Predictive microfluidic control of regulatory ligand trajectories in individual pluripotent cells

Abstract

Local (cell-level) signaling environments, regulated by autocrine and paracrine signaling, and modulated by cell organization, are hypothesized to be fundamental stem cell fate control mechanisms used during development. It has, however, been challenging to demonstrate the impact of cell-level organization on stem cell fate control and to relate stem cell fate outcomes to autocrine and paracrine signaling. We address this fundamental problem using a combined in silico and experimental approach in which we directly manipulate, using laminar fluid flow, the local impact of endogenously secreted gp130-activating ligands and their activation of signal transducer and activator of transcription3 (STAT3) signaling in mouse embryonic stem cells (mESC). Our model analysis predicted that flow-dependent changes in autocrine and paracrine ligand binding would impact heterogeneity in cell- and colony-level STAT3 signaling activation and cause a gradient of cell fate determination along the direction of flow. Interestingly, analysis also predicted that local cell density would be inversely proportional to the degree to which endogenous secretion contributed to cell fate determination. Experimental validation using functional activation of STAT3 by secreted factors under microfluidic perfusion culture demonstrated that STAT3 activation and consequently mESC fate were manipulable by flow rate, position in the flow field, and local cell organization. As a unique demonstration of how quantitative control of autocrine and paracrine signaling can be integrated with spatial organization to elicit higher order cell fate effects, this work provides a general template to investigate organizing principles due to secreted factors.

The developing embryo uses many spatially and temporally regulated mechanisms of signal propagation, including autocrine, paracrine, and extracellular matrix-mediated signals to control the proliferation and differentiation of progenitor cells. Based on our understanding of in vivo development, in vitro strategies attempt to mimic developmental mechanisms and establish artificial environments or niches that promote specific cell fates. Despite considerable progress in our ability to control pluripotent cell fate in vitro, significant variability and heterogeneity in differentiation protocols exist. One reason for this is thought to be our inability to mimic the temporally and spatially diverse signaling environments that occur in the embryo. Herein we use mouse embryonic stem cells (mESC) cultures as a model system to reveal a role for autocrine and paracrine signaling in cell fate control and to demonstrate how endogenous signaling and cell organization interact to create higher order local cellular environments, or niches.

Mouse ESC cultures normally include the soluble interleukin-6 (IL-6) ligand family member leukemia inhibitory factor (LIF). IL-6 ligands such as LIF signal through the Janus kinase-signal transducer and activator of transcription (Jak-STAT) pathway in self-renewing mESCs and result in the phosphorylation (p) of STAT3, inducing expression of many members of the Jak-STAT pathway, along with the direct and indirect transcription of genes associated with pluripotency (Fig. 1A) (1, 2). By controlling the bulk concentration of LIF and other regulatory factors added to the culture media, mESC can be either maintained in their pluripotent state or guided along particular differentiation pathways.

Fig. 1.

Overview of experimental and computational strategies for investigating autocrine and paracrine signaling in static and perfused mESC culture. (A) LIF signals by forming a LIFR-gp130 heterodimeric receptor complex, leading to the recruitment and phosphorylation (p) of STAT3, which can be directly measured and related to ligand binding (4). Nuclear translocation of pSTAT3 induces the transcription of members of the Jak-STAT pathway (13), as well as genes needed for self-renewal (1). (B) Schematic representation of the simulated cell culture system. Cells are treated as flat disks of radius r_cell with total and free receptors R_t and R, respectively, complex number C_n, and binding rate constant κ. Ligand capture boundary layer is at position z = δ. For additional simulation details, please see SI Appendix, Section S.3. Inset: Schematic depicting the different predictions made by deterministic vs. stochastic models of diffusion. In a deterministic model, a source S of diffusible ligands produces a Gaussian concentration gradient [L] such that all cells at position x experience an identical concentration [L_x] of the ligand (left). In contrast, a stochstic model will result only in a certain probability P[L_x] < 1 that the ligand concentration will be equal to L[_x].

