A microfluidic system was developed to study cellular quiescence under medium flow. To obtain sufficient numbers of cells for flow cytometry analyses, a microfluidic device was designed featuring a straight channel 420 μm in height, 4 mm in width, and 4 cm in length. The microdevices, made of optically transparent polydimethylsiloxane (PDMS, Sylgard 184, Dow Corning Corporation, 3097358-1004), also allow real-time imaging of cells during experimentation.

The device fabrication process, illustrated in Figure 1, started with the fabrication of a master mold. The mold with features of microchannel patterns was made in an aluminum block using a computer numerical control (CNC) machine based on a 3D Computer-Aided Design (CAD). PDMS mixture, consisting of 10:1 base and curing agent, was poured onto the mold. After air bubble removal from the mixture under vacuum, the PDMS was cured at 55°C for 3 h. The cured PDMS substrate was then peeled off the mold with formed microchannel grooves (Figure 1A). After punching inlet and outlet holes at the two ends of a channel, the PDMS microchannel was bonded with a glass slide following oxygen plasma treatment of the bonding surfaces (Figure 1B). Next, a pair of inlet and outlet tubing adapters was assembled for each device to connect the microchannel to the external flow control system. The device fabrication and packaging were completed with incubation at 55°C for an hour to enhance the bonding strength (Figure 1C). Prior to experiments, the microfluidic devices were sterilized by flowing ethanol through the microchannels, followed by UV irradiation for 1 h inside a biosafety hood. The inner surfaces of the microchannel were coated with 2% (w/w) fibronectin to enhance the adhesion of cells to the bottom surface.

The total volume of medium in a microdevice (including tubing at the inlet/outlet of the channel but not connectors, Figure 1C) is approximately 140 μl, and the medium volume in the microfluidic channel alone is about 67 µl. In this study, a continuous medium flow with a fixed flow rate (5 or 20 μl/h) was fed into the channel to mimic the typical interstitial flow velocity in soft tissues (Swartz and Fleury, 2007) unless otherwise noted. Correspondingly, the flow rate, rather than the priming volume, is used to characterize the flow effect. We also consider the concentration of the bulk fluid is uniform spatially, and local diffusion and convection at the interfaces between the fluid and cells can be neglected.

Pressure-driven flow in a microchannel presents a non-uniform velocity profile, which gives rise to shear stress. The shear stress for a Newtonian fluid is directly proportional to the product of the velocity gradient and fluid viscosity. Assuming a 2-D parabolic velocity profile in a microchannel with a rectangular cross-section, the wall shear stress, τ _w , experienced by cells attached on the bottom surface of the microchannel, is given by: τ w = 6 μ Q W H 2 (1) where W and H are the microchannel width and height, respectively, μ is the fluid viscosity, and Q is the volumetric flow rate. For a fixed medium viscosity, estimated to be μ = 0.73 cP at 37°C, and given the microchannel dimensions, W = 4 mm and H = 420 μm, the shear stress is linearly proportional to the fluid flow rate. Thus, the two flow rates used in this study, Q = 5 and 20 μl/h, correspond to shear stress values τ _w = 0.09 × 10⁻³ and 0.35 × 10⁻³ dyne/cm², respectively (Figure 1D).

In Eq. 1, for a fixed flow rate and microchannel dimensions, wall shear stress is linearly proportional to the medium viscosity. Dextran (Sigma, D5251; ∼ 500,000 average molecular weight) was dissolved in the medium in various final concentrations to obtain correspondingly various medium viscosities. Table 1 summarizes the resultant dextran-containing medium concentrations, viscosity at 37°C, and corresponding shear stress values for the two flow rates (Carrasco et al., 1989).

REF/E23 cells used in this work were derived from rat embryonic fibroblasts REF52 cells as a single-cell clone containing a stably integrated E2f1 promoter-driven destabilized GFP reporter (E2f-GFP for short), as previously described (Yao et al., 2008). Cells were maintained at 37°C with 5% CO₂ in the growth medium: DMEM (Coning, 15013-CV supplemented with 2x Glutamax (Gibco, 35050)) containing 10% bovine growth serum BGS (HyClone, SH30541.03).

