in concentration of active common regulator or the R² value between the model simulations and the in vitro experimental data. (A–C) are plotted on a linear x-axis. (D) is plotted on a base-10 logarithmic x-axis.

Then, a stimulus sensitivity analysis focusing on the R² value was conducted to quantify the effect of varying the magnitude of each stimulus on the degree of agreement between the model and in vitro experimental data (Equation [16]) (Fig. 7b). This was done in order to determine the influence of each stimulus on the trends in directedness and speed across different stimuli as opposed to the concentration of active common regulator (which determines the magnitudes of directedness and speed). The influence of CCL2 on the R² value was over four times that of IF, which itself was slightly greater than that of IL-8. This analysis suggests that while IF had the greatest influence on the concentration of active common regulator, CCL2 had the dominant influence on the trends in directedness and speed across different stimuli. Taken together, the considerable difference in the influence of the three modeled extracellular stimuli suggests that each plays a different role in the regulation of the downstream directedness and speed signals.

Focusing on the kinetics of individual reactions, a parameter sensitivity analysis was conducted to analyze how a change in a parameter affected the concentration of active common regulator (Equation [17]) (Fig. 7c). Additionally, parameters were classified according to their associated signaling protein or motif to assess the influence of reactions associated with each network element on the overall downstream effect. Results revealed that parameters associated with common regulator and G protein activation and turnover were in general the most influential. Among G protein-associated parameters, those governing CCL2-induced G protein activation (k₅ and n₅) were particularly influential. Other highly influential parameters included S_5,tot, which dictates the total concentration of CCL2 receptor, CCR2, and two parameters associated with the common regulator activation in response to CCL2 signaling (k₆ and n₆), which were the first and third most influential parameters, respectively. Overall, this analysis suggests an important role for G protein-mediated signals, especially those driven by CCL2 signaling, in the regulation of the common regulator and thus migration directedness and speed.

A second parameter sensitivity analysis was conducted to quantify how varying the magnitude of each parameter changed the R² value between the in vitro experimental data and model outputs (Equation [18]) (Fig. 7d). This analysis sought to determine the influence of each parameter on the trends in directedness and speed across different stimuli as opposed to the concentration of active common regulator. Again, parameters were classified according to their associated signaling protein or motif. The most influential parameter was n₇, the Hill coefficient associated with FAK-induced common regulator activation. Other parameters associated with common regulator activation and turnover were also among the most influential, including the second most influential parameter S_8,tot, the total concentration of common regulator. Parameters associated with G protein activation and turnover were additional influential parameters, including S_7,tot, the total concentration of G proteins, and c₇, the combined degradation and dilution rate constant for G proteins. Notably, the third and fourth most influential parameters on the R² value were k_S and r_S, both of which govern the speed response to common regulator activity. In contrast, among the least influential parameters were those associated with the directedness response to common regulator activity. The disparate influence between migration speed and directedness on the R² value suggests that trends in speed across different environmental conditions are more sensitive to changes in speed regulation than are trends in directedness sensitive to changes in directedness regulation. Furthermore, this disparate influence between speed- and directedness-associated parameters suggests that migration directedness is more directly driven by the concentration of active common regulator. On the other hand, migration speed, although driven by the concentration of active common regulator, is governed by a more nonlinear processing of that signal. Overall, these analyses suggest that common regulator and G protein activation and turnover play a dominant role in determining the trends across different stimuli and thus the agreement between in vitro experimental data and the simulated cell migration behaviors based on the model. Furthermore, the analyses suggest that although speed and directedness are regulated by the concentration of active common regulator, these exhibit very different responses to that signal.

DISCUSSION

IF is an important tumor-associated biophysical factor that contributes toward cancer progression and poor patient survival [1, 11–14]. Recent evidence suggests that IF also promotes the pro-tumor M2-polarization and migration activity of macrophages [51]. Moreover, clinical data demonstrate that macrophage density strongly correlates with increased metastasis [27]. Such findings suggest a plausible link between IF, macrophage activity (including their migration), and cancer metastasis, a research area that has not been widely studied [27]. In addition, macrophage migration is driven by tumor-secreted cytokines [36–40], which suggests that IF could act jointly with biochemical cues to affect macrophage migration. In this study, we demonstrate, for the first time, that IF can act in concert with tumor-secreted cytokines or factors (TSF) to regulate macrophage migration through a 3D in vitro TME-related ECM.