Established methods in which mESC colonies of different sizes are randomly arranged on the culture surface can lead to significant heterogeneity in the cell specific gp130 ligand exposure. This in turn leads to heterogeneities in cell fate throughout a culture (3). We have previously demonstrated, using micro-contact printing, that colony size and distribution directly regulate the activation of the Jak-STAT pathway, indicating the spatial distribution of cells is a critical determinant of ESC fate (4). Similarly, different levels of endogenous factor secretion cause differences in human pluripotent stem cell commitment to cardiac lineage cells (5). Controlling this heterogeneity is thus a difficult but important task in pluripotent stem cell biology, and the ability to decouple the associated effects of secreted factors and cell organization may reveal many insights into stem cell behavior, both in vitro and in vivo.

In this study, we explore a microfluidic approach in which we modulate the diffusion of endogenously secreted ligands with flow and demonstrate the effect of changes in ligand capture probabilities on mESC pluripotency and differentiation within spatially heterogeneous colonies. Our approach was to use a hybrid model wherein the Brownian motion of ligands under flow is linked to deterministically specified levels of gp130-mediated intracellular STAT3 signaling. This strategy allowed us to predict flow-rate dependent effects on the heterogeneity of cell signaling and fate determination. Our model further predicted a gradient of these effects in the direction of flow and predicted that the contribution of endogenously secreted factors to the maintenance of pluripotency would be inversely related to the local cell density. We experimentally validated these model predictions using media perfusion within a microfluidic culture device, demonstrating that fluid flow could be used to control STAT3 activating ligand trajectories and consequently cell fate. Importantly, the model prediction that increasing flow rates should increase the amount of differentiation was validated in our experimental system, indicating that autocrine and paracrine factors are critical determinants in maintaining mESC pluripotency.

Collectively, our study demonstrates how a small set of probabilistic rules for individual ligands can give rise to colony-level cellular responses, directly demonstrating a role for endogenous factor secretion in pluripotent cell maintenance and providing an analytical framework to study endogenous factor-mediated cell fate regulation.

Model

To provide insight into the flow regimes appropriate for controlling ligand trajectories, we first developed a hybrid model of our microfluidic culture system based on a combination of a stochastic 3D Brownian dynamics simulation of ligand movement and a deterministic model of gp130 ligand-mediated signaling (Fig. 1B). The use of a stochastic approach here is unique, because models of perfusion culture to date have characterized ligand movements using deterministic mass transport theory (6, 7). While informative, these models treat cultures as uniform surfaces with a single value representing ligand uptake by cells. Additionally, these models are unable to accurately predict the random trajectories followed by individual ligand molecules after release from a cell and are therefore inadequate for exploring the effects of cell population spatial heterogeneity.

Accordingly, we develop an extension of a previously described stochastic model of diffusive ligand transport in static culture, which provided (i) the ability to track the trajectories of individual ligands, (ii) the ability to analyze arbitrary cell distributions, and (iii) a scalable method with respect to both the physical size of the system and the number of ligands present (8, 9). We build upon this approach by analyzing the effects of flow on the trajectories and uptake of individual ligand molecules, thereby allowing us to decouple the impact of endogenously secreted factors and cell organization on mESC signaling and fate determination.

To maximize its predictive capabilities, our model system geometry was designed to mimic the microfluidic culture device used to validate our predictions (for details on the experimental device, please refer to SI Appendix, Section S.1). Thus, the system includes a channel with walls treated as ligand-reflecting surfaces and mESC modeled as partially absorbing disks on the culture surface (Fig. 1B). Simulations were initiated with two types of mESC cell maps. The first, designed to evaluate the general behavior of the system, used cell positions randomly selected from a uniform distribution with a specific cell density σ, defined as the proportion of the surface area covered by the partially absorbing disks. The second sets of maps were used to validate the ability of the model to predict experimental outcomes and were derived from the experimentally determined positions of cells seeded on the microfluidic device.

Our algorithm, implemented for each ligand in the system and outlined in SI Appendix, Fig. S10, is briefly described as follows. Each simulated cell i was randomly assigned a total number of receptors (R_t)_i between 300–700 and an initial number of receptor-ligand complexes (C_n)_i < R_t. Ligand secretion (v_l) and receptor-ligand complex degradation within individual cells (k_deg) were treated as random and independent events in the cell population. All simulations began with no ligands present in the system. Ligands were subsequently secreted by cells at a random time calculated according to a Gaussian distribution centered at the mean secretion rate, v_l per cell, and were assumed to be Brownian particles that undergo random fluctuations in the fluid stream at magnitudes proportional to the simulation time step Δt and their diffusion coefficient D. We further assumed ligands diffuse freely without colliding with one another—reasonable, given the long time scales for collision and the low expected concentrations of secreted ligands.