To induce cellular quiescence, growing cells were trypsinized (Coning, 25052-CI), and 70 μl of cell suspension (0.6 million cells/ml) was seeded into a microfluidic channel; after cell attachment on the bottom surface of the channel overnight, growth medium inside the channel was replaced by a continuous flow of serum-starvation medium (0.02% BGS in DMEM) at a designated flow rate controlled by a programmable syringe pump (Harvard PHD 2000). Cell morphologies were found comparable across the flow rate range (0–20 μl/h) (Supplementary Figure S1A). To induce quiescence exit, following serum starvation, the microdevice was disconnected from the flow-feeding setup (syringe and pump), and serum-stimulation medium (1–4% BGS in DMEM) was gently flowed into the micro-chamber using a pipette and a tip at the inlet tubing of the device. The medium change step is fast (<1 min for 140 µl medium) and identical to all quiescent cell groups, avoiding the bias in the exposure time of cells to the stimulation medium (if otherwise using slow flows at different flow rates, 5 or 20 μl/h). Cells were then incubated with serum-stimulation medium at static condition (again, identical to all quiescent cell groups). After 26 h of serum stimulation, cells inside the channel were harvested, and the intensities of E2f-GFP signals from individual cells were measured using a flow cytometer (BD LSR II). Flow cytometry data were analyzed using FlowJo software (version 10.0).

The percentage of cells with the E2f at the “On” state (E2f-On%) in a cell population after serum stimulation was used as an index for quiescence depth before stimulation: the smaller the E2f-On%, the deeper the quiescence depth prior to serum stimulation (Kwon et al., 2017). Consistent with our previous studies in static-medium experiments (Kwon et al., 2017; Wang et al., 2017; Fujimaki et al., 2019), E2f-On% was found comparable to the percentage of cells with EdU incorporation (EdU+%) in the microfluidic experiments under continuous flows (Supplementary Figures S1B,C). In the EdU incorporation assay, 1 µM EdU was added to the serum-stimulation medium at 0 h, and the EdU signal intensity was measured 30 h after serum stimulation by the Click-iT EdU assay following the manufacturer’s protocol (ThermoFisher, C10634).

To account for the effects of extracellular fluid flow on quiescence depth, the fluid flow-associated terms were added to the serum response terms in our previously established Rb-E2F bistable switch model (Supplementary Table S1) (Yao et al., 2008). Based on the resultant ordinary differential equation (ODE) framework (Supplementary Table S1), a Langevin-type stochastic differential equation (SDE) model was constructed as follows (Gillespie, 2000; Lee et al., 2010): X i ( t + τ ) = X i ( t ) + ∑ j = 1 M ν ji a j [ X ( t ) ] τ + θ ∑ j = 1 M ν ji   ( a j [ X ( t ) ] τ ) 1 / 2 γ + δω τ 1 / 2 (2) where the first two terms on the right account for deterministic kinetics, and the third and fourth terms represent intrinsic and extrinsic noise, respectively. X ( t ) = ( X 1 ( t ) ,   … , X n ( t ) ) is the system state at time t. X i ( t ) is the molecule number of species i  ( i = 1 ,   … ,  n ) at time t. The time evolution of the system is measured based on the rates a j [ X ( t ) ] ( j = 1 , … , M ) with the corresponding change of molecule number j described in v ji . Factors γ and ω are two independent and uncorrelated Gaussian noises. Scaling factors θ and δ are implemented for the adjustment of intrinsic and extrinsic noise levels, respectively (unless otherwise noted, θ = 0.4, δ = 40, as selected to be consistent with the experimental data presented in Figure 3). Units of model parameters and species concentrations (Supplementary Table S2) in the ODE model were converted to molecule numbers. The E2f-On state was defined as the E2f molecule number at the 26th h after serum stimulation reaching beyond a threshold value of 300. All SDEs were implemented and solved in Matlab.