Previously, Li et al. observed that IF-exposed mouse macrophages migrated faster than non-treated control macrophages [51]. Following their work, we were interested to explore the results generated using a co-culture setup of tumor cells and human primary macrophages, which more closely resemble the dynamic exchange between these cell types in the in vivo human TME. Using a two-gel channel setup with tumor cells and macrophages in co-culture in adjacent but separate channels, we could delineate between the effects of TSF and tumor-originating IF on macrophage migration. We observed that IF-exposed macrophages migrated faster and with increased directedness than non-treated controls, which agrees with Li et al.’s work. To our knowledge, our model is the first co-culture system that investigates the role of tumor IF on immune cell migration.

The Panc1 cell line was used to create the in vitro co-culture IF system. Panc1 originates from PDAC, which clinically represents one of the most malignant of cancers with one of the highest death rates [78, 79]. PDAC metastasis correlates with a high macrophage infiltrate [55, 80–84]. There are also numerous reports of cytokines underlying PDAC’s aggressive biology [85–88]. Therefore, PDAC seemed an appropriate cancer-immune model for investigating the effect of macrophage migration in response to PDAC-specific TSF, where the effect of IF can additionally be assessed. Also, our study integrated in silico and in vitro methods, an approach that has been highly effective in deriving insight into cell migration mechanisms [89–92]. Specifically, we demonstrated that by simulating in vitro conditions, an in silico signaling network model could be obtained associating key TSF (specifically IL-8 and CCL2), IF, and macrophage migration. In turn, the in silico model predictions were confirmed in vitro by adding different concentrations of exogenous IL-8/CCL2 or blocking antibodies against these cytokines and evaluating macrophage migration.

In our study, we first observed that the exposure of macrophages to IF or TSF induced a comparable increase in their migration directedness and speed. Interestingly, the non-additive effect of combining IF and TSF suggests that both IF and TSF could commonly regulate downstream macrophage migration when these stimuli are at saturating levels. Then, through a multiplex cytokine array of tumor-conditioned media, we identified IL-8 and CCL2 as the most probable cytokines driving the migration activity that we observed in the 3D in vitro system. In PDAC, acquisition of IL-8 and its receptors CXCR1 and CXCR2 on tumor cells [93, 94] and macrophages [95, 96] correlates with tumor invasion [97–99] and the metastatic potential of solid tumors in murine models [100–105] and patients [106, 107]. Similar to IL-8, the secretion of CCL2 and macrophage expression of its receptor CCR2 has been observed in the tumor tissues of patients with advanced metastasis [108–114]. Moreover, CCR2 blockade in a PDAC mouse model could deplete macrophages from the primary tumor to reduce metastasis [115]. Therefore, we focused on IL-8 and CCL2 in our study by virtue of their important role in regulating macrophage migration and PDAC metastasis. Notably, because IL-8/CCL2 is also implicated in the biology of other cancer types [42, 116, 117], our present findings can also be generalized to other cancers.

To understand the migration mechanism underlying our in vitro observations, we developed an in silico signaling network model to associate IL-8, CCL2, IF, and macrophage migration. To develop this model, we first referenced key literature describing the intracellular signaling pathways associated with IL-8 and CCL2 [38–40] and studies concerning IF-induced cell migration mechanisms based on these cytokines [51, 77, 118]. Our findings show that IL-8 [67, 69, 70] and CCL2 [73, 119] activate signaling that results in the posttranslational regulation of small monomeric GTPases of the Rho-family, leading to macrophage migration through the polymerization and retraction of the actin cytoskeleton. Specifically, in CCL2 signaling, extracellular chemokine CCL2 binds to and activates the chemokine receptor CCR2 expressed on the cell membranes of macrophages. Subsequently, the C-terminal intracellular domain of CCR2 activates intracellular signaling proteins, including phosphatidylinositol-3-kinase (PI3K), which eventually results in the activation of various Rho GTPases, in particular Rac, regulating cytoskeletal reorganization and cell migration [39, 68, 71, 72, 119]. In the case of IL-8 signaling, extracellular chemokine IL-8 binds to and activates receptor CXCR1/2, activating heterotrimeric small G proteins, G(α, β, γ), which then promote the activation of Rho GTPases. Notably, another signaling activity downstream of CXCR1/2 and G(α, β, γ) also activates PI3K and FAK.