Individual trajectories for all unbound ligands within the system were simulated by calculating the probable particle position (x, y, z) at each time point t using the Smoluchowski diffusion equation (SDE) with drift (10). Trajectories end when the ligand is either captured by a cell or escapes from outflow region. Capture was implemented by calculating the probability that the ligand will not bind to a cell surface receptor before diffusing to the next position. Also known as the ligand survival probability, this parameter is dependent on the binding rate constant and the ligand’s proximity to a nearby cell and is calculated as the ratio of the probability density function of the ligand position when it is above a cell surface to that when no cell is present. The analytical solution and computational implementation of the SDE for these boundary conditions are detailed in SI Appendix, Section S.3 and expand upon those reported previously for static conditions (11, 12).

Ligand capture physically manifests as the formation of receptor-ligand complexes, which determines the nuclear level of pSTAT3 according to our deterministic Jak-Stat signaling model (4, 13, 14). Briefly, this model consists of a set of 21 nonlinear differential equations that reflect the known and validated structure of the Jak-STAT signaling pathway that is functional within mESC. General components of this pathway and their interactions are depicted in Fig. 1A. Because this portion of the model was completely deterministic, it was implemented as a look-up table in which specific values of C_n > 10 led to associated pSTAT3 levels in a given cell.

It is important to note that there are no cell-colony-specific rules in this hybrid multiscale model. Cells that may be part of a single colony are treated individually with respect to ligand secretion and uptake, thus any higher order organization observed in functional signaling (STAT3 phosphorylation) are meta properties of the system behavior.

Results

Brownian Dynamics Effectively Simulates Heterogeneous Ligand Concentration Profiles.

To guide the subsequent perfusion experiments, the soluble microenvironment was first simulated in silico for a series of random cell coverage maps spanning low to medium cell densities (0.05 ≤ σ ≤ 0.2) (Fig. 2A), and perfusion flow rates of between 0 μL min^-1, corresponding to nondimensional Péclet numbers (see SI Appendix, Section S.3 for definition) of 0 ≤ Pe ≤ 100 that range from diffusion- to convection-dominated flow regimes.

Fig. 2.

Cell density and secreted factor trajectory simulations. Representative 2D projections of ligand trajectories in the xy plane as a function of Pe and σ (flow is from left to right). Inset i and ii: Magnified view of selected ligand trajectories.

To evaluate the behavior of our simulated culture system, we first plotted the 3D evolution of individual ligand trajectories as a two-dimensional projection in the xy plane for the first 30 s of simulation time (Fig. 2B). As expected, we observed that the absolute number of ligands was proportional to the cell coverage σ, and heterogeneous ligand concentrations were observed in many regions. Under static conditions, ligand trajectories resembled Brownian random walk, as each ligand diffused in the local area of its originating cell. Under constant perfusion, trajectories were translated in the axial dimension for each (x, y, z) position of the random walk at a rate equal to the local flow velocity. For diffusion-dominant (i.e., low Pe) regimes, ligand trajectories were similar to the static condition and exhibited a small mean axial translation at each time step. Conversely, in convection-dominant (high Pe) regimes, the randomness inherent to Brownian motion was overwhelmed by the effect of laminar flow. These results indicate that our simulation allows us to quantitatively analyze the time-dependent position of individual ligands within a simulated microfluidic device.

Simulated Nuclear pSTAT3 Profiles Change as a Function of Cell Distribution and Medium Flow.

To assess the impact of the cellular spatial context and microenvironment on intracellular signaling, we next analyzed the single cell data depicting the ligand-receptor complex numbers, (C_n)_i. In the diffusion-controlled no-flow limit, complex number was observed to be dependent on local cell density (Fig. 3A). At low cell densities, little difference was observed between the distribution of C_n resulting from the different simulated flow rates (Fig. 3B). As expected, higher cell densities resulted in greater overall levels of receptor-ligand complex number but also produced a wider range of (C_n)_i values. Importantly, both the mode and the width of the C_n distribution increased as flow rates decreased, indicating that receptor-ligand complex number became more heterogeneous as flow rates approached the diffusion-limited regime. When considered along with the ligand trajectory data, these observations demonstrate that the higher concentration of ligand associated with regions of high cell density lead to an increase in the number of captured ligands and further show how colony growth is advantageous for autocrine-responsive cells in the diffusion-limited case.