To test whether and how extracellular fluid flow affects cellular quiescence, we cultured REF/E23 cells in microfluidic devices under medium flow (Figure 1). Two flow rates (Q = 5 and 20 μl/h) were used in this study; they generated average velocities of 0.82 and 3.33 μm/s on the microfluidic platform, respectively, which are on the order of typical interstitial flow velocity in soft tissues (Swartz and Fleury, 2007). Cells were seeded in microfluidic devices, and cell quiescence and proliferation status were assessed using a previously established and stably integrated E2f-GFP reporter (Yao et al., 2008), which was validated by standard EdU-incorporation assay in regular cell cultures (Kwon et al., 2017; Wang et al., 2017; Fujimaki et al., 2019) as well as here on the microfluidic platform (Supplementary Figures S1B,C; see Methods).

To induce quiescence, cells in microfluidic devices were cultured in serum-starvation medium (0.02% serum) for 4 days under a given extracellular fluid flow (5 or 20 μl/h). In these conditions, about 95% of cells or more entered quiescence (Figures 2A,B, 0.02% serum, 4-days), as indicated by the Off-state of the E2f-GFP reporter (E2f-Off for short, the lower/left mode of the E2f-GFP histograms in Figure 2). Quiescent cells were subsequently stimulated to reenter the cell cycle with serum at varying concentrations (without flow, see Methods for details). Cells were harvested after 26 h of serum stimulation, and the E2f-GFP reporter activity was measured by flow cytometry. With increasing serum conconcentrations (0.02–4% serum, 4 days, Figure 2), higher percentages of cells exited quiescence and reentered the cell cycle, as indicated by the On-state of the E2f-GFP reporter (E2f-On for short, the higher/right mode of the E2f-GFP histograms in Figure 2). The observations that cells entered quiescence upon serum deprivation under an extracellular fluid flow and then reentered the cell cycle upon serum stimulation are consistent with the cell behaviors in conventional static medium (Coller et al., 2006; Yao et al., 2008).

We next compared cells induced to quiescence by 8 vs. 4 days of serum starvation in the presence of extracellular fluid flow. Previous work, including ours, showed that cells moved into deeper quiescence when they remained quiescent for longer durations in conventional static-medium cell cultures (Augenlicht and Baserga, 1974; Owen et al., 1989; Kwon et al., 2017; Fujimaki et al., 2019). One may wonder, however, whether this phenotype was caused by the gradual depletion of nutrients in the static culture medium in vitro, which may behave differently in vivo under an interstitial fluid flow replenishing nutrients. In the microfluidic platform under a constant fluid flow (either 5 or 20 μl/h) during serum starvation, we found cells that remained quiescent for a longer period of time (8 days) entered a deeper quiescent state and became less likely to exit: they had a smaller E2f-On% upon a given serum stimulation than those that remained quiescent for a shorter time (4 days, Figure 2). Together, these results showed that cellular behaviors in 1) serum signal-dependant quiescence entry and exit and 2) quiescence deepening over time are consistent regardless whether cells are in microfluidic devices exposed to extracellular fluid flows or in conventional static-medium cultures.

To examine whether and how extracellular fluid flow may affect cellular quiescence depth, we compared the cells induced to quiescence by serum starvation under different medium flow rates but otherwise in the same conditions. Specifically, cells in microfluidic devices were cultured in serum-starvation medium (0.02% serum) for 4 days under an extracellular fluid flow (0, 5, or 20 μl/h); serum-starvation medium was then replaced by serum-stimulation medium (1–4% serum) using a pipette—this medium change procedure in each microfluidic device was completed within 1 min (compared to otherwise more than 20 and 5 h under a pump-driven slow flow of 5 and 20 μl/h, respectively); cells were then cultured in static medium during serum stimulation. This identical serum-stimulation condition was applied in this study (see Methods for details), so that the subsequent cell cycle reenter and thus the assessment of quiescence depth were not biased by different effective exposure time of cells to the serum-stimulation medium (if the medium was fed by different pump-driven flows) and thus comparable across different quiescent cell groups (which were induced by serum starvation under different medium flow rates).