In addition, IF triggers a process known as outside-in signaling where it engages multiple extracellular signals to activate cell membrane-bound integrins that then initiate intracellular cytoplasmic signaling [118]. These extracellular signals include the binding of integrins to respective ligands in the ECM, and various mechanical forces originating from IF including fluid shear stresses. Specifically, each stimulus induces a conformational change in integrin, activating the cytoplasmic signaling element of the protein and allowing it to interact with other signaling molecules involved in intracellular signaling cascades [118]. Additionally, the activation of integrin activates FAK and Src, stimulating Rho GTPases, which drive macrophage cytoskeletal reorganization and migration [51, 77]. Based on these findings, we hypothesized that IL-8, CCL2, and IF commonly regulate a group of Rho GTPases, including CDC42, Rac1, and/or RhoA [38–40], and this regulates macrophage migration. Additionally, the similar trends exhibited by both directedness and speed in response to all tested stimuli could be explained simply by a common regulator, as opposed to more complex interactions between largely independent signaling pathways. Finally, any attempt to fully model the highly complex signaling associated with migration regulation (that is downstream of this common signaling point) might greatly complicate the model with no added insight about how these signals are integrated. Thus, we depicted directedness and speed as phenomena indirectly induced by this common regulator, with intermediate signaling described by respective response functions that depend on the concentration of active common regulator.

To gain additional insight from our modeling framework, we conducted a number of simulations and model analyses. We first compared the model results to the trends of directedness and speed that we observed in vitro in response to the exposure to various combinations of IL-8, CCL2, and IF in order to determine the level of agreement between the modeled and experimental results. Quantifying this agreement by calculating the R² value across all modeled directedness and speed data, we determined that the model successfully accounts for over 85% of the variation in the experimental data. In line with in vitro experimentally observed macrophage migration behaviors, our model also displayed an OR gatelike behavior, where the exposure to a single stimulus (of biologically consistent magnitude) results in maximum common regulator activation. We highlight that such behavior is essential for integrating multiple inputs to produce a stable output regardless of input number. It is also an important, though conditional, example of redundant signaling where multiple signaling pathways lead to the same downstream effect.

Although TSF contains cytokines in addition to IL-8 and CCL2, the connections between the IL-8, CCL2, and IF-induced, integrin-β2-mediated signaling appear to suitably explain the in vitro experimentally observed macrophage migration. The relatively dominant role of IL-8 and CCL2 is reflected in a second set of experimental data where in vitro antibody blockade of IL-8 and/or CCL2 substantially inhibited the TSF-mediated increase in migration. Moreover, the simultaneous exposure of macrophages to sub-saturating concentrations of both IL-8 and CCL2 was able to achieve a similar effect on migration directedness and speed as their exposure to only TSF. Of note, we recognize that IF and TSF do not appear to act additively in the tumor cell-macrophage co-culture setup where cytokines are likely to be at saturating levels (confirmed by the similar increase in directedness/speed between the TSF condition and concentration of 100 ng/mL IL8 or CCL2 that was used to intentionally achieve saturation, Supplementary Fig. S3). Instead, the increase in directedness/speed with either (1) a combination of IL-8 and CCL2 with each cytokine at a sub-saturating level (25 ng/mL) or (2) sub-saturating level of either cytokine with IF suggests that synergies are possible at non-saturating cytokine concentrations. Such synergies have been previously demonstrated experimentally for macrophages and have been determined to depend on the unimpaired activity of both CXCR1/2 and CCR2 receptors, suggesting the intracellular integration of both cytokine signals as the primary synergistic mechanism [75].

A comparison of model predictions and in vitro data of these antibody blockade and sub-saturating concentration experiments further confirms our network architecture and kinetics assumptions. First, consistent with experiments, the behavior with saturating cytokine concentrations was not observed in response to diminished concentrations. Furthermore, by accurately capturing the signaling instigated by intermediate and sub-saturating cytokine concentrations, our model showed that it is not a simple all-or-nothing OR-gate, but a nuanced model that can capture the response across a gradient of stimuli. Second, the model produced simulated migration behaviors that were consistent with the in vitro antibody blockade of IL-8 and/or CCL2, reinforcing its capability to simulate experimentally relevant phenomena and capture intermediate signaling with diminished cytokine concentrations (as quantified by the R² values between modeled and in vitro experimental data).

We then conducted a number of sensitivity analyses to determine the most influential aspects of the network on the network response magnitude and the data trends. Stimulus sensitivity analysis revealed that IF was more influential than either cytokine on the concentration of active common regulator, whereas CCL2 was the most influential extracellular stimulus on the directedness and speed trends between various extracellular stimuli (as quantified by the R² values between modeled and in vitro experimental data). Parameter sensitivity analysis then revealed that reactions associated with common regulator and G protein activation and turnover were the most influential on the resulting concentration of active common regulator as well as the trends between various extracellular stimuli (quantified by the R² values between modeled and in vitro experimental data). Reactions associated with CCL2 signaling were also shown to be among the most influential on the resulting concentration of active common regulator. Additionally, parameters associated with the migration speed response to the concentration of active common regulator were very influential on the trends between stimuli, whereas parameters associated with the migration directedness response were not. This suggests a more nonlinear processing of common regulator signals in the regulation of migration speed than of directedness. Notably, although the magnitude of IF velocity has significant influence on the concentration of active common regulator, the parameters associated with IF-induced signaling were not among the most influential parameters on the concentration of active common regulator.