Fig. 3.

Simulations predict a flow-rate-dependent gradient of gp130 complex numbers and pSTAT3 concentrations. (A) Absolute levels of receptor-ligand complexes increase with cell density and decreasing flow rate. (B) Increasing the density of a uniformly distributed cell population produces a concomitant increase in the heterogeneity of complex number across the population, whereas increasing flow rate results in less variation across the cells. (C) Whereas the mean theoretical pSTAT3 levels were uniforn along the channel under passive diffusion, the STAT3 activation per cell increased significantly with respect to axial distance under all flow conditions (*), indicating the formation of a gradient of cell fate responses. (D) When normalized to the number of neighboring cells, the impact of flow on the predicted mean pSTAT3 levels is significantly diminished. That the normalized levels of pSTAT3 are lower when cell density is higher suggests that each neighboring cell contributes less to the maintenance of colony pluripotency than cells located within a less cell-dense local environment.

Mean complex number was uniform along the longitudinal axis of the channel under static conditions at all cell densities. Interestingly, the number of ligands captured increased in the direction of flow at all Pe values and cell densities, but the rate of increase was lowest at Pe = 100. This relationship between flow rate and C_n is likely due to the spatial dimensions of our system, because the highest flow rates would force ligands further downstream than the lower rates, resulting in their removal from our system and lower overall increases in the downstream complex number.

To determine the effect of flow rate on cell signaling, we next calculated the mean nuclear pSTAT3 level as a function of complex number along the perfusion axis, according to our previously published model of LIF-dependent STAT3 activation (13). Under the no-flow static conditions, a uniform level of pSTAT3 activation was observed along the device in the direction of flow, consistent with a random cell arrangement selected from a uniform distribution (Fig. 3C). In agreement with the simulated (C_n)_i values, increased flow rates resulted in a lower global pSTAT3 profile, indicating a greater likelihood of ligands flowing out of the system before becoming trapped by a cell. Importantly, we observed a small but significant gradient of pSTAT3 activation along the axis of perfusion under all flow rates examined, with the steepest gradient observed under the Pe = 10 condition.

It is noteworthy that while heterogeneity in the local cell density creates regions of high ligand concentration and pSTAT3 response, normalizing pSTAT3 activation to the number of nearest neighbors (SI Appendix, Section S.3.2) (4) eliminated these local cell density effects (Fig. 3D). The similarity between cell density-normalized pSTAT3 response profiles among all cell maps used in this study suggests that perfusion results can be generalized to a wide range of cell distributions, whether simulated or experimental. Moreover, this result implies that the local effects of endogenously secreted ligands resulting from changes in cell density can be effectively decoupled from the effects due to perfusion. Importantly, these results also support the hypotheses that secreted autocrine factors from individual cells contribute to colony-level responses in diffusion-dominated regimes and that the appropriate level of laminar flow perfusion within a microfluidic device (in this case, Pe > 100) can be used to disrupt diffusive transport and remove autocrine factors from the system. Thus, the underlying system response (in this case, Jak-STAT activation) can be modulated by laminar flow.

Microfluidic Perfusion Control of Cell Fate.

To validate our simulated results and demonstrate perfusion-mediated cell fate control, we first seeded mESC in a microfluidic device under perfusion with saturating levels of exogenous LIF to allow for cell attachment and proliferation (see SI Appendix, Section S.1 for complete methods). For experiments depicted here, flow rates were in the range of 0.011 μL min^-1 to 1 μL min^-1 (corresponding to Pe = 1 - 100), and the cell coverage fraction was determined empirically by microscopy-based cell counting. These values were then used along with empirically measured maps of cell distributions within the device to simulate the experimental conditions.