Upon serum stimulation (with 1, 2, or 4% serum), the fraction of cells reentering the cell cycle from quiescence, as indicated by E2f-On% in Figure 3, were positively correlated with the medium flow rate applied to cells during quiescence induction (serum starvation). These results suggest that a higher extracellular fluid flow rate leads to shallower quiescence, from which cells are more likely to reenter the cell cycle upon stimulation.

Fluid flow introduces two types of cues to cells: 1) hydrodynamic shear stress (physical cue), and 2) continuous replenishment of nutrients and other compounds dissolved in the fluid and removal of local cell-secreted substances (collectively as extracellular factor replacement; biochemical cue). To determine whether these physical and biochemical cues act agonistically or antagonistically (thereby potentiating or attenuating the combined effect) in affecting cellular quiescence depth, we next conducted experiments to delineate the effect of each of the two cues.

To isolate the effect of mechanical shear stress from that of extracellular factor replacement on cellular quiescence depth, the viscosity of the culture medium was varied while its flow rate (and thus the pace of extracellular fluid replacement) was maintained at a constant level. The flow-induced shear stress is linearly proportional to the viscosity of working fluid (Eq. 1), which can be manipulated by varying the amount of high-molecular-weight dextran dissolved in the medium (Table 1).

Accordingly, REF/E23 cells were first induced to quiescence by culturing them in the serum-starvation medium containing 0, 25, 50, or 100 mg/ml high molecular weight ( ∼ 500,000) dextran, respectively, for 4 days under 5 or 20 μl/h flow rate. The cells were then stimulated with 2% or 4% serum for 26 h, and the fraction of cells that exited quiescence (E2f-On%) was measured. As shown in Figures 4A,B, E2f-On% increased with increasing dextran concentration in the serum-starvation medium under either 5 or 20 μl/h flow rate. By contrast, cells cultured in static serum-starvation medium containing the same higher dextran concentration entered deeper rather than shallower quiescence (Supplementary Figure S2; see Discussion). These results suggest that the dextran-induced shallow quiescence in the presence of extracellular fluid flow was primarily due to the viscosity-dependent shear stress (instead of other dextran-associated effects such as being a metabolic source). The higher dextran concentration, thus higher viscosity, of the medium flow generates higher shear stress under a continuous flow rate (5 or 20 μl/h, see Table 1; but not static 0 μl/h). Put together, our results showed that increasing only the fluid flow shear stress, while keeping the same flow rate and pace of extracellular factor replacement, leads to shallower quiescence.

The effect of continuous extracellular factor replacement on cellular quiescence depth was examined next. Some of the extracellular factors (such as nutrients) are expected to facilitate quiescence exit and cell cycle reentry, while others may play inhibitory roles (such as certain extracellular matrix (ECM) factors secreted by fibroblasts). To assess the net effect of extracellular factor replacement, while decoupling it from the effect of mechanical shear stress, we set up two test configurations. In the first “recycled-medium” configuration, a total fluid volume of either V = 120 or 480 μl oscillated back-and-forth through the microchannel at a constant flow rate of either Q = 5 or 20 μl/h, respectively. Thus, when the flow direction was switched every 24 h, the complete fluid volume V passed through the microchannel once. In the second “fresh-medium” configuration, the fluid oscillated exactly as in the first configuration, but fresh medium of volume V was supplied to replace previous medium at each flow direction switch. In both the recycled-medium and fresh-medium experiments, cells were serum-starved for 4 days at a given flow rate Q (5 or 20 μl/h) and subsequently stimulated with serum (1 and 2%, respectively) for 26 h.

The quiescence depth measurements are shown in Figure 5. The fractions of cells exiting quiescence and reentering cell cycle (E2f-On%) were significantly higher in ‘fresh-medium’ than in “recycled-medium” at a given serum stimulation condition. These results were obtained at the same flow rate (either 5 or 20 μl/h) and thus under the same mechanical shear stress. The difference that the cells experienced was medium replacement: once per 24 h during the 4-days serum-starvation in the fresh-medium configuration, whereas no medium replacement during the same period in the recycled-medium configuration. These results suggest that with the flow rate and shear stress being equal, extracellular factor replacement alone (as in “fresh-medium”) induces shallower quiescence than without such a replacement (as in “recycled-medium”).