Importantly, our findings substantiate the idea that IF contributes to cancer invasiveness through enhancing macrophage migration. Indeed, as macrophages would have a heightened capacity to migrate through the 3D ECM, there would be increased likelihood for them to interact with and hence support cancer cell migration in the process of metastasis. The supportive function of macrophages toward cancer metastasis was previously demonstrated, where media from tumor-conditioned macrophages increased the expression of EMT genes in a low EMT-score tumor cell line [55]. Moreover, media conditioned from IF-exposed macrophages could increase the speed of cancer cell migration through a 3D matrix [51], suggesting that IF could support the capability of macrophages to promote tumor cell invasion. These findings support the view that macrophages play a pivotal intermediary role between the stimulus of IF and the output of cancer cell invasion through 3D ECM. Notably, other stromal cells in the TME may also respond to IF and further influence macrophage and/or cancer cell migration. For example, cancer-associated fibroblasts (CAFs) can secrete ECM to remodel the TME matrix, and this can influence cell migration in the TME [120]. Future studies could therefore incorporate other TME-related cells, such as CAFs, to evaluate their contribution to the relationship between IF and the metastasis process.

Our model was established using cancer cell lines and macrophages derived from the in vitro differentiation of blood-isolated monocytes. By incorporating patient-derived tumor explants and autologous macrophages, our platform could potentially facilitate high-throughput preclinical screening of therapies for personalized treatment. For example, a preclinical screen can be performed of single or combined antibody blockade against CCL2, IL-8, and/or β-integrin. Then, the patient-specific response to these interventions can be quantified through measuring macrophage migration across the different treatments. As such, our work potentially forms the basis for developing a companion diagnostic that comes with a biophysical component such as IF for identifying patient responders. In addition, as IF presents a physical barrier to the effective penetration of drugs into deeper regions of the TME, our model could be used to screen and guide the design of therapeutics to optimize their transport efficiency.

Notably, there are some challenges that arise in the implementation of a patient-derived approach, including the optimization of cell culture media for culturing multiple cell types and the fine tuning of the gel matrix composition. However, unlike murine models, microfluidic systems allow for the precise control of spatial, pressure, and chemical gradients that can be tailored to the specific application [121, 122]. Moreover, although a microfluidic model system may not fully recapitulate human in vivo dynamics, it can allow for the creation of a 3D patient-specific environment that is closer to human in vivo settings than 2D in vitro models. Microfluidic-based screening is also more rapid and less costly compared to utilizing humanized murine models [121, 122].

Therefore, our work presents an integrated in silico-3D in vitro approach to evaluate the effect of IF and TSF on macrophage migration. Here, we developed a signaling network model identifying key stimuli and intermediary proteins that drive macrophage migration, thus identifying potential therapeutic targets for inhibiting macrophage migration (which evidently associates with their capability to support cancer cell invasion). Importantly, this work contributes toward an improved understanding of the signaling mechanism associating IF, macrophage motility, and cancer metastasis, an area that should be studied more extensively to improve cancer treatment.

Funding Support

This work was supported by the National Research Foundation (NRF), Prime Minister’s Office, Singapore, under its CREATE program, SMART BioSystems, and Micromechanics (BioSyM) IRG [to S.L and R.K.], a core grant to Singapore Immunology Network (SIgN) from Agency for Science, Technology and Research (A^*STAR) [to S.L., A.T., D.K., W.S.C. and G.A.], the Biomedical Research Council (BMRC) [IAF 311006 and BMRC transition funds #H16/99/b0/011 to SIgN Immunomonitoring platform], the National Cancer Institute (NCI) [NCI-U01 CA214381–01 to R.K. and NCI-U01 CA177799 to R.S., F.L., M.Z. and R.K.].

Author Contributions

S.L., W.S.C., G.A., and R.K. designed the study and in vitro experiments. S.L., G.A., and A.T. conducted in vitro experiments. R.S., F.L., and F.S. developed the computational model. R.S. implemented the model and conducted simulations. D.K. transfected the human cell lines used in the study. S.L. and R.S. analyzed the results. W.S.C., G.A., M.Z., and R.K. supervised the study and acquired funding. All authors interpreted the results and reviewed and edited the manuscript.

Conflict of Interest

R.K. is a cofounder and has significant financial interest in AIM Biotech, a company that manufactures microfluidic systems.