To first ensure that media perfusion had no effect on cell behavior during our experiments, we compared the expression of the pluripotency-related protein Oct4 under high-flow and static condition using immunofluorescent microscopy, and we observed no significant differences in its levels (SI Appendix, Section S.2). We also mapped the location of all cells in the device immediately after the seeding period and again after 24 h of continuous perfusion at Pe = 100. We observed no consistent channel-length related differences in cell distribution (SI Appendix, Fig. S6), that could be attributed to media perfusion. Finally, we constructed a second, novel microfluidic device in which shear was periodically altered by oscillations in channel width (SI Appendix, Fig. S7) and observed no correlation between pSTAT3 levels and shear stress along the device channel. Combined, these results indicate that any spatial differences in cell behavior observed during the subsequent experiments would be the result of flow-induced ligand transport rather than shear effects, detachment, or cell movement.

To determine how cell signaling and fate responded under various conditions within the straight-channel devices, we measured pSTAT3 after 3 h of perfusion in -LIF media conditions, and we observed that levels decreased with higher flow rates (Fig. 4A). At Pe = 1, STAT3 activation was comparable to the static plate control in the absence of LIF (Fig. 4C), indicating that the steady state rate of gp130 ligand removal due to perfusion was likely lower than the secretion rate. At Pe = 10 and Pe = 100, mean pSTAT3 levels were significantly lower than the static control and decreased monotonically with flow rate (p < 0.01). These results, and the cell density normalized pSTAT3 levels at each flow rate were in agreement with simulation predictions and were not dependent on local cell density (Fig. 4B).

Fig. 4.

Experimentally determined cell responses closely match theoretical predictions. (A) Mean and (B) local cell density normalized pSTAT3 levels in microchannel under test (-LIF) and control (+JakI) conditions closely follow the simulated results. Blue line represents mean normalized simulated data. Data represent mean ± s.d. (C) pSTAT3 levels in static controls. (D) Representative choropleth map of simulated STAT3 activation under Pe = 1 flow using an empirically determined cell map. A gradient of cell response is apparent. Correponding plots for other flow rates can be found in SI Appendix, Section 3.2. (E) Mean STAT3 activation along the axial distance reveals a graded response of cell fate under all perfusion regimes that is similar to those predicted by the model simulation. Data points with solid lines show experimentally determined values, while dashed lines depict the simulation predictions. All data are normalized to +LIF condition under static conditions.

Importantly, pSTAT3 levels at Pe = 100 in -LIF conditions were comparable to the Jak inhibitor (JakI) control condition under static culture, indicating that the effects observed due to perfusion could be mimicked by inhibiting the activation of STAT3. This result demonstrates that the changes we observed in our device were mediated by gp130 ligand transport effects rather than shear stress within the device and also indicates that baseline Jak-STAT signaling is rapidly established under convective flow.

To further evaluate the effects of perfusion on cell signaling, the longitudinal profile of STAT3 activation was next examined. Simulation results using the computer-generated cell maps (Fig. 3) suggested that a secreted ligand concentration profile forms under perfusion conditions, which would directly affect the level of pSTAT3 in a spatially dependent manner. When simulations were performed using the experimentally seeded cell maps and the appropriate perfusion conditions, we observed significant (p < 0.01) gradients of pSTAT3 levels under all flow rates (Fig. 4D). As for the uniform cell maps, the shallowest slope was observed under the Pe = 100 conditions, although some areas of high cell density exhibited higher than average STAT3 activation levels. These results are consistent with our calculations performed using uniform cell maps and indicate that gradients of cell behavior develop under flow regardless of cell organization in the cultures.

To evaluate the ability of the model to predict cell fate under perfusion, we directly compared the calculated pSTAT3 levels to those measured in the cultured cells (SI Appendix, Fig. S12B). At low flow rates, the graded response we observed in the simulations was not detectable in the experimental profile. Instead, pSTAT3 response at Pe = 1 was uniform along the longitudinal dimension and was comparable to static controls. At Pe = 10, the pSTAT3 response was similar to the simulated results, as exemplified by gradually increasing levels of pSTAT3 that reached levels comparable to those observed for Pe = 1 at the distal end of the culture device. At higher Pe values, the measured levels were likewise similar to the calculated responses, as the graded response apparent at lower flow rates was greatly decreased. Importantly, when pSTAT3 activation was normalized to the local cell density, the experimental responses were linear and closely matched theoretical predictions (Fig. 4E), demonstrating that the predicted flow-controlled ligand-activated cell signaling matched experimental measurements. Furthermore, these results indicate that the effects of cell organization and density could be effectively decoupled from perfusion in both our simulations and the cell culture device and highlight the ability of our model to faithfully capture the heterogeneity in cellular responses that results from differences in local cell density. We next explored the longer-term impact of these signaling gradients.