We next sought to develop a mathematical model to gain potential mechanistic insight into the effects of extracellular fluid flow on cellular quiescence depth. Previously, we have shown that the Rb-E2f pathway functions as a bistable gene-network switch that converts graded and transient serum growth signals into an all-or-none transition from quiescence to proliferation (Yao et al., 2008; Yao et al., 2011). Specifically, the minimum serum concentration required to activate this Rb-E2f bistable switch (the E2f-activation threshold for short) determines quiescence depth (Yao, 2014; Kwon et al., 2017). The experimental results in this study suggested that extracellular fluid flow generates or changes physical (mechanical shear stress) and biochemical (extracellular substances) cues that drive cells to shallow quiescence. We hypothesized that these flow-associated cues boost the cellular responses to serum growth signals and thereby reduce the serum level required to activate the Rb-E2f bistable switch, which results in shallow quiescence.

Accordingly, our previously established mathematical model of the Rb-E2f bistable switch (Yao et al., 2008) was extended, incorporating the extracellular fluid flow effects (FR) into the serum signal terms in the governing ordinary differential equations (ODEs) (Supplementary Table S1). The augmented model was utilized to simulate the responses (E2f-On or -Off) of cells to serum stimulation under the influence of extracellular fluid flow varying in rate. The simulations were carried out following the chemical Langevin formulation of the ODE framework, which considered both intrinsic and extrinsic noise in the system (see Methods for detail), and the results are shown in Figure 6.

A direct comparison between Figure 3B and Figure 6A demonstrates that the simulation results, based on the fluid flow-incorporated Rb-E2f bistable switch model, are qualitatively and quantitatively in good agreement with the experimental measurements. This finding supports our hypothesis regarding how extracellular fluid flow may sensitize cells to serum growth signals and activate the Rb-E2f bistable switch, and thus, reduces quiescence depth. Simulation results further show that the effect of extracellular fluid flow is more pronounced than that of mechanical shear stress alone in promoting quiescence exit (E2f-On%, Figure 6B). The “delta” between the two curves (orange minus blue) presumably reflects the effect of extracellular factor replacement in reducing quiescence depth (dotted grey curve, Figure 6B); this effect also increases with a higher flow rate (thus, an increasing pace of fluid replacement). Although how shear stress and extracellular factor replacement promote quiescence exit is unknown, taking a simple assumption that shear stress and extracellular factor replacement alone effectively corresponds to a portion (0.75 and 0.85, respectively) of the extracellular fluid flow term FR in the model (Supplementary Table S1), the simulation results are reasonably (although not perfectly) consistent with the experimental observations (regarding the shear stress effects, Supplementary Figure S3). Together, our modeling and experimental results suggest that the flow-induced shear stress (physical cue) and replacement of extracellular factors (biochemical cues) contribute agnostically to the effect of extracellular fluid flow in promoting quiescence exit by lowering the activation threshold of the Rb-E2f bistable switch.

The good agreement between simulations and experiments motivated the application of the model for predicting the cell responses to higher fluid flow rates above 20 ul/h, under which cells started to partially detach from the microchannel bottom surface and hence excluded from the current experimental study. The simulation results show that the additive effect of extracellular fluid flow to a given serum signal on quiescence exit (E2f-On%) can be well fitted with a Hill function (Figure 6C). Namely, E2f-On% increases monotonically with increasing flow rate but is asymptotically bound by a serum concentration-dependent level. By contrast, with sufficiently high serum concentration, the entire cell population can exit quiescence (i.e., E2f-On% approaches 100%) in our model even without extracellular fluid flow (Figure 6D). This latter result is consistent with what we experimentally observed previously in REF/E23 cells under static medium (Yao et al., 2008; Kwon et al., 2017; Fujimaki et al., 2019). Therefore, it appears that extracellular fluid flow facilitates quiescence exit by reducing the E2f-activation serum threshold, but unlikely to fully replace the role of serum growth factors in this process.