Selective Loss of Pluripotency Under Long-term Perfusion.

In mESC culture, loss of STAT3 activation upon LIF removal occurs rapidly and precedes the down regulation of the pluripotency factor Oct4 (13). The formation of a STAT3 activation gradient along the axial dimension of the microfluidic culture chamber after 3 h of perfusion suggests that sustained convective transport of gp130 ligands downstream in the culture chamber over a longer period of time would result in a graded level of mESC differentiation in the direction of flow. To test this hypothesis, perfusion experiments were run for 24 h in -LIF media conditions at Pe = 10 and Oct4 expression and STAT3 activation were measured over the length of the culture device. Perfusion with +LIF medium produced uniform Oct4 levels, indicating a maintenance of pluripotency under those conditions (Fig. 5A) and that shear stress had no significant effect on cell fate. In contrast, -LIF medium resulted in a graded pattern of Oct4 expression along the device, with upstream cells expressing little to no Oct4, while those downstream remained Oct4+. Activation of pSTAT3 was significantly lower in the -LIF condition compared to the +LIF condition at 24 h (p < 0.01, Fig. 5B). Static controls show that pSTAT3 in the -LIF case was comparable to the +JakI case, which were both significantly lower than the +LIF case, while Oct4 expression was lower in the -LIF and +JakI conditions (Fig. 5C). Fluorescence micrographs of representative cell colonies from upstream and downstream regions of the culture chamber demonstrate the positional difference in Oct4 expression (Fig. 5 D–E) This longitudinal dependence of Oct4 down regulation suggests that gp130 ligands are transported downstream at a rate favorable for capture rather than for elimination from the culture device. Together, these data demonstrate that fluidic control can be used to concentrate autocrine ligands and impact cell fate in a manner that is predictive by single cell based Brownian dynamic factor secretion.

Fig. 5.

Molecular consequences of fluidic-controlled pSTAT3 gradients. (A) Levels Oct4 expression along the length of the microchannel indicate that downstream cells maintain their pluripotent state in the absence of LIF. The red line denotes the threshold set for determining Oct4+ expression levels in undifferentiated cells (13). (B) Mean STAT3 activation under moderate perfusion indicates the overall level of pluripotent cells decreases in the absence of LIF. (C) Under static conditions, Jak inhibition results in pSTAT3 and Oct4 levels comparable to those of the -LIF condition, suggesting complete inhibition of signaling occurs due to LIF deprivation. (D and E) Representative fluorescent images of cells stained with Hoechst 33342 and anti-Oct4 after 24 h perfusion in -LIF conditions demonstrates different cell after distributions in upstream (D) and downstream (E) regions of the channel.

Discussion

The stem cell microenvironment consists of the localized interactions of physical and biochemical signals that affect stem cell behavior in a temporally and spatially dependent manner. Heterogeneity in these signals ultimately impacts our ability to understand and control stem cell fate. In this study, a microfluidic device was developed with the objective of directly manipulating local secreted ligand concentrations in a manner that would allow validation of theoretical models of cell- and ligand-specific autocrine and paracrine secretion. Specifically, we examined the effects of gp130 ligand removal from mESCs under perfusion in the absence of exogenous LIF delivery along with subsequent Jak-STAT pathway activation.

To our knowledge, the results presented here are a unique application of Brownian dynamics for the purpose of simulating system response in an agent-based manner for stem cell culture. There have been numerous reports of applying plug flow and surface reaction-type solutions to microchannels, which involves solving a system of partial differential equations for fluid flow and mass transfer (6, 15, 16). However, simulations limited to bulk concentration effects cannot capture differences in local concentration created by underlying cellular activities. For example, the level of endogenous signaling in ESCs is influenced by local cell density, as shown by controlling cell colony size using micropatterning (4, 17, 18).

We have advanced these previous studies by creating a model and cell culture system to demonstrate that a small set of probabilistic rules for individual ligands can give rise to colony-level cellular responses. This higher order organization due to endogenous secreted factors is reminiscent of the role of endogenous signaling important during tissue morphogenesis. For example, the specification of germ cells requires spatial association between the extraembryonic ectoderm and the epiblast and is more efficient when the epiblast is closely packed or contains more than approximately 40 cells (19).

In our approach, we explicitly account for spatial heterogeneity by computationally analyzing the effect of ligands secreted by both arbitrarily positioned cells and by cells with positions determined experimentally. Accordingly, we were able to reliably predict the heterogeneous responses in STAT3 signaling levels that are exhibited by cells inhabiting different microenvironments in the culture system. This analysis demonstrates the importance of the cell coverage in the regulation of cell responses and demonstrably explains why heterogeneity is a predominant observation in stem and primary cell culture. Interestingly, normalizing pSTAT3 to local cell density revealed that perfusion allowed decoupling of cell organization from fluid flow, in that perfusion culture was able to overcome the local cell density effects inherent in randomly seeded cells.

That the theoretically predicted and empirically measured pSTAT3 levels do not match exactly across all values of flow rate and cell density (Fig. 4) suggests that our model does not capture all the details present within the cellular system under study. Incorporating our previous work identifying a positive-feedback mechanism (13) that controls the abundance of LIF-signaling pathway components into the model may address this discrepancy. However, because our simulations match experimental observation well, we suggest that the current model contains the key factors involved; including further molecular signals and components should yield improvements in the model predictions.

The analytical framework presented herein should be applicable to the study of autocrine and paracrine regulation during pluripotent cell differentiation and generally useful for describing ligand capture across populations of cells, providing insight into intercellular communication mechanisms during development and disease. For example, devices such as ours may be useful in determining threshold levels of endogenous ligands necessary to drive specific cell fate decisions. By using perfusion to remove the endogenously secreted factors, one could change media formulation to determine the minimal compensatory amount of that ligand required to drive cells toward a desired fate. Alternatively, the model and perfusion device may be particularly useful in the analysis and production of tissues that require a flow of molecules between different cell types to guide differentiation or to maintain a targeted cell state.

Materials and Methods

Microfluidic Culture and Analysis of mESC.

Microfluidic devices were fabricated using standard soft lithography techniques (20). R1 mESC were seeded as a single cell suspension (10⁶ mL^-1) on devices coated with 25 μg mL^-1 bovine fibronectin and 50 μg mL^-1 bovine gelatin in ddH₂O and incubated 4 h to allow cell attachment. ESC maintenance media was then perfused at 0.5 μL min^-1 per culture chamber for 24–36 h, followed by perfusion with experimental media (ESC culture medium with 15% KnockOut™ Serum Replacement [KOSR, Invitrogen] substituting for 15% FBS, supplemented with either 0 or 500 p LIF, or 1,000 n Jak inhibitor 1 [Calbiochem]) for 3–24 hrs. Static controls were cultured in standard 96-well tissue culture plates under comparable conditions.

Quantitative Immunocytochemistry.

On-chip immunostaining was performed using standard solutions. Cells were fixed in 3.7% formaldehyde in PBS, permeabilized, incubated overnight in 10% FBS and stained overnight at 4° C with 1∶200 mouse anti-Oct4 and 1∶200 rabbit anti-pSTAT3 antibodies. After staining with goat antimouse IgG Alexafluor 546, goat antirabbit IgG Alexafluor 488 (both, 1∶200 dilution), and 0.1 μg mL^-1; Hoechst 33342, cells were imaged using a Thermo Fisher Cellomics ArrayScan V^TI High Content Screening platform using the Target V3 algorithm to quantify single cell fluorescence of Oct4 and pSTAT3.

Quantitative Methods.

Simulations of ligand trajectories were performed using Python 2.6 on a dual-Xeon based workstation under Red Hat Enterprise Linux 5.0. Binned data are reported as mean ± standard deviation, and other data represented as means with error bars representing nonparametric 95% bootstrap confidence levels.

Complete computational and experimental methods can be found within SI Appendix.

Note.

While this paper was under review, Voldman and colleagues reported alternative microfluidic culture systems to examine the role of FGF (21) and ECM (22) on ESC fate control.